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Macy's to shutter 125 stores in massive retooling
Macy's press materials
Declaring 2020 a "transition year," Macy's on Tuesday released a plan "designed to stabilize profitability and position the company for growth" that includes shuttering 125 underperforming stores over the next three years (29 of which had already been announced for 2020).
Some 2,000 employees will lose their jobs in the process, as the company reduces its "corporate and support function headcount" by 9%, according to a company press release. All told the moves should generate annual gross savings of about $1.5 billion, fully realized by year-end 2022. Costs of executing the changes will be about $450 million to $490 million, most recorded in 2019.
The strategy also entails abandoning Macy's Cincinnati headquarters and maintaining a sole head office in New York City, home to its Herald Square flagship. Its Macys.com e-commerce office in San Francisco will also close and shift to New York, with much of its tech operations moving to an expanded presence in Atlanta. Customer service hubs and other facilities will also close and be consolidated, the company said.
Macy's is embarking on a project that goes well beyond the 100-store reduction to its fleet that for a while seemed like it would be its most dramatic slim-down.
What hasn't changed much is the retailer's slipping sales. Its dismal third quarter gave way to a tepid holiday quarter. On Tuesday the company updated its fourth-quarter results, saying that store comps fell 0.6%, and fell 0.8% for the year ending Feb. 1.
As the department store wrapped up those earlier closures, which it previously said were finished in early 2019, it also unveiled a "store segmentation" strategy that split stores into three basic categories, flagships (like those in New York and San Francisco), "Growth150" stores (which were remodeled and represent half of its revenue), and "neighborhood stores." Its Backstage off-price effort has been mostly forged within Macy's stores.
But Macy's on Tuesday said that is now getting an overhaul, too. Plans for the neighborhood stores that do remain open are to shift to non-mall shopping centers, after testing the first such location in Texas. Backstage will expand, with plans this year to open 50 more store-within-store spaces and seven off-mall standalone stores.
The company isn't as bad off as rivals burdened with debt. A "conservative financial policy" that has entailed debt reduction of more than $2.7 billion in the past three years "has provided support to its credit profile in the face of weakening operating performance," Christina Boni, vice president and Moody's lead analyst for Macy's, said in emailed comments.
"Macy's is taking major steps to stabilize its operating performance through sizeable cost reduction efforts as well as earmarking 125 of its least productive stores for closure over the next three years. Macy's, like its major department store competitors, is working to accelerate change after a weak 2019," she also said.
But more than doubling the store closure count of a few years ago may not be dramatic enough, according to Nick Egelanian, founder and president of the retail real estate consulting firm SiteWorks. He called 125 closures "a pretty good downpayment" toward what he believes will eventually be as many as 500 to 600.
"Their future is on the coasts, in the flagship stores, and in the 150 or 100 stores that they themselves say gives them 50% of their sales and by the way probably 75% of their profits," he told Retail Dive in an interview. "They should be remerchandising and updating those stores, reinventing the core Macy's stores in A malls on the coasts, and not competing head to head with TJX or Kohl's." | {
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When the Jew-bashers are Jews
Sharon Kleinbaum, rabbi of New York's Beit Simchat Torah—the world's largest LGBTQ congregation. Source: Facebook/Beit Simchat Torah.
Their values turn Jewish principles of justice and truth on their heads, and their Israel-bashing is but a thin veneer for a hatred of other Jews or Judaism itself.
(August 12, 2021 / JNS) The latest move by President Joe Biden to appall many American Jews as an act of wanton hostility is his appointment of the progressive rabbi, Sharon Kleinbaum, to the U.S. commission on International Religious Freedom.
Kleinbaum has been accused of repeatedly using her pulpit at New York's Beit Simchat Torah—the world's largest LGBTQ congregation—to demonize Israel.
During Israel's "Operation Protective Edge" in Gaza in 2014, Kleinbaum read a list of Palestinian and Israeli casualties, including the names of Hamas terrorists, in special prayers during her synagogue's services. A number of members quit the synagogue in protest.
Her other half, Randi Weingarten, who is president of the American Federation of Teachers, distinguished herself in turn by saying in April that American Jews were part of an "ownership class" in the United States who want to take opportunities away from others.
Kleinbaum is but the latest in a series of anti-Israel appointees by the Biden administration. The twist in the knife is that she is a Jew and even boasts the title of rabbi.
Such Jewish individuals are routinely used as human shields by Jew-bashers on the left. In Britain, the former Labour Party leader Jeremy Corbyn, who presided over an eruption of Jew-baiting and Israel-bashing in his party, boasted as his friends certain anti-Israel Jews—particularly if they were religious—in order to rebut accusations that he was an anti-Semite.
Those who know nothing about Judaism may therefore think that the malevolent views such Jews express about Israel represent authentic Jewish values. Certainly, many of these anti-Israel Jews themselves think that.
In fact, their values turn Jewish principles of justice and truth on their heads, and their Israel-bashing is but a thin veneer for a hatred of other Jews or Judaism itself.
Part of the explanation for this is the influence of Marxist ideology that now dominates left-wing thinking through "social justice" (which is anything but). Since most American Jews subscribe to this view of the world, they are not only increasingly turning against Israel; they assume, shockingly, that the anti-Jewish precepts of leftist ideology are Jewish ones.
Today, this muddle takes vicious form through the doctrine of intersectionality. This grotesquely demonizes Israel and the Jewish people as representatives of white supremacism, colonialism and racism and holds that their victims are people of color, the LGBTQ community and Palestinian Arabs.
However, the phenomenon of Jews turning against each other reaches deeply back into history with innumerable examples. The very first blood libel is thought to have been promoted by a Jewish convert to Christianity in medieval England.
In his essay On the Jewish Question, Karl Marx wrote: "Money is the jealous god of Israel, in face of which no other god may exist."
The financier George Soros, who has been the target of much anti-Jewish prejudice, has nevertheless funded anti-Israel initiatives through his Open Society Foundation and nauseatingly blamed the resurgence of anti-Semitism in Europe on Israel's behavior.
There are many different reasons for such problematic attitudes towards the Jewish people among some Jews.
Marx was the son of Jewish parents who converted to Christianity, itself a principal historical driver of demonization and persecution of the Jews. Soros's complex personality was almost certainly forged in his experiences in Holocaust-era Hungary.
Today's intersectional Jew-bashers subscribe to the view of Jews as predators that itself derives in large measure from Marx.
But the distortions go far deeper. Such Jews are often called "self-hating," but this is a misnomer because they tend to be intensely narcissistic. Moreover, there's one part of their Jewish ancestry that they do embrace; this is their identification with Jewish victimhood, which they think gives them moral nobility.
So they will talk up their family's victimization in the Holocaust; or in Britain, they may wheel out as evidence of their "proud" Jewish identity the fact that during the 1930s, their fathers marched against British fascists in London's East End.
But they don't like much else about being Jewish. They don't like its moral codes getting in the way of the free and easy life they want to lead. They don't like being associated with attributes associated with Jews by disdainful polite society, such as materialism, pushiness or vulgarity. Above all, they don't like being viewed as different from the rest of society—and similarly, certain Israelis don't like their country being seen as different from any other.
Of course, other people revolt against their own religion, culture or nation. With the Jewish Judaism-haters, however, this takes pathological form. They obsessively seek to expunge Jewish particularism from themselves and the world.
Anti-Jewish Jews are perhaps the greatest danger facing the Jewish people today. Despite being on the left, they make common cause with neo-Nazis and jihadists in seeking to harm the Jews. Wildly over-represented in the universities and cultural elites, they are to be found at the very forefront of campaigns designed to damage the Jewish people.
Take the recent announcement by Ben & Jerry's that the company would no longer sell its ice-cream in what it calls "the occupied Palestinian territories."
Although Ben Cohen and Jerry Greenfield sold their eponymous company years ago to British-owned Unilever, they have said that this illegal and discriminatory boycott, which will hit both Jewish and Arab residents of the disputed territories, is "one of the most important decisions the company has made in its 43-year history."
The boycott was applauded in turn by Kenneth Roth, the Jewish director of Human Rights Watch, which obsessively and maliciously demonizes Israel with serial falsehoods.
And to combat the furious pushback, the Ben & Jerry's board has brought in Peter Beinart, a Jew who now notoriously argues for Israel's dissolution and advocates that it should be stripped of its nuclear capability—its last-ditch deterrent against a second Jewish genocide.
In his book The Oslo Syndrome: Delusions of a People under Siege, the psychiatrist Kenneth Levin provides a magisterial analysis of the psycho-pathology of the anti-Israel and anti-Jewish Jew.
Much of this pathology is deeply defensive. Blaming Israel for the murderous war waged against it, writes Levin, provokes an illusion of control over a situation that otherwise would be unbearably terrifying. It's easier for certain Israelis and Diaspora Jews to believe they can stop the violence by getting Israeli policy changed than it is to cope with the reality that millions of fanatics are bent on Israel's extermination.
Similarly, such Diaspora Jews believe they can fend off anti-Jewish attacks by ingratiating themselves with the enemies of the Jewish people. Identifying with fashionable social causes appears to offer protection against the charge that the Jews are concerned only with their own interests. Which is why so many subscribe to the "social justice" agenda, equate anti-Semitism with Islamophobia and relativize the Holocaust.
As Levin observes, however: "Yet the path they advocate is no less delusional than that of abused children who blame themselves for the abuse they experience. All too often such children doom themselves psychologically to lives of self-abnegation and misery. In the case of Jews indicting Israel for the hatred directed against it, the misery they cultivate goes far beyond themselves and ultimately, undermines Israel's very survival."
Perhaps the most savage analysis of the anti-Jewish Jew was written by Uzi Silber in Ha'aretz more than a decade ago. Jewish anti-Semitism, he wrote, was a condition in which being "more sensitive to pain suffered by members of a group other than (one's) own metastasizes into a malignant emotional and moral identification with people committed to (one's) annihilation."
No other people does this to itself. Attitudes expressed by the likes of Kleinbaum, Beinart, Roth and a myriad others constitute a particular and devastating Jewish tragedy.
Melanie Phillips, a British journalist, broadcaster and author, writes a weekly column for JNS. Currently a columnist for "The Times of London," her personal and political memoir, "Guardian Angel," has been published by Bombardier, which also published her first novel, "The Legacy." Go to melaniephillips.substack.com to access her work.
Anti-Israel Bias | {
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Huntington, Collis P(otter)
born Oct. 22, 1821, Harwinton, Conn., U.S.
died Aug. 13, 1900, Raquette Lake, N.Y.
U.S. railroad magnate.
He worked as a peddler before becoming a prosperous merchant in Oneonta, N.Y. In the gold rush year of 1849, he moved to Sacramento, Calif., and joined Mark Hopkins in a firm that specialized in miners' supplies. In the late 1850s he became interested in a plan to link California with the eastern U.S. by rail. In 1861 he joined Hopkins, Leland Stanford, and Charles Crocker (1822–1888)
a group later known as the "Big Four"
to form the Central Pacific Railroad. During its construction (1863–69), Huntington lobbied for the company in the east, securing financing and favourable legislation from the federal government. In 1865 the Big Four formed the Southern Pacific Railroad. In 1869 Huntington bought the Chesapeake and Ohio Railway, which he later extended to link with the Southern Pacific, forming the first transcontinental railroad. He became president of the Southern Pacific–Central Pacific system in 1890.
Huntington chorea
Huntington, Samuel P(hillips)
Huntington, Collis P(otter) — (22 oct. 1821, Harwinton, Conn., EE.UU.–13 ago. 1900, Raquette Lake, N.Y.). Magnate ferroviario estadounidense. Fue vendedor ambulante antes de convertirse en un próspero comerciante en Oneonta, N.Y. En 1849, el año de la fiebre del oro, se… … Enciclopedia Universal
Huntington — ► C. del NE de E.U.A., en el estado de Nueva York, en la costa N de Long Island; 200 571 h. Huntington, Archer Milton * * * (as used in expressions) Huntington Beach Huntington, Collis P(otter) Huntington, corea de Huntington, Samuel P(hillips)… … Enciclopedia Universal
Potter — (as used in expressions) Aiken, Conrad (Potter) Huntington, Collis P(otter) Potter, (Helen) Beatrix Potter, Dennis (Christopher George) Stewart, Potter Martha Beatrice Potter … Enciclopedia Universal
United States — a republic in the N Western Hemisphere comprising 48 conterminous states, the District of Columbia, and Alaska in North America, and Hawaii in the N Pacific. 267,954,767; conterminous United States, 3,022,387 sq. mi. (7,827,982 sq. km); with… … Universalium | {
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Maximum five files to be uploaded.
File name to include the name of participant.
Awards won during last 5 years only.
Attach a scanned copy of news covering of the achievement, if any.
Accepted file types: jpeg, jpg, png, docx, doc, rtf, pdf, xls, xlxs. | {
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Home University Affiliates Institute for Social Development and Policy Research, Seoul National University Non-series Others (The Institute for Social Development and Policy Research, Seoul National University)
Others (The Institute for Social Development and Policy Research, Seoul National University)18
Survey on Family, 1974
Institute for Population and Development, Seoul National University
Survey on Geographical and Social Mobility on the Way of Modernization, 1968
Survey on the Perception of Noblesse Oblige, 2009
Yee, Jaeyeol
Institute for Social Development and Policy Research, Seoul National University
Records on the Seminar of the Urban-Rural Gap in the Late 1960s in Korea, 1969
Survey on Urban Population Adjustment, 1964
Institute for Population, Seoul National University
Survey on City Dwellers' Attitude towards Society, 1968
Department of Sociology, Seoul National University
Survey on Population and Life in Urban Areas, 1966
Survey on Adaptation to Urbanization, 1970
Preliminary Survey on Social Welfare, 1968
Lee, Man-Gap
Social Security Committee, Ministry of Health
National Safety Awareness Survey for the Development of a Social Safety Index, 2005
Survey on Family Life in Suburban New Towns of Seoul, 1965
Lee, Hae Young
Social Survey on Newspaper Readership, 1964
Korea Newspaper Research Institute
Public Opinion Survey on the 10 Years Following the Financial Crisis, 2007
Chung, Chin-Sung
Survey on Migration and Urban Life, 1971
Youths Values Survey, 1970
Han, Wan Sang
Comparative Study on Values and Attitudes of Korean and American University Students, 1972
Institute for Population and Development, Seoul National University ; Department of Sociology, North Carolina State University
Survey on the Attitudes of Korean University Students, 1970
Survey on Safety Consciousness in Korean Society, 2008 | {
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Borland Groover's team of specialists have trained and worked as faculty and researchers in leading hepatology and gastroenterology facilities throughout the US and abroad.
We have 68 board-certified physicians to choose from, specializing in all areas of gastroenterology. That means you can rely on us for everything from colonoscopies to serious digestive health conditions, including liver concerns.
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Kyle Etzkorn, M.D., F.A.C.P., C.P.I.
Jose Nieto, D.O., A.G.A.F., F.A.C.P., F.A.C.G., F.A.S.G.E.
Hong Taing Tek, M.D., A.G.A.F. | {
"redpajama_set_name": "RedPajamaC4"
} |
Marivic Lesho is a content editor for the International Institute for Innovative Instruction. She earned her PhD in linguistics from the Ohio State University. Before coming to Franklin, she was a postdoctoral researcher at the University of Bremen, specializing in dialectal variation in American and Philippine English as well as other Philippine languages. She also has experience in teaching linguistic methods and theory, editing academic publications, and working as a freelance editor. As part of the i4 team, she edits courses and provides LMS support to Franklin students and faculty as well as working on projects for external clients. | {
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VFW (2020) Review
Spoiler-free so you can read before you watch
Horrorific content by Jaredsoto on March 25th, 2021 | Movie Review | Survival, Mutant, Revenge, Gore, Splatter, B-Horror
Add VFW (2020) to your Watchlist
It's about a group of war veterans who must defend their local VFW post and an innocent teenager, from a psychotic drug dealer and his army of drugged up punks.
VFW was directed by John Begos (Bliss) and stars Stephen Lang (Don't Breathe,Avatar), William Sadler (The Mist, Machete Kills), Fred Williamson (From Dusk Till Dawn, Starksy and Hutch), and Martin Kove.
Who said I was dead?
Have you ever walked into a movie completely blind? (No, that was not intended as a Stephen Lang "Don't Breathe" pun) Because that's exactly what I did here with this 1 hour and 32 minute film called "VFW." Did I regret it? Let's talk about it!.
VFW is about a group of old war buddies. Sounds fun right? A couple of old pals who meet up daily at their local VFW post and throw back a couple of brewski's and talk about the good old days. Meanwhile, we go to the location across the street, where chaos and absurdity linger. We are introduced to the wacko drug dealer who goes by the name of Boz (Hammer), as well as a couple of his lackeys. Their lair is run down and filled to the brim with drugged out punks, who are addicted to this trendy new drug that turns them into mindless, jacked up zombies. Something happens to some of the drugs and this really pisses off Boz and his people. He learns that the war veterans across the street may have something to do with it, so he decides to take action.
I really did have a good time with this movie. It's on the lower side of the film budget, but I'm a huge fan of indie horror and they really have something nice going on here despite being an independent film. The cast is all around solid and is made of movie vets! Their chemistry on screen is great. The writing is well done and not super complex. With that being said, it's a pretty straight forward movie that aims at entertaining the viewer. Overall, I was happy with this product, even if it's far from perfect (lighting crew I'm looking at you). It really keeps you engaged and never really slows down when it gets started. Did I mention the violence in this is pretty top notch as well? Nothing too wild, but definitely enough to satisfy the gorehounds out there! I guarantee if you watch this during a movie night with some friends and a few drinks, you will have a fun, bloodsoaked time.
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EVEN MORE HORRORRandom Spoiler-free Review
Worth Watching?
Definitely! It's a weird, good old time. Whether it be during a movie night, or maybe you just came across it randomly, I'm 96.5 percent sure that you will have a fun experience with this film. Filled with body parts and geriatric humor, VFW is one I recommend from here on out.
VFW Review (2020) Worth Watching? - ALL HORROR Tweet it
JaredSoto
-Independent filmmaker -Lover of all things horror
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We would be delighted to hear from you regarding your child's education and future at Cambridge International School. Providing we have a space, it is possible to join CIS at any point during the school year, although our main intake is in September.
For further information regarding our admissions procedure or for any further information on registering your child for a place, please contact us on [email protected] or call 01223 832719.
Alternatively, you can complete the contact form below. We will contact you as soon as we can to discuss your enquiry and your child's future with us. | {
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} |
This project consists of the construction of a 19,700 square foot tilt-wall building to provide space for both retail and restaurant usage. Architectural features include arched canopies, Lampasas sandstone with EIFS accents, and contemporary sconce lighting.
OWNER: Sea Island Real Partners, Ltd. | {
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} |
Agencies launch 'massive response' after Typhoon Haiyan devastates Philippines
by Tim Wyatt
Aftermath: a devastated downtown area in Tacloban city, on Leyte Island, on Sunday
AID agencies are mounting a "massive response" as the scale of the devastation caused by Typhoon Haiyan in the Philippines becomes clear.
Officials are now warning that up to 10,000 people may have died when the typhoon tore through the central Philippines on November.
The charity World Vision said in a statement that it was aiming to provide life-saving essentials to 1.2 million people in the aftermath of the storm, which some are calling the most powerful ever to ever hit land.
Many of their Philippines staff, the charity said, are also victims of the typhoon: 37 of them had suffered damage to their homes. One World Vision worker, Erna Tupaz, said: "The typhoon totally destroyed our house. We're living with neighbours now. I can't do anything but to cry." A World Vision emergency specialist, Aaron Aspi, said: "It was like waking up from a nightmare."
Grace Baloro, a World Vision worker with family on the island of Leyte, which was badly hit by the storm, said: "I'm worrying about my two children. I don't have any contact with them yet. I left them with their nanny."
The Government announced on Sunday that it would donate £6 million to provide "crucial humanitarian aid", but the head of the Philippines Red Cross, Richard Gordon, told the BBC that the situation was "absolute bedlam". "There's an awful lot of casualties; a lot of people dead all over the place; a lot of destruction," he said. "It's absolute bedlam right now, but hopefully it will turn out better as more and more supplies get into the area."
Speaking on Friday, Alwynn Javier, a Christian Aid senior programme officer in the capital, Manila, said that the damage was likely to be colossal. "This is on a scale never been seen before. It has covered a vast area, including islands where the infrastructure was already limited. Air and seaports are closed, and power lines are down, cutting off entire provinces and leaving many communities stranded."
A regional emergency manager for Christian Aid, Coree Steadman, said that the organisation had not been able to get in touch with its local partners because of the devastation caused by the storm.
"It is not just the strength of the typhoon," she said, "but the scale of it - it has affected 15 provinces, two of which were also hit by the earthquake. Our priority now is responding to immediate needs: food, household items, blankets, and shelter materials. We will also be looking at the extent of the damage to livelihoods as part of our assessment. In the next few weeks, we will be able to respond for longer term rehabitation."
The storm struck the central Philippine islands of Leyte and Samar, and northern parts of Cebu. A spokesman for World Vision said that the charity had been unable to contact staff in Tacloban City, in Leyte. The charity said that it would be sending relief teams to the Visayas region, which was worst hit by the typhoon, as well as continuing its support of up to 7000 families affected by last month's earthquake. The BBC is reporting that Tacloban has been flattened by the storm, and that bodies are piling up in the streets as aid struggles to reach the town.
The chief executive of Tearfund, Matthew Frost, asked the charity's supporters to pray for the relief effort in the Philippines. "As well as the urgent and practical things, like helping people have a roof over their heads, we know that there will be a lot of grief as people come to terms with bereavement," he said. "We must pray for the thousands of people who are grieving and ask God how he wants each of us to respond to their needs.
"Please also pray for the churches who are sending teams out, many of whom will travel long distances by motorbike, that their teams would stay safe and well on their travels, and that they would be able to bring hope to the people they meet."
On Monday, the Archbishop of Canterbury sent a message of prayer and solidarity to all those affected by Typhoon Haiyan:
"The news of the devastating storm in the Philippines is tragic, and my heart goes out to the people there. We are all deeply shocked and saddened to hear of the loss of thousands of lives and of the suffering of millions as a result of Typhoon Haiyan.
"Our prayers are with all who have lost loved ones and all those who are traumatised by the disaster and in desperate need of food, water, shelter and medical attention. We pray for those who are most vulnerable in this crisis: children separated from their parents, the sick and injured, the disabled and the elderly.
"As a Church, we will stand beside the people of the Philippines at this devastating time, offering all we can in practical and spiritual support as the scale of the disaster unfolds.
"I note that the relief work has already commenced and my prayer is that governments, agencies, churches and individuals will respond generously to help the people of the Philippines to recover and rebuild their shattered lives.
"May the victims of this terrible storm know God's comfort and derive strength from their faith."
Haven provided
Dr Billy Graham gives his last blessing on film
Photo: Vigilant
Cyclone 'hit 14 million'
Welby tells of longing for church unity
World news in brief
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Stapleford is a lively, evangelical parish between Nottingham and Derby. We are praying for a vicar who will be able to help us rebuild our congregations and inspire us, post covid, to move forward with new vision and energy to deepen faith within our three very different | {
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National Agents Alliance Hotspots - Mobile, AL- NAA Training & Opportunity Meeting!!
Mobile, AL- NAA Training & Opportunity Meeting!!
7:00pm - 8:00pm - NAA Opportunity!! 8:00pm - 10:00pm - NAA Training!! 10:00pm - 11:00pm - President's Club Night Owl!! | {
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What a beautiful shape! Here is one stem of a fern unfurling, unfolding, becoming. If I came back next week and photographed this exact fern, it would look very different. If I could take a photo every few minutes and view it as stop motion video it wouldn't look so still. We would see it was constantly moving, restless, stretching, curling and uncurling, spreading its leaves in the sun.
This single fern is a wonderful example of how, if we want to really know an individual, we have to follow them through their unfolding. Single moments, isolated snapshots of existence only hint at the complexity, the movement, the development which is at the heart of all Life. | {
"redpajama_set_name": "RedPajamaC4"
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Back Stories » Saigon » Uniqlo's First Store in Vietnam Will Be at Parkson Saigon Tourist Plaza
Uniqlo's First Store in Vietnam Will Be at Parkson Saigon Tourist Plaza
Friday, 18 October 2019.
After a year of waiting, fast-fashion fans in Vietnam will be able to purchase Uniqlo products in a flagship outlet in the very near future.
Just yesterday, Uniqlo's Vietnamese subsidiary announced on their Facebook page the location of its first store in Vietnam to excited reactions by the local cybersphere. According to the update, the outlet will be based in Parkson Saigon Tourist Plaza on Le Thanh Ton Street, spanning three stories and occupying the department store's entire front façade.
The brand adds that the total retail space of the first store is 3,000 square meters, enough to house the brand's entire LifeWear line, targeting shoppers of all ages. Along with the announcement, a Vietnamese-language website has also been set up, though it's still bare-bones at the moment.
A screenshot of the Vietnamese Uniqlo website.
Uniqlo is a Japanese casual wear brand famous for its minimalist style and affordable price tags. Even before the brand announced plans to expand to Vietnam, it has already been loved by local consumers, despite its rather questionable ethical track record.
More than a year ago, the Japanese company confirmed its intention to establish a presence in Vietnam and promised a fall 2019 arrival date. "The Southeast Asia region has been an important driver of growth for us, and we are pleased and optimistic about our opportunity to be a part of such an exciting economy and retail market," Tadashi Yanai, the chairman and CEO of Uniqlo's parent company Fast Retailing, told Nikkei Asian Review in an interview last year.
Apart from Vietnam, the fast-fashion brand also entered India at the beginning of this month to tap into the South Asian market's 1.3 billion customers. It's hoped that the expansions will help cushion Uniqlo's lagging business elsewhere. Most recently, the tit-for-tat trade war between Japan and South Korea has negatively impacted the brand's sales in Korea as local consumers boycott Japanese goods.
[Top image via Facebook page Uniqlo Vietnam]
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The trees that were cut down last July during construction of the metro station in front of the Saigon Opera House are making a comeback in the form of benches.
2 Men Arrested In HCMC For Trying To Ship Gun and Grenade In Guitar Case
Two local men were arrested last Tuesday after attempting to ship a rifle, grenade and 5 bullets to Hanoi in a guitar case. Surprisingly, neither of the men were Antonio Banderas. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} |
Episode 10 - dave mossop
Dave Mossop is the cofounder of Sherpas Cinema, one of the most - if not the most cutting edge, innovative outdoor film production studios out there. In fact Sherpas has been cited as redefining what is possible in outdoor film. Dave and his team have created some of the most stunning imagery I've ever seen, and likely a lot of what you've seen but may not know it. With big productions like All I Can, Into the Mind, Imagination, and their latest film - Loved By All - Sherpas has received countless top awards from most of the well-known Outdoor Film Festivals globally. They also work with some of the biggest house hold names out there: Google, Audi, The North Face, Asics, the list goes on and on.
What I loved about this conversation is that Dave has such an authentic and palpable appreciation for the things he cares about. Whether its the places he visits, or the new filming techniques he's learning, or the people he's met and lost along the way, whatever it is - there's this deep sense of gratitude for the opportunity, which I just find really cool.
With this episode, you get a little bit of everything - just the way I like it. We zig in and out of self-actualization, living life to the fullest, the role of art in outdoor film, virtual reality, and of course some good old dirt bag stories too.
Show Resources:
Sherpas Cinema Website
Dave Mossop's Instagram
Sherpas Cinema Instagram
Apa Sherpa
Dave Shuman
Conrad Anker
Eric Rosland and Malcolm Sangster (CoFounders Sherpa Cinema)
Brian Hendricks (Film Professor)
Sherpas Cinema Portfolio
JP Auclair
Flyover Canada
Landon Bassett | {
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} |
After consuming milk, cheese and yoghurt for most of her life, this writer was diagnosed with osteoporosis. How does a woman who consumed dairy for years have Osteoporosis by her mid-forties?
Let's look at some chilling facts about dairy consumption. Read on and you'll see we should perhaps have a media campaign that asks ... "Is dairy bad for you?"
One woman's journey from food addiction, using food to get through the day, to losing 30kg and returning to her natural weight without dieting or even trying!
Food choices: what does your whole body have to say?
Reward, comfort, stimulation or true nourishment – what do you want from your food and what is driving your food choices?
Nutritional Dogma – Food rules or loving impulse?
When we categorise foods and diet into 'good' and 'bad', are we truly supporting ourselves or creating restrictions and dogma?
Dairy – think "pasteurised pus, antibiotics, inflammation and cancers"
Dairy is addictive, inflammatory and a catalyst for cancer – time to drop dairy. | {
"redpajama_set_name": "RedPajamaC4"
} |
U.S. Army Corps of Engineers (USACE) released details of a closed-door June 8 meeting where options for reopening Canyon Dam's popular service road were discussed by representatives from USACE's Canyon Lake and Fort Worth offices, U.S. Senator John Cornyn's office, Guadalupe Blanco River Authority (GBRA), Comal County and Water Oriented Recreation District of Comal County (WORD).
USACE closed the road to public access without warning on May 21, citing safety concerns. Thousands of area residents as well as tourists walk the trail/road annually to enjoy its spectacular views of Canyon Lake and the Texas Hill Country, and its closure sparked a petition on Change.org that quickly drew 17,500 signatures.
Tim MacAllister, Fort Worth District operations chief, described the Corps' decision to cordon off the road as "difficult" but warned USACE may not be able to obtain funding for upgrades needed to bring the road into compliance with federal guidelines.
In a press release posted to USACE's Fort Worth District website, USACE said it is meeting with stakeholders included discussion of alternatives and funding sources that would make the service road "safe" for mobility devices like wheelchairs and scooters as well as for bicycles, strollers and children's wagons.
Reacting to the announcement on her Facebook page, Jen Crownover, Comal County Commissioner, Pct. 4, told her constituents the Corps and other stakeholders are 100-percent committed to getting the access road reopened.
"Before that happens, some adjustments will need to be made, and we are already at work on those details," she said.
USACE blockaded the road after reaching an impasse with U.S. Access Board over a May 22, 2017 complaint alleging the Corps violated the Architectural Barriers Act.
U.S. Access Board said pedestrian access points to reach Canyon Dam Crest Trail were not accessible to mobility devices, and charged the Corps with flatly refusing to make the trail accessible by widening pedestrian access points to 36 inches and providing greater maneuvering clearance.
Speaking publicly for the first time about its decision, MacAllister said the complaint brought to light safety concerns for all users.
"Having concern for the safety of all users and not wanting to discriminate, the Corps made the difficult decision to close the dam service road to all users until the appropriate safety features and accessibility features could be put into place," he said in the press release.
"Alternatives discussed included constructing a wider pedestrian walk-through to allow wheeled assistive devices such as wheelchairs and scooters to pass through, yet prohibiting motorcycles and other motorized vehicles.
A second measure would include guard rails on both sides of the entire length of the dam service road to provide safety measures for the steep slopes along the service road.
Crownover said in an earlier interview the Corps would seek public funding to help reopen the service road. No cost estimates are yet available.
With this kind of logic, all city, state and national parks will be closed. This is just another example of political correctness gone amok. Common sense is extremely uncommon these days. I thought the American voters spoke out loud and clear that this senseless behavior is not wanted or acceptable any longer. Has anyone asked our current President how he would handle this issue. I doubt it. Seems like the holdovers from the previous administration ( the lost eight years) are still in " so called charge" here.
USACE in Ft Worth is just dragging its feet (as usual). We need to ask Sen Cruz to put pressure on Department of the Army to intercede. Motorcycles can be handled differently than motorized wheelchairs if USACE wants to help us out. Now it is a matter of pride for them.
Why does it need gard rails now but has been fine seance 1964.how meany people have gone over the side of the road?I think the hard rails are over kill. | {
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} |
Today, I woke up with this song in my mind another under rated band, in my opinion ladies and gentlemen, I give you: Dredg.
This is a great idea Cosmin, keep on doing it! I'll check each and everyone of them!
Thunbs up for the good chaps at 'Godmode' - nice Romanian band and their guest Mr. Adi Despot - friend of mine and famous vocalist in my country.
Great music Cosmin! I don't comment but I check this thread every day! Keep the songs coming!
Another pretty underrated band - Dark New Day, and their song 'Follow the sun down'. These guys have been friends for a long, long time and have waited about 12 years to make this band. All of them activated in various other famous groups (Creed, Sevendust, Stereomud). Too bad they disbanded after 2 albums and an unreleased one.
Ummm, Sinisa, is that a bad thing?
Probably, that she was born in America or England, would be greater star than Madonna !
Great thread cosmin Some killer songs/bands that I'd have probably never come across otherwise. Keep it up!
Just to throw something wacky in the mix, here is AUSTRIAN DEATH MACHINE (An Aaaahhnold tribute band) with "Get to the choppa!"
I liked the Godmode song a lot. Romanian sounds very cool when sung.
Hahahah when I'm with Voodoo, we have a thing for Schwartzie's style. This is so awesome I'll keep the stuff coming mates thanks!!
May I suggest 2 songs from Shinedown?
I still don't know how to put the videos in here and not the link if you can do it (and teach me how to do it) would be great!!! | {
"redpajama_set_name": "RedPajamaC4"
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There is a clear need for a democratic system for the election of the government in the UK, as the government has coercive power. However, it is much less clear that a purely democratic system should operate in the business world too. This would mean that companies would be controlled by large boards representing a range of interest groups with varying views about the strategy of the business. This would mean that the purpose of the business would become unclear, thus possibly having a negative impact on profits. Most directors feel that the current general structure of boards elected by shareholders is the most appropriate for competitive private enterprise.
Institutional investors in the UK are increasingly tending to overlook smaller quoted companies, even though these companies employ 2 million people and produce 9 billion pounds sterling a year in profits. Smaller quoted companies may not communicate very well with fund managers, and there is a lack of understanding between the two sides. Waning institutional interest in smaller quoted companies may place restrictions on the ability of many companies to raise equity by securing a listing. Smaller quoted companies seeking to attract investors should provide more information and direct their presentations at specific audiences.
Online banking is becoming more accessible to smaller businesses in the United Kingdom and it can save time and cuts costs. Online services offered vary from bank to bank and can be geared to individual companies, and the charges also vary. Online services for larger firms became common in the late 1980s. Software improvements and reductions in charges have meant that smaller firms are increasingly using these services. Packages are more advanced and user-friendly and technophobia is being combated. | {
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Professor Roger Durham (Ph.D., University of Oregon) joined the Aquinas Community in Fall of 1996. He teaches the international relations and comparative politics courses and coordinates the International Studies Degree. His research interests include: Post- Cold War dynamics between strong andweak states; development issues; theories of the state; international political economy, human rights issues and American Foreign Policy. On campus he is Chair of the Political Science Department, Advisor to the Polis Political Studies Club, Pi Sigma Alpha – Political Science Honor Society, Model United Nations and Model Arab League. He serves on many committees including the Haiti Connection Committee through which he has twice accompanied AQ students on a service learning trip to Haiti. He has twice been honored with the AQ Student Senate Outstanding Faculty Award for the years 1996-97 and 1998-99. He has been nominated by AQ President Knopke for the prestigious CASE Award for Teaching Excellence. He is a member of the International Studies Association, the American Political Science Association and has presented research at several conferences. He is past President of the Michigan Conference of Political Scientists. | {
"redpajama_set_name": "RedPajamaC4"
} |
Operating fields: medical imaging across art and science
The exhibition is a collaboration with NTNU and the interdisciplinary research projects Inside out: New images and imaginations of the body and Picturing the brain: Perspectives on neuroimaging. Both projects explore the intersections of art and science in the field of medical imaging. The collaboration involves scientists, researchers and artists. A closing conference for the projects will be held at Dokkhuset on the 3rd and 4th of September and will include artist talks by the exhibiting artists.
At Babel Christina Lammer presents two video installations. Mirror Mirror (2014) where a young facially paralyzed girl performs her exercises at home in front of the mirror. She is already several years after nerve and muscle transplantation. Hand Movie 0 (2012) is part of a video series that was produced in the operating theatre of plastic and reconstructive surgery where the artist explores gestures of surgeons. With her camera she follows touching moments of surgical treatment and illuminates aesthetic and particularly empathetic aspects in the operating field.
Andrew Carnie's installation Magic Forest is a dreamlike journey through a growing brain's development and its organizing of neurons. Based on scientific results, 162 slides show how neurons expand into a shape resembling trees and other organic material. The installation was made after a collaboration with neuroscientists at Kings College and was presented at the Science Museum in London in 2002.
Andrew Carnie works visually with pictures of the brain and neurons both in painting and larger installations. He is a well-known artist and academic working closely with scientists and research results. Carnie lives and works in Winchester and London as an artist and lecturer. He studied chemistry and painting, zoology, psychology before gaining a BA in Fine Art from Goldsmiths College and an MA in painting at the Royal College of Art. He often works with time-based installations that slowly unfold their narrative. http://www.andrewcarnie.co.uk
Carnie, Andrew
8b71b0b4-5dc7-4ce9-8914-332402077859
(2014) Operating fields: medical imaging across art and science.
Record type: Art Design Item
Submitted date: 28 August 2014
Organisations: Winchester School of Art
Learn more about Winchester School of Art research
PURE UUID: 8f01a5ba-c4f7-47ae-837c-e43c0ab24305
Date deposited: 08 Feb 2016 14:34
Other: Andrew Carnie
Faculties (pre 2018 reorg) > Faculty of Business, Law and Art (pre 2018 reorg) > Winchester School of Art (pre 2018 reorg)
Current Faculties > Faculty of Arts and Humanities > Winchester School of Art > Winchester School of Art (pre 2018 reorg)
Winchester School of Art > Winchester School of Art (pre 2018 reorg) | {
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Have you read the Goalkeepers' Report ?
The Education Support Forum (TEDSF) is a South African registered Non Profit Orgainisation (186-593-NPO) and Public Benefit Organisation (PBO No. – 930061043). TEDSF exists to support human development efforts in Africa through bridging the gap between stakeholders for optimal results in the quest to eradicate poverty.
© The Education Support Forum is a South African registered Non Profit Orgainisation (186-593-NPO) and Public Benefit Organisation (PBO No. – 930061043). | {
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This map of Hood Canal in Washington highlights major interstate and state highways, cities and towns. Find scenic points of interest including Olympic National Forest and Olympic National Park. Click on any to city or town to find more information on accommodations and lodging, activities and outdoor recreation, attractions, food and beverage, visitor information and shopping venues. Utilize the left column to find more information on Hood Canal and more Washington maps. | {
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White House Home stay is located at Kumai Maurey Fari Forest Village, Near Naxal Forest Check Post. We offer cosy home-style rooms for a silent adventure.
White House Home Stay is located at Mourey Village Forest near Naxal Forest check post Dist Kalimpoong Jaldhaka Power Project Road Dooars. Its located in the valley based village from where you can have spectacular view of Himalayas of Bhutan Border and also has a river close by which flows between India and Bhutun where guests can enjoy Fishing as well as Swimming. We also provide activities like Fishing , BBQ, Bonfire and many more like Jungle Safari at Chapramari Wildlife in Dooars.
Kumai is the place of national bird habitat where people can grow everything but economically backward and dependable on agriculture and tea garden. People are honest and kind hearted.
Kumai Pin code is 734319 and postal head office is Lava .
Rongo ( 5 KM ) , Dalim ( 13 KM ) , Gorubathan ( 16 KM ) are the nearby Villages to Kumai. Kumai is surrounded by Matiali Block towards South , Nagrakata Block towards South , Mal Block towards South , Reghu Block towards North .
Mal , Kalimpong , Gangtok , Mainaguri are the near by Cities to Kumai. | {
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Paris 2024 Olympics tickets will go on sale worldwide this week
Martin Belam
Photograph: Marc Piasecki/Getty Images
The organisers of the Paris 2024 Olympic Games have announced that anyone in the world will be able to apply for tickets from Thursday 1 December in a new approach to ticketing for the showpiece event. In a significant change, tickets will be obtainable from a single platform worldwide and will not be available through ticket resellers.
Instead of entering a ballot for tickets for specific sessions or events, those who want to experience the games enter one global draw. Those selected will then be able to have their pick of what they want to see within a specific sales window. "We really wish to make Paris 2024 the first 'Games Wide Open', and we are fully dedicated to bringing this concept to life," said Tony Estanguet, president of Paris 2024.
Related: 'It's been in my mum's attic': iconic GB London 2012 kit set for charity auction
Three million tickets will be available in this phase of sales, representing about 80% of the tickets sold to the public, and applications are open until 31 January 2023. Half of the tickets will cost €50 (£43) or less, while prices for a three-session package start at €72 (£62). Two types of tickets for people with disabilities will be included – wheelchair access places, and accessible places for people with disabilities or reduced mobility who do not use a wheelchair, but who need an accessible seat with minimal steps close to accessible facilities.
However, organisers say that tickets for the opening and closing ceremonies, as well as "for some specific sports sessions", will not be available during this sales phase, and will go on sale in May 2023. "These tickets will be for the opening and closing ceremonies and the premium sessions, such as the 100 metres finals in athletics and swimming, or the basketball final, for example," Michael Aloisio, chief of staff to Estanguet, said.
From 15 February 2023, fans who have been selected by the draw will receive an email with a specific time slot giving them access to what the organisers call "Make Your Games packs" sales for 48 hours. The "Make Your Games packs" allow a visitor to select up to three sessions that they want to attend, and purchase the tickets directly. The first four days of sales will be reserved for members of the Club Paris 2024, which is free to sign up to. People will be able to buy a maximum of 30 tickets across all of the sales phases.
Ticketing has been an issue at many recent Olympic games, with no shows often leading to empty stands in early morning sessions, despite claims the event is sold out. The London Olympics were marred as visitors sometimes had to queue up to six hours to collect tickets from the agencies handling the sales. Paris 2024 will be the first summer Olympics to welcome overseas visitors since Rio in 2016, after the pandemic-impacted Tokyo Games held in 2021 restricted sales to domestic fans.
The Paris ticketing arrangements apply to the Olympic Games, which run from Friday 26 July to Sunday 11 August in 2024. Organisers say that with nearly 10m tickets available in total, this marks the largest number of tickets ever on sale for a sporting event. Sales arrangements for the Paralympics will be announced in autumn 2023.
Dog walker's 'traumatic' cause of death revealed at inquest after mauling in park
Natasha Johnston, 28, was attacked by dogs at a beauty spot in Caterham, Surrey
Bournemouth Echo UK
Dorset rail passengers urged to make new arrangements for upcoming strikes
DISRUPTION to rail services in Dorset is expected at the start of February amid strike action.
Why declutter queen Marie Kondo giving up on tidying is a good thing
To clutter or not to clutter? Marie Kondo's "kind of given up" tidying at home, due to the birth of her third child.
Police offer £10,000 reward for information that tracks down missing couple and baby
Police believe they are still in the country and fear they could be sleeping rough in a tent
Antony Blinken says US opposes anything that puts two-state solution 'further from reach' after violence in Jerusalem
The United States will "continue to oppose anything" that puts a two-state solution "further from reach" after one of the bloodiest months in the West Bank and East Jerusalem in several years, the US secretary of state has said. Antony Blinken said the US opposes Israeli settlement expansion and any moves towards the annexation of the West Bank. The US secretary of state spoke at a news conference in Jerusalem on the second day of a two-day visit to the region where he met Israel's leader Benjamin Netanyahu and the Palestinian president Mahmoud Abbas.
The Last of Us's gay love story breaks new ground for an entire genre
COMMENT: HBO's thrilling post-apocalyptic drama took a detour this week to chart the tender romance between Bill (Nick Offerman) and Frank (Murray Bartlett). It's an incredibly bold move, writes Louis Chilton, one that represents the very best of what adaptation can achieve
Wife of jailed Bolivian opposition leader claims prison 'intimacy' filmed
The wife of a jailed Bolivian opposition leader accused the government Monday of having used a hidden camera to film "intimacy" between her and her husband on a prison visit.The 30-year-old, who married Camacho in May last year, claimed that with "hidden cameras, the government recorded my intimacy as a woman and our intimacy as a couple."
Chuck Todd has fiery exchange with Jim Jordan over difference between Biden and Trump documents
'Biden didn't defy a subpoena, congressman'
Ukraine war a 'massive wakeup call' for British Army, say veterans and experts
Rishi Suna has come under fire from veterans and members of his own party after a US general said the army could no longer defend the UK
Glasgow Times
WATCH: Herd of escaped COWS spotted walking down busy road
A HERD of cows have been spotted making their way along a busy road in Airdrie.
Isle of Wight County Press
Man to stand trial accused of punching ex-girlfriend
The Isle of Wight man is accused of assault by beating and criminal damage in Brading.
Tesco buys Paperchase brand after stationery chain collapses into administration
Hundreds of jobs remain at risk as supermarket will not buy Paperchase's stores
Mickelson 'at peace' if never plays PGA, Ryder Cup again
Phil Mickelson says he will be "at peace" if he never plays in a PGA Tour event or Ryder Cup again, nearly one year after his explosive remarks about the Saudi-funded LIV golf series triggered uproar."If I were never to play another PGA Tour event, I'm totally at peace with it," Mickelson said. | {
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A part of the area covered by this zone of the city is the Historic Site of El Toscal, which is aligned around three main axes heading south to north: Calle de la Rosa, Calle Santiago and Calle San Miguel.
Along Avenida Francisco la Roche you can find a wide range of gastronomy and leisure. On the other hand, at the end of this Avenue you will find the road that leads to the neighbourhood of San Andrés, Las Teresitas Beach and Anaga Rural Park (declared a Biosphere Reserve by UNESCO).
In this zone of the city it is worth highlighting the following places:
North of the city centre, at the end of Calle San Francisco is a more or less triangular-shaped promontory that dropped sharply down El Naciente over what was previously called Roncadores beach, along the edge of which ran the path of San Andrés. Its shortest side faced the city and the earth part overlooked the ravine of Ancheta, which shortly before reaching the sea joined -and still joins under Las Ramblas- with that of La Leña, resulting in a single channel at its mouth. That more or less flat and shallow area where the waves broke, was initially called Playa del Varadero (boatyard beach), as it was where ships were built and repaired in the 16th century. The pilot and owner of one of those boats was Juan de Almeida, and it is very possible that the current place is named after this figure, as was the case with the Cove of Blas Díaz and the Ravine of Santos.
On the side overlooking the sea, since at least the 17th century there has been a vegetable garden named Huerta de los Melones, and the path leading from it, which climbed the slope alongside the right-hand side of the Ancheta ravine was named after it, as was the artillery battery on the same side of the ravine, the Los Melones battery. This is the first precedent of Almeida Fortress, whose construction began in 1859 under the management of the General of the Engineer Unit Salvador Clavijo y Plo, with two main objectives. Firstly, faced with the fact that war ships had powerful artillery that could destroy an entire open gun emplacement or one barely defended behind battlemented parapets with a single hit, it was essential to protect coastal defences facing such attacks with strong fortifications. Secondly, for the first time there was a need to protect the plaza from both sea and land attacks, in case the enemy managed to land via other entry points, as had occurred with Nelson´s first assault on the Bufadero. Had Clavijo´s project been fully carried out, Santa Cruz would have had the most significant fortification in the Canaries, but financial restrictions made it impossible to be completed.
At present, what remains of the entire defensive complex is the central building, the underground casemates of the sea front and little else. In memory of the place´s past activity, the adjoining street is named Calle del Saludo (Salute Street), in remembrance of the salutes that were performed there, from the wall overlooking the sea, to the ships reaching port.
With the construction of several pavilions for housing troops and services, for years the place served as the quarters of the Mixed Artillery Regiment no.93 until it was moved, and it is currently the headquarters of the Centre of Military History and Culture and the Military History Museum of the Canaries.
The Centre acts as a focal point and coordinator for all the cultural activity of the Armed Forces in the Canaries and it has collaboration agreements with the universities of La Laguna and Las Palmas de Canaria. It carries out notable work in the field of publications and organisation of conference series, covering historical and cultural issues in addition to military ones. The Military History Museum operates under the centre. It is one of the best in the country, and was founded by Colonel Juan Arencibia de Torres in 1988, when he was in charge of the regiment.
In the rooms of the former fortress, the public can view countless testimonies, materials, pictures and documents from the history of the Canaries, notably including the monumental model of Santa Cruz de Tenerife which represents the city that the Englishman Vice Admiral Horatio Nelson attempted to storm in 1797, including audio-visual effects. It is also possible to view the famous "El Tigre" cannon temporarily on display in the area under Plaza de España, and the British flags captured from the enemy during their attempt to conquer the island.
These rooms are no longer big enough to exhibit all the available material, so a solution for fitting out the underground casemates -which have an original building typology- is now being sought for a necessary extension. In any case, it is necessary to bear in mind that both the central building and the casemates, once properly restored, are in themselves elements that constitute a part of the wealth of museum treasures in the area.
On the other hand, the entire area of the former quarters is an integral part of the museum, as the heavy materials which do not fit into the display rooms are exhibited outside.
The pavilions which once housed the troops and services of the Artillery Regiment have been properly fitted out and are now home to a large library of historical and military material and the comprehensive Historical Military Archive, containing two million documents made available to researchers and those interested in historic matters, who can use the study and consulting rooms.
LOS LAVADEROS (WASH HOUSES)
During the first two centuries of its existence, the inhabitants of Santa Cruz who lacked wells or cisterns in their homes had to do their laundry by using the currents of the ravines and gullies. This situation was alleviated in 1706 when residents were provided with a public fountain that they could take water from. Despite this, the custom of washing in the ravines remained in force, and it was not until 1820 that the municipal representative Vicente Martinón asked the Council to build public wash houses, an initiative that took more than twenty years to come to fruition.
In 1835 an agreement was reached to request a license from the King to apply to the construction of municipal wash houses, for the time required, half of the taxes charged on wine and spirits in order to pay for the maintenance of the public drains. The following year, the commissioned councillor, Gregorio Asensio Carta, presented the project with a budget and requested that the site for its construction be allocated. The Council took a long time to decide on a location, and another three years to provide a suitable plot of land at the side of the Ancheta ravine, land that was purchased from the Grandy family, right in the place where the drain supplying the city reached to.
However, financial problems and the difficulty supplying wood for construction, delayed its opening until 1842. The revenue from the new facility was auctioned every year for a modest sum that was used to swell the municipal coffers, however the municipality often had to administer the wash houses due to a lack of bidders.
This point was assigned as the terminal for the measurements carried out periodically to determine possible losses from the drain, between the volume that flowed from the source of Mount Aguirre and that which reached the city, which sometimes barely exceeded fifty percent. Throughout its not very dazzling history -complaints due to a lack of hygiene, water restrictions, lack of maintenance, etc.- from 1900 on the facilities were occasionally assigned to a wide range of uses, such as a warehouse, stable for stallions or a public kitchen during epidemics.
The installation resulted in the neighbourhood that now bears its name – Los Lavaderos- founded on the right-hand side of the ravine. Created with a square floor plan, it has sixty basins, fifteen for slapping laundry, and the cistern is located in the centre. It is a special example and authentic relic of unique industrial architecture in the Canary Islands. Following restoration, it is in quite a good state of conservation and remains a municipal property. It is currently used as an art gallery and exhibition space named "Los Lavaderos" (The Wash Houses) and is located on Calle Carlos Chevilly.
Hotel Náutico
It is located on Avenida Profesor Peraza Ayala no. 13. It was opened in 1990 and renovated in 2006. It has a total of 40 rooms. | {
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package org.renjin.primitives.annotations.processor;
import com.google.common.collect.Lists;
import com.google.common.collect.Maps;
import com.sun.codemodel.*;
import org.renjin.eval.Context;
import org.renjin.eval.EvalException;
import org.renjin.eval.Session;
import org.renjin.primitives.annotations.SessionScoped;
import org.renjin.primitives.annotations.processor.args.ArgConverterStrategies;
import org.renjin.primitives.annotations.processor.args.ArgConverterStrategy;
import org.renjin.sexp.Environment;
import org.renjin.sexp.SEXP;
import java.util.Collections;
import java.util.List;
import java.util.Map;
import static com.sun.codemodel.JExpr._new;
import static com.sun.codemodel.JExpr.lit;
public class OverloadWrapperBuilder implements ApplyMethodContext {
protected JCodeModel codeModel;
protected JDefinedClass invoker;
private PrimitiveModel primitive;
private int arity;
private List<JVar> arguments = Lists.newArrayList();
private JVar context;
private JVar environment;
public OverloadWrapperBuilder(JCodeModel codeModel, JDefinedClass invoker, PrimitiveModel primitive, int arity) {
this.codeModel = codeModel;
this.invoker = invoker;
this.primitive = primitive;
this.arity = arity;
}
public void build() {
JMethod method = invoker.method(JMod.STATIC | JMod.PUBLIC, codeModel.ref(SEXP.class), "doApply")
._throws(Exception.class);
context = method.param(Context.class, "context");
environment = method.param(Environment.class, "environment");
for(int i=0;i!=arity;++i) {
JVar argument = method.param(SEXP.class, "arg" + i);
arguments.add(argument);
}
/**
* Tests the arguments given against those of each Java overload
*/
IfElseBuilder matchSequence = new IfElseBuilder(method.body());
List<JvmMethod> overloads = Lists.newArrayList( primitive.overloadsWithPosArgCountOf(arity) );
/*
* Sort the overloads so that we test more narrow types first, e.g.,
* try "int" before falling back to "double".
*/
Collections.sort( overloads, new OverloadComparator());
for(JvmMethod overload : overloads) {
/*
* If the types match, invoke the Java method
*/
invokeOverload(overload, matchSequence._if(argumentsMatch(overload)));
}
/**
* No matching methods, throw an exception
*/
matchSequence._else()._throw(_new(codeModel.ref(EvalException.class))
.arg(typeMismatchErrorMessage(arguments)));
}
private JExpression typeMismatchErrorMessage(List<JVar> arguments) {
JInvocation format = codeModel.ref(String.class).staticInvoke("format");
format.arg(lit(typeMessageErrorFormat(arguments.size())));
for(JVar arg : arguments) {
format.arg(arg.invoke("getTypeName"));
}
return format;
}
private String typeMessageErrorFormat(int nargs) {
StringBuilder message = new StringBuilder();
message.append("Invalid argument:\n");
message.append("\t").append(primitive.getName()).append("(");
for(int i=0;i<nargs;++i) {
if(i > 0) {
message.append(", ");
}
message.append("%s");
}
message.append(")\n");
message.append("\tExpected:");
for(JvmMethod method : primitive.getOverloads()) {
message.append("\n\t");
method.appendFriendlySignatureTo(primitive.getName(), message);
}
return message.toString();
}
private Map<JvmMethod.Argument, JExpression> mapArguments(JvmMethod overload) {
Map<JvmMethod.Argument, JExpression> argumentMap = Maps.newHashMap();
int argumentPos = 0;
for(JvmMethod.Argument argument : overload.getAllArguments()) {
if(argument.isContextual()) {
if(argument.getClazz().equals(Context.class)) {
argumentMap.put(argument, context);
} else if(argument.getClazz().equals(Environment.class)){
argumentMap.put(argument, environment);
} else if(argument.getClazz().equals(Session.class)) {
argumentMap.put(argument, context.invoke("getSession"));
} else if(argument.getClazz().getAnnotation(SessionScoped.class) != null) {
argumentMap.put(argument, context.invoke("getSingleton").arg(JExpr.dotclass(codeModel.ref(argument.getClazz()))));
} else {
throw new UnsupportedOperationException(argument.getClazz().getName());
}
} else {
argumentMap.put(argument, convert(argument, arguments.get(argumentPos++)));
}
}
return argumentMap;
}
private void invokeOverload(JvmMethod overload, JBlock block) {
if(overload.isRecycle()) {
new RecycleLoopBuilder(codeModel, block, primitive, overload, mapArguments(overload))
.build();
} else {
invokeSimpleMethod(overload, block);
}
}
/**
* Invokes with the JVM method simply (without recycling) using the
* provided arguments.
*/
private void invokeSimpleMethod(JvmMethod overload, JBlock block) {
JInvocation invocation = codeModel.ref(overload.getDeclaringClass())
.staticInvoke(overload.getName());
Map<JvmMethod.Argument, JExpression> argumentMap = mapArguments(overload);
for(JvmMethod.Argument argument : overload.getAllArguments()) {
invocation.arg(argumentMap.get(argument));
}
CodeModelUtils.returnSexp(codeModel, block, overload, invocation);
}
private JExpression convert(JvmMethod.Argument argument, JVar sexp) {
return ArgConverterStrategies.findArgConverterStrategy(argument)
.convertArgument(this, sexp);
}
/**
* Compute the expression that will test whether the provided arguments
* match the given overload.
*/
private JExpression argumentsMatch(JvmMethod overload) {
JExpression condition = JExpr.TRUE;
List<JvmMethod.Argument> posFormals = overload.getPositionalFormals();
for (int i = 0; i != posFormals.size(); ++i) {
ArgConverterStrategy strategy = ArgConverterStrategies
.findArgConverterStrategy(posFormals.get(i));
JExpression argCondition = strategy.getTestExpr(codeModel, arguments.get(i));
if(condition == null) {
condition = argCondition;
} else {
condition = condition.cand(argCondition);
}
}
return condition;
}
@Override
public JExpression getContext() {
return context;
}
@Override
public JExpression getEnvironment() {
return environment;
}
@Override
public JClass classRef(Class<?> clazz) {
return codeModel.ref(clazz);
}
@Override
public JCodeModel getCodeModel() {
return codeModel;
}
}
| {
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} |
You are here: What's On > Christian Heritage Weekly Walking Tours
Christian Heritage Weekly Walking Tours
The Round Church
We have been running our highly acclaimed walking tours of Cambridge for nearly 20 years. Come along to explore the beautiful streets and buildings of the city, and learn about some of the people who helped to shape Western civilization.
Walks are held on Saturdays and Sundays at 2.30PM and Mondays at 2.00PM. Each tour lasts around 90 minutes. The cost is £10 per person and £8 for students. This includes entry into the Round Church Visitor Centre.
You are welcome to reserve a spot in advance for these walks through our website: www.roundchurchcambridge.org
Christian Heritage Weekend Walking Tours (1 Jan 2019 - 31 Dec 2019)
Type -- Any -- Cambridge University Events Classical Music Clubs Comedy Exhibitions and Displays Family Festivals Food & Drink Live Music Music and Theatre Outdoor Events Religious Events Sporting Events Stage Talks/Lectures Walks, Tours & Punting Workshops
Start Date Day: 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Month: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year: 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029
End Date Day: 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Month: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year: 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029
Any date in the future
St John's College
St John's College was founded in 1511 by Lady Margaret Beaufort, mother of…
Cambridge Early Music
Cambridge Early Music is a registered charity which offers concerts and…
The Bridge of Sighs
Neo-gothic covered bridge linking the new court of St. John's with the… | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} |
By buying this product you can collect up to 37 loyalty points. Your cart will total 37 points that can be converted into a voucher of 9,25 €.
Start your event with us, enjoy yourself and girls in very special party costumes!
Each one of you will be becam a some misterious character - a princess, a police officer, a franch maid, or a cat-woman! Make a great photos, play special games with a bride, have fun and enjey beginning of your party!
Open up your champagne, make photoshoot in the party costumes and have fun in fantasy fashion studio!
After party it can be ordered a special party car for your company - a limo, medical bus or police car to drive you in the city, Jurmala or other place you want to continue yout event! | {
"redpajama_set_name": "RedPajamaC4"
} |
// Copyright 1998-2016 Epic Games, Inc. All Rights Reserved.
#pragma once
#include "Curves/RichCurve.h"
#include "MovieSceneSection.h"
#include "IKeyframeSection.h"
#include "MovieSceneMpcFloatSection.generated.h"
/**
* A single floating point section
*/
UCLASS( MinimalAPI )
class UMovieSceneMpcFloatSection
: public UMovieSceneSection
, public IKeyframeSection<float>
{
GENERATED_UCLASS_BODY()
public:
/**
* Updates this section
*
* @param Position The position in time within the movie scene
*/
virtual float Eval( float Position ) const;
/**
* @return The float curve on this section
*/
FRichCurve& GetFloatCurve() { return FloatCurve; }
const FRichCurve& GetFloatCurve() const { return FloatCurve; }
public:
//~ IKeyframeSection interface
void AddKey( float Time, const float& Value, EMovieSceneKeyInterpolation KeyInterpolation );
bool NewKeyIsNewData(float Time, const float& Value) const;
bool HasKeys( const float& Value ) const;
void SetDefault( const float& Value );
public:
//~ UMovieSceneSection interface
virtual void MoveSection(float DeltaPosition, TSet<FKeyHandle>& KeyHandles) override;
virtual void DilateSection(float DilationFactor, float Origin, TSet<FKeyHandle>& KeyHandles) override;
virtual void GetKeyHandles(TSet<FKeyHandle>& OutKeyHandles, TRange<float> TimeRange) const override;
virtual TOptional<float> GetKeyTime( FKeyHandle KeyHandle ) const override;
virtual void SetKeyTime( FKeyHandle KeyHandle, float Time ) override;
private:
/** Curve data */
UPROPERTY()
FRichCurve FloatCurve;
};
| {
"redpajama_set_name": "RedPajamaGithub"
} |
module ChefSpec::API
# @since 4.6.0
module ChocolateyPackageMatchers
ChefSpec.define_matcher :chocolatey_package
#
# Assert that a +chocolatey_package+ resource exists in the Chef run with the
# action +:install+. Given a Chef Recipe that installs "7zip" as a
# +chocolatey_package+:
#
# chocolatey_package '7zip' do
# action :install
# end
#
# The Examples section demonstrates the different ways to test a
# +chocolatey_package+ resource with ChefSpec.
#
# @example Assert that a +chocolatey_package+ was installed
# expect(chef_run).to install_chocolatey_package('7zip')
#
# @example Assert that a +chocolatey_package+ was installed with attributes
# expect(chef_run).to install_chocolatey_package('git').with(
# version: %w(2.7.1),
# options: '--params /GitAndUnixToolsOnPath'
# )
#
# @example Assert that a +chocolatey_package+ was _not_ installed
# expect(chef_run).to_not install_chocolatey_package('flashplayeractivex')
#
# @param [String, Regex] resource_name
# the name of the resource to match
#
# @return [ChefSpec::Matchers::ResourceMatcher]
#
def install_chocolatey_package(resource_name)
ChefSpec::Matchers::ResourceMatcher.new(:chocolatey_package, :install, resource_name)
end
#
# Assert that a +chocolatey_package+ resource exists in the Chef run with the
# action +:remove+. Given a Chef Recipe that removes "7zip" as a
# +chocolatey_package+:
#
# chocolatey_package '7zip' do
# action :remove
# end
#
# To test the content rendered by a +chocolatey_package+, see
# {ChefSpec::API::RenderFileMatchers}.
#
# The Examples section demonstrates the different ways to test a
# +chocolatey_package+ resource with ChefSpec.
#
# @example Assert that a +chocolatey_package+ was removed
# expect(chef_run).to remove_chocolatey_package('7zip')
#
# @example Assert that a specific +chocolatey_package+ version was removed
# expect(chef_run).to remove_chocolatey_package('7zip').with(
# version: %w(15.14)
# )
#
# @example Assert that a +chocolatey_package+ was _not_ removed
# expect(chef_run).to_not remove_chocolatey_package('7zip')
#
#
# @param [String, Regex] resource_name
# the name of the resource to match
#
# @return [ChefSpec::Matchers::ResourceMatcher]
#
def remove_chocolatey_package(resource_name)
ChefSpec::Matchers::ResourceMatcher.new(:chocolatey_package, :remove, resource_name)
end
#
# Assert that a +chocolatey_package+ resource exists in the Chef run with the
# action +:upgrade+. Given a Chef Recipe that upgrades "7zip" as a
# +chocolatey_package+:
#
# chocolatey_package '7zip' do
# action :upgrade
# end
#
# The Examples section demonstrates the different ways to test a
# +chocolatey_package+ resource with ChefSpec.
#
# @example Assert that a +chocolatey_package+ was upgraded
# expect(chef_run).to upgrade_chocolatey_package('7zip')
#
# @example Assert that a +chocolatey_package+ was upgraded with attributes
# expect(chef_run).to upgrade_chocolatey_package('git').with(
# version: %w(2.7.1),
# options: '-params "/GitAndUnixToolsOnPath"'
# )
#
# @example Assert that a +chocolatey_package+ was _not_ upgraded
# expect(chef_run).to_not upgrade_chocolatey_package('flashplayeractivex')
#
# @param [String, Regex] resource_name
# the name of the resource to match
#
# @return [ChefSpec::Matchers::ResourceMatcher]
#
def upgrade_chocolatey_package(resource_name)
ChefSpec::Matchers::ResourceMatcher.new(:chocolatey_package, :upgrade, resource_name)
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} |
The legend John Digweed will make his debut at Project 301 on Friday.
The English DJ will deliver his heaven scent beats in between sets at Coachella last weekend and this Sunday.
"It's probably the biggest festival in the U.S. and certainly one of the most respected," Digweed said in an email interview with the El Paso Times. "The Yuma tent where I played was incredible, a purpose built air-conditioned nightclub in the desert. Sound and lighting was amazing and the crowd really up for a party."
There seems to be a lot in store this year for the 49-year-old Digweed. He is preparing for a fall tour with Sasha to celebrate the 20th anniversary of "Northern Exposures". Fans appear ecstatic after seeing the two play first set together since 2010. Digweed and Sasha played a surprise back-to-back set at the Ministry of Sound's Easter Bedrock Party.
After more than two decades, Digweed weathers the changes in the scene.
"It's great," Digweed said. "To be honest the fact that it constantly changes and new artists arrive all the time keeps it fresh and me on my toes."
Digweed was ranked the No. 1 DJ in 2001's DJ Magazine Top 100 rankings. He maintained a spot in the top 10 from 1998 to 2008. The Englishman's well of creativity never runs dry, it still provides after a long career.
"I love what I do and get a real buzz from being in front of a crowd who wants to hear me play," Digweed said.
The EDM business has become commercialized, definitely not as underground as it used to be. The only way to differentiate the real from the fakes is to identify "someone who plays from the heart and with passion, rather than someone who wants the spotlight and lifestyle," Digweed said.
Digweed also owns a label, Bedrock Records. Somehow between touring, he finds time to balance it all. With much more music coming out, it can be a challenge to find talent.
"Yes and no, a bad track is still a bad track so finding those stand out tracks is where the skill comes in," Digweed said.
The journey continues for Digweed.
"For me clubbing is my life 24/7-365 (days a year)," Digweed said. "I am as inspired now as I was when I first saw a pair of technics."
Kristopher Rivera may be reached at 546-6121; [email protected]; @kgrivera on Twitter. | {
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} |
Q: Angular2-crumbs and lazy loading component I am trying to use Angular2-crumbs with lazy loader components in my project. Somehow breadcrumb is working fine but my lazy loader component doesn't load and not throwing any error in the console either.
What I have understand from the Angular2-crumbs code that it works only with children components. Since my requirement is to use lazy loading so what I did is that I am redirecting from app to root component where I have all lazy loading components under the children of root component.
The arrangement of my code is given below:
app.routing.modules.ts
export const routes: Routes = [
{path: '', redirectTo: 'root', pathMatch: 'full'}
];
@NgModule({
imports: [RouterModule.forRoot(routes)],
exports: [RouterModule]
})
export class AppRoutingModule {
}
app.module.ts
@NgModule({
declarations: [
AppComponent
],
imports: [
CoreModule,
BrowserModule,
BrowserAnimationsModule,
RouterModule.forRoot(routes)
]
providers: []
bootstrap: [AppComponent]
})
export class AppModule {
}
app.component.ts
import { Component } from '@angular/core';
@Component({
selector: 'my-app',
templateUrl: './app.component.html',
styleUrls: ['./app.component.css']
})
export class AppComponent {
title = 'app';
}
app.component.html
<router-outlet></router-outlet>
root-routing.module.ts
@NgModule({
imports: [
RouterModule.forChild([
{
path: '', component: RootComponent, children: [
{ path: '', component: HomeComponent },
{
path: 'screen/home', component: HomeComponent, data: { breadcrumb: 'Home' }, children:[
{ path: 'orders', loadChildren: './../app/orders/module#Module', data: { breadcrumb: 'Order management'} },
{ path: 'stocks', loadChildren: './../app/stocks/module#Module', data: { breadcrumb: 'Stock management' } },
]
}
]}
])
],
exports: [ RouterModule ]
})
export class RootRoutingModule {}
root.module.ts
@NgModule({
declarations: [
HomeComponent,
RedirectComponent,
RootComponent
],
imports: [
CoreModule,
BrowserModule,
BrowserAnimationsModule,
BreadcrumbModule.forRoot(),
HttpClientModule,
RootRoutingModule
],
providers: [
BannerService,
BlockService,
CanDeactivateGuard,
ConfirmationService,
CoreService,
GenericService,
HttpClient,
MessageService,
RedirectComponent,
]
})
export class RootModule {
}
root.component.ts
import { Component, OnInit } from '@angular/core';
@Component({
selector: 'root',
templateUrl: 'src/root/root.component.html',
styleUrls: ['src/root/root.component.css']
})
export class RootComponent implements OnInit {
constructor() { }
ngOnInit() {
}
}
root.component.html
<breadcrumb></breadcrumb>
<router-outlet></router-outlet>
There is no extra documentation provided in the Angular2-crumb repo so I don't have any clue how to solve this problem.
If anyone can help me I would appreciate you in advance.
Thanks!!!
A: I have solve this issue by doing some minor changes in root-routing.modules.ts below:
root-routing.modules.ts
@NgModule({
imports: [
RouterModule.forChild([
{ path: '', component: HomeComponent, pathMatch: 'full' },
{
path: 'screen/home', component: RootComponent, data: { breadcrumb: 'Home' }, children: [
{ path: 'orders', loadChildren: './../app/orders/module#Module', data: { breadcrumb: 'Order management'} },
{ path: 'stocks', loadChildren: './../app/stocks/module#Module', data: { breadcrumb: 'Stock management' } },
]}
])
],
exports: [ RouterModule ]
})
export class RootRoutingModule {}
So my conclusion after checking the Angular2-crumbs code again is that it works with first children component.
A: There is a simple solution to this.
Track the last index in the *ngfor loop of the breadCrumb component.
Angular exposes local variables for ngfor to track elements of the loop.
https://angular.io/api/common/NgForOf
Replace the customizable code mentioned in the angular-crumbs customizable code. I am demonstrating below using a bootstrap example.
From:
<breadcrumb #parent>
<ol class="breadcrumb">
<ng-template ngFor let-route [ngForOf]="parent.breadcrumbs">
<li *ngIf="!route.terminal" class="breadcrumb-item">
<a href="" [routerLink]="[route.url]">{{ route.displayName }}</a>
</li>
<li *ngIf="route.terminal" class="breadcrumb-item active" aria-current="page">
{{ route.displayName }}</li>
</ng-template>
</ol>
</breadcrumb> }
Change To:
<breadcrumb #parent>
<ol class="breadcrumb">
<ng-template ngFor let-route [ngForOf]="parent.breadcrumbs" let-lastIndex="last">
<li *ngIf="!lastIndex" class="breadcrumb-item">
<a href="" [routerLink]="[route.url]">{{ route.displayName }}</a>
</li>
<li *ngIf="lastIndex" class="breadcrumb-item active" aria-current="page">
{{ route.displayName }}</li>
</ng-template>
</ol>
</breadcrumb> }
The value of lastIndex will be a boolean value. Here, when we know the breadcrumb ngfor loop is at last value, mark it as active.
That is how you solve the fantastic angular-crumbs library problem with Lazy Loading. Let me know if you need an example.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} |
Stormzy Headlines Friday
Stormzy Headlines Day 2 at Glastonbury
Stormzy's history making headline set at Glastonbury has attracted praise from his fellow stars and politicians alike.
The 25-year-old grime star is the first British black male to headline Glastonbury and the second youngest person ever to play the slot.
Nik Fisher, 28, from east London, said: "It was insane. It was out of this world. He did so well. The vibe and energy was incredible so we're really happy about it. We saw him two years ago as well, it was definitely a level up from that. It was unbelievable."
Jordain Edwards, 23, from south London, said: "I've seen him about five or six times before. I think the first time I saw him was eight years ago when I was about 16 or 17. So to see him now on the Pyramid Stage was insane.
"It's a moment for the whole community, the whole culture, it's crazy."
Across Twitter, fans called him a king, a hero, and a national treasure.
One said the set was a moment to be remembered in Black British history.
And Labour leader Jeremy Corbyn tweeted: "The performance was political, iconic and the ballet was beautifully powerful. It won't just go down in Glastonbury history - it'll go down in our country's cultural history."
Labour MP for Tottenham, David Lammy, praised Stormzy for sampling a speech he had given about black men and the justice system.
He tweeted: "@stormzy using his headline spot at #glastonburyfestival2019 to speak out about the injustice of young black kids being criminalised in a biased and disproportionate justice system. Humbled and inspired that he sampled my speech. Salute #Merky."
Writing on his Instagram story, Canadian rapper Drake said: "@Stormzy headlining Glastonbury and that. Madness congrats."
Stormzy's girlfriend, the TV presenter Maya Jama, tweeted: "ICONICCCCCCCC."
Ghetts tweeted: "God bless Stormzy and long live the culture the ones before and the ones after this is a moment for everyone who laid a brick to help build our house."
Tottenham-born rapper Wretch 32 tweeted: "Champions league the league of champions."
Hip-hop star Konan, also from the London grime scene, said: "This crazy man the feeling I have in my chest right now watching this I have to watch this again."
Ed Sheeran shared a picture of the rapper, real name Michael Omari, on stage, and wrote: "First black British solo artist to headline Glastonbury, second youngest to ever headline, and just an inspiration to so many.
"This is just the start, congrats big Mike, looking forward to see you do more achievements like this."
A449 Castle Street - Worcester, Worcestershire
Tim Haycock playing Whitesnake - Here I Go Again | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} |
5G is untested, intrusive, and being forced on Us with disingenuousness, lies, and omissions. I interviewed Annie Logical (YouToilet channel: Logical Annie) who is a 5G researcher and activist against this hideous technology, which is really the ability to "crowd control" Us at the push of a button. Can We doubt that there are psychopaths in control?
I highly recommend We ALL push this technology into the waste bin - for Our sake, and the sake of Our children.
sometimes an article or vid supports two or more threads.im so glad i came across it at lop.5g is the devil.its 3.2 mm bandwidth kills birds and creates pain if more than one antenna is pointed at people and animals.the newest antennas have robotically tilting and panning equipment on them to increase signal strength in temporary high density population areas.these could be used to police or harass.
as my experience proves,this technology cannot be trusted even in police hands.thus this equipment should be banned.along with radar guns.
if a hacker got access it could get bad and im one thats knowledgable enough of the system to know its easily hackable.imagine swarms of bugs.this technology can swarm insects.like in the days of moses.by turning it off,then turning it on.then concentrating it into a focal area while slowly panning it could cause minor irritation to bugs of whichever one chose based on eyes or nerves of the critter.these plagues could then be migrated to one individual location.such as swarming rats onto one apartment or business location.
this technology should be in no ones hands!
It's ghastyly unEthical, it is. Like GMO. Indeed, is will be used for "crowd control..." And worse.
Ah, the havoc money creates in this world. Along with promoting psychopaths to power.
EDIT to add: I ponder this article, as it looks much like part of the play the psychopaths are putting on here on the literal world STAGE. And given CHINA is a corporation, like all the rest of the "governments," and is owned by the same psychopaths that own the rest, I doubt "espionage" is a necessary thing... More script to sell Us as "reality," I wager.
We really need to fight this, for Humanity's sake! Thanks for adding more data, robo.
top microwave scientist.saying what i was living.what ive been saying about bugs also.
Yes indeed! 5G is NOT for the benefit of Humanity. Cui bono...? The psychopaths in control.
i know hes a gatekeeper but i thought video was relavent for its mainstream awakening.
my personal story is so unbelievable and i hope my effort shows that the things that have happened in my life ive stated are believable.i really was a radio tower climber for twenty years.im really a hobbiest physicist.i really did have a neighbor shoot me with a dew weapon.i really do have a schizophrenic wife whos triggered by cop radar guns and microwave.i hear it as tinnitus.
now two years later government politicians are taking notice of the threats surrounding us.i hope 5g doesnt overshadow the entire emf spectrum of danger.especially nexrad radar units pointing south in regards to inversion.
i worry of that too amy.just a dulled spear point.thing is my politicians know of this board and read it.thats why they are two of the top congressmen.cruz and gohmert.along with wyomings legislatures.thats why the anti drilling bills passed so fast for around yellowstone.they were having governors race and i sent link of yellowstone thread to governors competition.lol.it works.a new law was created and passed in weeks!
this forum is read by people who cant be named but see the facts and react to them accordingly.5g is very dangerous and thats a fact.all microwave is.
Just curious how You know They're reading My humble little forum... LOL! If You can't say, I will endure not knowing. Haha!
But I do hope that enough of Them are fully Human (and not psychopaths) and really want to do something for Humanity on Our planet. I don't have HIGH hopes on that, but hopes nonetheless. Maybe They can help create better on Our planet.
May 5G die a rapid death!
Oh yes, 5G is not healthy for children or other living things. Just like war. In fact... It is a war on Humanity.
notice in one pic of man holding antenna,if you notice the spacing of circles,that 3.2 mm wide.the pain ray.the spacing is how you tell what wavelength,then a chart of emf will show you the frequency.
its the wavelenth that matters.it tells you the depth and width of harm on the human body.this means 3.2 mm wide and 3.2mm deep is the least damage you will get.anything more conductive than air,like blood,goes even deeper,lol,but not funny.now think of a thousand antennas under emergency control all focusing on you.or i dont know,maybe a hacker having a bad day.
like a grape in a microwave oven.
oh, the gov lottery decided it was your day to die?
nice website and im a believer hes on to something.
chest tightening ,sounds familiar.more of an anxiety at the frequency i was exposed to.
Indeed, it is not just stupid, it is unEthical. "Evil." Ghastly. Hideous. Planned and being implemented. By the psychopaths in control. | {
"redpajama_set_name": "RedPajamaC4"
} |
Date this page was last updated: 03/12/2012
River Loadout Safety
One of the greatest worries at the river docks has to be falling into the river and being crushed between the coal barge and the dock barge. Barges have completely vertical sides and are deep into the water, about 9 feet. Dock workers are often working near this dangerous, narrow area while changing out empty and loaded barges and while measuring the draft as the barge is being loaded. Even a strong swimmer would not have a chance of escape if caught between the long coal barge as it floated against the dock barge.
One company, Kanawha River Terminals (KRT), has developed a device they call a "Smash Box" (see photographs below) in an effort to counter this hazard. The smash box is stored close-to-hand at the river edge of the dock, ready to be thrown into the water between the coal barge and the dock barge. The aluminum box floats and is strong enough to prevent the barge from closing against a person who may have fallen into the area of danger.
Smash Box in use at Kanawha River Terminals (photographs: WVMHST)
In addition to the smash box, each person's life jacket is equipped with a Man Overboard Alert System that sounds an alarm in the tug boat and in the loadout operator's station. Crews are trained to immediately stop all barge and boat movements when the man overboard alarms sounds. After a quick look into the water, the smash box is thrown into the water to keep the narrow space open between the barges while the person is being rescued. Throw Rings are also available at various locations at the facility.
The wire ropes used to move the coal barge during the loading operations are another recognized hazard. The rope used to stabilize the barge, called the "monkey rope" can suddenly flex inward toward the walkway along the dock. The can happen when the barge attachment rope or pulley fails. KRT has installed heavy steel posts between the monkey rope and the dock walkway as a safety precaution to protect persons using the walkway. For further information contact Kanawha River Terminals at the following address:
Kanawha River Terminals, Inc.
150 Dairy Lane
Belle, WV 25015
The "Smash Boxes" and Man Overboard Alert System can be obtained from:
Smash Boxes Man Overboard Alert Systems
Parson's Machine Co. Emarld Marine Products
Ashford, WV Seattle, WA
304-836-5612 1-800-426-4201 or 206-781-9450
(Roger Parsons) (Page Read)
Note: This is a non-promotional, informational listing only. There may be other companies which provide similar products.
UPDATE: In January 2006 the U>S> Coast Guard approved an innovative personal-flotation device which allows for quicker response and greater reach for water rescue. The Personal Retriever is an authorized substitute for the orange or white ring buoys. It is an aerodynamic disc made of expanded polyethylene foam. The device can be deployed by hand out to 100 feet in 10 seconds or less. (from the GCMA News January/ February 2006) Find out more about this device by contacting: The Gulf Coast Mariners Association P.O. Box 3589, Houma, LA 70361-3589 website: www.gulfcoastmariners.org. Or Life-Safer, Inc (www.lifesafer.com)
The State of West Virginia and the West Virginia Office of Miners' Health Safety and Training does not maintain these sites and is not responsible for their content or management. If you would like to report a problem, please call the West Virginia Office of Miners' Health Safety and Training at 304.558.1425.
[MHS&T Homepage] [ Publications Page] [ Frequently Asked Questions] | {
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The Boat Table Lamp is part of our collection of coastal living lighting for your beach cottage or bungalow. This lamp measures 32"H and is UL/CUL listed and approved...and so affordable!
Shown in Cottage with Navy accent and finial. | {
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This Saturday 19, 2013 we held at the Aula Magna of the Universidad Peruana de Ciencias Aplicadas the first SAP CodeJam Lima.
We have around 20 people and I talked about SAP HANA.
As I'm from Peru…and haven't come back in 2 years and 8 months…I decided to start the day with a little session called "From Lima to Montreal…from Consultant to Development Expert" to tell people about my experiences, motivations, problems and successes.
This SAP CodeJam was a replicate of the one I did in Montreal as I simply translate the whole Workbook into Spanish…we talk about Tables, Views, Attribute, Analytical and Calculation Views, connection with Microsoft Excel and SQLScript.
As always, I tried to show people how versatile and easy to use SAP HANA is with some examples and real life applications. | {
"redpajama_set_name": "RedPajamaC4"
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"redpajama_set_name": "RedPajamaCommonCrawl"
} |
8.You can download the code here,modify and compile programs by keil ,then burn the program by STC-ISP-V4.86.
First,choose the right MCU (STC12C5A60S2).
Second,open the file of .HEX .
Third,choose the right COM (Automatic Identification) .
Fourth,Start burning,when click 'ISP programming',at the same time press the power button twice, power off and then power on .
Note : Download the microcontroller when the need for cold start (meaning that the microcontroller needs to power off and then re-power to download), the power switch as a cold start on the line, download the device is connected to the need to disconnect the switch and then re-power can be downloaded, Host computer connection method (no cold start, do not dial the power cord and then plug), with the power cord directly on the line.
This page was last modified on 21 November 2017, at 04:02.
This page has been accessed 24,285 times. | {
"redpajama_set_name": "RedPajamaC4"
} |
Patient leaders from around the world meet at 3rd RDI Annual Meeting in Barcelona
The RDI Membership Meeting 2017 Barcelona (3rd Annual Meeting) was held on June 4th, 2017 in Castelldefels, Barcelona, Spain. Over 50 participants from 23 countries were able to network with patient advocates from around the world, learn more about recent developments in international rare disease advocacy and receive information to become further involved in RDI activities.
The first part of the meeting was reserved for members only. The objective was to inform members of the activities undertaken by the Alliance in 2016 as well as the Work Plan and Budget for 2017. This was also the ideal moment to discuss with them outreach and recruitment plans to give more visibility to RDI and attract additional members to the Alliance, which counts 47 members to date. Representatives of member organisations present, were also able to meet personally the two most recently-elected members of the Council: Ritu Jain, President of DEBRA Singapore and Board Member of DEBRA International and Kin Ping Tsang nominated by RETINA International and President of the Hong Kong Alliance for Rare Diseases.
The second part of the meeting was open to all umbrella patient groups and other stakeholders interested in working in the field of rare diseases at the international level. Participants received information about the latest advocacy actions community to put rare diseases in the global health and development agenda. In particular, feedback from the first Rare Disease Policy Event in Geneva in February and the launch of the NGO Committee for Rare Diseases at the United Nations in New York last November. At the meeting, participants were also able to discuss ways in which they could contribute to these efforts through their Ministries of Health and Foreign Affairs or through their Permanent Representations to the UN in New York or Geneva. This session was also the ideal opportunity to further understanding of the UN system and the synergies between rare diseases and the Sustainable Development Goals 2030 Agenda with its mission to 'leave no one behind'. The session also included information about the different types of UN Resolutions and strategies to obtain a UN Resolution on Rare Diseases.
The broader UN perspective was followed by an environmental scan of rare disease policy at the national and regional levels. 12 patient leaders from Asia (India, Iran, Hong Kong, Malaysia and Singapore); Latin America (Colombia, Mexico and the Iberoamerican Alliance for Rare Diseases); Africa (South Africa), North America and Europe (USA, Canada and Spain) gave an overview of rare disease policy, trends and challenges in their region of the world.
The country panels were introduced by a presentation of the Report on the State of the Art of Rare Disease Activities in Europe (RD –ACTION) by Victoria Hedley of Newcastle University. The presentation triggered a discussion on the importance of data collection at country level and the development of a pilot project to include non-EU countries in this survey.
The final part of the meeting was intended to highlight examples of the advocacy work of RDI members in order to gauge the advocacy priorities for the rare disease patient community at the international level. Presentations included the advocacy work that has been undertaken by the World Federation for Hemophilia, the International Niemann-Pick Disease Alliance, the BLACKSWAN Foundation and the rare disease national alliances of Argentina and Colombia.
15 RDI fellows from India, Malaysia, South Africa and 6 Latin American countries, stayed on to attend the ExPRESS 2017 Expert Patient and Researcher EURORDIS Summer School (English and Spanish versions) that took place in Barcelona the week following the RDI annual meeting (June 5-9, 2017).
Global Environment: Advances and Opportunities
RDI Joint Declaration: Rare Diseases: An International Public Health Priority – Lisa Phelps, Secretary of the Council of Rare Diseases International and Director of Marketing and Community Relations, National Organization for Rare Disorders
Understanding the UN system and UN SDGs 2030 – Clara Hervás, Public Affairs Junior Manager, EURORDIS-Rare Diseases Europe
NGO Committee for Rare Diseases, New York – Yann Le Cam, Chief Executive Officer of EURORDIS – Rare Diseases Europe and Member of the Council of Rare Diseases International
RDI Rare Disease Day Policy Event Geneva – Paloma Tejada, Senior Manager, Rare Diseases International
A United Nations General Assembly Resolution: an introduction to the concept – Clara Hervás
Strategy towards a UN Resolution on rare diseases – Yann Le Cam
Review of 11 National Policies for Rare Diseases in the Context of Key Patient Needs, Safiyya Dharssi, Director – International Public Affairs, Rare Disease & Inflammation/Immunology, Pfizer Inc
Presentation of the Report on the State of the Art of Rare Disease Activities in Europe, and pilot project to extend beyond the European Union, Victoria Hedley, RD ACTION, Newcastle University, UK
Environmental Scan of Rare Diseases Around the World: Advances and opportunities
Rare Diseases South Africa
Federacion Colombiana de Enfermedades Raras
Alianza Iberoamericana de Enfermedades Raras (ALIBER)
Federación Mexicana de Enfermedades Raras (FEMEXER)
Advocacy Opportunities: Where and How Do We Go Forward?
Building on Grassroots successes and initiatives
Christoph Poincilit, International Niemann-Pick Disease Alliance (INPDA)
Chiara Ciriminna, BLACKWSAN Foundation
Mark Brooker, World Federation of Hemophilia (WHF)
Angela Chaves Restrepo, Federación Colombiana de Enfermedades Raras (FECOER)
Review of 11 national policies for rare diseases in the context of key patient
Presentation of the Report on the State of the Art of Rare Disease Activities in
Rare Diseases International Membership Meeting 2017 https://t.co/JllN9ohGjl
— RDI (@rarediseasesint) 4 juin 2017
Environmental Scan of Rare Diseases Around the World: Advances and
Rare Connect and RDI | {
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Galerie Stephan Witschi
Jungjin Lee
Jungjin Lee's latest series Unnamed Road approaches the contested territories of Israel and the West Bank through landscape photography imbued with an elemental vastness that is at once powerful and serene.
"My project focuses on the deserts and the land that contains layers of history. The land has always been changing, but there are some fundamental truths that have never changed. This aspect of Israel was what I wanted to concentrate on and reveal through my photographs.
You can feel the history of the country in the land. The land embraces fragments of past lives. What remains in the present gives you a feeling of what has happened there in the past. In that sense, the diverse terrain can be approached both physically and emotionally.
What I am searching for in my photographs is something about life. It's about the solitary state of being human. Life changes on the surface, like an ocean. You have the constant movement of water on the surface. But deep down, at the core, there is no movement."
- Jungjin Lee
Lee's Unnamed Road series is included in This Place a traveling exhibition of twelve photographers including Thomas Struth, Jeff Wall and Josef Koudelka. "This Place" travels to the Tel Aviv Museum of Art, Brooklyn Museum of Art, Norton Museum of Art and other museums in Europe, the USA and Asia through 2016.
Jungjin Lee is one of the most celebrated Korean photographers of our time. Her work is in the collections of the Metropolitan Museum of Art, Whitney Museum of Art, L. A. County Museum of Art, National Museum of Contemporary Art in Korea, and others.
www.stephanwitschi.ch
Zwinglistrasse 12
Stephan Witschi
[email protected]
Jungjin Lee, | {
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CDA 2.0.4 (31st October 2017).
CDA 2.0.5 (1st December 2017).
CDA 2.0.6 (2nd February 2018).
CDA 2.0.7 (23rd February 2018).
CDA 2.0.8 (20th April 2018).
LIXI continues to seek involvement in order to refine and extend this standard from industry participants. If you are interested in joining this collaborative effort, please email Louise Harper. | {
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Kurnool: A video clip showing money 'being rained' on public at a political meet at Sirivella village in Allagadda constituency went viral on Thursday. The party in question was reportedly YSRC.
There was intense fight between YSRC candidate Gangula Bijendra Reddy and TD candidate Bhuma Akhila Priya. Villages which were once pocket burrows of Bhuma family have now been rallying behind Gangula family.
An enthusiastic supporter reportedly took out a wad on Rs 10 notes and rained it on the audience in front of him apparently pleased by the enormous support galvanised for Gangula Bijendra Reddy.
Allagadda DSP said that a complaint had been lodged on Thursday by a TD worker and a case was registered. It is being viewed as an election offence, he said.
The video clip and the details there of were being enquired into, the DSP said. | {
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Q: Machine Public IP I already had a small code that does this but it seems like it was not doing what i really needed it to do.
I was using the following commands to get Public IP.
dig +short myip.opendns.com @resolver1.opendns.com
curl ipinfo.io/ip
Sadly, these give me the Public IP that the rest of the world can see my machines/servers as. In reality, they all have different public ip addresses. Sadly, i have no idea how i can get it from Linux terminal.
Right now i have:
redmine XXX.XXX.XXX.238
mail XXX.XXX.XXX.234
git XXX.XXX.XXX.237
But when i use the commands i mentioned below, i get
XXX.XXX.XXX.227
This is also the public IP that everyone sees us as, thats why these commands don't work. Any suggestions?
A: You may want to read about NATs (https://en.wikipedia.org/wiki/Network_address_translation). You did not share the entire IP, so I can only suspect, but I believe the IPs for redmine, mail and git are private IPs (only inside your network), while the one ending in 227 is the public one for all 3 services.
Does the following command return the same .227 IP address from both redmine, mail and git servers (if you SSH into them)? If so, then you are behind nat and that is the public IP for all 3 machines.
curl v4.ifconfig.co
How about the v6 IP? Is it the same for all 3?
curl v6.ifconfig.co
| {
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Each year the Computerworld Honors Program recognizes individuals and organizations that create and use information technology to promote and advance public welfare, contribute to the greater good of society and change the world for the better.
We are proud to say that four Cisco nominees from public sector, including one school district and one university, were selected as Gold Medal Laureates because of their innovative uses of collaboration technology. Brief descriptions of all four are listed below.
Every year, the California Correctional Health Care Services (CCHCS) provides healthcare for over 166,000 inmates at 33 adult correctional facilities throughout California. However, many of the prisons under CCHCS' care are located in rural areas, where healthcare specialists are in short supply. To tackle this healthcare discrepancy, the CCHCS implemented a robust solution: the CCHCS Telemedicine Program. Through the Telemedicine Program, CCHCS contracts with private healthcare entities to provide virtual specialty care services to California inmates—an initiative that necessitates collaborating with over 7,000 California healthcare and prison staff including doctors, nurses, administrative staff and pharmacists.
MGSD in North Carolina encompasses eight schools and over 5,500 students in grades K-12. Of the 115 school districts in North Carolina, MGSD ranks 99th on the state's per-pupil-expenditure (with first place spending the most). Additionally, the district faces a high poverty rate. MGSD developed and launched a revolutionary strategic program—the Digital Conversion Program—to employ technology resources to improve teaching and learning with a focus on academic achievement, engagement, opportunity and equity. Since the Digital Conversion Program's 2008 implementation, student achievement at MGSD has skyrocketed.
The Ninth Judicial Circuit in Florida serves Orange County (Orlando) and Osceola County (Kissimmee) and represents a population of over 1.37 million. To address the rising demand for interpreters and create efficiencies in the court process, the Ninth Circuit developed a remote, centralized interpreting system that provides on-demand virtual language interpretation services to courts. By integrating video and audio technology into the court, the Ninth Circuit was able to change the entire system of interpreter service provision, effectively aligning supply and demand in a way that has allowed the Court to eliminate unnecessary expenditures, cover more transactions and improve the quality of interpretation within the judicial system.
USM is a comprehensive doctoral and research-extensive university. The devastation of Hurricane Katrina, the BP oil spill, and the following flood that inundated the Mississippi Sound caused faculty and staff to leave the region, and required some classes to be taught in trailers. With faculty having to travel between sites, office hours for students seeking help suffered. Travel budgets were exhausted and travel between the various locations became an inefficient process—hindering those critical sessions of collaboration between staff that enable a university to grow and develop. USM created the Distance Learning and Collaboration (DLC) initiative to bridge the gap between disparate USM faculty and staff members at the various campuses, university and teachers, and the university and surrounding K-12 districts.
An awards gala will be held on June 4, 2012 at Andrew W. Mellon Auditorium in Washington, D.C. to recognize the Laureate Class of 2012.
We congratulate this year's recipients and are proud to see how Cisco technology benefiting society! | {
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At this page you will find information about our 2017 meetings. To the best of our ability, we present the minutes for each general meeting, the attendance records for each general meeting where available, and the minutes of each executive meeting beginning with June 2017 where available.
Nonmember attendees: Kathleen Spaine, Tristan Shields, Brigita Sebold, Debra White, Teresa White, Jacob Bennington, Olivia DuVall, and Dave Bell.
To the best determination of 2018-2019 Chair Ben Hixon, records of attendance for July 2017 are unavailable.
To the best determination of 2018-2019 Chair Ben Hixon, records of attendance for September 2017 are unavailable.
October 2017 Executive Meeting minutes unavailable.
To the best determination of 2018-2019 Chair Ben Hixon, records of attendance for November 2017 are unavailable. | {
"redpajama_set_name": "RedPajamaC4"
} |
Bids/contracts
Caltrain
Local Shuttles
Local Shuttles Resources
Dumbarton Rail
Local Streets
Grade Separation
Peds & Bikes
Congestion Relief
Call for Projects
SB Grade Sep
RT1 Calera Pkwy
101-Broadway
101-Ralston Bridge
101-Aux Lanes
HMB Highway
Oyster Point
RT92 Climbing Lanes
280 Overpass
280-Eastmoor
SMCTA Board Calendar/Meetings
Measure A
Measure W
CAC Calendar
> smcta.com > About > Media Relations > News > Transportation Authority Signs Off On BAIFA Deal, Authorizes $53 Million Loan to Complete Express Lanes Project
Transportation Authority Signs Off On BAIFA Deal, Authorizes $53 Million Loan to Complete Express Lanes Project
The San Mateo County Transportation Authority (TA) Board of Directors took two actions to advance the San Mateo US 101 Express Lanes Project at their meeting last Thursday. The Board voted to execute a four-party agreement for toll system design services with the Bay Area Infrastructure Financing Authority (BAIFA), the City and County Association of Governemnts of San Mateo County (C/CAG) and the San Mateo County Express Lanes Joint Power Authority (SMCELJPA), and also authorized a $53 million loan for the project.
The agreement tasks BAIFA with the responsibility to complete the toll system design for the project, covering both the hardware and software that will be used to operate the toll system. The four parties agreed to a cost of $3 million for this aspect of the project, which will be funded by bridge toll revenue. The toll system design is targeted to be complete by December of this year.
The loan will fund the remainder of the $514.3 million project, with the rest coming from local, state, federal and private sector sources. This loan will be paid back by future toll revenues generated by the express lanes.
The San Mateo US 101 Express Lanes Project, currently slated for completion at the end of 2022, will build an express lane in each direction on US 101 from the San Mateo/Santa Clara County line to Interstate 380, a distance of about 22 miles.
Express lanes will allow carpools with three or more people and buses, including SamTrans express routes like the recently-launched FCX, to travel for free. Others can travel in the lane for a toll, while maintaining a targeted 45 mph traffic flow.
Construction is under way on the south segment from the Santa Clara County line to Whipple Avenue in Redwood City, and should be complete by early 2020. Construction will begin on the north segment from Whipple Avenue to Interstate 380 in 2020 and will be complete late 2022.
About the TA: Created to administer Measure A, San Mateo County's ½ sales tax, the Transportation Authority provides funding for transportation and infrastructure improvement projects. In 2004, more than 75 percent of San Mateo County residents voted to reauthorize Measure A for an additional 25 years.
Media Contact: Dan Lieberman, 650-508-6385
Call for Projects - Archives
Citizens Advisory Committee Calendar
View meetings calendar
4:30 PM TA Citizens Advisory Committee Meeting
5:00 PM Transportation Authority Board Meeting
View Past Meetings Calendar
Copyright ©2019 | Privacy Policy | San Mateo County Transit District | {
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"redpajama_set_name": "RedPajamaC4"
} |
My interesting is art. I am arial photographer and video maker. My department is advertising, wedding photograph and movie. My company name is Medyaprodü[login to view URL] thank you.
I require a small Boys wear clothing range from sizes 1-7. I require patterns for each style and design prints.
Phonegap client. Online and offline map. I meed show a map and draw point on it. Also if the user is for fist time in the aplication is going to have the map online, but the option to download the map and used offline. Also i meed to draw some point in the map.
Our Project name is E-Skyway. Its online or offline Typing work process . Simple medical form filling work. Process is for 10 Months. Task mode and Payment mode will be monthly.
Hi, The project consists on making the pattern and grading (sizes S, M, L, XL) from a picture/photo of the clothes, ready to be printed on a plotter, for later fabric cutting. Clothes: 1 Apron - Japanese style.
We need a m...kept CONFIDENTIAL at all times now and in the future - the work you do for us should not be quoted as reference to anybody nor should be advertised or listed anywhere online/offline. If you have any questions, feel free to ask. We prefer someone with a good track record who has done this work before and would like to get started asap.
...Our current solutions are offered only to other businesses currently and we are searching for more partners. We can offer solutions to providers for online English learning, offline English learning and a combination of both. As many of these companies may be Chinese, being able to read and write Chinese is a bonus. Note: Chinese market is our focus.
I...for the people that know how to assemble a game. I would give all the art of the game (visuals, music, sounds, etc...) and I need someone to take those and build it in Game Maker or another platform in order to release it for PC, Mac and Linux. DISCLAIMER: ONLY PEOPLE WITH GREAT OR EXCELLENT BACKGROUND, I WILL NOT GIVE ALL MY WORK TO ANY PERSON.
Hello, The project is to create an offline data entry form. The form should be able to accept text, attach multiple photos to it, and capture GPS locations. After the form is filled, the data can be extracted into an excel sheet.
looking for a shoes designer. I've got my designs and technology at hands, whats missing is the shoe maker. I want shoes in bulk and the budget is price per shoe. | {
"redpajama_set_name": "RedPajamaC4"
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Tag Archives: human rights
Limiting Power
November 14, 2018 Constitutionaccountability, Constitutional change, human rights, international corporationsSheila
Credit where credit is due: not only has the Trump administration rekindled civic engagement (scholars tell us that the number of people on the streets protesting exceeds the number who protested the Vietnam War), but his accidental ascension to the Presidency has highlighted the need to revisit constitutional provisions that no longer serve their intended purposes.
The problem, of course, is that We the People are too divided and too historically and civically illiterate to be trusted with the task of constitutional revision.
When–and if–the time ever comes that we are capable of making careful revisions to our foundational document, there are a number of issues to consider. The most obvious, of course, is the Electoral College, but there are also several aspects of federalism that should be reconsidered in light of contemporary technology and transportation. For example, there is no reason elections should continue to be administered by the states. A national, nonpartisan agency could maintain a national registration database, ensure standardized procedures and hours, and dramatically curtail partisan game-playing of the sort we've seen in Georgia and the incompetence Hoosiers experienced in Porter County, Indiana.
There is an even more significant assumption that we need to re-think.
The American Constitution limits the power of the state. It was written at a time when governments were the entities wielding the most power, and focusing on the state made sense because constraining power was the whole point. The protection of personal autonomy–our individual right to direct our own lives, so long as we don't harm the person or property of others and so long as we are willing to let others do the same–was the goal, and it required restraints on power.
I thought about that when I read this article from Common Dreams. Today, many governments are less powerful than multi-national corporations.
As corporations in the United States and around the world continue to reap record profits thanks to enormous tax cuts, widespread tax avoidance schemes, and business-friendly trade and investment policies, an analysis by Global Justice Now (GJN) published Wednesday found that the world's most profitable companies are raking in revenue "far in excess of most governments," giving them unprecedented power to influence policy in their favor and skirt accountability.
Measured by 2017 revenue, 69 of the top 100 economic entities in the world are corporations, GJN found in its report, which was released as part of an effort to pressure the U.K. government to advance a binding United Nations treaty that would hold transnational corporations to account for human rights violations.
"When it comes to the top 200 entities, the gap between corporations and governments gets even more pronounced: 157 are corporations," GJN notes. "Walmart, Apple, and Shell all accrued more wealth than even fairly rich countries like Russia, Belgium, Sweden."
As difficult as it can be to subject governments to the rule of law, constitutions and legal systems do provide mechanisms to hold them accountable. By contrast, it is incredibly difficult for citizens to hold powerful corporations to account. Increasingly, as the article notes, trade and investment deals allow corporations to demand that governments do their bidding rather than the other way around.
"From a coal mine in Bangladesh that threatens to destroy one of the world's largest mangrove ecosystems to hundreds of people at risk of displacement from a mega-sugar plantation in Sri Lanka, corporations and big business are often implicated in human rights abuses across Asia" and the world, Friends of the Earth Asia Pacific noted in a blog post on Wednesday, describing the U.N. treaty as a potential "game-changer."
"Companies are able to evade responsibility by operating between different national jurisdictions and taking advantage of corruption in local legal systems, not to mention the fact that many corporations are richer and more powerful than the states that seek to regulate them," Friends of the Earth concluded. "We must right this wrong."
The question, of course, is how?
It is becoming increasingly clear that massive reforms to global law and governance will be required if human liberty is to survive the changes that increasingly confront us. Given the numbers of people who have an overwhelming fear of change and who respond by embracing tribalism and autocracy, the odds of a successful "reboot" look pretty daunting.
Human Rights, Equal Rights, Political Rights
May 12, 2017 Constitution, Public Policy and GovernanceColumbus, gerrymandering, human rights, Indiana, Milo SmithSheila
Last night, I spoke at the annual dinner of the Columbus, Indiana, Human Rights Commission. Here's what I said (sorry for the length…):
Over the past several years, American political debate has become steadily less civil. Partisan passions have overwhelmed sober analysis, and the Internet allows people to choose their news (and increasingly, their preferred realities). During the recent election cycle, it was clear that in many cases, Americans were talking past each other rather engaging with opponents through thoughtful public discourse.
I am firmly convinced that an enormous amount of this rancor and partisan nastiness is a result of what I call civic illiteracy—widespread ignorance of the historical foundations and basic premises of American government. I don't want to belabor this lack of civic literacy, but I do want to share some statistics that should concern all of us. A few years ago, the Oklahoma Council of Public Affairs asked high school seniors in that state some simple questions about government. Let me share a few of those questions and the percentages of students who answered them correctly:
What is the supreme law of the land? 28%
What do we call the first ten amendments to the Constitution? 26%
What are the two parts of the U.S. Congress? 27%
Who wrote the Declaration of Independence? 14%
What are the two major political parties in the United States? 43%
We elect a U.S. senator for how many years? 11%
Who was the first President of the United States? 23%
Only 36 percent of Americans can name the three branches of government. Fewer than half of 12th graders can describe federalism. Only 35% can identify "We the People" as the first three words of the Constitution. Only five percent of high school seniors can identify or explain checks on presidential power. (There's a lot more depressing research on IUPUI's Center for Civic Literacy website.)
Why does it matter? Well, for one thing, productive civic engagement is based on an accurate understanding of the "rules of the game," especially but not exclusively the Constitution and Bill of Rights– the documents that frame policy choices in the American system.
Understanding the history and philosophy that shaped what I call "the American Idea" is critically important for understanding the roots of our national approach to human rights.
The American Constitution was a product of the 18th Century cultural, intellectual and philosophical movement known as the Enlightenment. Most of us know that the Enlightenment gave us science, empirical inquiry, and the "natural rights" and "social contract" theories of government, but what is less appreciated is that the Enlightenment also changed the way we understand and define human rights and individual liberty.
We are taught in school that the Puritans and Pilgrims who settled the New World came to America for religious liberty; what we aren't generally taught is how they defined liberty. Puritans saw liberty as "freedom to do the right thing"—freedom to worship and obey the right God in the true church, and their right to use the power of government to ensure that their neighbors toed the same line. The Founders who crafted our constitution some 150 years later were products of an intervening paradigm change brought about by the Enlightenment and its dramatically different definition of liberty.
America's constitutional system is based on an Enlightenment concept we call "negative liberty." The Founders believed that our fundamental rights are not given to us by government; instead, they believed that rights are "natural," meaning that we are entitled to certain rights simply by virtue of being human (thus the term "human rights") and that government has an obligation to respect and protect those inborn, inalienable rights.
Contrary to popular belief, the Bill of Rights does not grant us rights—it protects the rights to which we are entitled by virtue of being human against infringement by an overzealous government. The American Bill of Rights is essentially a list of things that government is forbidden to do. For example, the state cannot dictate our religious or political beliefs, search us without probable cause, or censor our expression—and government is forbidden from doing these things even when popular majorities favor such actions.
In our system, those constraints don't apply to private, non-governmental actors. As I used to tell my kids, the government can't control what you read, but your mother can. Public school officials can't tell you to pray, but private or parochial school officials can. If government isn't involved, neither is the Constitution. Private, non-governmental actors are subject to other laws, like civil rights laws, but since the Bill of Rights only restrains what government can do, only government can violate it. I'm constantly amazed by how many Americans don't understand that.
Unlike the liberties protected against government infringement by the Bill of Rights, civil rights laws represent our somewhat belated recognition that if we care about human rights, just preventing government from discriminating isn't enough. If private employers can refuse to hire African-Americans or women, if landlords can refuse to rent units in multifamily buildings to LGBTQ folks, if restaurants can refuse to serve Jews or Muslims, then the broader society is not respecting the human rights of those citizens and we aren't fulfilling the obligations of the social contract that was another major contribution of Enlightenment philosophy.
The Enlightenment concept of human rights and John Locke's theory of a social contract between citizens and their government challenged longtime assumptions about the divine right of kings. Gradually, people came to be seen as citizens, rather than subjects. The new concept of human rights also helped to undermine the once-common practice of assigning social status on the basis of group identity.
The once-radical idea that each of us is born with the same claim to human rights has other consequences. For one thing, it means that governments have to treat their citizens as individuals, not as members of a group. America was the first country to base its laws upon a person's civic behavior, not gender, race, religion or other identity or affiliation. So long as we obey the laws, pay our taxes, and generally conduct ourselves in a way that doesn't endanger or disadvantage others, we are all entitled to full civic equality, no matter what our race, religion, gender or other identity. When our country has lived up to that guarantee of equal civic rights, we have unleashed the productivity of previously marginalized groups and contributed significantly to American prosperity. And I think it is fair to say that—despite setbacks, and despite the stubborn persistence of racial resentments, religious intolerance and misogyny, we have made substantial progress toward a culture that acknowledges the equal humanity of the people who make up our diverse nation. So on that scale, good for us!
In addition to civic equality, however, respect for human rights also requires democratic equality—an equal right to participate in self-government. We now recognize—or at least give lip service to—the proposition that every citizen's vote should count, but on this dimension of human rights, we not only aren't making progress, we're regressing, as anyone who follows the news can attest.
One element of civic literacy that gets short shrift even among educators is the immense influence of systems in a society—an appreciation of the way in which institutions and conventions and laws shape our understanding of our environments, and obscure our recognition of social problems. Right now, longstanding practices are obscuring the degree to which American democracy is becoming steadily less democratic—and the extent to which we are denying citizens the human right to participate meaningfully in self-government.
Vote suppression has been on the rise, especially but not exclusively in Southern states that have not been required to get preclearance from the Justice Department since the Supreme Court gutted the Voting Rights Act. Thanks to population shifts, the current operation of the Electoral College gives disproportionate weight to the votes of white rural voters, and discounts the franchise of urban Americans. Ever since Buckley v. Valeo, which equated money with speech, and especially since Citizens United, which essentially held that corporations are people, money spent by special interests has overwhelmed the votes and opinions of average citizens.
The most pernicious erosion of "one person, one vote" however, has come as a consequence of gerrymandering, or partisan redistricting. There are no "good guys" in this story—gerrymandering is a crime of opportunity, and both political parties are guilty.
Those of you in this room know the drill; after each census, state governments redraw state and federal district lines to reflect population changes. The party in control of the state legislature at the time controls the redistricting process, and they draw districts that maximize their own electoral prospects and minimize those of the opposing party. Partisan redistricting goes all the way back to Elbridge Gerry, who gave Gerrymandering its name—and he signed the Declaration of Independence—but the process became far more sophisticated and precise with the advent of computers, leading to a situation which has been aptly described as legislators choosing their voters, rather than the other way around.
Academic researchers and political reformers alike blame gerrymandering for electoral non-competitiveness and political polarization. A 2008 book co-authored by Republican Norman Orenstein and Democrat Thomas Mann argued that the decline in competition fostered by gerrymandering has entrenched partisan behavior and diminished incentives for compromise and bipartisanship.
Mann and Orenstein have written extensively about redistricting, and about "packing" (creating districts with supermajorities of the opposing party) "cracking" (distributing members of the opposing party among several districts to ensure that they don't have a majority in any of them) and "tacking" (expanding the boundaries of a district to include a desirable group from a neighboring district). They have tied redistricting to the advantages of incumbency, and they have also pointed out that the reliance by House candidates upon maps drawn by state-level politicians has reinforced what they call "partisan rigidity"– the increasing nationalization of the political parties.
Interestingly, one study they cited investigated whether representatives elected from districts drawn by independent commissions become less partisan. Contrary to their initial expectations, the researchers found that politically independent redistricting did reduce partisanship, and in statistically significant ways, even when the same party retained control.
Perhaps the most pernicious effect of gerrymandering is the proliferation of safe seats. Safe districts breed voter apathy and reduce political participation. After all, why should citizens get involved if the result is foreordained? Why donate to a sure loser? (For that matter, unless you are trying to buy political influence for some reason, why donate to a sure winner?) What is the incentive to volunteer or vote when it obviously won't matter? It isn't only voters who lack incentives for participation, either: it becomes increasingly difficult for the "sure loser" party to recruit credible candidates. As a result, in many of these races, voters are left with no genuine or meaningful choice. Ironically, the anemic voter turnout that gerrymandering produces leads to handwringing about citizen apathy, usually characterized as a civic or moral deficiency. But voter apathy may instead be a highly rational response to noncompetitive politics. People save their efforts for places where those efforts count, and thanks to the increasing lack of competitiveness in our electoral system, those places often do not include the voting booth.
If the ability to participate meaningfully in self-governance is a human right, partisan game-playing that makes elections meaningless should be seen as an assault on human rights. And increasingly, it is.
Safe districts do more than disenfranchise voters; they are the single greatest driver of governmental dysfunction. In safe districts, the only way to oppose an incumbent is in the primary–and that almost always means that the challenge will come from the "flank" or extreme. When the primary is, in effect, the general election, the battle takes place among the party faithful, who also tend to be the most ideological voters. So Republican incumbents will be challenged from the Right and Democratic incumbents will be attacked from the Left. Even where those challenges fail, they create a powerful incentive for incumbents to "toe the line"— to placate the most rigid elements of their respective parties. Instead of the system working as intended, with both parties nominating candidates they think will be most likely to appeal to the broader constituency, the system produces nominees who represent the most extreme voters on each side of the philosophical divide.
The consequence of this ever-more-precise state-level and Congressional district gerrymandering has been a growing philosophical gap between the parties, each with an empowered, rigidly ideological base intent on punishing any deviation from orthodoxy and/or any hint of compromise.
A study done by researchers at the University of Chicago concluded that Indiana is the fifth most gerrymandered state in the country. We had a chance to change that system in the just-concluded legislative session; Representative Jerry Torr, a good government Republican, introduced a measure that was co-sponsored by Brian Bosma, the Republican Speaker of the House. Thanks to efforts by the League of Women Voters and Common Cause, the public came out in droves from all over Indiana in a massive show of support for the bill; however, the chair of the Elections Committee, Milo Smith, refused to allow his committee even to vote on it, and killed it.
In the United States, we tend to think of Human Rights in terms of legal rights: equality before the law, an equal right to participate in democratic governance and to have our preferences count at the ballot box. But most of us recognize the existence of non-legal challenges to full realization of equal human rights. Poverty is one; a citizen working two or three jobs just to put food on the table doesn't have much time for civic engagement, and in Indiana, that's a lot of people.
In 2014, the United Ways of Indiana took a hard look at "Alice." Alice is an acronym for Asset Limited, Income Constrained, Employed; it applies to households with income above the federal poverty level, but below the actual, basic cost of living. The report was eye-opening.
More than one in three Hoosier households cannot afford the basics of housing, food, health care and transportation, despite working 40 or more hours a week.
In Indiana, 37% of households live below the Alice threshold, with some 14% below the poverty level and another 23% above poverty but below the cost of living.
These families and individuals have jobs, and most do not qualify for social services or support.
The jobs they are filling are critically important to Hoosier communities. These are our child care workers, laborers, movers, home health aides, heavy truck drivers, store clerks, repair workers and office assistants—yet they are unsure if they'll be able to put dinner on the table each night.
ALICE families don't have time or energy for civic participation or political engagement through which to exercise their human and civil rights. Human Rights Commissions lack the jurisdiction to address ALICE inequities, but we all need to recognize that people preoccupied by a daily struggle for subsistence are unable to participate fully in the formation and conduct of civic society.
How can our civic institutions—including local Human Rights Commissions– help guarantee citizens' human rights?
Human Rights Commissions can act when employers or owners of public accommodations violate local ordinances. Indiana also has a civil rights law, although it currently omits protection against discrimination based upon sexual orientation and gender identity, and the federal government has several agencies charged with enforcement of civil rights—although recent statements from Administration officials have called their commitment to doing so into question. Local to federal, these agencies are important, and the work they do is critical to social stability and fundamental fairness.
Critical as they are, there are rights violations these agencies cannot address or solve. Reversing the erosion of America's democratic norms, turning back the assault on equal access to the ballot box, and fixing the gerrymandering that makes too many votes meaningless will require political action and persistent civic engagement by an informed, civically-literate citizenry. We all have a stake in improving civic knowledge and encouraging informed participation, because safeguarding human rights ultimately depends upon the existence of a civically-informed electorate.
It won't be easy, but We the People can do this.
Institutionalizing the 'Macaca moment'
May 29, 2012 Random Blogginghuman rights, Macaca moment, You TubeSheila
You'd have to be hiding under a rock not to notice the multiple ways in which the Internet has changed politics. Back when I first became politically active, I used to write direct mail pieces for candidates; that was a time when you could tailor one message for moms, one for firefighters, etc. Candidates who weren't too scrupulous could and did use direct mail to take positions that were–shall we say– inconsistent with each other. Candidates could also make speeches to certain audiences that they wouldn't necessarily want broadcast more widely.
The Internet has made that sort of micro-targeting virtually impossible.
The most-cited example: When George Allen was running for Senate from Virginia (yes, he's doing that again), he stopped mid-speech to point out a young man filming the talk for his opponent. The volunteer was an American of Indian ancestry, and Allen referred to him as 'macaca'–a term later determined to be a racist epithet in the country Allen's mother had come from. The young volunteer uploaded the film to You Tube, and the rest, as they say, is history: the clip went viral, prompting reporters to take a closer look at Allen's other racially-charged behaviors, Allen lost an election in which he had been heavily favored, and "macaca moment" became part of our political vocabulary.
Just as television brought the Viet Nam war into American living rooms, and arguably sparked the anti-war movement, You Tube and similar technologies give an immediacy and impact to events we might otherwise shrug off or ignore.
Now, You Tube has decided to play a more intentional role in world affairs. It has just announced a Human Rights channel. As the announcement put it:
In the case of human rights, video plays a particularly important role in illuminating what occurs when governments and individuals in power abuse their positions. We've seen this play out on a global stage during the Arab Spring, for example: during the height of the activity, 100,000 videos were uploaded from Egypt, a 70% increase on the preceding three months. And we've seen it play out in specific, local cases with issues like police brutality, discrimination, elder abuse, gender-based violence, socio-economic justice, access to basic resources, and bullying.
This is going to get interesting.
A Widespread Misunderstanding
March 4, 2012 ConstitutionBill of Rights, Constitution, human rights, rightsSheila
A recent comment posted to this blog demonstrates a widespread–and pernicious–misunderstanding of the role of the U.S. Constitution. The commenter demanded to know where there was any reference to healthcare in the constitution.
The answer, of course, is that no such reference exists–just as there's no reference to, say, smoking. Or marriage. Or the right to drive a car. Or the internet.
The constitution does not grant us rights. It limits the government's right to infringe on those rights. The founders believed that we have certain "inalienable" rights by virtue of being human (hence "human rights"). Some believed those rights were "endowed by the Creator." But Creator or no, those human rights preceded governments and their laws; the Bill of Rights was intended to constrain government from ignoring or invading them.
The bottom line is that government can pass laws and create programs that the legislature believes will advance the general welfare, so long as those laws and programs do not run afoul of the limits imposed by the document itself, or by the Bill of Rights. We are all free to disagree about the wisdom of government's policy choices; we are equally free to debate whether, in close cases, government has crossed the lines established by the constitution.
But when we look to the language of our constituent documents for permission–when we view government as the source of our rights–we betray a fundamental misconception of the role of government and law in these United States. | {
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If you agree that parts of Alameda look like the Leave It to Beaver set, then Scalise's is where Mrs. Cleaver would have gotten her meat cleaved. Occupying one end of the midcentury modern Encinal Market, the family-run meat counter has been an Alameda institution since 1935. The fifty-foot-long case is packed with USDA choice cuts of beef, lamb, natural chicken, seafood, and deli products, plus harder-to-find items such as quail, rabbit, and duckling. The "Papa Scalise" brand sausage and pasta sauce are made on the premises using family recipes from the homeland of Calabria, Italy. Other popular delicacies are the marinated tri-tips, stuffed chicken, and steak cordon bleu. Weekday mornings are the best time to shop. These are men who know their meat, and over-the-counter advice flows freely. Scalise's also offers catering -- keeping many demanding customers coming back for seconds, including most of the East Bay's Italian-American organizations. Other notable carnivores, the Oakland Raiders, are well represented with signed autographs on the wall. Says Joe Scalise: "They are hearty eaters, and they like good food." | {
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Horn Law Offices offers personal attention to our clients as we walk them through every step in the legal process. Your initial consultation is FREE, and the legal fees and costs are always explained during the first visit.
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The investigation into who hit a 12-year-old boy on his bike last month is getting a major break as police are revealing only to 7 Action News who they believe is responsible for this terrible crime.
He U.S. Marshals say Dominique Amos may be the most heartless fugitive we've ever searched for – his actions right here last month, changing a 12 -year-old boys life forever and now they need your help to find justice.
He's one of Detroit's Most Wanted. | {
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CAREER: Civil Engineer
February 9, 2019 – When asked to define servant leadership, how that applies to his life now, and his future career, Jules Cesar said: "I would define servant leadership as a form of leadership which involves more understanding than commanding. As the leader puts himself/herself in the followers' shoes before making any decision. Simply put, it is leading with a follower's perspective. Personally, I live a life of a servant leader almost every day, and it has impacted me positively, both inside and outside. I remember last year, with few high school friends, we started a group that would help us connect with each other and help one another in any case. It was tiresome, and demanded a lot of commitment to make it work. After few weeks, one of them came up to me and told me how exemplary I was to him, it was a minor gesture but it made me look back at what made him do so. And surprisingly, it was because I was a servant leader. In my career, I am planning to strengthen my servant leadership because I will work with many humble people and sometimes who are not even literate. So, if I don't focus on that, I may end up asking one of the bricklayers why he hasn't acquired a smartphone or doesn't know how to use certain engineering software. While it couldn't be possible, due to a number of reasons that I just can't understand because I am not leading from his perspective."
November 19, 2018 – Jules Cesar wants to be known as a person who succeeded despite all the challenges and obstacles he faced! He wants to inspire others to persist and never give up! This semester, he plans to focus on improving his social skills and punctuality!
July 7, 2018 – This last school year the thing that was the most challenging Jules Cesar was time management. He said he can vividly remember a time when he had multiple things to do in one day, he had meetings, had to pick up his phone from being repaired, and had to take a test in a class. He unfortunately ended up messing things up that day, however he was able to make his meeting with Auntie Jackie who gave him advice about time and stress management. He is now able to better prioritize and let go of what he cannot control, which has helped with his school and to know his limits in terms or taking on extra responsibilities. He has two big goals he wants to accomplish this summer, the first is to learn Spanish and the second is to learn how to drive a car! Outside of these two things he is looking forward to being home with his family and being able to cook with them, he said from what he can tell so far it's going to be an amazing summer!
May 12, 2018 – The two things Jules Cesar values most are people and God, because he said that those are the two things he would sacrifice everything for. It is also because of those two things that he has been able to accomplish all of his achievements and is where he is in life now!
March 25, 2018 – When Jules Cesar was younger, he wanted to be a pilot because his father told him he would be a great pilot since he was doing so well in math! In five years, he hopes to be a good engineer that is serving his community and the country!
Feb 27, 2018 – Jules Cesar said that it is the love of his family and friends what inspires him to be better and to always go the extra mile! He wants to always push for a better and brighter future for those around him.
Jan 25, 2018 – Jules Cesar said the most interesting book he read was, Things Fall Apart by Chinua Achebe. One of his favorite lines is, "The sun rises for those who are already awake."
Dec 18, 2017 – The main things Jules Cesar says people do to celebrate Christmas is eating special foods, usually made up of meat and rice, and wearing new clothes! Jules Cesar says the word he thinks his friends would use to describe him is "happy" because he always tries to have a smile on his face!
Nov 11, 2017 – Jules Cesar is thankful for what God has provided for him, and is excited for Christmas because it is a time where everyone gets together to spend time with family.
Oct 8, 2017 – Two things Jules Cesar says he was blessed by this summer was to be a part of the These Numbers Have Faces family, and to have had the chance to hear the word of God from an inspirational pastor. Jules Cesar is excited about starting a new life and to strive to be a great ambassador of his family as well as his community.
MESSAGE jules
Jules'S CIRCLE
G. & J. Thurston – Portland, OR
Prince of Peace Lutheran Church – Portland, OR
Jules Cesar could have given up hope of education when his mom passed away in 2011 leaving a newborn baby to care for, but he knew that he must focus on the future. His vision stayed firmly on a career in civil engineering as a career that would provide for his family's financial needs and his country's infrastructure needs.
Wise beyond his years, Jules Cesar is excited to study Civil Engineering at university and to learn leadership skills with These Numbers have Faces because, "you cannot make bricks without straw, and you cannot make a community a better place without knowledge."
Outside of school, Jules Cesar serves as a representative on the National Youth Council for his community — ensuring the wellbeing of students and representing the youth people of his town on a national level. He also co-founded a club called Inspire250 where they work on touring secondary schools around the area, inspiring the next group of students!
The Kykers • California
"We believe These Numbers Have Faces is doing some of the best work on the continent." | {
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Some people come for just a few sessions: others come over a longer period of time. An initial session provides the opportunity to consider if counselling might be of benefit to you.
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bauxite mali
Geography of Mali Wikipedia
Mali is a landlocked nation in West Africa, loed southwest of Algeria, extending southwest from the southern Sahara Desert through the Sahel to the Sudanian savanna zone. Mali's size is 1,240,192 square kilometers. Desert or semidesert covers about 65 percent of Mali
CORRECTEDMali more than triples bauxite reserves estimate
Apr 04, 2017 · BAMAKO, April 4 (Reuters) Bauxite reserves in Mali's Falea project are now estimated at 1.63 billion tonnes, which is equivalent to 572 tonnes of refined aluminium following several new
China to Develop Guinea Port The Maritime Executive
China Harbour Engineering Company (CHEC) signed a $770 million contract with Guinea's government last Monday to upgrade the port in the capital, Conakry, expanding Chinese economic influence in
Guinea Wikipedia
The sovereign state of Guinea is a republic with a president that is directly elected by the people and is head of state and head of government.The unicameral Guinean National Assembly is the legislative body of the country, and its members are also directly elected by the people. The judicial branch is led by the Guinea Supreme Court, the highest and final court of appeal in the country.
Africa :: Mali — The World Factbook Central Intelligence
Slowing Mali's population growth by lowering its birth rate will be essential for poverty reduction, improving food security, and developing human capital and the economy. Mali has a long history of seasonal migration and emigration driven by poverty, conflict, demographic pressure, unemployment, food insecurity, and droughts.
Guinea List of African Countries
Guinea is loed on the Atlantic Coast of West Africa and is bordered by GuineaBissau, Senegal, Mali, Côte d'Ivoire, Liberia, and Sierra Leone. The country is divided into four geographic regions: a narrow coastal belt (Lower Guinea) the pastoral Fouta Djallon highlands
Reuters: Guinea News
Reuters is your source for breaking news, business, financial and investing news, including personal finance and stocks. Reuters is the leading global provider of news, financial information and technology solutions to the world's media, financial institutions, businesses and individuals.
RARE AFRICAN AUTHENTIC KHOMISSAR PENDANT TUAREG NECKLACE
AFRICAN RITUAL NECKLACE HEIRLOOM KHOMISSAR LEATHER PENDANT JEWELRY. Materials : LEATHER, BAUXITE, BLACK HORN PIPES. The Tuareg were recorded by the Greek historian Herodotus in the 5th Century BC. Ethnically related to Berbers and often described as "lightskinned," Tuareg culture dates back centuries.
Mining industry of Mali Wikipedia
The mining industry of Mali is dominated by gold extraction which has given it the ranking as the third largest in Africa. Artisanal miners play a large part in the mining of diamonds. The other minerals extracted are rock salt and semiprecious stones. Phosphates are mined in the Tilemsi Valley.
Camec discovers 439Mt bauxite resource in Mali
JOHANNESBURG (miningweekly) – Londonlisted Central African Mining & Exploration Company (Camec) has discovered an inferred bauxite resource of 439million tons in Mali, the company
Nalco to Open New Bauxite Mine at Panchpatmali – Aluminium
A senior official in India's government told domestic media this week that stateowned National Aluminium Company Limited (Nalco) recently begun the process of opening a new mine at its operations in Panchpatmali. Citing the delays encountered by the firm in obtaining a new mining area, the unnamed official said such a move would help Nalco []
Mali Triples Bauxite Estimates to 1.63 Billion MT
After a series of significant discoveries, the Republic of Mali's Chamber of Mines now estimates a tonnage of 1.63 billion metric tons lies beneath the surface of its Falea project, which it says is equivalent to 572 million metric tons of primary aluminium. Chamber of Mines President Abdoulaye Pona informed Reuters earlier this week that []
The Mismanagement & Abuse Of Africa's Natural Resources
Jul 19, 2002 · The problems of Africa continues to grow and its solution is not clear or well articulated. African leaders continue to depend on foreign countries to solve their problems. Not only that African
Bauxite – Ministry of Mines and Geology Republic of Guinea
Set to become a world leader in bauxite and alumina Guinea holds substantial worldclass reserves of bauxite, both in terms of quality and quantity, and was the world's fifth highest producer of the ore in 2014 (source: World Bank, Commodity Markets Outlook, January 2016). With the recent entry of a number of new industrial players into production and an increase in the production capacity
France does not need Mali's uranium despite all conspiracy
Jan 24, 2013 · There is a meme circulating on web claiming that France's intervention in Mali can be traced to a desire to capture the country's uranium resources.That idea is complete and utter rubbish that can only be believed by people who have done no math and no research to recognize whether such a theory can be supported by facts and logic.
screening of bauxite sale Mali DBM Crusher
Guinea Mining Annual Review bauxite ore crusher machine for sale in GuineaBissau11 Mar 2000 Mining saprolite ore at Soci233t233 Mini232re de Dinguiraye's Karta open pit in northeastern Guinea neighbours are GuineaBissau Senegal and Mali and to the east economy Sales of bauxite alumina gold value while equipment and consumables that are . Get Price
Mali Resources and power Britannica
Mali Resources and power: Mali's mineral resources are extensive but remain relatively undeveloped. Exploited deposits include salt (at Taoudenni), marble and kaolin (at Bafoulabé), and limestone (at Diamou). The most important exploited mineral is gold, a significant source of foreign exchange. Gold is mined primarily in the southwestern areas of the country, on the Mandingue Plateau.
Mali Map and Satellite Image Geology
Mali is loed in western Africa. Mali is bordered by Senegal and Mauritania to the west, Algeria to the north, Niger to the east, and Burkina Faso, Guinea, and Cote D'Ivoire (Ivory Coast) to the south. If you are interested in Mali and the geography of Africa our large laminated map of Africa
Guinea GraphicMaps
Guinea is an African country covering 245,857.00 km2 of which 0.06% is water and 245,717.00 km2 is land. This makes it the 77th largest country in the world and slightly smaller than Oregon. Its geographic coordinates are 11 00 N, 10 00 W and Conakry is the capital city.
Bauxite: Freetown, Accra and Abidjan aspire to match
Wanting to make the most of this current trend, Mali's minister of mines, Tiemoko Sangare, has pointed out to investors that his country holds 1.2 billion tonnes of bauxite. Interest in Mali, however, remains subdued. Only Comifa and Mali Mineral Resources hold bauxite titles.
Bauxite Beads – The Bead Chest
Bauxite is a type of aluminium ore. All African bauxite beads are hand made and drilled, making these beads very labor demanding. Bauxite beads like these have been imported from Africa for decades. African Bauxite beads are known for their unique bauxite color and bauxite texture. Also known as "African pipestone" th
Bauxite mining comes to halt at Hindalco mine Business
Bauxite mining by Aditya Birla owned Hindalco Industries has came to a grinding halt in the Mali Parbat area near Semiliguda in south Odisha's Koraput district with the district administration imposing prohibitory orders under Section 144 of CrPC.. The prohibitory orders have been clamped in the area on August 21 in the wake of tussle between pro and antimining groups over mining of bauxite
Bauxite Mali vbl
Bauxite Archives AfricaBusiness. Mali's Growing Mining Sector Upcoming Prospects October 10, 2017 Africa Business 0. Following the news of several new discoveries which have tripled the estimates of the nation's Bauxite reserves, the mining prospects of Mali is poised for massive growth.
Mali Economic Outlook African Development Bank
Mali continues to face a moderate risk of debt distress. Inflation slowed to an estimated 1.7% in 2018 thanks to lower prices of foodstuffs and imported oil products. In the external sector, the current account deficit rose slightly from 6.0% in 2017 to an estimated 6.5% in 2018, with import growth (9.3%) outpacing export growth (7.2%).
Guinea: Mining, Minerals and Fuel Resources
Guinea is a major exporter of diamonds, bauxite, alumina, and gold, with major export partners including China, Ghana, India, Spain, and The United Arab Emirates as of 2017. Unfortunately, the country is a victim of poor mining practices which have resulted in considerable environmental damage.
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pressure washer with sand attachment | {
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Q: ¿Cómo hacer llamadas a una función desde un array en C++? Quiero almacenar varias llamadas a una función en un array, para así, utilizarla de forma repetida llamando a la posición concreta del array.
El problema es que en C++ hay que especificar el tipo de dato del array.
int llamadaFuncion [] = {
funcion(1, 10),
funcion(45, 50),
funcion(56, 43),
funcion(56, 10)};
}
Esto es solo un ejemplo, el tipo de dato no me importa, lo que necesito es poder llamar a una función en posiciones de un array.
A: Tienes dos opciones:
*
*Creas un array de punteros a función
*Usas std::function. Es un wrapper que encapsula los punteros a funciones
Un ejemplo con std::function
#include <functional>
#include <iostream>
void func1(int value)
{ std::cout << "func1 - " << value << '\n'; }
void func2(int value)
{ std::cout << "func2 - " << value << '\n'; }
int main()
{
std::function<void(int)> array[2] {
func1,
func2
};
for(int i=1; i<10; i++)
{
for (auto func : array)
{
func(i);
}
}
}
Puedes verlo funcionando aqui
El problema que tienes aquí (independientemente de la solución que uses) es que todas las funciones deben tener exactamente la misma interfaz, es decir, no te va a funcionar si una función no tiene parámetros, la otra recibe un int, otra un float y otra varios string
Si tu idea es que se llame a las funciones con unos parámetros por defecto, puedes usar lambdas:
#include <functional>
#include <iostream>
void func1(int value)
{ std::cout << "func1 - " << value << '\n'; }
void func2(int value)
{ std::cout << "func2 - " << value << '\n'; }
int main()
{
std::function<void(void)> array[] {
[]() { func1(1); },
[]() { func1(2); },
[]() { func2(3); },
[]() { func2(4); },
};
for (auto func : array)
{
func();
}
}
Puedes verlo funcionando aqui
En este caso sí que podrás usar funciones de cualquier tipo, ya que al final lo que se invocan son las lambdas, las cuales sí que tendrás que garantizar que tienen todas la misma interfaz
| {
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Dan Baker is a producer with experience in delivering projects, festivals and outdoor work from Fringe to large-scale, and is currently Creative Producer for Barbican Theatre Plymouth. He is Producer and co-founder of Toast, a theatre development agency for Plymouth and founders of the Plymouth Fringe Festival – an annual theatre and performance festival taking place annually since 2015.
Dan has delivered touring productions, outdoor work and international partnerships, and has been employed as a producer for organisations including the Old Vic Theatre, Bush Theatre and Greenwich + Docklands Festivals. He has also developed an extensive portfolio of freelance producing work, including the Outpost pop-up theatre season with New Model Theatre (2014, 2015 & 2016), extensive touring work for the MolinoGroup - most recently their award-winning Edinburgh Fringe show Much Further Out Than You Thought (2015) - and work across the UK for Agent 160 Theatre, including presenting twelve specially commissioned pieces by female playwrights for Fun Palaces at the Wales Millennium Centre (2014).
In addition to his work as a producer, Dan has a background in work with young people and in community settings - having delivered activities for organisations including Arts Council England, Theatre Royal Plymouth and Almeida Theatre. | {
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Temptation by Fire(8)
By: Tiffany Allee
Gray hair ran along the sides and back of his head, light against his dark skin. The glare from the streetlight overhead glinted off the exposed skin on top, where hair hadn't grown since long before I'd met him. Crow's feet crinkled around his eyes during the rare times he smiled. But it was the deep wrinkles that cleaved his mouth when he frowned that I was familiar with.
A hard man, but a good one.
"Franklin." I nodded to him, and he jerked his head for me to follow him inside.
Franklin hadn't only taught me the ropes, he'd saved me from aimlessly wandering the streets without a hope of ever getting some payback. After my family was killed, I'd worked for months on my own. A damn waste of time. But Franklin had noticed me one night, pulled me off the street, and into his Venator cell. And he'd taught me how to kill demons.
He gave me my first tattoo with his own hands.
"How are things progressing?" Franklin headed past the small area where, during working hours, patrons would wait in line to pay a cover charge, before he went through an open doorway into the club proper.
I pulled off my jacket and tossed it onto an empty table. It landed with a dull thud. Knives only—I didn't throw guns. "They're progressing as they should—mostly."
"Mostly?"
"There was a girl—"
"Hell, son, I can understand that, but I don't think right now is the time to be worrying about some pretty thing."
I barked out a quick laugh. When was the last time I'd thought of a woman for longer than the time it took to get off? Not since I'd become a Venator, that was for sure. Hell, I'd enjoyed myself, burned off some steam with random women when there were no demons around to take out some of my pent-up energy on, but even that never lasted longer than the night. I couldn't afford to get attached. And that was a reality I always made clear before making so much as a move.
I might be an asshole, but I wasn't a total dick.
"It's not like that. A woman we saw today. She had some sort of a fit, then started muttering about Thomas dying in a fire."
Franklin's eyes widened slightly, and my stomach tensed. As difficult as it was to get a reaction from the old man, he might as well have shouted or screamed.
"Give me details, son."
"I went to the hospital with Thomas. He was meeting with the hospital's director—no doubt going to donate money to build some goodwill there. Give him an excuse to spend a lot of time at the hospital. Get an 'in' there." An "in" he'd no doubt use to hunt victims. People leaving the hospital would be easy marks, especially when Thomas didn't have the time or inclination to hunt more difficult prey.
By the time I finished describing her trance—or whatever the hell it had been—Franklin was pacing.
"She wasn't a Venator, then?"
"Not that I could figure."
"And you're sure she wasn't a demon?"
"I'm not sure of anything. But if she was, she's the best damn actor I've ever seen." Something in my chest constricted at the thought of the brave woman being taken by a demon. That much moxie being distorted into something…else. I shook off the thought.
"This doesn't feel like a random coincidence, considering your timeline."
"Maybe we should bring her in. Question her. Find out if she's a Venator—part of a different cell." A flash of something lit Franklin's eye, like he almost relished the idea, but then was gone so quickly I couldn't be sure I'd even seen it. But I felt every muscle in my body tense in response.
"I'll see what I can find out," I lied. I'd had no plans to find Ava again. "But maybe you can look into other possibilities first."
The request stung my tongue in a way the lie didn't. Lying didn't bother me, not anymore. But bending to Franklin's authority was getting harder to deal with by the day. That was the thing about branding yourself with demon blood. You lost the conscience, but gained an authority complex.
"I'll ask around. She wouldn't be the first Venator who'd fucked around with another's job." His eyes turned shrewd. "Don't think I don't know why you're doing this, son. You could have cut Thomas's head off a dozen times by now, but you want to go for the exorcism. See if you can save the human that parasite has latched onto."
<--Pre14567 8 9101112...98 Next--> | {
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Research Article: Filariasis in Travelers Presenting to the GeoSentinel Surveillance Network
Date Published: December 26, 2007
Author(s): Ettie M. Lipner, Melissa A. Law, Elizabeth Barnett, Jay S. Keystone, Frank von Sonnenburg, Louis Loutan, D. Rebecca Prevots, Amy D. Klion, Thomas B. Nutman, Maria Yazdanbakhsh
Abstract: BackgroundAs international travel increases, there is rising exposure to many pathogens not traditionally encountered in the resource-rich countries of the world. Filarial infections, a great problem throughout the tropics and subtropics, are relatively rare among travelers even to filaria-endemic regions of the world. The GeoSentinel Surveillance Network, a global network of medicine/travel clinics, was established in 1995 to detect morbidity trends among travelers.Principal FindingsWe examined data from the GeoSentinel database to determine demographic and travel characteristics associated with filaria acquisition and to understand the differences in clinical presentation between nonendemic visitors and those born in filaria-endemic regions of the world. Filarial infections comprised 0.62% (n = 271) of all medical conditions reported to the GeoSentinel Network from travelers; 37% of patients were diagnosed with Onchocerca volvulus, 25% were infected with Loa loa, and another 25% were diagnosed with Wuchereria bancrofti. Most infections were reported from immigrants and from those immigrants returning to their county of origin (those visiting friends and relatives); the majority of filarial infections were acquired in sub-Saharan Africa. Among the patients who were natives of filaria-nonendemic regions, 70.6% acquired their filarial infection with exposure greater than 1 month. Moreover, nonendemic visitors to filaria-endemic regions were more likely to present to GeoSentinel sites with clinically symptomatic conditions compared with those who had lifelong exposure.SignificanceCodifying the filarial infections presenting to the GeoSentinel Surveillance Network has provided insights into the clinical differences seen among filaria-infected expatriates and those from endemic regions and demonstrated that O. volvulus infection can be acquired with short-term travel.
Partial Text: Parasitic diseases are widespread throughout the developing world and are associated with a heavy burden of morbidity and mortality. Human filariae, nematodes transmitted by arthropod vectors, are endemic in tropical and subtropical regions of the world. With an estimated 80 million people who travel to developing countries each year [1], exposure to filarial parasites is likely to become more common. It has been suggested that infection with filariae requires prolonged and intense exposure to the vectors that transmit them [2]. Moreover, when comparing nonendemic visitors who have acquired filarial infections with those born in endemic regions, the nonendemic visitors appear to have greater numbers of objective clinical symptoms and fewer clinically asymptomatic (or subclinical) infections [3]–[7].
From a total of 43,722 individual patient encounters, filarial infections were diagnosed for 271 (0.62%) persons who presented to GeoSentinel sites from August 1997 through July 2004. The reporting of cases to GeoSentinel was lowest in 1997 and 1998 (3.7% and 8.9% respectively); from 1999 through 2004, filariasis as a proportion of morbidity (ill patients reporting to the clinics) fluctuated between 11% (n = 30) and 17.5% (n = 47). Of the 271 patients with filarial infections, 37% were diagnosed with O. volvulus, 25% were infected with L. loa, and another 25% were diagnosed with W. bancrofti. Among all filarial infections, 5.5% were identified as other filarial species, (e.g., Mansonella, Brugia spp.), and 5.5% of all filarial infections reported in the database were unspecified. Three patients were coinfected with L. loa and other filarial species; one patient presented with O. volvulus and L. loa coinfection (Figure 1). Overall, 122 (45%) patients were female; gender was not recorded for 17 (6.3%) patients. Patient mean age was 34.9 years (range 0–84). The region of acquisition among filaria-infected individuals was assigned when possible (n = 230). The majority (75%) of infections were acquired in Africa (both Northern Africa and Sub-Saharan Africa) and 10% in South America (see Table 1). The remaining individuals were exposed in, Oceania, the Caribbean, South Central Asia, and Central America. Of all filarial infections reported to the GeoSentinel ntwork (n = 271), the majority were reported by the North American sites (76.4%); 18.5% were reported from European sites, and the remainder were reported from GeoSentinel sites in the Middle East, Australia/New Zealand, and South Central Asia.
While filarial infection and disease are most frequently diagnosed among native residents of endemic regions, the risk of infection acquisition among travelers from nonendemic regions is sizeable. Filarial species are found in tropical and sub-tropical regions of the world and, as travel to these regions becomes more popular, filarial infection among nonendemic visitors becomes increasingly common as well. We describe here important epidemiologic characteristics of filarial infections acquired by world travelers from nonendemic regions as reported to the GeoSentinel network. While clinical presentation of filarial disease is known to differ between visitors to and natives of endemic regions [3], our analysis also provides a quantitative assessment of filarial acquisition among travelers and helps describe the differences in clinical presentation between those native to filaria-endemic regions and those traveling to those regions.
In addition to the authors, members contributing data include: | {
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HomeOperating ProjectsRise & Shine International
Rise & Shine International
Funders 31
Rise & Shine International resources hope through education and micro enterprise among the Palestinians and other people groups in destabilized situations, and to also be a voice for the disenfranchised among these peoples. We are motivated by our relationship with Jesus Christ, whose love for us and for these others compels us to work for creative educational and economic solutions.
The Palestinian situation is a painful stalemate with global repercussions. In the middle of it, families try to raise their young and build a future, like families everywhere. Every step forward has brought two steps back with new constraints. Israeli settlements relentlessly shrink West Bank area designated as Palestinian Territory. Unemployment soars behind the wall. The high wall, with guard towers and check points, weaves its way through the area, eating up more Palestinian land, sometimes cutting through a farm or neighborhood. It chills the heart and soul of Palestinian fathers, eager to provide for their families. The wall and checkpoint process generates fear and cuts deep into the previously thriving tourism-based economy. This high unemployment, low opportunity reality kills the hopes of youth that see no future, hence no reason to try. Without dreams, people perish.
By presenting options that tap into the creativity and talents of the people, hope is reborn and, with it, focus on a future that is better than the present or past.
Rise & Shine International, a small project at present, relates directly with a few families - within relationship: love, joy, and respect from across the sea. So much gain from such a relatively small investment! Families are growing healthy and hopeful - together!
It would be better if this work had grown faster, from its humble start in 2010, but - we are here now! The question arises - are we going to build on this beta test, or look the other way and let the dream die? We have students in elementary school and a teenager in tutoring and academic enrichment classes. Our commitment to the several students is growing as they progress through the grades; there are (many) more that would benefit and add momentum to this trend. Regional peace hangs in the balance. We can no longer do this alone - we need YOU!
Mary Chico
Connect/More Info
Funding Period
Start Date: ---
End Date: 14 July 2020
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raised of $ 6000.00
Donate Now To This Project
Fundraise For This Project What's this? | {
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St Clair College is a member of the Ontario Colleges Athletic Association. The Saints men compete in baseball, basketball, rugby, soccer and volleyball. Saint's women compete in basketball, soccer, volleyball and softball. Other sports include curling, golf, and cross country.
The St. Clair College Saints call the SportsPlex home, it's a state-of-the-art facility featuring a triple gymnasium, 10,000 sq. ft. fitness centre, elevated walking track, workout studios, 12 team rooms, classrooms and more!
St Clair College schedule of events can be found on the In Play! sports calendar. | {
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Patti Rocks est une comédie américaine sortie en 1988. Il a été réalisé par David Burton Morris
Synopsis
C'est un road movie mettant en scène deux copains partis dans la nuit pour l'histoire foireuse survenue à l'un d'eux avec une fille sans intérêt. Bientôt se révèle que la fille sans intérêt est une grande histoire d'amour pour l'autre, un être humain qui apporte l'espoir dans une vie où il n'existait plus et que le premier est un type minable. C'est l'amour qu'on trouve là où on ne l'attendait pas.
Fiche technique
Titre : Patti Rocks
Réalisation : David Burton Morris
Scénario : John Kenkins, Karen Landry, David Burton Morris et Chris Mulkey d'après les personnages de Victoria Wozniak
Musique : Doug Maynard
Photographie : Gregory M. Cummins
Montage : Gregory M. Cummins
Production : Gregory M. Cummins et Gwen Field
Société de production : FilmDallas Pictures
Pays :
Genre : Comédie dramatique
Durée : 86 minutes
Dates de sortie :
:
:
Distribution
Karen Landry : Patti Rocks
Chris Mulkey : Billy Regis
John Jenkins : Eddie Hassit
Ralph Estlie : le vieux poivrot
Joy Langer : la fille de Steambeast
Mae Mayhew : la vieille femme
Joe Minjares : le mécanicien chicano
Buffy Sedlachek : Steambeast
Notes et références
Liens externes
Film américain sorti en 1988
Comédie dramatique américaine
Film récompensé au Festival du cinéma américain de Deauville | {
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Country of Origin: USA
UK TV Premiere Date
Latest/Next UK Season: 3b (returning after mid-season break)
Latest/Next UK TV Air Date: 04 February 2020 at 9:00 pm
UK Channel: Sky Witness
Previous UK Premiere Dates
Season 1 – Sky Living – 27 October 2017 at 9:00 pm
Season 1b – Sky Living – 02 March 2018 at 9:00 pm
Season 2b – Sky Witness – 29 January 2019 at 9:00 pm
Season 3 – Sky Witness – 15 October 2019 at 9:00 pm
US TV Premiere Date [BETA]
The US TV information is currently being added. Please bear with us!
Latest/Next US Season: 3b (returning after mid-season break)
Latest/Next US TV Air Date: January 13, 2020 at 10:00 pm
US Channel: ABC
Previous US Premiere Dates
Season 3 – ABC – September 23, 2019 at 10:00 pm
Renewal/Cancelled?
Next Season If Renewed: 4
Click here to see the full list of UK TV Premiere Dates.
Click here to see the full list of Cancelled/Renewed Shows.
Additional Airing Notes:
Medical Drama From House's David Shore starring Bates Motel's Freddie Highmore about a young surgeon with autism and savant syndrome.
6 Responses to "The Good Doctor"
I love the series and Can not wat for the next series!!!
Vanessa O'Connor says:
Can't wait love Shaun and co…
Anthony Darren Daniel says:
when do we see the rest of season one in the UK has only saw 13 episodes. where are the rest that where meant to be on sky1.
When does good dr season two come back to sky Living
When does it restart?
H Holdsworth says:
It's Richard Schiff. Get it now!!! | {
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Tim Twentyman: Three high-potential Lions picks trumps one Patrick Peterson
Tim Twentyman
Allen Park — The best thing that happened to the Lions during last week's draft is what didn't happen.
The Lions reportedly tried to move up from the 13th pick to the Cardinals' fifth pick in order to draft LSU cornerback Patrick Peterson.
Peterson was by far the best corner available in the draft and getting him would have instantly fulfilled a need for the Lions.
But at what cost?
The Lions offered their first, second and fourth-round picks to move up the eight spots.
The Cardinals, obviously, scoffed at the offering and a deal was not made. They selected Peterson themselves.
We got a good idea of what it would have taken to get the pick when the Falcons made a trade to move into the Browns' No. 6 spot — the pick just after the Cardinals'.
The Falcons wanted Alabama receiver Julio Jones and paid exceedingly for him. They gave up five picks: this year's first, second and fourth-round selections, and next year's first and fourth-rounder.
That's a lot picks to hand over for one player, even though they'll likely be late-round picks.
Let's just pretend for a moment that the Cardinals had accepted the Lions offer of three picks in this year's draft. The Lions would have gotten Peterson, but wouldn't have had another pick until the third round (75th overall).
That means no Nick Fairley, and likely no Titus Young or Mikel Leshoure.
I'm not saying Fairley is going to be a better player than Peterson, but it's not out of the realm of possibility. Did anyone see the national championship game?
What the Lions would have had to give up to get Peterson just wasn't worth it, especially after evaluating the Lions haul afterwards. Most experts gave the Lions rave reviews for this year's class.
I think Fairley is going to be a terrific player and I think the Lions have solidified their defensive front for the next five or six years, at least.
Mix in the explosive third receiver (Titus) and power rusher (Leshoure) that the Lions snagged in the second round, and I'm just fine with how things worked out.
The Lions know that cornerback is the deepest position in this year's free-agent class.
Filling three needs with terrific talent in the first two rounds makes more sense to me than getting one great player at one position of need.
It's simple math.
[email protected]
Author SA SportswriterPosted on May 8, 2011 Categories In The NewsTags Allen Park, cornerback, Detroit Lions, fairley, fourth rounder, in the news, Julio Jones, mikel, Mikel Leshoure, national championship game, news, patrick peterson, terrific player, Tim Twentyman, Titus Young, twentyman
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Q: How to properly animate code for a three-body system? I am trying to write a program that animates the simulated motion of three objects and I have found that the easiest way for me to achieve that was to define the motion of the objects with a looping function that populates the positional arguments a1,a2,a3 for the three different objects. Each "a" is a list of the position of the objects as they move through time; a1=[[x0,y0],[x1,y1],[x2,y2],...]
#Function populating position data#
fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize = (10,10))
axes.set_ylim(-1.5, 1.5)
axes.set_xlim(-1.5, 1.5)
plt.style.use("ggplot")
def animate(j):
axes.plot(a1[0],a1[1], color="red", linewidth=1)
axes.plot(a2[0],a2[1], color="gray", linewidth=0.5)
axes.plot(a3[0],a3[1], color="blue", linewidth=1)
ani = animation.FuncAnimation(fig, animate, interval=10)
plt.show()
For some reason, all I get is a static straight line which doesn't correspond to the positions of any of the objects defined by the position lists a1, a2, or a3. I've combed through the data populating function, and have not found any problems with populating the positions of the objects, so I am assuming that I must have messed up my coding of the animation function. Can someone please lend me a hand and guide me in the right direction?
Edit: I can add the function populating the position data if its needed, but I am just trying to figure out how to animate motion through time along x and y, given positional data.
| {
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Once you know you're ready for a tandem, it's time to dream of what you can do together. This tandem will take you there!
The frame of every tandem needs to be strong, not just for the riders and possible cargo, but also for handling and safety. Cannondale's SmartFormed aluminum frame tubes on the RT2 tandem are butted with the expectation that two powerful riders will take it through its paces. Cornering won't feel rubbery with a stong tandem frame, and braking will feel progressive and powerful. A massive 1.5" head tube/steerer tube interface adds handling precision, espcially during high-speed turns and descents. Rack and water bottle mounts are found throughout the RT2, giving the tandem versatility for longer rides and trips to the farmer's market. A 3D forged fork soaks up road vibration, keeping the captain more comfortable.
The drivetrain of the RT2 consists of 10-speed Shimano 105 components, including the dual-control levers, front triple derailleur and long-cage rear derailleur. An FSA Gossamer tandem 52/39/30T crankset and Shimano Tiagra 12-30T cassette adds a massive gearing range to the bike, making challenging climbs less fearsome. 36-spoke alloy DT Swiss wheels are wrapped with Continental's legandary 700x25c GatorSkin tires, bringing puncture-resistant confidence to every mile. Shimano's R515 cable-operated disc brake calipers clamp onto 203mm front and 180mm rear rotors, ensuring excellent stopping power in all conditions, rain or shine. Cannondale's alloy C3 Compact road handlebars, alloy stoker bars, adjustable alloy stoker stem, alloy seatposts and Prologo T2.0 saddles complete this brilliant bicycle built for two. | {
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Decoupled Momentum was first discovered as an apparently inexhaustible source of energy by the Anchorage based research labs of the EqerCell company in 2065.
The discovery lead to the invention and marketing of the PermaCell, or 'Nole'®, as a replacement for the company's range of electro-chemical batteries.
The initial research into the possibility of Decoupled Momentum was originally inspired by Milus Blondel using the now infamous technique of Invention by rumour. Milus was desperately in need of a high power, long lasting, portable power source in order to remove the static restrictions placed on the EMTI of having to be wired into an electrical mains supply or suffer very high battery drainage and short power cycles. He seeded each of two companies; Duragizer and EqerCell with the 'inside' information that each of them were secretly developing compact power sources with an almost infinite life-cycle based on the technology of decoupling momentum from sub-atomic particles, specifically, higher level orbiting electrons.
Milus, had enough theoretical knowledge to convince each company that this technology was not only possible, but actually close to being reliably reproduced by their competitors. The induced paranoia was sufficient to overcome the loud protestations from all of the respective and respected research scientists employed by both companies. Prof. Ed Panard, the then head of the EqerCell Research Labs was quoted as saying; "we all knew DM as a concept was absolute garbage and provably impossible - but as we were also convinced those bastards at Duragizer were on the brink of a major breakthrough in this area, we threw everything at it."
The actual technology for manufacturing PermaCells has been one of the closest guarded secrets ever maintained by any industrial corporation. No patents have ever been filed because any such filing requires the publication of the methodology. Any attempts to tamper with the PermaCell in order to investigate its construction, results in its instantaneous collapse into nothingness. This strategy maintains EqerCell as one of Earth's most enduring and profitable companies.
The discovery had been made by a computer which had been programmed to encrypt the experimental data with an algorithm and key known only to itself, therefore there were no human researchers who knew exactly how it was done. With no one to bribe or coerce and no way of getting at the data, the secret has been maintained ever since. It is claimed as the first machine-made scientific discovery although that term fell into disuse after it became politically incorrect to refer to a computer as a mere 'machine'.
The fact that their scientists had developed an almost eternal power supply that needed no maintenance or replacement was both extremely good news and extremely bad news to a company who had previously made almost all of their income from selling devices that were specifically designed to rapidly wear out and leave the consumer with useless containers of toxic chemicals they had been expressly warned not to throw away. The decision not to patent was made by unanimous board consensus when it was explained to them by their legal advisors that they had two choices; they could patent their invention, and protect themselves for a very short period of time, after which their company would become as valueless as, say, a spent battery, or they could protect their trade secret and charge an exorbitant amount for each device sold. The directors reckoned on the fact that only a company with similar resources and expertise to themselves would be able to figure out how to make a DM device and that company would be equally concerned about putting themselves out of business so would want to keep it a secret too.
It is hard to find anything that doesn't have a Decoupled Momentum device in it somewhere. On Earth, however, it was usually cheaper to connect fixed appliances to the world energy grid (see Polar Rosette) because of the exorbitant purchase price of the PermaCell. The autonomous EqerCell company became the first MaxedOut onSlab corporation in 220 PD, thereafter making their main flagship product free to all.
The apparently inexhaustible power of the Nole and its very small size has facilitated the ubiquitous use of sub-neural implants for Slabwide communication and data access. Complete reliance on this technology gave rise to the saying "I need that like I need a Nole® in my head" being the exact opposite meaning of its former usage.
This page was last edited on 2 January 2016, at 10:15. | {
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A lady came to my house and saw my kettle. To the naked eye it looks like a regular ordinary kettle, nothing spectacular, but to the lady who was doing the looking she thought it was better than hers and wanted one just like it. I was perplexed. How did she get there? Were we looking at the same thing?
What she did with the kettle we too often do with each other. We only see the outside, and use that as the basis for our perceptions which then feeds our inadequacies, most of the time. Sometimes it has the opposite effect.
The reality is that kettle was quite tarnished on the inside; as the water boiled metal chips would get in to the water and sometimes in to a cup of tea. It was on its last leg just before being tossed (but I was holding on, because I'm cheap). Because of the polished exterior, she wanted what I had.
Don't we do that all the time? We take a snapshot of someones' life at an instant in time and say that's what we want. We don't see the metal chipping - the sickness, sadness, disagreements, worry, fear, failure - we only see what we want to see because it's in a pretty package. The mind is dangerous because at this point we then say, "Why can't I have what they have? Why isn't my marriage as happy as theirs? Why aren't my children as successful as hers? How come she got the good job and I didn't?"
The opposite effect can happen also, though this did not happen with the kettle. It's not far fetched to think that someone could say, "I'm so glad I don't have that kettle, mine is so much better." Replace kettle with position (for example) and you would be like the Pharisee mentioned in this parable.
There is a danger in comparing; instead accept who you are, accept your circumstances and work from there. When we accept we let go of the burden of comparison.
Do you find yourself inadvertently comparing yourself to others? Do you think it's more prevalent in the age of social media? How do you prevent yourself from becoming envious or bigheaded? Have you figured out how to be content?
I think knowing that nothing is as it appears has helped me in that regard. It's so easy to compare, nature of the man. But I think remembering and knowing that helps a lot. | {
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Matthäus Heilmann (* 10. Mai 1744 in Hofheim am Taunus; † 10. März 1817 in Mainz) war ein Mainzer Klavier- und Orgelbauer. Er gilt als einer der Schüler des Johannes Kohlhaas des Älteren.
Leben
Matthäus Heilmann wurde am 10. Mai 1744 als Sohn des Wendel Heilmann und dessen Frau Anna Katharina in Hofheim am Taunus geboren. Seine Lehrzeit verbrachte er bei dem domkapitelschen Orgelmacher Johannes Kohlhaas dem Älteren in Mainz, der nicht nur ein angesehener Orgelbauer war, sondern auch das Schreinerhandwerk virtuos beherrschte.
Am 25. Juni 1777 heiratete Heilmann die Mainzer Bürgerstochter Apollonia Müller. Am 12. Juli 1777 wurde er in die Mainzer Bürgerschaft und am 12. Dezember 1777 in die Mainzer Goldschmiedezunft aufgenommen, der auch die Orgelbauer traditionell angehörten. Nicht nur die hohe Anzahl der von Heilmann gebauten Klaviere spricht dafür, dass er gut verdient haben dürfte. Ihm gehörte 1785 bereits das Haus in der Welschnonnengasse 6, schon während seiner Zeit als Hoforgel- und Instrumentenmacher (1789 bis 1797) wohnte er auf der Tiermarktstraße, der heutigen Schillerstraße, und besaß ab 1794 auch noch ein weiteres Haus in der Rochusstraße. Bereits im März 1789 beantragte Heilmann, Gesellen in seine Werkstatt aufnehmen zu dürfen.
Seit seiner Ernennung zum Hoforgel- und Instrumentenmacher durch Dekret vom 3. April 1788 war Heilmann als Angehöriger der Hofkapelle mit der Stimmung und der Erhaltung aller Instrumente am Hofe des Kurfürsten und Mainzer Erzbischofs Friedrich Karl Joseph von Erthal betraut.
Werk
Außer der 1772–1774 oder 1777–1779 für die kath. Pfarrkirche St. Aureus und Justina in Büdesheim gebauten Orgel, die sich seit 1847 in der Stiftskirche in Pfaffen-Schwabenheim befindet, lassen sich seiner Werkstatt vier Hammerflügel sicher zuordnen. Ein weiterer Hammerflügel wird Heilmann lediglich zugeschrieben.
Hammerflügel
Von den Hammerflügeln, die Heilmanns Werkstatt sicher zugeordnet werden können, befinden sich einer im Germanischen Nationalmuseum in Nürnberg (Werknr.: 231 um 1795), einer im National Music Museum an der Universität von South Dakota/USA (Werknr.: 252, um 1790) und zwei in der Colt Clavier Collection in Bethersden/Kent (Werknr.: 64, um 1775–80 und Werknr.: 194, 1775 oder 1790, letzterer 1970 durch Tausch aus der Sammlung Johann Christoph Neupert erworben, die sich im Germanischen Nationalmuseum Nürnberg befindet). Seit Frühjahr 2017 befindet sich Werknr. 194 im Museum Geelvinck in Heerde (Niederlanden). Ein weiterer Hammerflügel, datiert auf etwa 1780, in der Sammlung Neumeyer-Junghanns-Tracey in Bad Krozingen wird der Werkstatt Heilmann lediglich zugeschrieben. Die hohe Anzahl der gebauten Hammerflügel ist vor dem Hintergrund zu verstehen, dass diese im späten 18. Jahrhundert als Hausinstrument des Bürgertums immer beliebter wurden. 1976 und 1979 wurden in der Museums-Werkstatt von Derek Adlam und Richard Burnett in Goudhurst/Kent Nachbauten von Hammerflügeln Heilmanns gefertigt, die weltweit bei Konzerten eingesetzt werden.
Orgel
Heilmann orientierte sich bei der Einteilung seiner 22-registrigen Orgel in Haupt- und Unterwerk mit flankierenden Pedaltürmen; ihrer Aufstellung als Emporenbrüstungsorgel mit seitlicher Spielanlage; ihrer Dispositionsgestaltung sowie ihrem Pedalumfang von nur einer Oktave offenkundig am Mainzer Orgelbaustil, der von Johann Jakob Dahm, Johann Anton Ignaz Will sowie den Orgelbauerfamilien Kohlhaas und Onimus geprägt war. Auch die Gestaltung des Orgelprospekts orientiert sich mit seinen Pedaltürmen in Form von Harfenfeldern am Stil des mainfränkischen Barocks, der für Mainz typisch ist.
Abgesehen von den Zungenregistern gibt es nach gegenwärtigem Forschungsstand keine Beziehungen zu dem Orgelbaustil der Werkstatt Stumm. Das Register Krummhorn 8′ ist eines von nur zwei Zungenregistern, die überhaupt aus der barocken Epoche des Mainzer Orgelbaus noch erhalten sind.
Matthäus Heilmann hat mit seiner einzigen bekannten Orgel ein Musikinstrument hinterlassen, das für den Mainzer Orgelbau des 18. Jahrhunderts typisch ist und das eine Bereicherung der rheinhessischen Orgellandschaft darstellt, die von Werken der Orgelbauerfamilien Stumm aus Rhaunen-Sulzbach; Kohlhaas und Onimus aus Mainz und Geib aus Saarbrücken bzw. Frankenthal sowie der Mainzer Orgelbauer Johann Jakob Dahm und Johann Anton Ignaz Will geprägt ist.
Die Heilmann-Orgel ist eine der wenigen Barock-Orgeln der Region, die noch einen über 80-prozentigen originalen Pfeifenbestand, einschließlich sämtlicher Prospektpfeifen, aufweist. Aus dem historischen Bestand stammen außerdem das Gehäuse, die Spiel- und Registermechanik, die Spielanlage und die Windladen. Aus späterer Zeit stammen lediglich ein Salicional 4′ (später als Gemshorn 4′ bezeichnet) aus dem Jahre 1816 von Johann Heinrich Engers (* 1771; † 1851), Waldlaubersheim, dessen Werkstatt ab 1854 von Johann Martin Schlaadt weitergeführt wurde, sowie wahrscheinlich aus dem Jahre 1847 von Johann Heinrich Schäfer (* 1810; † 1877 in Heilbronn), eine Oktave 2′ und ein Subbass 16′, dem eine originale Trompete 8′ weichen musste, die aber 1964 wieder rekonstruiert wurde. Die Veränderungen durch Schäfer wurden 1847 durchgeführt, nachdem er die Orgel von Bingen-Büdesheim nach Pfaffen-Schwabenheim überführt hatte.
Der bekannte Mainzer Musikwissenschaftler Adam Gottron urteilte im Jahre 1959 über die Heilmann-Orgel wie folgt:
Einspielungen des Organisten Wilhelm Krumbach auf der Heilmann-Orgel wurden vom Südwestfunk, Landesstudio Mainz, am 2. Oktober 1967 aufgenommen und am 25. März 1968 ausgestrahlt.
Disposition seit 1964
Durch eine Manualkoppel ist das Pedal fest an das II. Manual angehängt.
Die kursiv gesetzten Register gehören zur Originaldisposition von 1779.
Zur Originaldisposition
Die Originaldisposition ist nicht bekannt, allerdings liegt ein Rekonstruktionskonzept von Adam Gottron vor (siehe Dispositionsvergleich). Die in der oben stehenden Tabelle kursiv gedruckten Register stammen von Heilmann. Das Salicional 4′ (so Pfeifengravur, später als Gemshorn 4′ bezeichnet) stammt von Engers aus dem Jahre 1816; Oktave 2′ und Subbass 16′ stammen vermutlich von Schäfer aus dem Jahre 1847 (siehe "Orgel"). Diese Veränderungen aus dem 19. Jahrhundert sind so qualitätvoll, dass sie bei der notwendigen denkmalpflegerischen Restaurierung nicht wieder rückgängig gemacht würden.
Im Zuge der heute kritisch beurteilten Instandsetzungsarbeiten von 1964 baute Karl Borchert (Ingelheim) für die Orgelbaufirma von Emanuel Magnus Kemper (* 1910; † 1978) das Sesquialtera II (ist kein Sesquialter, Repetition bei c°) und die Mixtur IV–V in das Unterwerk sowie das Großgedackt 8′, die Cimbel IV und die Trompete 8′ in das Hauptwerk ein. Außerdem installierte er einen Schwimmerbalg und reduzierte den Winddruck um die Hälfte.
Dispositionsvergleich
Bestandsaufnahme (2000)
Die Bestandsaufnahme wurde am 26. Juni und 27. Juli 2000 durch Achim Seip, Orgelsachverständiger im Bistum Mainz, durchgeführt.
Spielanlage, seitl. rechts; Manualtasten neu belegt, Registerschilder neu (Aug. Laukhuff), Registerzüge möglicherweise alt. Beschriftung "Copula" 19. Jahrhundert; Pedal an Hauptwerk angehängt; Tasten klapperig mit seitlichem Spiel; Pedalklaviatur von Borchert/Kemper (1964), Beläge stark ausgespielt.
Windladen, original Heilmann (1779) mit erneuerten Spunddeckeln und Rastern (Borchert/Kemper, 1964)
Gehäusetüren auf der Rückseite durch Pressspanplatten ersetzt (Borchert/Kemper, 1964)
Spielmechanik: Abstrakten (Holz) und Abzugsdrähte (vermutl. Borchert/Kemper, 1964); der liegende Wellenrahmen original Heilmann (1779).
Registermechanik: Schwerter original Heilmann (1779), Stangen und Koppel vermutl. Schäfer (1847)
Technische Daten
Stimmhöhe: a' = 472,0 Hz bei 21,1 °C und 72 % relativer Luftfeuchtigkeit (gemessen am 9. August 2001 durch Mitarbeiter von Förster & Nicolaus Orgelbau, Lich);Winddruck: 70 mmWs (gemessen am Kanal zum Unterwerk am 9. August 2001 durch Mitarbeiter von Förster & Nicolaus Orgelbau, Lich)
Literatur
Adam Gottron: Mainzer Musikgeschichte von 1500 bis 1800. (= Beiträge zur Geschichte der Stadt Mainz. Band 18). Mainz 1959, S. 157 f.
Achim Seip: Alte und neue Orgeln im Bistum Mainz. Mainz 2003, ISBN 3-8053-2838-9, S. 94, 95.
Quellen
Bischöfliches Ordinariat (Mainz)/Dezernat IX/5 (Abt. Orgeln und Glocken)/OA
Dom- und Diözesanarchiv, Best. 47,6
Handbuch des Bistums Mainz 1931, S. 184.
Adam Gottron: Die Orgeln des Bistums Mainz. 1936.
Achim Seip, Gutachten über eine Denkmal-Orgel (Heilmann-Orgel, Pfaffen-Schwabenheim) vom 2. März 2007.
Einzelnachweise
Klavierbauer
Orgelbauer (18. Jahrhundert)
Orgelbauer (Deutschland)
Person (Hofheim am Taunus)
Deutscher
Geboren 1744
Gestorben 1817
Mann
Orgellandschaft Pfalz | {
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Proposition 2 : the administrator must handle two types of administrativetasks, both (a) those concerned with the long-run health of the company and(b) those concerned with its smooth and efficient day-to-day operation (9).5. (1942)..
Response of linear systems to stochastic inputs. Finite Element Analysis for Engineering Design (EGM 4350) 3 credits Prerequisites: EML 4500 or EOC 3410C or CES 3102C with minimum grades of "C" Fundamental concepts of..
Russian authorities pressed criminal separatism charges against several people, including for online remarks about Crimea being part of Ukraine. The term dedovshchina refers to systematic abuse of new conscripts by more long-serving soldiers. 5..
two contrasting places. tags: Their Eyes Were Watching God Essays Free Essays 632 words (1.8 pages) Preview - Freedom Through the Pursuit of Dreams in Their Eyes Were Watching God After the Civil War and the emancipation of the slaves, the ex-slaves could not find enough good. 20) vlpa Advanced study in Spain in approved foreign study programs. tags: Their Eyes Were Watching God Essays Powerful Essays 2985 words (8.5 pages) Preview - The Charater of Janie in Their Eyes Were Watching God In Zora Neale Hurston's Their Eyes Were Watching God, Janie Crawford is the heroine. In looking at Janies interaction with her tree, I chose to focus on the passage on page 11, beginning with She was stretched on her back beneath the pear tree. Grandmas worship of Jesus and the Good Lawd, Joe Starks worship of himself, Mrs. According to this definition, any attempt to maintain one's original values, beliefs, ways of thinking, feelings, or behaviors constitutes mental illness or "maladaptation" (p. .
2 The interactive acculturation model represents one proposed alternative to the typological approach by attempting to explain the acculturation process within a framework of state policies and the dynamic interplay of host community and immigrant acculturation orientations. Instructors: Mercer View course details in MyPlan: span 415 span 416 Spanish Literature: 1900 to the Present (5) vlpa Spanish literature of the twentieth century prior to the Civil War to the present. "Rethinking the concept of acculturation: Implications for theory and research". In other words, Kramer argues that one need not unlearn a language in order to learn a new one, nor does one have to unlearn who one is in order to learn new ways of dancing, cooking, talking and so forth. tags: Their Eyes Were Watching God Essays Free Essays 429 words (1.2 pages) Preview - Character Development in Chapter Two of Their Eyes Were Watching God In Zora Neale Hurston's novel, Their Eyes Were Watching God the character of Nanny dies in the. Emphasis on critical reading, vocabulary expansion, and grammar review. Back to the years of slavery, African-American couldn't get too much freedom, and they were treated as goods by their white masters. Instructors: Mercer View course details in MyPlan: span 482 span 483 Latin American Literature: Origins to Independence (5) vlpa. | {
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THIS IS A PARCEL OF 2 STONES MINED IN BRAZIL. RULITE IS A MAJOR ORE OF TITANIUM, WHICH IS A METAL, USED HIGH TECH ALLOYS. IT OFTEN FORMS NEEDLE LIKE CRYSTALS INCLUSIONS INSIDE QUARTZ. THIS FORM OF QUARTZ IS KNOWN AS RULITED QUARTZ AND IT LOOKS LIKE SMALL BARS OF IMBEDDED GOLD. RULITE IS A 6 MOHS SCALE BECAUSE OF THE DIFFERENCE IN HARDESS BETWEEN THE TWO MATERIALS AND BECAUSE OF THE WAY RULITE FORMS INSIDE, THIS CAN BE A DIFFICULT STONE TO ATTAIN A SMOOTH SURFACE WITHOUT PITS. RULITED QUARTZ HAS BEEN REFERRED TO HAVE CUPIDS DARTS, VENUS HAIR STONE AND FLETCHERS D'AMOUR.
SIZE OF LARGEST STONE : 20 x 18 x 6 MM APPROX.
WEIGHTOF PARCEL: 50 CTS APPROX. | {
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6 p.m. ,and will discuss the beginning of the 2019 legislative session.
The town hall meeting is an opportunity for the citizens of Johnson, Carter, and Sullivan Counties to hear updates and ask questions about legislative priorities and talk about other important issues.
Timothy Hill represents Tennessee House District 3, which includes Johnson, and part of Carter and Sullivan Counties. Hill can be reached by email at: [email protected] or by calling (615) 741-2050. | {
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Bhubaneswar: Protest over the Kunduli incident took an ugly turn today as several BJP workers tried to barge into Naveen Nivas, the residence of Odisha Chief Minister Naveen Patnaik.
Hundreds of activists of the party took out a mass rally from Ram Mandir Square here and marched towards Naveen Nivas holding banners, party flags and placards. They raised slogans against Patnaik and demanded his resignation over the issue.
A scuffle ensued between them and policemen after they reached near the residence of the Chief Minister and attempted to enter inside it forcefully. Many workers of the saffron party were then detained by police. | {
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Home / Cruise Lines / Oceania Cruises / Insignia
North Atlantic Passage
Ship: Insignia
Departure: Monday, September 6, 2021
Departs: Amsterdam
Returns: New York (Manhattan)
1 Monday, September 6, 2021 Amsterdam, Netherlands Embark 7:00 PM
Originally a dam in the river Amstel, Amsterdam today is the capital and largest city of the Netherlands, as engineered dams, sea gates, and the 19-mile dyke walling out the Zuider Zee prevent this low-lying country from being reclaimed by the North Sea. Interestingly, the 17th century canals of Amsterdam located in the heart of the city have been added to the UNESCO World Heritage List. The main tourist attractions are undoubtedly the famous Museums such as the Rijksmuseum, the Van Gogh Museum, and the Stedelijk Museum. However, there is much more to be seen and appreciated. Read more about Amsterdam, Netherlands
2 Tuesday, September 7, 2021 Zeebrugge, Belgium 7:00 AM 5:00 PM
The port city of Zeebrugge is a harbour town at the western end of the Belgian coast and a subdivision of the city of Bruges - one of the best preserved cities in Europe - for which it is the modern port. The new port has reinvigorated the city as an art and tourist centre for northern Europe. Upon visiting Bruges you will immediately notice that this city has always carefully cherished its architectural and artistic treasures from the past, but what makes Bruges so unique though is the way it deals with this past today. There is something for everybody. Read more about Zeebrugge, Belgium
3 Wednesday, September 8, 2021 Le Havre, France 8:00 AM 8:00 PM
Le Havre is a city in the NW of France, situated on the right bank of the mouth of the Seine River and 170 km from Paris. Best known for being the ferry terminal for the English Channel crossings, it should not be quickly dismissed. This city was devastated during WWII, but was rebuilt in modernist style and designated a UNESCO World Heritage Site in 2005. The innovative use of concrete, blended with the sheer sense of space, with the sea visible at the end of almost every street and open public space and expanses of water at every turn, it can be exhilarating. Read more about Le Havre, France
4 Thursday, September 9, 2021 St Malo, France 8:00 AM 6:00 PM
St Malo (aka Saint-Malo, Sant-Maloù, Saent-Malô) on the English Channel in Brittany in the NW of France, is an amazing, historic, ancient walled city. With its tall granite mansion blocks lining the attractive lanes and squares, its numerous ramparts that offer amazing views, and its cobbled streets brimming with restaurants, bars and shops, it is considered to be the most attractive channel port in France. The Citadel, aka the Old Town, was originally built on a rocky island at the mouth of the Rance estuary, a strategic position for defence, but today the modern harbour connects the citadel to the mainland. Read more about St Malo, France
5 Friday, September 10, 2021 At Sea
6 Saturday, September 11, 2021 Oporto, Portugal 8:00 AM 6:00 PM
Located in the scenic estuary of the Douro River with swathes of vineyards clinging to the hills, Oporto - aka Porto - is Portugal's second largest metropolis, and one of Europe's most charismatic cities. The city is home to monuments by leading world architects from the past and the present, and some fantastic baroque carvings. Then there's the world-famous sweet wine, and Ribeira - Its historical centre - that was awarded World Heritage status by UNESCO. Understandably, it is considered the economic and cultural heart of the entire region. Read more about Oporto, Portugal
7 Sunday, September 12, 2021 At Sea
8 Monday, September 13, 2021 At Sea
9 Tuesday, September 14, 2021 At Sea
10 Wednesday, September 15, 2021 At Sea
11 Thursday, September 16, 2021 At Sea
12 Friday, September 17, 2021 At Sea
13 Saturday, September 18, 2021 St George's, Bermuda 9:00 AM 12:00 AM
St George's is an island and town of the same name in the British Overseas Territory of the archipelago Bermuda in the North Atlantic Ocean. It was founded in 1612 and served as the capital of Bermuda until eclipsed by Hamilton in 1815. St George's is the oldest continually inhabited English settlement in the New World, and the second largest town. The island is in the hurricane belt and prone to severe weather. Read more about St George's, Bermuda
14 Sunday, September 19, 2021 St George's, Bermuda 12:00 AM 2:00 PM
15 Monday, September 20, 2021 At Sea
16 Tuesday, September 21, 2021 New York (Manhattan), USA 8:00 AM Disembark
New York's port on the Hudson River in Manhattan is four blocks from Central Park. New York is situated on the Atlantic coast of NE United States. With its world-class museums, big statues, even bigger buildings - certainly the Manhattan skyline with its many skyscrapers is universally recognizable - and being the most linguistically diverse city in the world, the Big Apple's hyperactive rush keeps drawing more and more people to it. The City of New York is a densely packed mass of humanity and all this living on top of one another makes the New Yorker a special kind of person. Read more about New York (Manhattan), USA
Insignia Overview
(from 1 verified customers)
Newly refurbished in 2019, the 30,277 GT Insignia carries just 688 passengers. This is a 'small ship' boasting many big-ship features. Dress is informal in a luxurious setting, with an accent on personalised service and five-star cuisine.
Insignia Cabins
F, G
Size: 160 sq. ft. / 14 sq. mt. Features: Ultra Tranquility Bed, an Oceania Cruises exclusive. Bulgari amenities. Twice daily maid service. Belgian chocolates with turndown service. Complimentary 24-hour room service. Flat-screen television with DVD player and extensive media library. Wireless Internet access and cellular service. Writing desk and stationery. Plush cotton towels, robes and slippers. Handheld hair dryer. Security safe. All Suites and Staterooms are Smoke-Free.
C1, C2, D, E
A1, A2, A3, B1, B2
Size: 216 sq. ft. / 20 sq. mt. Features: Ultra Tranquility Bed, an Oceania Cruises exclusive. Free and unlimited soft drinks replenished daily in your refrigerated mini-bar. Free still and sparkling Vero Water. 24-hour Butler service in all suites. Bulgari amenities. Free room service menu 24 hours a day. Signature Belgian chocolates with nightly turndown service. Wireless Internet access. Expanded lunch and dinner room service menu from the Grand Dining Room. Free laundry service – up to 3 bags per stateroom. Priority Noon ship embarkation. Complimentary welcome bottle of Champagne. Priority online specialty restaurant reservations. Unlimited access to the Aquamar Spa Terrace. iPad® upon request for your enjoyment on board (limited availability). Complimentary Oceania Cruises logo tote bag. Cashmere lap blankets, perfect for relaxing on your veranda. Complimentary pressing of garments upon embarkation (certain limitations apply). Complimentary shoe shine service. All Suites and Staterooms are Smoke-Free.
OS, VS, PH1, PH2, PH3
Size: 1,000 sq. ft. / 92 sq. mt. Features: Ultra Tranquility Bed, an Oceania Cruises exclusive. Free and unlimited soft drinks replenished daily in your refrigerated mini-bar. Free still and sparkling Vero Water. 24-hour Butler service in all suites. Bulgari amenities. Free room service menu 24 hours a day. Signature Belgian chocolates with nightly turndown service. Wireless Internet access. Free laundry service – up to 3 bags per stateroom (restrictions apply). Priority 11am ship embarkation with priority luggage delivery. 24 hour Butler Service. Complimentary in-suite bar setup with 6 full-size bottles of your choice of premium spirits and wines from our suite beverage menu (certain limitations apply). Complimentary welcome bottle of Champagne. Fresh fruit basket replenished daily. Priority online specialty restaurant reservations. Unlimited access to the Aquamar Spa Terrace. iPad® upon request for your enjoyment on board. Bulgari gift set and variety of amenities. Choice of daily printed newspaper. Cashmere lap blankets. Choice of pillow from a luxurious selection. Complimentary shoe shine service. Complimentary pressing of garments upon embarkation (certain limitations apply). All Suites and Staterooms are Smoke-Free.
Deck Plans for Insignia
Deck Eleven
Deck Ten
Deck Eight
Deck Seven
Deck Six
Deck Five
Deck Four
Deck Three
Quad with Pullman
Quad with Sofabed
Triple with Pullman
Triple with Sofabed
Current promotions for Insignia
Oceania O Life Choice Fare
O Life Choice fare is available on all cruises at all times.
• Enjoy Free Internet *Plus*
Select one of these generous amenities:
• FREE Shore Excursions,
• FREE House Beverage Package or
• Shipboard Credit.
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Cruiseline: Oceania Cruises Ship: Insignia Departure: Monday, September 6, 2021 Nights: 15 nights Departs: Amsterdam Returns: New York (Manhattan) | {
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In Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface. This is a static solution, meaning that it does not change over time. It was discovered by Karl Schwarzschild in 1916, who earlier had found the exterior Schwarzschild metric.
Mathematics
The interior Schwarzschild metric is framed in a spherical coordinate system with the body's centre located at the origin, plus the time coordinate. Its line element is
where
is the proper time (time measured by a clock moving along the same world line with the test particle).
is the speed of light.
is the time coordinate (measured by a stationary clock located infinitely far from the spherical body).
is the Schwarzschild radial coordinate. Each surface of constant and has the geometry of a sphere with measurable (proper) circumference and area (as by the usual formulas), but the warping of space means the proper distance from each shell to the center of the body is greater than .
is the colatitude (angle from north, in units of radians).
is the longitude (also in radians).
is the Schwarzschild radius of the body, which is related to its mass by , where is the gravitational constant. (For ordinary stars and planets, this is much less than their proper radius.)
is the value of the -coordinate at the body's surface. (This is less than its proper (measurable interior) radius, although for the Earth the difference is only about 1.4 millimetres.)
This solution is valid for . For a complete metric of the sphere's gravitational field, the interior Schwarzschild metric has to be matched with the exterior one,
at the surface. It can easily be seen that the two have the same value at the surface, i.e., at .
Other formulations
Defining a parameter , we get
We can also define an alternative radial coordinate and a corresponding parameter , yielding
Properties
Volume
With and the area
the integral for the proper volume is
which is larger than the volume of a euclidean reference shell.
Density
The fluid has a constant density by definition. It is given by
where is the Einstein gravitational constant. It may be counterintuitive that the density is the mass divided by the volume of a sphere with radius , which seems to disregard that this is less than the proper radius, and that space inside the body is curved so that the volume formula for a "flat" sphere shouldn't hold at all. However, is the mass measured from the outside, for example by observing a test particle orbiting the gravitating body (the "Kepler mass"), which in general relativity is not necessarily equal to the proper mass. This mass difference exactly cancels out the difference of the volumes.
Pressure and stability
The pressure of the incompressible fluid can be found by calculating the Einstein tensor from the metric. The Einstein tensor is diagonal (i.e., all off-diagonal elements are zero), meaning there are no shear stresses, and has equal values for the three spatial diagonal components, meaning pressure is isotropic. Its value is
As expected, the pressure is zero at the surface of the sphere and increases towards the centre. It becomes infinite at the centre if , which corresponds to or , which is true for a body that is extremely dense or large. Such a body suffers gravitational collapse into a black hole. As this is a time dependent process, the Schwarzschild solution does not hold any longer.
Redshift
Gravitational redshift for radiation from the sphere's surface (for example, light from a star) is
From the stability condition follows .
Visualization
The spatial curvature of the interior Schwarzschild metric can be visualized by taking a slice (1) with constant time and (2) through the sphere's equator, i.e. . This two-dimensional slice can be embedded in a three-dimensional Euclidean space and then takes the shape of a spherical cap with radius and half opening angle . Its Gaussian curvature is proportional to the fluid's density and equals . As the exterior metric can be embedded in the same way (yielding Flamm's paraboloid), a slice of the complete solution can be drawn like this:
In this graphic, the blue circular arc represents the interior metric, and the black parabolic arcs with the equation represent the exterior metric, or Flamm's paraboloid. The -coordinate is the angle measured from the centre of the cap, that is, from "above" the slice. The proper radius of the sphere – intuitively, the length of a measuring rod spanning from its centre to a point on its surface – is half the length of the circular arc, or .
This is a purely geometric visualization and does not imply a physical "fourth spatial dimension" into which space would be curved. (Intrinsic curvature does not imply extrinsic curvature.)
Examples
Here are the relevant parameters for some astronomical objects, disregarding rotation and inhomogeneities such as deviation from the spherical shape and variation in density.
History
The interior Schwarzschild solution was the first static spherically symmetric perfect fluid solution that was found. It was published on 24 February 1916, only three months after Einstein's field equations and one month after Schwarzschild's exterior solution.
References
Exact solutions in general relativity
de:Schwarzschild-Metrik#Innere Lösung | {
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Detroit: Become Human Connor&Hank Find this Pin and more on Gaming by Play Free Online 32. This scene straight up killed me. Why did I think choosing the wrong answers on purpose would be a …... Yeah, I usually think Alex's opinions are pretty reasonable even if I don't exactly agree with him, but I really don't see why he's soooo harsh on Detroit. It's far and away the most coherent and least derpy game that Quantic Dream has made, by a country mile.
Explore Detroit: Become Human game detail, demo, images, videos, reviews. Travel to the near-future metropolis of Detroit – a city rejuvenated by an exciting technological development: androids. Shape an ambitious branching narrative, making choices that will not only determine your own fate, but that of …... Carl treats Markus as if he were human, teaches him to paint, exposes him to literature and music; develops the android's spirit a little each day. Eventually Carl comes to think of Markus like a son, much to the dissatisfaction of Carl's biological son, Leo.
Carl treats Markus as if he were human, teaches him to paint, exposes him to literature and music; develops the android's spirit a little each day. Eventually Carl comes to think of Markus like a son, much to the dissatisfaction of Carl's biological son, Leo. how to make him fear losing you Our Verdict: Detroit: Become Human looks and sounds great, and includes key player choices throughout, though it could have benefited greatly from a tighter script.
This guide shows how to get the Detroit: Become Human Survivors Trophy (Everyone is alive at the end). None of the characters listed below is allowed to die over the course of the game. If you lose someone, quit out to the main menu and replay the chapter from the last checkpoint. | {
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By now you must know I am a total film nerd. There is nothing more I love than snuggling up with some popcorn and catching up with a film. Movie nights are the most fun when you share them with the ones you love. That's just what we did too. One of the best things about children is teaching them about all the awesome things you loved when you were little so when we had the pleasure of a visit from Me K's son we decided to school him in the ways of pure classics. My favourite film growing up was Labyrinth and with the recent passing of the legendary Bowie it seemed so much more important to share.
No good movie night is complete without snacks and we were spoilt with popcorn, retro sweets, pizza and fizzy pop. There's something about watching a movie and sharing food that just fills me with love.
J was so excited by the puppets in the labyrinth and we sang along to the songs which even he was singing by the end. Although secretly I think he just loved the big of eternal stench it was really magical to watch him get shocked and wonder if Sarah would ever get to the castle.
What films would you watch on a movie night?
Such a great thing to do! I've been loving Todd Hayne's "Carol" this year - such a beautiful and aesthetically pleasing film. | {
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Belief in the authority and reliability of the Bible as the inspired and infallible Word of God. The Bible is the complete and final revelation of God concerning all matters of faith, truth and practice. All truth is God's truth (II Timothy 3:16; II Peter 1:20-21).
Belief in the omnipotent, omniscient and omnipresent God who is sovereign over all (Revelation 4:2; Psalm 45:6; 139:8; Isaiah 66:1). His sovereignty is seen in acts of creation (Genesis 1:1,31), salvation (John 6:44), and continual care (Matthew 10:29-31; Hebrews 7:25).
Belief in the Trinity, of the one true God (Matthew 28:19), the deity of Jesus Christ (I Timothy 3:16; John 1:1; 10:30), His virgin birth (Luke 1:30-35), sinless life (Romans 8:3; Hebrews 4:15), miracles (Mark 1:27; John 2:11), atonement for our sins by His blood sacrifice (Matthew 26:28), His bodily resurrection (John 20:1-9), ascension, His personal return in power and glory (Mark 16:19, 13:26).
Belief in the Holy Spirit as teacher of God's Truth (John 14:17) and as giver of new life in Christ and who unites all believers in Christ (Titus 3:5).
Belief that man is the crown of God's creation. God endowed man with His image and gave him the responsibility to rule the earth (Genesis 1:26-27). Belief that sin has severely broken the relationships between God and man (Romans 3:23), man and himself, man and other men (James 4:1), and man and nature (Romans 8:20-22).
Belief that Jesus Christ, the eternal Son of God, came to earth to offer cleansing for man's sin, and to heal these broken relationships through His cross(Romans 5:1-2).
Belief that man cleansed through Christ must seek to live out his life in total commitment to Jesus Christ as Lord of life, which involves reestablishing all the original relationships God intended for him (Ephesians 4:1).
Belief in a need for clearly defined goals and objectives centered in the Word of God for the development and growth of the whole person (spiritual, mental, emotional, social and physical) and for the establishing of proper priority in an individual's life (Proverbs 1:7; I Corinthians 10:31).
Belief that God established the family as the basic unit of society. Parents are ultimately responsible for the instruction and discipline of their children. The Christian School is simply an extension of the educational process of the family and the church providing a supportive basis of encouragement to the family and the church (Ephesians 5:22-33;Proverbs 22:6).
Belief that a personal commitment to Jesus Christ and God's Word is necessary for those who are involved in the educational process (faculty, staff, administration and board) (II Timothy 3:16).
We believe a true Christian is one who has received Jesus Christ as Savior and Lord by faith. We believe good works to be the inevitable result of true faith (Romans 10:9; Ephesians 2:8; James 2:17-18;I John 2:3-4). | {
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This snakeskin inspired wrap dress is just that, a true wrap dress! This dress features a deep V neckline and fun pattern. Super flattering on any body type this long sleeved dress will quickly become a wardrobe staple. The super soft slinky fabric will have you wondering how you ever lived without it.
Model is shown wearing her usual size medium, she is 5'7 and a size 6 for reference. | {
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It is our policy that participants arrive on time to class and do not leave until class is completed. Parents are not allowed in the gym during class, unless they are participating in one of our Parent/Tot classes. This policy is in place to maintain concentration of the coaches as well as the participants and it allows us to run a safe gym with minimal distractions. If you have an issue with something that is happening during class, please contact us at [email protected].
Registration is done through the Achieve Front Desk, in person or over the phone at (720) 330-2200. Payment is due at the time of registration. After the initial registration, you are able to pay through our Customer Portal for future sessions during the Preferred Registration Week, which is the 5th week of every session.
During the 5th week of each session, your child(ren) are automatically enrolled in their same class for the next session. To continue in the following session, you must pay on or before the last day of Preferred Registration Week (PRW).
Achieve Gymnastics does not typically provide refunds for any activity (class, practice, clinic, camps) once it has started. We do review all refund requests, on a case by case basis, due to special circumstances and hardships.
We request that parents or guardians accompany their gymnast(s) to and from the building for practice. This request is for your child's safety. ALL participants are to remain inside the building with our staff until an adult arrives to pick them up. We have never had an incident and feel this is partly due to the presence of parents.
Your child(ren) do not have to wear a leotard, although it is recommended. They can wear form fitting tee shirts and shorts, leggings or sweats. No jeans or khakis are allowed, even if they are shorts. Clothes without buttons, snaps or zippers are preferred. No jewelry, socks or shoes are allowed during class time. We have cubbies in the gym for students to put their belongings in.
We do not offer make-ups for missed classes. Enrollment in our recreation program is with the understanding that you are paying for the spot in your child's specific class and not the number of days attended during the session. Many of our classes are full and have wait lists, which makes it difficult to allow make ups and keep our 8:1 ratio of students to coach intact. Achieve Gymnastics will not prorate the session tuition for any missed classes.
If Achieve Gymnastics has to cancel a planned class, we will credit your account for that class.
The ONLY drink that should be brought into the gym is water. The water should be in a container with a lid. There should not be ANY food items brought into the gym.
We hope that everyone coming to our gym will respect the belongings of others. However, since valuables cannot be protected in the gym, we ask that all valuables and money stay at home. | {
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A Pair of Book Stamps
On June 22, 2017 June 10, 2021 By trinitycollegelibrary1695In Features, Library Curios
Curio B15: A Pair of Book Stamps with the Arms of John Hacket
John Hacket (1592-1670) was a member and fellow of Trinity College. As Bishop of Lichfield and Coventry he oversaw the rebuilding of the cathedral, contributing £3,500 and raising far more. He was also generous towards his former college making a bequest of £1200 in his will towards the rebuilding of the 'ruined' Garret Hostel. The work was completed in 1671 and the building was known thereafter as Bishop's Hostel. Hacket's will also stated that rental income from the new building should go to the college Library for the purchase of books. At the time the Library was housed in Great Court, but Hacket's bequest appears to have been an impetus towards the building of the new Wren Library. Work began in 1676 and was completed just under 20 years later in 1695. These two book stamps were purchased in 1677, almost certainly so that the Library could mark those books which came to it under the terms of the bequest.
Volume R.17.6 bears the impression of the larger of the two stamps on the front and back covers.
R.17.6, front cover
Inside it contains a copy of a letter written by Hacket announcing his intention to leave a gift to the college (f. 3r). It also includes a copy of accounts from Bishop's Hostel from the late 17th century. This includes an item from 1677 detailing the purchase of the book stamps for £1 15s.
Detail from R.17.6, f. 4r
A portrait of Hacket given by his son, Andrew Hacket hangs at the far end of the Wren Library.
The Junior Bursar's accounts for 1679-80 record a payment of 6s 6d 'for the carriage of Bishop Hackett's picture from London'. Hacket is depicted in Bishop's clothes, holding an unrolled scroll with a red seal. The writing on the scroll records the detail of Hacket's bequest to the college. In the background there are paintings of Lichfield Cathedral and Bishop's Hostel.
John Hacket, ascribed to Valentine Ritz, oil on canvas
The Bishop's Hostel accounts record that in 1681, £10 was spent on books from Dr Isaac Barrow's Library. These included, as examples, a work on physics by Marino Ghetaldi (T.10.6) and Hypomnemata Mathematica by Simon Stevin (Q.16.91.t1). The bindings of these books do not, however, bear the mark of either of the book stamps.
The Library also owns Hacket's small 13th-century Bible in two parts (B.10.24 and B.10.25) as well as a number of other books which were written by him including a volume of his sermons, his play Loyola published in 1648 which had been performed in Cambridge before James I in 1623, and a number of copies of his longest work – Scrinia reserata– on the life of his patron Archbishop John Williams. The volume of sermons, published posthumously in 1674, contains a frontispiece portrait of the author. The Library also owns the copper plate used for printing this portrait. By the time it was reused in a volume dated 1702 the wording on the bottom had been scratched out. Hacket's portrait was presumably included in the later volume (which was not written by him) because it had been bought for the Library under the terms of his bequest.
I.11.14
N.16.27
Archbishop of YorkB.10.24B.10.25Bishop of Coventry and LichfieldBishop's HostelIsaac BarrowJohn HacketJohn Williamswren library
From the Crewe Collection: Jonas Hanway and his bookbindings
The King's Scholars
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Kuduro (eller kuduru) är en typ av musik och dans som ursprungligen utvecklades i Angola på 1980-talet. Den kännetecknas som energisk med upptempo i snabb 4/4-takt.
Kuduron föddes ursprungligen i Malange, Angola i slutet av 1980-talet. Inspirationen kom inledningsvis från karibisk musik som soca och zouk från Karibien samt Semba från Angola. Med den angolanska invandringen till Portugal under inbördeskriget kom den att fortsätta utvecklas i Europa och utvecklas i mer elektronisk inriktning.
Externa länkar
Artikel om Kuduro-musikens historia och utveckling (på engelska)
Angolas historia hörs i den hårda kuduron Musikmagasinet, SR P2, 18 oktober 2014
Källor
Musikgenrer
Musik i Angola | {
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Blood, Metal and Dust: How Victory Turned into Defeat in Afghanistan and Iraq (Paperback)
By Ben Barry
This title is likely unavailable. Email or call for price and availability.
SHORTLISTED FOR THE DUKE OF WELLINGTON MEDAL FOR MILITARY HISTORY 2021, THE BRITISH ARMY BOOK OF THE YEAR 2021, AS A FINALIST FOR THE 2020 ARMY HISTORICAL FOUNDATION DISTINGUISHED WRITING AWARDS. FIRST RUNNER UP IN THE TEMPLER MEDAL BOOK PRIZE 2021.
'With a soldier's eye for telling operational details, Ben Barry offers an authoritative, compelling and inevitably bleak account of the American and British campaigns in Iraq and Afghanistan.' Sir Lawrence Freedman, Emeritus Professor of War Studies, King's College London
Newly revised and updated with in-depth analysis of the current situation in Afghanistan after American withdrawal, Blood, Metal and Dust is an authoritative account of how the wars in Iraq and Afghanistan were played out, explaining their underlying politics and telling the story of what happened on the ground.
From the high-ranking officer who wrote the still-classified British military analysis of the war in Iraq comes the authoritative history of two conflicts which have overshadowed the beginning of the 21st century. Inextricably linked to the ongoing 'War on Terror', the wars in Iraq and Afghanistan dominated more than a decade of international politics, and their influence is felt to this day.
Blood, Metal and Dust is the first military history to offer a comprehensive overview of the wars in Afghanistan and Iraq, providing in-depth accounts of the operations undertaken by both US and UK forces. Brigadier Ben Barry explores the wars which shaped the modern Middle East, providing a detailed narrative of operations as they unfolded. With unparalleled access to official military accounts and extensive contacts in both the UK and the US militaries, Brigadier Barry is uniquely placed to tell the story of these controversial conflicts, and offers a rounded account of the international campaigns which irrevocably changed the global geopolitical landscape.
The International Institute for Strategic Studies is an influential independent international think tank. As Senior Fellow for Land Warfare, Ben Barry has written extensively for IISS publications including Survival, its journal, and Strategic Survey, its annual assessment of world affairs. He is one of the authors of the annual Military Balance, an authoritative assessment of global military affairs. He was the author of 'Combat and Capability: Military Trends since 9/11', published in the 2012 Military Balance. This flagship essay was a concise analysis of the decade of military conflict war from 2001 to 2011.
He left the British Army in October 2010. He wrote A Cold War: Frontline Operations in Bosnia describing his battalion's operational tour under both UN and NATO flags in the mid-1990s. The book was shortlisted for the British Army Book of the Year 2009. His final appointment was leading the British Army's analysis of the lessons of the Iraq campaign, which informs Blood, Metal and Dust.
History / Wars & Conflicts / Afghan War (2001-2021)
History / Wars & Conflicts / Iraq War (2003-2011)
History / Middle East / Iraq
Publisher: Osprey Publishing
Publication Date: February 22nd, 2022
"At one level Blood, Metal and Dust is a clear, dispassionate and succinct military history of the post-9/11 wars in Iraq and Afghanistan. But it is much more important than that. As the US and UK turn their backs too quickly on both wars, they are in danger of disregarding the lessons and so failing to profit from their experiences. This book puts that right. Ben Barry is forthright in his criticisms and depressingly correct in his conclusions. Blood, Metal and Dust is essential reading." - Sir Hew Strachan FBA FRSE, Professor of International Relations at the University of St Andrews and former Chichele Professor of the History of War at All Souls College, Oxford
"With a soldier's eye for telling operational details, Ben Barry offers an authoritative, compelling and inevitably bleak account of the American and British campaigns in Iraq and Afghanistan." - Sir Lawrence Freedman, Emeritus Professor of War Studies, King's College London
"Blood, Metal and Dust is a seminal work that exploits newly available archival material to produce a riveting account of the allies' wars in Iraq and Afghanistan. Armed with a keen scholarly eye and long military experience, Ben Barry dissects key decision points and pitched battles ranging from Tora Bora, Operation Medusa and Wanat in Afghanistan to the US Marines' Anbar campaign, Operation Viking Hammer in Kurdistan, and the Sadr City battle of 2008. His unsparing judgments should inform future war planning, making this book required reading for the policymaker and the practitioner alike." - Linda Robinson, Senior International/Defense Researcher, RAND Corporation and author of 'Tell Me How This Ends'
"The telling of this particular audit of war is accomplished with precision and with dispassionate honesty. This book is required reading." - Mark Barnes, War History Online
"This is without doubt the best military history of the campaigns in Iraq and Afghanistan I have read to date." - Wavell Room
"Blood, Metal and Dust is an essential, landmark work." - Mungo Melvin, The RUSI Journal
"Blood, Metal and Dust is the essential account of the 21st-century wars in Afghanistan and Iraq." -Martin Purbrick, Asian Affairs
"This is a must-read." - This England
"Lucid, wide-ranging and thorough, for students of the West's recent wars in Iraq and Afghanistan it will remain an indispensable resource for years to come." - International Journal of Military History and Historiography | {
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Williams Takes His Turn in Dubai Tour Breakaway
Race: Dubai Tour, Stage 4
Start/Finish: Dubai/Hatta Dam, United Arab Emirates
Distance: 172 kilometers
Hatta Dam, UAE —Friday's 172-kilometer race served as the Dubai Tour's queen stage and it saw Team Novo Nordisk's Chris Williams feature in the day's main breakaway.
Immediately from the Stage 4 start, Williams and two other riders attacked. Quickly three riders joined them. The six-man group earned a maximum gap of 6:30.
Williams took top honors through the first intermediate sprint and was runner-up through the second intermediate sprint. Following the second sprint, Williams and another rider dropped back to the peloton in anticipation of the climb up Hatta Dam.
Eventually, only Brandon McNulty (Rally Cycling) remained off the front from the initial breakaway. Heading into the final kilometer, it appeared the American would pull off an upset, but a reduced chase group caught him in the final 150 meters.
Sonny Colbrelli (Bahrain-Merida) took the win while Charles Planet finished in that elite front group.
Charles Planet
"Today was good for my confidence; it felt good to be there with the best guys in this race. After two days in the breakaway and 300 kilometers off the front, I didn't know what to expect out of my legs. My teammates helped me all the way to the climb. My legs felt good and I moved up to the first group. I finished in the top 20, but I know I can do better. I did learn some valuable lessons today, specifically about positioning in the crucial moments on the climb."
Team Novo Nordisk, the world's first all-diabetes pro cycling team, wraps up racing at the Dubai Tour on Saturday with Stage 5. The final 132-kilometer stage begins at Skydive Dubai and features two intermediate sprints before a sprint finish at City Walk. Team Novo Nordisk's Planet, Williams and Quentin Valognes are all still in contention to win the intermediate sprint jersey.
Stage 4: Rider CGM Data*
Chris Williams: 3:54:53 (Chris spent 134km of the 172-km queen stage in the breakaway)
1st: Sonny Colbrelli (Bahrain-Merida): 3:40:50
2nd: Magnus Cort Nielsen (Astana Pro Team): same time as Colbrelli
3rd: Timo Roosen (Team LottoNL-Jumbo): same time as Colbrelli
19th: Charles Planet: same time as Colbrelli
(Photos: ©TDWSport/Getty Images)
*This image is solely for informational purposes and is not intended as medical advice. It is not a substitute for the advice of a health care professional. If you have diabetes or suspect having any health problems, you should consult a qualified health care professional.
Tags: dubai tour Tour of Dubai
"I did learn some valuable lessons today, specifically about positioning in the crucial moments on the climb."
Team Novo Nordisk Returns to the World Tour at the Inaugural UAE Tour
Race: UAE Tour (February 24-March 2, 2019) Country: United Arab Emirates Total Distance: 1,090 kilometers Race Class: WT Team Novo Nordisk is taking a mixed squad of sprinters and climbers to the inaugural UAE Tour when the seven-day race kicks off on Sunday, February 24th. "The UAE Tour has it all with a team time…
Chris Williams: Injury Update
Team Novo Nordisk rider Chris Williams gives an update on his recovery after fracturing his right ankle on stage 5 of Dubai Tour. Chris Williams: "I went in for surgery a couple of days after I returned to Australia, as my fractured ankle was slightly displaced, so I have been getting around on crutches since then. The swelling in…
Brais Dacal Visits Diabetes Center in Dubai
Following the 2018 Dubai Tour, Team Novo Nordisk ambassador Brais Dacal got a chance to visit two local Dubai schools and the Boston Diabetes Center of Dubai and bring some much-needed inspiration to kids affected by diabetes in the United Arab Emirates. Brais Dacal: "Meeting with students at the Dubai British School and the Bradenton Preparatory Academy was a tremendous opportunity to inspire and empower young people…
2018 Dubai Tour – Stage 5 Recap
Watch Team Novo Nordisk rider Quentin Valognes come from behind to win the UAE Intermediate Sprint Classification jersey at the 2018 Dubai Tour. | {
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I will give a brief description of the materials used on each page. On the first page there are leaves cut and painted from a phone book page with a leaf cut from a leftover of my mixed media quilt Illustrated Document No. 1.
Sprout painted with textile paint on fabric, next page black and white tissue paper and left overs from a mixed media vessel.
Collaged, painted paper overlapped by painted flower on the canvas.
A piece of rust dyed silk organza from Jane LaFazio that I drew floral images on with a permanent marker.
Dark tea stained tea bag drawn on with permanent marker.
Another leaf from the vessel, black and white tissue paper and colored art papers.
Tea bag drawn on with a red marker collaged over a paper image. Painted leaves and a strange bug I created in photoshop printed on paper with some washes of acrylic paint.
Old engravings on paper, painted with fluid acrylics and leaves cut from painted fabric leftovers.
I will be working on the metal for the next book in Open Studios at Quilt Festival, so you will have to wait to see the next one.
Fiber Art for A Cause earned $6,250 for the American Cancer Society! This is better than anyone could have imagined and a great addition to the $165,000 that Virginia has raised so far. Thank you, thank you to all those special people out there who made it possible!
I began by tearing canvas into 4" x 8 " pieces and painting both sides with gesso. I think if I were to start again I would tear them into 4 " x 8 1/2" pieces to allow for the bulk of paint and collage. When the pages were folded in half the book got fairly fat and the pages were a little short in width.
I painted the pages with fluid acrylic washes.
These are the semi finished pages for two books, the blue on the left will be Birds & Bees the yellow on the right is Flora.
There are images that are drawn, painted and transfered onto tea bags, pieces of rice paper, printed tissue paper, wrapping paper, pieces of painted fabric, scraps from other projects, transfers on fabric, painted canvas and a sewing pattern. All adhered with gel medium and machine stitching.
I folded the canvas pages in half and clamped them to help set the fold.
I tore 4" x 2" strips of canvas to use on the binding. Since the canvas was not painted I did some zigzag stitching around the edge, then positioned it over the center of the stack of pages, taping it in place to secure it for stitching.
I stitched through the four layers on my Bernina sewing machine (my Janome would not sew through the bulk).
I clamped the stitched book again to help it hold the fold.
Walnut Hollow sells a very strong double sided tape to adhere the metal to other surfaces. I found that it will even stick to canvas. I attached the tape and burnished it well to the canvas and then peeled away the paper backing to stick it to the metal, burnishing it to make a good bond with the metal.
I finished the binding by adding some cloth book binding tape.
My next post will show the whole book page by page.
The Donations are coming in!
Here's an uplifting note in a time when we have felt so down about the economy. Fiber Art For A Cause is off to a fabulous start with two pieces sold on opening day and another two this morning.
Linda Teddlie Minton's artwork raised $1800, Rayna Gilman's - $1600, Marjorie DeQuincy's - $800 and mine - $450 for the fight against cancer. That's an incredible start to this fundraiser!
Tomorrow is the last day of the Reverse Auction and the minimum donation will drop by another third. Will the artwork you desire still be there???
Donations are made directly to the American Cancer Society with an immediate electronic receipt sent to donors. Thank you for your support of Fiberart For A Cause, fundraising for the American Cancer Society.
The Fifth and Final Reverse Auction featuring my artwork "I Beelieve" opens today at 10 a.m. CST.
100% of the proceeds are donated directly to the American Cancer Society through Fiberart For A Cause. The minimum donation drops each day; wait too long and my artwork might be gone!
This is the bee panel partially done. In this photo I have gone over all my lines on the front side of the metal with the pointed stylus and begun adding some stippling with the tiny ball stylus to the background on the left side. This helps the image to pop up and be defined. In the next photo, the metal design is finished. The raised areas of the design are worked from the back side of the metal. On the bees wings and the leaves, I used a large ball shaped stylus to give extra dimension.
The tool kit from Walnut Hollow has a lot of different metal working tools to add texture and shaping to the metal. I have only used a few of the tools so far as I figure out how each one can be used. It is an awesome little kit with a ruler, scissors, two tool handles with multiple tips that screw into both ends and a couple plastic embossed border shape plates that metal can be burnished over with a paper stump. I like to make my own designs , so I haven't used those, but they are nice patterns. All in all it is everything you would need to do some serious metal work.
This is a design I made on a piece of copper metal using the Alcohol Inks, the felt pad tool and the blending solution. Here is a great little video with Tim Holtz demonstrating alcohol inks.
I am working on making a couple small canvas books with copper metal covers. I am using 4 inch square copper metal, it is a heavier weight metal than the aluminum I use for Fiesta Ornaments.
I have drawn several designs to use for front and back covers for two books, one titled Flora, the other Birds & Bees.
I begin by taping the metal to a foam mat and then taping the drawing in place over the metal. I transfer my image to the metal by tracing over my pencil lines with an embossing tool. I remove the paper and use the embossing tool to deepen the lines on the metal and add details by working on the front and the back side of the metal, creating dimension. I like to make a small outline around my whole design and fill in the background with stippling by tapping the point of the tool repeatedly over the surface of the copper. This helps the main design stand out from the background. I found the best product to color metal is Adirondack Alcohol Inks. You can apply inks using a felt pad or paint brush. I wanted to paint color in specific areas so I used a brush to apply the ink. You don't need much when working with the inks, just drop a few drops of ink onto a paint tray and use a paint brush to apply the ink to the metal. The ink goes on very bright. If you decide that you want less color, dip your brush in a little of the Alcohol Ink Blending Solution and go back over the area previously painted and the color becomes lighter as it removes the ink. Or you can add the blending solution to the ink on the tray and lighten it before painting it on the metal.
The inks dry very quickly and can be reconstituted in the tray by adding a little blending solution. To rinse my brush between colors I dipped it in the alcohol blending solution and wiped it on a paper towel. On the copper design with the waterlilies I lightened the ink to make a soft pastel tint on the copper and I painted the ornate floral design brightly to look more like the metal ornaments you see in Mexico.
Natalya Aikens, Gerrie Congdon, Marjorie DeQuincy, Rayna Gillman, Carol Larson, Linda Teddlie Minton, Susie Monday, Judy Coates Perez, Leandra Spangler and Roxane Stoner have all donated their artwork.
All proceeds from the sales go directly to the American Cancer Society.
All artwork will begin at a fixed minimum donation. This minimum donation is reduced by a fixed (and very generous) percentage of the original minimum donation each day until the artwork is chosen by a generous patron.
"Having lost my husband to cancer nine years ago, I wanted to make some small contribution to something that is so close to my own heart, as well as a joyful way to remember my husband and other friends and relatives who have fought this disease. Since fiber art is both my vocation and my avocation, this seemed a perfect match for me. I was honored to be asked to contribute to the Invitational Reverse Auction, and delighted to accept," said Linda Teddlie Minton.
Fiberart For A Cause has now donated more than $165,000 to the American Cancer Society in the last four years and was the second highest national fundraiser for the 2007 American Cancer Society Cancer's Relay for Life.
For more information on Invitational Reverse Auction and Fiberart For A Cause, contact [email protected].
Please go visit the website on Tuesday and place a bid on a piece of art for this worthy cause.
Just a reminder that I will be teaching two classes at the International Quilt Festival Chicago in April.
In this class we will cover a variety of painting techniques such as creating smooth gradations of color, glazing and adding fine details, with lots of tips for getting the best results from different types of paint.
I would love to have you in one of my classes, check your Quilt Festival catalog and sign up now.
Last month I made a canvas book after seeing Jane LaFazio's segment on Quiting Arts TV. Jane used artist canvas as a base for a mixed media collage. I have not worked much on canvas and thought it would be a lot of fun to try using it as a base for a book.
I bought a yard of canvas at the art store and tore it into two 12" x 24" strips and two 6" x 16" strips and painted a coat of Gesso on each side of the canvas. Gesso creates a surface to paint on, so all your paint doesn't soak into the canvas.
Next I put color on each side of the canvas, so I would not be working on blank pages. A blank white page can be so intimidating. I also collaged some paper images onto the pages with gel medium and stitched a couple pieces of painted canvas to the pages.
Then I stacked the pages together and sewed them together on the sewing machine. I found that my Janome was not happy sewing through the layers of canvas, but the Bernina plowed right through four layers of painted canvas with no problem.
This book was not meant to have a theme, just be a place to try new things, new techniques and randomly add things, a continuous work in progress.
This page has a paper bird from wrapping paper in the upper corner and a painted bird in the bottom corner, painted with textile paints. The patterns and text were printed with thermofax. I had never printed with thermofax screens before. The images printed a little more distressed on the bumpy surface of the canvas. But I love the layer of texture. I can see why so many people love working with thermofax screens.
The photos of the women, here, on the cover and the back of the book are from acetate transfers using matte medium that Lesley Riley gave me. The one on this page was transferred onto a piece of buckram.
The cicada drawn on the red fabric and the patterns drawn on the leaf were made using a ruling pen. This was a great tip from Melanie Testa, I had forgotten all about ruling pens. I used to use them all the time years ago for inking things. I have several of them that have sat unused in a box for the last 20 years. I even have my dad's ruling pen and drafting tools that he used in his days as an engineer for the Navy. I am thrilled to rediscover the ruling pen, it is a great tool for drawing fine lines with paint or thickened dye.
In Jane's QATV segment she also used stencils to add more visual texture to her collages. When I was at Blick I saw a set for $2.99 how could I resist? I numbered my pages with them using the number as a design element on each page.
I drew the bee on the page with a permanent brown pen and painted it using transparent glazes of textile paint.
This center page has a thermofax print on a piece of wool felt and a scrap from the fabric I made to create the apron I posted about a couple weeks ago.
On page 12 I sewed a machine felted fabric collage.
On my last page I sewed a pocket so that I could keep things I want to add to the book in the future.
This book is still far from finished, I am planning to keep adding to it indefinitely.
It has been a fun experiment, canvas takes paint so differently from fabric. You can push paint around on its surface and pick it up again with a cloth making interesting textures in ways that you can't on cotton fabric. I also like the body the canvas has for book pages, flexible, yet sturdy. I can see a lot of ways one could explore using canvas for books. | {
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Petazon Business Directory list of hotels in Harrisville, NH and motels in Harrisville, NH. A comprehensive directory of resorts and accomodations in Harrisville, NH that allow you to bring your dog, cat or other pet.
Below is a compilation of information for travelers with pets to Harrisville, NH.
If you are looking for lodging in Harrisville, NH - please see our list above. | {
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If there is one thing Metroid is known for above all else, it's atmosphere. The sense of isolation you share with series heroine Samus Aran is deep and oppressive. A great deal of this atmosphere is derived from an excellent soundtrack that perfectly compliments the landscapes of planets such as Zebes and Talon IV. When these soundscapes are remixed and combined with some amazing fan made CGI animation, the results are nothing short of stunning. SamoStudios has created a gorgeous music video for their song "Beyond The Glass" from the recently released Harmony Of A Hunter: 101% Run. The song and video are by Sam Dillard and is based on the Maridia theme from Super Metroid and a must for any Metroid fan. Enjoy! | {
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Godfrey Manar, paramount chief of Vanua Lava, shows a special round stone that is used only by chiefs when they want to relax. The chief takes a victory leaf and slaps it on the round stone, which makes it spin on top of another stone. He then sings and dances.
Description : Godfrey Manar, paramount chief of Vanua Lava, shows a special round stone that is used only by chiefs when they want to relax. The chief takes a victory leaf and slaps it on the round stone, which makes it spin on top of another stone. He then sings and dances. | {
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OK, maybe he misheard the question; it's Monday right?
So on Tuesday, Jeb goes on Hannity to clear things up.
Blah blah blah, but as to knowing what we know now?
So mistakes were made, and apparently by that mysterious entity known as the third person, and a refusal to answer.
Now many times it's fair to say that hypothetical questions shouldn't be answered, however the Iraq War wasn't hypothetical, it was real, and an answer to that question is an excellent proxy to all sorts of foreign policy views.
Particularly if your last name is Bush.
He was later asked about comments aired by Fox News on Monday that he would have ordered the Iraq invasion even knowing how the war unfolded and that intelligence used to justify the war was faulty. On Tuesday, Bush clarified his comments, saying he had misunderstood the question.
"Rewriting history is hypothetical," Bush replied.
"And I answered it honestly and I answered it the way I answer it all the time, which is that there were mistakes made, but based on the information we had, it was the right decision," he said.
Bush also dismissed "hypothetical" questions about the origins of the Iraq war as a "disservice" to U.S. troops who died or were injured in the war, and to their families.
By Thursday, Jeb was in Arizona and finally seemed to suspect that he might actually be asked about Iraq, and he had better come up with an answer.
If we're all supposed to answer hypothetical questions: Knowing what we now know, what would you have done? I would not have engaged. I would not have gone into Iraq.
As I've argued here and here, Jeb Bush is mentally unprepared to be President. All he cares about are illegal immigrants and when he's not talking about that, it's as if he's never thought of the issue before, even when the issue is the most predictable question any potential candidate has ever gotten.
I had cut on the Sean Hannity Show this afternoon, and caught the show midway through a discussion between Hannity and his producer, Lynda about the pros and cons of Ashley Madison, the cheating website. "Again?" I thought. It seemed like more than once I had heard Hannity either talking about the website or arguing with the Ashley Madison CEO Noel Biderman, about the website. Was Hannity going through a mid-life crisis? After berating Anthony Weiner for a half hour, was Hannity now one red corvette away from having his own affair?
The discussion between Hannity and his producer waged on for what I thought was an uncommonly long while. Air time is valuable and with Zimmerman-IRS-Immigration going on this week, I would expect the time would be allotted to those tidbits rather than Lynda the producer taking a pro Ashley Madison position and Hannity of course taking the disapproving Catholic, finger wagging position. Considering how much the very concept of a website to facilitate cheating on your spouse apparently offended Hannity, why would he give so much free air time to promote a business he morally opposed?
Knowing how careful radio hosts are about spending airtime to promote businesses that are not sponsors, I got a little bit suspicious. Could Ashley Madison, the red warning sign of the decline of Western Civilization, and promoter of the disintegration of the American Family, be a paid advertiser of the Sean Hannity radio show?
I did a little snooping on Hannity's website. No banner ads from Ashley Madison with cute adverts like, "get your cheat on." were visible. However I did see that the Ashley Madison CEO had been on the Hannity show quite a few times: Today, July 24, 2013, May 17, 2013, June 15, 2011, and May 12, 2010, at least from the archaic search function on the site, so I suspect it's probably more than that.
In my opinion, only an act of desperation would tempt Limbaugh's show to take the offer. Ironic as it might be, he speaks for those who fancy themselves the "family values" party. The largest segment of his demographic is 65+. I don't know how well Grandpa and particularly Grandma will take to his biggest sponsor being a website geared toward adulterers. Ashley Madison does advertise on Sean Hannity and Howard Stern.
OK, Howard Stern I get. If ever there was a natural fit, it would be between Ashley Madison and the Howard Stern Show, but Sean Hannity?
Doing an on-air plug is not only the best sort of radio advertising; it's generally the most expensive, since the radio show host, who presumably you trust since you are listening to their show, is telling you how great the product or service is. But in this case, the host is telling you how terrible the service is. But he's telling you over and over.
Still, it has an air of dishonesty to it. Hannity's finger waging of disproval doesn't seem as nearly as disapproving if he's collecting a big fat check for it.
This post brought you to you by the Sean Hannity Show. Hannity, for all your conservative needs (j/k).
I agree. Although Cruz was talking about budget negotiations, to me it applies to the issue of immigration more than any other issue. That's because so many Republicans are not only prepared to vote for amnesty, they are actively campaigning for it, even though it is not only damaging public policy, but damaging to those same Republican's political futures.
At least with the Democrats, I perfectly understand their motivations for wanting amnesty, and frankly, from their perspective they seem totally logical to me. It's bad public policy for the nation, but its great political policy. For the Democrats, out of a possible 11 million new voters 10 to 15 years from now, 9 million will vote for Democrats. That's enough to turn the rest of the Southwest, including Texas, deep blue. Without Texas, the Republicans are no longer viable as a national party.
And from a policy perspective, that adds 11 million more citizens in which ¾ of them don't even have a high school diploma and virtually none of them have the high tech skills required for the 21st century workplace. That means most of them will live and die below the mean income level, and will be major consumers of social programs. That's voting gold for the Democrats. The Democratic Party was never stronger as when FDR saw "one third of a nation, ill housed, ill clad, ill nourished." Importing millions to fill that gap helps create the very conditions of income inequality and widespread poverty that is the fertile ground for Democratic power.
But what do the Republicans get out of it?
That is the real head scratcher. Of course there are some aspects of big business that do use unskilled and semi skilled labor that really like the downward push on working class wage rates that increased numbers of unskilled workers provide. Certainly the Wall Street Journal Opinion page is filled with pro illegal immigration editorials. But for most businesses interested in immigration, the demand isn't for millions of unskilled workers but for hundreds of thousands of skilled workers, which current immigration law limits to a mere trickle.
Politically, it seems to make even less sense. There isn't any evidence that pro illegal immigration positions help Republican candidates. A recent CIS study showed that Latinos in pro-immigration Republican Districts were no more likely to vote for Republicans than Latinos living in anti-illegal immigration Republican Districts. Certainly it didn't help Senator John McCain in his 2008 Presidential bid. And of course, what is the political advantage of ensuring that your political party remains a minority party for the foreseeable future?
And yet… Republicans, including conservatives, are falling all over each other to support the Gang of 8 bill. Fox talker Sean Hannity even hosted a one hour special for Marco Rubio last Friday that did little more than pimp the bill with friendly "questions" and a generally pro bill agenda. Hard as I try, I can't see a rational reason to support this. Bad public policy, bad political strategy… what am I missing?
My suspicion is that I'm not missing much, and that the real problem with Republicans is that they think they can buy Latino votes with the bribery that has proven so successful for the Democratic Party for decades. But the Democrats can't be outbid. There is no line that Republicans can draw that Democrats won't cross to buy more votes. Republicans were just as delusional in 1986 when they accepted a "one time' amnesty with the promise that this would be the last one and that Latinos would now love Republicans.
Instead we lost California permanently. Well, if Republicans regard Texas as an embarrassment they can't wait to be rid of, they are well on their way. The Democrats won't be embarrassed by Texas at all once they own it. | {
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Buzz announces extensive This Machine Kills Artists summer tour!
Buzz has just confirmed a seven-week U.S. tour, which kicks off June 10 in San Diego, CA! This will be in support of his full length solo acoustic album "This Machine Kills Artists" which will be coming out on June 3rd via Ipecac. He'll be documenting his tour through an ongoing travelogue on Noisey.com.Tickets for most shows will go on sale this Friday, April 4th. Buzz will also be playing the Scion A/V Rock Fest along with Big Business and others in Pomona, CA, it's a free show but you have to RSVP!
The A.V. Club has also premiered a song from Buzz's album for streaming, Drunken Baby! | {
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Grange wants statue for reggae icon in MoBay
Published:Monday | April 1, 2019 | 12:11 AM
Culture and Entertainment Minister Olivia 'Babsy' Grange addressing the audience at the unveiling of Jimmy Cliff Boulevard at a ceremony held at the Old Hospital Park in Montego Bay.
WESTERN BUREAU:
Culture and Entertainment Minister Olivia 'Babsy' Grange has expressed her desire to see a statue of musical icon Dr James 'Jimmy Cliff' Chambers erected in Montego Bay, St James, to honour his work.
"I would like to see a statue of Jimmy Cliff in the heart of Montego Bay," Grange told reporters while attending a ceremony to unveil the Jimmy Cliff Boulevard sign, in honour of the reggae artiste, at the Old Hospital Park in Montego Bay on Thursday.
"We must have monuments so that future generations can recognise and look at those monuments as inspiration, and it would be fitting and most appropriate to have a statue of Jimmy Cliff here in Montego Bay."
The newly named boulevard, formerly known as Gloucester Avenue and popularly called the 'Hip Strip', was renamed in recognition of Chambers' role in exposing Jamaica's culture on the global stage.
"It is my pleasure to be a part of this renaming ceremony from Gloucester Avenue to Jimmy Cliff Boulevard, reflecting our own history and our own pride," Grange said while addressing the function.
"Today, we pay homage to a musical giant in declaring the new Jimmy Cliff Boulevard, in recognition and celebration of a musical genius whose creative imagination and forceful character have brought fame, not only to himself, but to Montego Bay, St James, western Jamaica and to Jamaica, land we love."
Grange also indicated that more monuments should be similarly erected to honour other Jamaican icons, as had been done with the unveiling of a statue of the late Louise 'Miss Lou' Bennett-Coverley in Gordon Town, St Andrew, last September.
"We have commissioned and mounted statues of our athletes, we have started in treating with our culture, a statue of Louise Bennett-Coverley, and so there will be many more statues to come," said Grange.
A.F.
«Jimmy Cliff will now get greater recognition – mayor
Tourism ministry to receive plans for new MoBay performing arts centre » | {
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G+T named in AFR Most Innovative Companies List
G+T has been named 12th Most Innovative Company in the Australian Financial Review's (AFR) list of the top 50 firms at the cutting edge in 2017.
Cementing the firm's reputation as delivering the most innovative legal services in Australia, Gilbert + Tobin was the only law firm to make the 2017 list.
The awards, now in their 6th year recognised Gilbert + Tobin for its innovation program which led to the development of its flagship Smart Search suite of tools that automate searches for client-based due diligence work; and the Smart Counsel app - a free digital platform providing expert tips, example clauses and usage guides for in-house counsel.
The Smart Counsel app represents an unprecedented move by a major Australian law firm to provide free access to intellectual property for its clients and the broader legal community.
This recognition proves once again that Gilbert + Tobin's comprehensive innovation strategy is not only adding value for clients but also leading the way in transforming the legal industry.
Managing Partner Danny Gilbert said it was an honour to be recognised in the list of top-ranking companies who are pushing the boundaries on game-changing innovations and embedding an innovation mindset in everything they do.
"We are thrilled to be named among the top most innovative companies in Australia and New Zealand and a stand-out in the legal industry. We continue to challenge ourselves to raise the bar when it comes to integrating technology into our business and disrupting traditionally labour intensive and low-value tasks to enable our lawyers to focus on more high-value legal support for our clients."
G+T Innovate | {
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The Ministry of Economic Development (MED) has released a discussion document on the fees and levies to fund the Financial Markets Authority (FMA), External Reporting Board, Companies Office and Insolvency and Trustee Service.
The amounts involved are significant, and the basis for calculation is contestable, so we recommend that you take the opportunity to have your say.
Submissions are due by 5pm, 8 July. The new fee scale will take effect from 1 February, 2012 and will be reviewed after two years.
MED is not seeking feedback on the split between state and user-pays funding as that decision was taken in the budget.
$680 AFA, both associated with a QFE or independent, and QFE Category 1 adviser.
All fees would be paid on registration and then annually.
There will also be an FMA levy to fund the FMA's general monitoring, supervision, surveillance and investigative roles. Four options are offered.
Option One (MED's preferred option) would take a narrow focus and would levy only providers who are required to be registered under the Financial Service Providers (Registration and Dispute Resolution) Act (FSPA) and issuers who are required to file financial statements under the Financial Reporting Act (FRA).
Option Two would be broad-based and would capture all companies, limited partnerships, building societies, credit unions, industrial, provident and friendly societies and contributory mortgage brokers.
Options Three and Four would reflect this distinction but would wind the FAA and the FMA levies into a single payment.
The cost differences generated by these different approaches are significant.
One $910 Providers registered under the FSPA and issuers under the FRA.
Two $20 All companies, limited partnerships, building societies, credit unions, industrial, provident and friendly societies, contributory mortgage brokers.
Three $1,800 As per Option One.
Four $40 As per Option Two.
whether the Option One levy should be graduated according either to the relative benefit groups derive from operating in a well-regulated market or to the level of risk they create for the FMA.
The main advantage of Options Three and Four are that they reduce dramatically the amount payable by each FAA entity or individual. But this is at the cost of other financial providers, companies and entities. The MED also says that a combined levy would put a disproportionate burden on smaller operators.
The FMA will also have an auditor oversight function from 1 July 2012. Proposed fees are $7,900 a year for each licensed auditor plus the actual costs of conducting the practice reviews mandated by the Auditor Regulation Act. MED anticipates auditors will pass on the auditor levy to issuers as part of the fee charged for their services.
The XRB will replace the Accounting Standards Review Board on 1 July, 2011 and will be responsible for all financial reporting and audit and assurance standard setting. The proposed levy is $10 a year, to be paid by all companies, limited partnerships, building societies, credit unions, industrial, provident and friendly societies, and contributory mortgage brokers, at registration and with their annual return.
The document proposes restoring a company annual return fee. This would be levied at $22.50 for companies and $40 for limited partnerships, building societies, credit unions, industrial, provident and friendly societies and contributory mortgage brokers.
The revenue from this would finance reduced registration fees (from $153.33 to $110 for companies and from $276 to $250 for the rest).
financing statements/renewals: $4 for wholesale clients and $9 for retail clients (both up from $3.07).
The proposed fee is $2.50 a year for each registered company for liquidation services provided by the Official Assignee. | {
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\section{Introduction}
This paper continues the investigations carried out in \cite{HV1}, \cite{HV2}, \cite{HW}, \cite{GH1} and \cite{GH2} concerning the Schwartz kernel of the boundary values of the resolvent $(P - (\lambda \pm i0)^2)^{-1}$, where $P$ is the (positive) Laplacian $\Delta_g$ on an asymptotically conic manifold $(M^\circ,g)$, or more generally a Schr\"odinger operator $P = \Delta_g + V$ where $V$ is a suitable potential function. This was done for a fixed real $\lambda$ in \cite{HV1} and \cite{HV2} (and valid uniformly for $\lambda$ in a compact interval of $(0, \infty)$), for $\lambda \to \infty$ in \cite{HW} and for $\lambda = ik$, with $k$ real and tending to zero, that is, inside the resolvent set but approaching the bottom of the spectrum, $0$, in \cite{GH1} (and also in \cite{GH2}, where zero eigenvalues and zero-resonances were treated). Here we treat the case $\lambda$ real and tending to zero.
One of the main reasons for doing this is to obtain results about the spectral measure, which can be expressed in terms of the difference between the outgoing and incoming resolvents $R(\lambda \pm i0)$, where $R(\sigma) = (P - \sigma^2)^{-1}$.
Very complete results about the singularity structure of the spectral measure are known from \cite{HV1}, \cite{HV2} and \cite{HW} for $\lambda \in [\lambda_0, \infty)$ for any $\lambda_0 > 0$. To complete the picture we derive the asymptotics as $\lambda \to 0$ here. We can then, at least in principle, analyze the Schwartz kernel of any function of $P$ by integrating over the spectral measure. In the present paper we use our result on the low-energy asymptotics of the spectral measure to deduce long-time asymptotics of the wave and Schr\"odinger propagators determined by $P$.
In future articles, we will
treat two aspects of functional calculus for Laplace-type operators on an asymptotically conic manifold: (i) restriction estimates, that is $L^p \to L^{p'}$ estimates on the spectral measure, and $L^p \to L^p$ estimates for fairly general functions of the Laplacian, and (ii)
long-time dispersion and Strichartz estimates for solutions of the Schr\"odinger equation on nontrapping asymptotically conic manifolds.
\subsection{Geometric setting}\label{sect:Geometricsetting}
The geometric setting for our analysis is the same as in \cite{GH1}, which we now recall. Let $(M^\circ, g)$ be a complete noncompact Riemannian manifold of dimension $n \geq 2$ with one end,
diffeomorphic to $S\times(0,\infty)$ where $S$ is a smooth compact connected manifold without boundary. (The assumption that $S$ is connected is for simplicity of exposition; see Remark~\ref{manyends}.)
We assume that $M^\circ$ admits a compactification $M$ to a smooth compact manifold with boundary, with $\partial M=S$,
such that the metric $g$ becomes a \emph{scattering metric} or \emph{asymptotically conic metric} on $M$. That means that there
is a boundary defining function $x$ for $\partial M$ (i.e.\ $\partial M=\{x=0\}$ and $dx$ does not vanish on $\partial M$) such that in a collar neighbourhood
$[0,\epsilon)_x\times\partial M$ near $\partial M$, $g$ takes the form
\begin{equation}\label{metricconic}
g=\frac{dx^2}{x^4}+\frac{h(x)}{x^2} = \frac{dx^2}{x^4}+\frac{\sum h_{ij}(x,y) dy^i dy^j}{x^2}
\end{equation}
where $h(x)$ is a smooth family of metrics on $S$. We then call $M^\circ$ an asymptotically conic manifold, or a scattering manifold.
Notice that if $h(x) = h$ is independent of $x$ for small $x < x_0$, then setting $r = 1/x$ the metric reads
$$
dr^2+ r^2 h(0), \qquad r > x_0^{-1},
$$
which is a conic metric; in this sense, the metric $g$ is asymptotically conic. For a general scattering metric taking the form \eqref{metricconic}, we view $r = 1/x$ as a generalized `radial coordinate', as the distance to any fixed point of $M$ is given by $r + O(1)$ as $r \to \infty$.
A metric cone itself is not an example of an asymptotically conic manifold, since cone points are not allowed, except in the case of Euclidean space, where the cone point is a removable singularity.
In spite of this, the methods of this paper apply to metric cones, and in fact we analyze the resolvent kernel on a metric cone as an ingredient of our analysis on asymptotically conic manifolds.
We let $V$ be a real potential function on $M$ such that
\begin{equation}\label{hyp2}
\begin{gathered}
V\in C^{\infty}(M), \quad V(x,y)=O(x^2) \textrm{ as }x\to 0,\\
\textrm{ with }\Delta_{\partial M}+\frac{(n-2)^2}{4}+V_0>0 \textrm{ on } L^2(\partial M, h(0)), \ \textrm{ where } V_0=(x^{-2}V)|_{\partial M}.
\end{gathered}
\end{equation}
Here, $\Delta_{\partial M}$ is the (positive) Laplacian with respect to the metric $h(0)$, we let $(\nu_j^2)_{j=0}^\infty$
be the set of increasing eigenvalues of $\Delta_{\partial M}+\frac{(n-2)^2}{4}+V_0$ and the condition in \eqref{hyp2} is that the lowest eigenvalue $\nu_0^2$ is \emph{strictly} positive. Notice that $V_0 \equiv 0$ is not allowed if $n=2$, but is allowed for $n \geq 3$, and indeed then $V_0$ could be somewhat negative: for example, any negative constant greater than $(n/2 - 1)^2$.
We shall further assume that
\begin{equation}
\Delta_g + V \text{ has no zero eigenvalue or zero-resonance.}
\label{hyp3}\end{equation}
(Recall that a zero-resonance of $P$ is a solution $u$ to $Pu = 0$ where $u \notin L^2(M)$, but $u \to 0$ at infinity. Zero-resonances do not exist when $V \geq 0$.)
Let $P = \Delta_g + V$.
Then $P$, with domain $H^2(M, dg)$,
is self-adjoint on $L^2(M,dg)$ and a consequence of \eqref{hyp2} and \eqref{hyp3} is that its spectrum is the union of absolutely continuous spectrum on $[0, \infty)$ together with possibly a finite number of negative eigenvalues. It is known that, for $\lambda > 0$, the limits
$$
R(\lambda \pm i0) := \lim_{\eta \downarrow 0} (P - (\lambda \pm i\eta)^2)^{-1}$$ exist as bounded operators from $x^{1/2 + \epsilon} L^2(M, dg)$ to $x^{-(1/2 + \epsilon)} L^2(M, dg)$, for any $\epsilon > 0$ \cite{Yafaev}. The Schwartz kernels of these operators determines that of the spectral measure of $P_+^{1/2}$, where $P_+ = \operatorname{1\negthinspace l}_{(0, \infty)}(P) \circ P$ denotes the positive part of $P$, according to Stone's formula
\begin{equation}
dE_{P_+}(\lambda) = \frac{\lambda}{\pi i} \Big( R(\lambda + i0) - R(\lambda - i0) \Big) \, d\lambda, \quad \lambda \geq 0.
\label{Stone}\end{equation}
\subsection{Asymptotics}
We just mentioned above that, for any positive $\lambda$, the boundary values $R(\lambda \pm i0)$ of the resolvent exist as bounded operators from $x^{1/2 + \epsilon} L^2(M, dg)$ to $x^{-(1/2 + \epsilon)} L^2(M, dg)$, for any $\epsilon > 0$. However, this is not true uniformly down to $\lambda = 0$ \cite{BH2}. Indeed, the limit $\lambda \to 0$ of the resolvent kernel is a singular limit, which can be seen e.g. from explicit formulae for the resolvent kernel on flat Euclidean space. The outgoing resolvent kernel on $\RR^n$ has (modulo constant factors) asymptotics
$$
\lambda^{(n-3)/2} e^{i\lambda |z-z'|} |z-z'|^{-(n-1)/2} + O(|z-z'|^{-(n+1)/2}),
$$
for fixed $\lambda > 0$ and $|z-z'| \to \infty$, and
$$
|z-z'|^{-(n-2)} + O(\lambda),
$$
for $\lambda \to 0$ and $z, z'$ fixed (provided $n \geq 3$). These asymptotics do not match, and there is a transitional asymptotic regime in which we send $\lambda \to 0$ while holding $\lambda |z-z'|$ fixed. In the special case of $\RR^n$ the resolvent kernel is given by
$$
\lambda^{n-2} (\lambda |z - z'|)^{(n-2)/2} \operatorname{Ha}^{1}_{(n-2)/2}(\lambda |z-z'|), \quad z, z' \in \RR^n,
$$
where $\operatorname{Ha}^{1}_{(n-2)/2}$ is the Hankel function of the first kind and order $(n-2)/2$. Thus in this case we can see explicitly the transitional asymptotic regime, interpolating between the oscillatory behaviour of the kernel for positive $\lambda$ and the polyhomogeneous behaviour at $\lambda = 0$.
In this paper, following \cite{GH1} and more generally Melrose's program \cite{Kyoto}, we analyze the different asymptotic regimes of the resolvent kernel by working on a compactified and blown-up version, denoted\footnote{In this notation, $k$ stands for the parameter $\lambda$. We write $k$ rather than $\lambda$ in this notation to agree with the notation of \cite{GH1}, where the same space was used to construct $(\Delta_g + k^2)^{-1}$, $k \geq 0$.} $\MMksc$, of the space
\begin{equation}
M^\circ \times M^\circ \times (0, \lambda_0]
\label{naturaldomain}\end{equation}
which is the natural domain of definition of the kernel $R(\lambda \pm i0)$ for $0 < \lambda \leq \lambda_0$. The idea is to realize asymptotic regimes geometrically so that each regime corresponds to a boundary hypersurface, and we consider the space \eqref{naturaldomain} to be ``sufficiently blown up" when the resolvent kernel lifts to be conormal at the lifted diagonal and either Legendrian, or polyhomogeneous conormal, at each boundary hypersurface. That means, in particular, that there is nothing ``hidden" at any of the corners, or in other words that if we have two intersecting hypersurfaces $H_1$ and $H_2$, that the expansion at $H_1 \cap H_2$ can be obtained by taking the expansion at $H_1$ and restricting the coefficients, which are functions on $H_1$, to $H_1 \cap H_2$, or conversely by taking the expansion at $H_2$ and restricting the coefficients to $H_2 \cap H_1$. In the example above, the expansions for $\lambda \to 0$ for fixed $z,z'$ and at $|z-z'| \to \infty$ for fixed $\lambda$ do not match, and this requires (in our approach) that the corner in between be blown up, to create a hypersurface on which the transitional asymptotics take place.
\subsection{Main results and relation to previous literature}
Expansions of the resolvent as $\lambda \to 0$ were first considered by Jensen-Kato \cite{JK} for Schr\"odinger operators on $\RR^3$ and generalized by Murata \cite{Murata} to general dimension and general constant coefficient operators. More recently, there have been several studies by Wang \cite{XPW}, Bouclet \cite{Bouclet, Bou}, Bony-H\"afner \cite{BH1, BH2} and Vasy-Wunsch \cite{VW} on resolvent estimates (based on commutator estimates and Mourre theory) at low energy, for asymptotically Euclidean or asymptotically conic metrics.
Wang's paper \cite{XPW} is particularly close in spirit to the current paper, and we discuss it further in Remark~\ref{Wang}.
To describe previous results from \cite{HV1}, \cite{HV2} and \cite{GH1}, we refer to figures \ref{mmkb} and \ref{fig:mmksc} which are illustrations of the manifolds $\MMksc$ and $M^2_{k,b}$, two blown-up versions of $M \times M \times [0, \lambda_0]$. Here, $\mathrm{lb}$, $\mathrm{rb}$ and $\mathrm{zf}$ are respectively the boundary hypersurfaces of $M \times M \times [0, \lambda_0]$ corresponding to $x = 0$, $x' = 0$ and $\lambda = 0$ (we use unprimed variables to refer to the left copy of $M$ and primed variables to refer to the right copy of $M$). The other hypersurfaces are created by blowup. Notice that $\mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0$ and $\mathrm{bf}_0$ are ``at $\lambda = 0$'', while the others are ``at positive $\lambda$''.
In \cite{HV1}, \cite{HV2} the boundary value of the resolvent, $R(\lambda \pm i0)$, for fixed $\lambda > 0$, was shown to be the sum of a pseudodifferential operator (in the scattering calculus of Melrose \cite{scatmet}) and a Legendre distribution of a certain specific type, with respect to several Legendre submanifolds associated to the diagonal and to the geodesic flow on $M$, or more precisely to a limiting flow at `infinity'. In terms of the picture in Figure~\ref{fig:mmksc} this means that, on a fixed $\lambda > 0$ slice, the kernel is oscillatory at the boundaries $\mathrm{bf}, \mathrm{lb}, \mathrm{rb}$ and can be written as an oscillatory function or oscillatory integral with respect to phase functions determined by geodesic flow on $M$.
On the other hand, in \cite{GH1} the resolvent $(P + k^2)^{-1}$ was analyzed for real $k \to 0$ on the space $\MMksc$. Because $k$ is in the resolvent set whenever $0 < k < k_1$ where $-k_1^2$ is the largest negative eigenvalue of $P$, the kernel of the resolvent has exponential decay away from the diagonal, and hence vanishes exponentially at the faces $\mathrm{bf}, \mathrm{lb}$ and $\mathrm{rb}$. However, the rate of exponential decay vanishes as $k \to 0$ and, consequently, the kernel has nontrivial expansions at $\mathrm{lb}_0, \mathrm{rb}_0$ as well of course at $\mathrm{zf}$ and $\mathrm{bf}_0$ (which meet the diagonal), and the focus of \cite{GH1} was the precise analysis of these (polyhomogeneous) expansions.
The point of the current paper is to unify the two constructions.
A precise statement of the result is given in Theorem~\ref{mainres}, after definitions of Legendre distributions on the space $\MMkb$ have been given. For now, let us say that a kernel is conormal-Legendrian on the space $\MMkb$ if it lies in the calculus of Legendre distributions given in Section~\ref{Leg}; roughly this means that it is oscillatory at the faces $\mathrm{bf}, \mathrm{lb}, \mathrm{rb}$ and polyhomogeneous conormal at the other faces, on which $\lambda = 0$.
\begin{theo}
The boundary value of the resolvent kernel, $R(\lambda \pm i0)$, is the sum of a pseudodifferential operator, i.e.\ a kernel on $\MMksc$, supported close to and conormal to the diagonal $\Delta_{k, sc}$, and a conormal-Legendrian on $\MMkb$.
\end{theo}
We determine the structure of the spectral measure by subtracting the incoming from the outgoing resolvent. There are two different cancellations that occur when we do this. First the singularity along the diagonal disappears (not surprisingly, since the spectral measure solves an elliptic equation) and secondly there is cancellation in the asymptotic expansion for fixed $z, z' \in M^\circ \times M^\circ$ as $\lambda$ goes to zero. The second cancellation is quite important in applications, such as in understanding the decay of the heat kernel or propagator for long time.
\begin{theo}\label{mainth}
The kernel of the spectral projection \eqref{Stone} is conormal-Legendrian on $\MMkb$, and vanishes to order $2\nu_0 + 1$ as $\lambda \to 0$ with $z, z' \in M^\circ$ fixed, where $\nu_0^2$ is the lowest eigenvalue of the operator \eqref{hyp2}. In particular, if $V = 0$ (or even if just $V_0 = 0$), the spectral projection vanishes to order $n-1$ as $\lambda \to 0$ with $z, z' \in M^\circ$ fixed.
More precisely, there is a nontrivial solution $w$ to $Pw = 0$, with $w = O(x^{n/2 - 1 -\nu_0})$ as $x \to 0$, such that the expansion at $\lambda=0$ is given by
\[dE(\lambda)= \Big(\lambda^{2\nu_0+1} w(z) w(z') |dg dg'|^{1/2} + O(\lambda^{\min(2\nu_0+2,2\nu_1+1)}) \Big)d\lambda.\]
where $\nu_1^2>\nu_0^2$ is the second eigenvalue of the operator \eqref{hyp2}. Moreover, if $V$ is identically zero, then $w$ is constant.
\end{theo}
See Theorem~\ref{mainsm} for a more precise statement of this result.
We now give two corollaries of Theorem~\ref{mainth} concerning the long-time behaviour of the wave and Schr\"odinger kernels associated to $P$.
We write $P_+$ for $\operatorname{1\negthinspace l}_{(0, \infty)}(P) \circ P$.
\begin{cor}\label{cor:waves}
Let $P = \Delta_g + V$ be as above, and
let $\chi \in C_c^\infty(\RR)$, with $\chi(t) \equiv 1$ for $t$ near $0$.
Let $w$ and $\nu_0, \nu_1$ be as in Theorem~\ref{mainth}.
Then the
solution operators for the wave equation, localized to low energy, satisfy as $t \to \infty$
\begin{equation}
\begin{gathered}
\operatorname{1\negthinspace l}_{(0, \infty)}(P) \chi(P) \frac{\sin(t\sqrt{P_+})}{\sqrt{P_+}}(z,z') = - \Gamma(2\nu_0 + 1) \cos(\pi(\nu_0 + 1)) t^{-(2\nu_0 + 1)} w(z) w(z') \\ + O(t^{-\min(2\nu_0 + 2,2\nu_1+1) }) ,\\
\operatorname{1\negthinspace l}_{(0, \infty)}(P) \chi(P) \cos (t \sqrt{P_+})(z,z') = \Gamma(2\nu_0 + 2) \cos(\pi(\nu_0 + 1)) t^{-(2\nu_0+2)}w(z)w(z')\\ + O(t^{-\min(2\nu_0+3,2\nu_1+2)}) .
\end{gathered}\label{waveexp1}
\end{equation}
Notice that the coefficient $ \cos(\pi(\nu_0 + 1))$ vanishes
when $2(\nu_0+1)$ is an odd integer.
In particular if $\partial M=S^{n-1}$ and $V_0=0$, then waves decay to order $t^{-(n-1)}$ if $n$ is even and $O(t^{-n})$ is $n$ is odd.
The implied constant in the remainders are uniform on compact subsets of $M^\circ \times M^\circ$. Moreover, if $(M,g)$ is nontrapping, then we can remove the energy cutoff $\chi(P)$: the Schwartz kernels of $\operatorname{1\negthinspace l}_{(0, \infty)}(P) \sin(t\sqrt{P_+})/\sqrt{P_+}$ and $\operatorname{1\negthinspace l}_{(0, \infty)}(P) \cos(t \sqrt{P_+})$ are given by the right hand side of \eqref{waveexp1}. \end{cor}
\begin{remark}
This result is closely related to Price's law, which is the statement that waves on a Schwarzschild spacetime, starting with localized initial data, decay to order $t^{-3}$ (outside the event horizon) as $t \to \infty$. This $t^{-3}$ decay was predicted in \cite{Pr1,Pr2} and has been proved recently by Donninger-Schlag-Soffer \cite{DSS,DSS1} for exact Schwarzschild using separation of variables and by Tataru \cite{Ta} for more general settings.
Although our result does not apply directly to the Schwarzschild case, it does apply to asymptotically flat manifolds
which are isometric to Schwarzschild near infinity, or more generally to asymptotically conic manifolds with a `gravitational' type metric at infinity, that is, of the form near $x=0$
\begin{equation}
(1 - 2Mx) \frac{dx^2}{x^4} + \frac{h(x)}{x^2}.
\label{grav}\end{equation}
The case $M \neq 0$ requires a minor extension to the analysis of Section~\ref{lerc} given in \cite[Section 5]{HV2}.\footnote{Note that, in \cite[Section 5]{HV2}, for a metric of the form \eqref{grav}, we have $q_l = q_r = 2M\lambda^2$, so the imaginary powers that show up have an exponent $i\alpha$ with $\alpha = O(\lambda)$ vanishing at $\mathrm{bf}_0$ and $\mathrm{zf}$.}
\end{remark}
\begin{comment}
\begin{remark}
The decay of waves in time in this setting is related to the so-called Price's law about the decay of waves on Schwarzschild background.
Indeed, the Schwarzchild metric is given by $g=-(1-\frac{2M}{r})dt^2+(1-\frac{2M}{r})^{-1}dr^2+r^2d\theta^2_{S^2}$ and thus one can reduce
the problem of wave decay to a stationary problem (see e.g. \cite{DSS,DSS1,Ta}) by considering the operator
\[ |g|^{\frac{1}{4}}(1-\frac{2M}{r})^{\frac{1}{2}} \Box_g (1-\frac{2M}{r})^{\frac{1}{2}}|g|^{-\frac{1}{4}}=-\partial_t^2+\partial_{r^*}^2-\frac{1}{r^2}(1-\frac{2M}{r})\Delta_{S^2}-\frac{2M}{r^3}(1-\frac{2M}{r})\]
on $L^2(dr^*d\theta_{S^2})$ where $r^*:=r+2M\log(r-2M)$ and $|g|:=|\det g|$. One easily sees that $r$ has a polyhomogeneous expansion in $r^*$ starting with
$r=r^*-2M\log(r^*)+O(\log(r^*)/r^*)$ and thus the operator above is of the form $-(\partial_t^2+P)$ where $P$ is an operator which fits in our setting\footnote{We technically did not discuss log terms in the operator coefficients here, but since the expansion is polyhomogeneous and the log terms start at order $x^4\log(x)$ at $x=1/r=0$, our analysis carries this out and only the index sets at lower orders would be modified in the expansion of the spectral measure at $\lambda=0$.}. Therefore our result implies that the waves, spectrally localized to low frequencies and localized spatially in compact sets decay to order $O(t^{-3})$ by Corollary \ref{cor:waves}. Our analysis also gives the $t^{-3-2\ell}$ decay on Schwarzchild if the initial data has no components in the $\ell-1$ first angular momenta on the sphere $S^2$, since then using the spectral decomposition on $S^2$ and the spherical symmetry of the operator $P$,
our $\nu_0$ becomes $1/2+\ell$ and $\nu_1=\nu_0+1$.
The high frequencies analysis is already contained for instance in Bony-H\"afner \cite{BH0}, the waves localized at frequencies $\geq 1$ decay (locally in space) to infinite order in time due to the resonances free region proved by S\'a Barreto-Zworski \cite{SBZ}.
The sharp result on $t^{-3}$ decay was predicted in \cite{Pr1,Pr2} and has been proved recently by Donninger-Schlag-Soffer \cite{DSS,DSS1} for exact Schwarzschild using separation of variables and by Tataru \cite{Ta} for more general settings.
Previous results on wave decay for Schwarzschild were obtained in \cite{KaWa,BlSt,Kr,DaRo,Lu}.
Recently, decay of waves on asymptotically Euclidean metrics have also been
studied in by Bouclet and Bony-H\"afner \cite{Bou,BH2}.
\end{remark}
\end{comment}
The corresponding result for the Schr\"odinger propagator $e^{itP_+}$ is as follows:
\begin{cor}\label{propagators}
The Schwartz kernel of the propagator $e^{itP_+}$, localized to low energy, satisfies
\begin{equation}
\operatorname{1\negthinspace l}_{(0, \infty)}(P) \chi(P) e^{itP_+}(z,z') = C t^{-(\nu_0 + 1)} w(z) w(z') + O(t^{-\min(\nu_0 + 3/2,\nu_1+1) }) , \quad t \geq 1,
\label{propexp}
\end{equation}
for some $C\not=0$. The implied constant in the remainder term is uniform on compact subsets of $M^\circ \times M^\circ$. Moreover, if $(M,g)$ is nontrapping, then we can remove the energy cutoff $\chi(P)$: the Schwartz kernel of $\operatorname{1\negthinspace l}_{(0, \infty)}(P) e^{itP_+}$ is given by the right hand side of \eqref{propexp}.
\end{cor}
\begin{remark}
Indeed, using results of \cite{HW}, if the metric $g$ is nontrapping, then the propagator localized away from low energy satisfies
$$
\big| (\Id - \chi(P)) e^{itP_+}(z,z') \big| = O(t^{-\infty}), \quad t \to \infty.
$$
Intuitively this is because when $z, z'$ are fixed and $t \to \infty$, then no signal starting at $z$ can end at $z'$ when there is a lower bound on the velocity. The same is true with $e^{itP_+}$ replaced by either of the wave solution operators.
We also remark that, instead of localizing the variables $(z,z')$ in compact sets, we could work instead in appropriately weighted Sobolev spaces.
\end{remark}
\begin{comment}
This allows us to remove the energy cutoff:
\begin{cor} Let $P = \Delta_g + V$ be as above, and suppose in addition that the metric $g$ is nontrapping.
Then the Schwartz kernel of the propagator satisfies
\begin{equation}
e^{itP_+}(z,z') = t^{-(\nu_0 + 1)} w(z) w(z') + O(t^{-(\nu_0 + 1 + \epsilon)}) , \quad t \geq 1,
\label{proplongtime}\end{equation}
for some $\epsilon > 0$, where $w$ and the $O(t^{-(\nu_0 + 1 + \epsilon)})$ term are as in \eqref{propexp}.
\end{cor}
\begin{remark}
Of course, we could equally well write down an expansion for $e^{itP}$, since
$$e^{itP} - e^{itP_+} = \sum_{k=1}^N e^{-it\mu_k} \Pi_k,
$$
where $\{ -\mu_k \}_{k=1}^N$ are the negative eigenvalues of $P$ and $\Pi_k$ is the orthogonal projection onto the $\mu_k$-eigenspace.
\end{remark}
\end{comment}
\begin{remark}\label{Wang} X. P. Wang's paper \cite{XPW} is quite close in spirit to the present paper. He also studies manifolds with (exactly) conical ends, and derives low energy asymptotics for the resolvent, as well as large time expansions for the propagator similar to the Corollaries above. In fact, his results are more general than ours in some respects, as he treats higher order asymptotic terms, and also allows zero modes and zero resonances. On the other hand, our results are more complete in that we consider expansions at all boundary hypersurfaces of $\MMksc$, while Wang only considers (in our terminology) expansions at the $\mathrm{zf}$ boundary hypersurface. Our expansions are also more explicit: for example, it does not seem easy to see from \cite{XPW} that the leading asymptotic for the propagator is a rank one operator (under our assumptions), as in \eqref{propexp}.
\end{remark}
Corollaries~\ref{cor:waves} and \ref{propagators} only use the expansion of the spectral measure at the $\mathrm{zf}$ face of $\MMkb$.
In the sequel, \cite{GHS2}, to this paper we shall prove the following
consequences of Theorem~\ref{mainth} that exploit the full regularity of the spectral measure, in particular its Legendrian nature at the ``positive $\lambda$" boundary hypersurfaces:
\begin{itemize}
\item
For any $\lambda_0 > 0$ there exists a constant $C$ such that the generalized spectral projections $dE(\lambda)$
for $\sqrt{\Delta}$ satisfy
\begin{equation}
\| dE(\lambda) \|_{L^p(M) \to L^{p'}(M)} \leq C \lambda^{n(1/p - 1/p') - 1}, \quad 0 \leq \lambda \leq \lambda_0
\label{restr}\end{equation}
for $1 \leq p \leq 2(n+1)/(n+3)$. Moreover, if $(M,g)$ is nontrapping, then there exists $C$ such that \eqref{restr} holds for all $\lambda > 0$ and the same range of $p$.
\item
Assume that $F\in C_c(0, T)$ and that for some $s>\max\{n(1/p-1/2),1/2\}$
$$
\|F\|_{H^s}< \infty,
$$
where $H^s$ is a Sobolev space of order $s$. Then there exists $C$ depending only on $T$, $p$ and $s$ such that
\begin{equation}
\|F(\sqrt{\Delta})\|_{p\to p} \leq C\|F\|_{H^s} .
\label{specmult}\end{equation}
Moreover, if $(M,g)$ is nontrapping, then \eqref{specmult} can be improved to
\begin{equation*}
\sup_{t > 0} \|F(t\sqrt{\Delta})\|_{p\to p} \leq C\|F\|_{H^s} .
\end{equation*}
\end{itemize}
\section{Geometric Preliminaries}
\subsection{The spaces $\MMkb$ and $\MMksc$}\label{5.1}
The construction of the Schwartz kernel of $(\Delta-\lambda^2)^{-1}$ takes place on a desingularized version of
the manifold $[0,1]\times M\times M$ where $[0,1]$ is the range of the spectral parameter $\lambda$. In geometric terms, this
corresponds to an iterated sequence of blow-up of corners of $[0,1]\times M\times M$; it was introduced in \cite{MS} and heavily
used in \cite{GH1}. For the convenience of the reader we recall quickly its definition but we refer to Section 2.2 in \cite{GH1} for
a detailed description of this manifold.
We denote by $[X;Y_1,\dots,Y_N]$ the iterated real blow-up of $X$ around
$N$ submanifolds $Y_i$ if $Y_1$ is a p-submanifold, the lift of $Y_2$ to $[X; Y_1]$ is a p-submanifold, and so on.
We shall denote by $\rho_H$ an arbitrary boundary defining function for a boundary hypersurface $H$ of $X$.
We now define the space $\MMksc$. Consider in $[0,1]\times M\times M$ the codimension 3 corner $C_3:=\{0\}\times\partial M\times\partial M$
and the codimension $2$ corners
\[C_{2,L}:=\{0\}\times\partial M\times M, \quad C_{2,R}:=\{0\}\times M\times\partial M,\quad C_{2,C}:=[0,1]\times\partial M\times\partial M.\]
We consider first the blow-up
\[M_{k,b}^2:=\big[[0,1]\times M\times M; C_3, C_{2,R},C_{2,L},C_{2,C}\big]\]
with blow-down map $\beta_b:M^2_{k,b}\to [0,1]\times M\times M$.
We have $7$ faces on $M^2_{k,b}$, the right, left, and zero faces
\[\mathrm{rb}=\mathrm{clos }\beta_b^{-1}([0,1]\times M\times\partial M),\quad
\mathrm{lb}:=\mathrm{clos }\beta_b^{-1}([0,1]\times\partial M\times M),\]
\[\mathrm{zf}:=\mathrm{clos }\beta_b^{-1}(\{0\}\times M\times M),\]
the `b-face' (so-called because of its use in the b-calculus) $\mathrm{bf}:=\mathrm{clos }\beta_b^{-1}(C_{2,C}\setminus C_3)$, and the three faces corresponding to $\mathrm{bf}, \mathrm{rb}, \mathrm{lb}$ at zero energy:
\[\mathrm{bf}_0:=\beta_b^{-1}(C_3), \quad
\mathrm{rb}_0:=\mathrm{clos }\beta_b^{-1}(C_{2,R}\setminus C_3), \quad
\mathrm{lb}_0:=\mathrm{clos }\beta_b^{-1}(C_{2,L}\setminus C_3).\]
\begin{figure}[ht!]
\begin{center}
\input{Mk2b2.pstex_t}
\caption{The manifold $M^2_{k,b}$. The arrows show the direction in which the indicated function increases from $0$ to $\infty$.}
\label{mmkb}
\end{center}
\end{figure}
The closed lifted diagonal $\Delta_{k,b}=\mathrm{clos }\beta_b^{-1}([0,1]\times \{(m,m);m\in M^\circ\})$
intersects the face $\mathrm{bf}$ in a p-submanifold denoted $\partial_{\mathrm{bf}}\Delta_{k,b}$. We then define
the final blow-up
\begin{equation}
M^2_{k,\mathrm{sc}}:=\big[M^2_{k,b}; \partial_{\mathrm{bf}}\Delta_{k,b}\big],
\label{scblowup}\end{equation}
and denote the new boundary hypersurface created by this blowup $\mathrm{sc}$, for `scattering face'.
\begin{figure}[ht!]
\begin{center}
\input{M2ksc.pstex_t}
\caption{The manifold $M^2_{k,\mathrm{sc}}$; the dashed line is the boundary of the lifted diagonal $\Delta_{k, \mathrm{sc}}$}
\label{fig:mmksc}
\end{center}
\end{figure}
\subsection{Polyhomogeneous conormal functions and index sets}\label{sect:phg}
Below we use spaces of polyhomogeneous conormal functions. These are
defined on any manifold with corners $X$. Let $\mathcal{F}$ denote its set of boundary hypersurfaces. An \emph{index family} $\mathcal{E}$ consists of a subset $\mathcal{E}_H$ of $\CC \times \NN$ (an \emph{index set}) for each $H$ in the set $\mathcal{F}$ of boundary hypersurfaces of $X$, satisfying two conditions: (a) for each $K \in \RR$, the number of points $(\beta, j) \in \mathcal{E}_H$ with $\Re \beta \leq K$ is finite and (b) if $(\beta, j) \in \mathcal{E}_H$ then $(\beta + 1, j)\in \mathcal{E}_H $ and if $j > 0$ then also $(\beta, j-1) \in \mathcal{E}_H$. Then the space of polyhomogeneous conormal functions with index family $\mathcal{E}$, denoted $\mathcal{A}_\mcE(X)$, is the space of functions $f$ that are smooth in the interior of $X$ and possess expansions in powers and logarithms of the form
$$
f = \sum_{{z,p} \in \mathcal{E}_H \text{ s.t. } \Re z \leq s} a_{(z,p)} \rho_H^z (\log \rho_H)^p +O(\rho_H^s)
$$
where $\rho_H$ is a boundary defining function for the boundary hypersurface $H$. See \cite{GH1} or \cite{cocdmc} for a precise definition. Condition (a) on the index set ensures that the sum on the left hand side is finite, and condition (b) ensures that the form of the sum is independent of the choice of local coordinates.
Let us recall from \cite{cocdmc} the operations of addition and extended union on two index sets $E_1$ and $E_2$, denoted $E_1 + E_2$ and $E_1 \extunion E_2$ respectively:
\begin{equation}\begin{gathered}
E_1 + E_2 = \{ (\beta_1 + \beta_2, j_1 + j_2) \mid (\beta_1, j_1) \in E_1 \text{ and } (\beta_2 , j_2) \in E_2 \} \\
E_1 \extunion E_2 = E_1 \cup E_2 \cup \{ (\beta, j) \mid \exists (\beta, j_1) \in E_1, (\beta, j_2) \in E_2 \text{ with } j = j_1 + j_2 + 1 \}.
\end{gathered}\end{equation}
We write $q$ for the index set
\begin{equation}
\{ (q + n, 0) \mid n = 0, 1, 2, \dots \}
\label{short}\end{equation} for any $q \in \RR$; note that in this notation, $0$ denotes the $\CI$ index set $\NN = \{ (0,0), (1,0), (2,0), \dots \}$.
For any index set $E$ and $q \in \RR$, we write $E \geq q$ if $\Re \beta \geq q$ for all $(\beta, j) \in E$ and if $(\beta, j) \in E$ and $\Re \beta = q$ implies $j = 0$. We write $E > q$ if there exists $\epsilon > 0$ so that $E \geq q + \epsilon$. We shall say that $E$ is integral if $(\beta, j) \in E$ implies that $\beta \in \mathbb{Z}$, and one-step if $E$ is such that $E = E' + (\alpha,0)$ for some $\alpha \in \CC$ and some integral index set $E'$. We write
$$\min E = \min \{ \beta \mid \exists \ (\beta, j) \in E \}.
$$
We say that $E'$ is a logarithmic extension of $E$ if $E \subset E'$ and if $(\beta, j) \in E'$ implies that $(\beta, 0) \in E$.
\subsection{Compressed cotangent bundle}\label{sect:compcotbundle}
We define a `compressed tangent bundle' and a `compressed cotangent bundle' on $\MMkb$. To define the compressed tangent bundle, denoted $\Tkb \MMkb$, it is helpful first to define the single space version. Thus we define the single space $\Mkb$ to be
$$
\Mkb = \big[ M \times [0, \lambda_0]; \partial M \times \{ 0 \} \big],
$$
that is, $M \times [0, \lambda_0]$ with the corner $\partial M \times \{ 0 \}$ blown up. (We always ignore the boundary at $\lambda = \lambda_0$.) We denote the boundary hypersurfaces of $\Mkb$ by $\mathrm{bf}$, the `b-face', the lift of $\partial M \times [0, \lambda_0]$; $\mathrm{zf}$, the `zero face', the lift of $M \times \{ 0 \}$, and $\mathrm{ff}$, the `front face', created by the blowup.
Recall that the space of scattering vector fields on $M$, denoted $\Vsc(M)$, are those of the form $x W$, where $x$ is a boundary defining function for $\partial M$ and $W$ is tangent to the boundary (i.e.\ is a b-vector field, $W \in \Vb(M)$). Let $\rho_{\mathrm{ff}}$ denote a boundary defining function for $\mathrm{ff} \subset \Mkb$.
We define the space (and Lie algebra) $\mathcal{V}_{k,b}(\Mkb)$ to be those smooth vector fields
generated by $\rho_{\mathrm{ff}}^{-1}$ times the lift of $\Vsc(M)$ to $\Mkb$, together with the vector field $\lambda \partial_\lambda + W$, where $W \in \Vb(M)$ is equal to $ x \partial_x$ near $\partial M$. Thus near $\mathrm{bf} \cap \mathrm{ff}$, using coordinates\footnote{We use $\rho$ to denote $x/\lambda$, and $r = \lambda/x$ throughout this paper.} $(\rho = x/\lambda, y, \lambda)$, such vector fields are smooth $\CI(\Mkb)$-linear combinations of
\begin{equation}
\rho^2 \partial_\rho,\quad \rho \partial_{y_i}, \quad \lambda \partial_\lambda \Big|_{\rho, y},
\end{equation}
while near $\mathrm{ff} \cap \mathrm{zf}$, using coordinates $(x, y, r = \lambda/x)$,
such vector fields are smooth $\CI(\Mkb)$-linear combinations of
\begin{equation}
x \partial_x \Big|_{r, y}, \quad \partial_{y_i}, \quad r \partial_{r}
\end{equation}
which in particular restrict to $\mathrm{zf}$ to give the b-vector fields on $M$.
This definition is independent of coordinates. These vector fields define a bundle $\Tkb \Mkb$, whose space of smooth sections is precisely $\mathcal{V}_{k,b}(\Mkb)$.
We observe some geometric properties of $\Mkb$ and $\Tkb \Mkb$:
\begin{itemize}
\item
To see why these vector fields are chosen, note that both $H$ and $\lambda^2$ vanish to second order at $\mathrm{ff}$, in terms of $\Tkb\Mkb$.
It is natural, then, to divide the operator by a factor of $\rho_{\mathrm{ff}}^2$;
we find that $\rho_{\mathrm{ff}}^{-2}(H - \lambda^2)$, which we can take to be $\lambda^{-2} H - 1$ near $\mathrm{bf}$ and $x^{-2} H - (\lambda/x)^2$ near $\mathrm{zf}$, is `built' out of an elliptic combination of sections of $\Tkb\Mkb$. Moreover, for Euclidean space, we have
$[\lambda\partial_\lambda + x\partial_x, \Delta - \lambda^2 ] = 2 (\Delta - \lambda^2)$, which shows that the resolvent and spectral measure are (in the Euclidean case) homogeneous with respect to this vector field.
\item A scattering metric \eqref{metricconic} on $M$ blows up at $\mathrm{ff}$ to second order. If we multiply by $\lambda^2$ and restrict to $\mathrm{ff}$, then it is easy to check that we get the \emph{exact} conic metric
\begin{equation}
\frac{d\rho^2}{\rho^4} + \frac{h(0)}{\rho^2}.
\label{exactconicmetric}\end{equation}
Thus a scattering metric on $M$ induces an exact conic structure on $\mathrm{ff}$.
\item At $\mathrm{zf}$, we have the Lie algebra of b-vector fields on $M$, but for a fixed positive $\lambda$, the vector fields tangent to $M \times \{ \lambda \}$ are the \emph{scattering} vector fields. Thus this Lie algebra interpolates between the b-calculus at $\lambda = 0$ and the scattering calculus for positive $\lambda$. This Lie Algebra was `microlocalized' to a calculus of operators in \cite{GH1}, with kernels defined on $\MMksc$. This calculus interpolates between the b-calculus at $\lambda = 0$ and the scattering calculus for fixed positive $\lambda$.
\end{itemize}
Now to define $\Tkb \MMkb$, we note that there are stretched projections $\pi_L, \pi_R : \MMkb \to \Mkb$; this can be proved
by noting that $\MMkb$ can be constructed from $\Mkb \times M$
by blowing up $\mathrm{ff} \times \partial M$, $\mathrm{ff} \times M$ and $\mathrm{bf} \times \partial M$ using Lemma 2.7 of \cite{asatet}. We define $\Tkb \MMkb$ to be that vector bundle generated over $\CI(\MMkb)$ by
\begin{equation}
\pi_L^*(\rho_{\mathrm{ff}}^{-1} \Vsc(M)), \quad \pi_R^*(\rho_{\mathrm{ff}}^{-1} \Vsc(M)) \text{ and }\lambda \partial_\lambda + x \partial_x + x' \partial_{x'}.
\label{VkbMMkb}\end{equation}
It is straightforward to check that the $\CI(\MMkb)$-span of these vector fields is closed under Lie bracket.
We denote this Lie Algebra by $\Vkb$.
We now define the compressed cotangent bundle $\Tkbstar \MMkb$. This is the dual bundle to $\Tkb \MMkb$. Near $\mathrm{bf}$ and $\mathrm{bf}_0$, but away from $\mathrm{zf}$, a basis of sections is given by singular one-forms of the form
\begin{equation}
\frac{d\rho}{\rho^2}, \quad \frac{d\rho'}{{\rho'}^2}, \quad \frac{ dy_i}{\rho}, \quad \frac{dy'_i}{\rho'}, \quad \frac{d\lambda}{\lambda}
\label{Tkbstar-basis}\end{equation}
where primed variables are coordinates on the right factor of $M$, and unprimed variables on the left factor of $M$ (lifted to $\MMkb$);
near $\mathrm{bf}_0$ and $\mathrm{zf}$, but away from $\mathrm{bf}$, a basis is given by
\begin{equation}
\frac{dx}{x}, \quad \frac{dx'}{{x'}}, \quad {dy_i}, \quad dy'_i, \quad \frac{d\lambda}{\lambda};
\end{equation}
and near $\mathrm{zf}$, and away from other boundary hypersurfaces,
\begin{equation}
dz_i , \quad dz'_i, \quad \frac{d\lambda}{\lambda},
\end{equation}
where $z = (z_1, \dots, z_n)$ are local coordinates on the interior of $M$.
Therefore, any point in $\Tkbstar \MMkb$ can be written
\begin{equation}
\nu \frac{d\rho}{\rho^2} +\nu' \frac{d\rho'}{{\rho'}^2}+ \mu_i \frac{dy_i}{\rho} + \mu'_i \frac{dy'_i}{\rho'} + T \frac{d\lambda}{\lambda}
\label{T}\end{equation}
in the first region,
$$
\tau \frac{dx}{x} + \tau' \frac{dx'}{{x'}} + \eta_i {dy_i} + \eta'_i dy'_i + T' \frac{d\lambda}{\lambda}
$$
in the second region, and
$$
\zeta_i dz_i + \zeta'_i z'_i + T'' \frac{d\lambda}{\lambda}
$$
in the third region. These expressions define local coordinates on $\Tkbstar \MMkb$ in each region.
\begin{remark} Here the coordinates $\mu, \nu, \mu', \nu'$ have a different meaning to that used in \cite{HV2}, due to the scaling in $\lambda$, since for example here $\mu_i$ is dual to $\lambda dy_i/x$ rather than $dy_i/x$. It is similar to how in the semiclassical calculus, the variable $\eta$ is dual to $dy/h = \lambda dy$ rather than $dy$, so the frequency corresponding to $\eta$ scales as $\lambda$. However, here we have the opposite situation in that $\lambda \to 0$, rather than infinity, so in a sense we are giving a meaning to the `semiclassical calculus with $h \to \infty$'!
\end{remark}
\subsection{Densities}\label{sect:densities}
We define the compressed density bundle $\Omegakb(\MMkb)$ to be that line bundle whose smooth nonzero sections are given by the wedge product of a basis of sections for $\Tkbstar(\MMkb)$. For example, near $\mathrm{bf} \cap \mathrm{bf}_0 \cap \Diagb$ this takes the form (using \eqref{Tkbstar-basis})
\begin{equation}
\Big| \frac{d\rho d\rho' dy dy' d\lambda}{\rho^{n+1} {\rho'}^{n+1} \lambda} \Big| \sim \lambda^{2n} \Big| \frac{dg dg' d\lambda}{\lambda} \Big|
\end{equation}
where $dg$, resp. $dg'$ denotes the Riemannian density with respect to $g$, lifted to $\MMkb$ by the left, resp. right projection;
near $\mathrm{zf}$, a smooth nonzero section takes the form
\begin{equation}
\Big| \frac{dx dx' dy dy' d\lambda}{x x' \lambda} \Big| \sim \Big| \frac{dg_b dg_b' d\lambda}{\lambda} \Big|
\end{equation}
where $dg_b$ is the Riemannian density with respect to the b-metric $$g_b = x^2 g$$ on $M$; near $\mathrm{lb} \cap \mathrm{lb}_0$, a smooth nonzero section takes the form
\begin{equation}
\Big| \frac{d\rho dy dx' dy' d\lambda}{\rho^{n+1} x' \lambda} \Big| \sim \lambda^n \Big| \frac{dg dg_b' d\lambda}{\lambda} \Big|,
\label{lblbo}\end{equation}
and so on.
\begin{remark} This differs from the density bundle used in \cite{GH1}. The density bundle defined here is more convenient; for example, it absorbs the $\rho_{\mathrm{sc}}^{n/2}$ factors put in `by hand' in Definition 2.7 of \cite{GH1}.
\end{remark}
\subsection{Fibrations and contact structures}\label{facs}
The Lie algebra $\Vkb$ gives rise to a fibration at each boundary hypersurface $\bullet$ of $\MMkb$, in the following way: the leaves of this fibration at $\bullet$ are precisely the maximal submanifolds on which the restriction of $\Vkb$ to $\bullet$ is transitive.
These fibrations are trivial (and therefore unimportant) on $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{rb}_0$ and $\mathrm{zf}$, i.e.\ the Lie algebra is transitive on these faces. We now describe the fibration at the remaining boundary hypersurfaces, namely $\mathrm{bf}$, $\mathrm{lb}$ and $\mathrm{rb}$.
At $\mathrm{bf}$, the Lie Algebra restricted to this face is given by multiples of $\lambda \partial_\lambda$, and therefore, the fibration is given by projection off the $\lambda$ factor. That is, in local coordinates $(y, y', \sigma, \lambda)$ on this face, where\footnote{We use the notation $\sigma = x/x' = \rho/\rho'$ throughout the paper} $\sigma = x/x'$, the fibration takes the form
$$
(y, y', \sigma, \lambda) \mapsto (y, y', \sigma).
$$
Thus $Z_{\mathrm{bf}}$ is the base of this fibration, i.e.\ $Z_{\mathrm{bf}}$ is the lift of the corner $(\partial M)^2$ to $M^2_b = [M^2; (\partial M)^2]$ (which can be identified with $\mathrm{bf} \cap \mathrm{bf}_0$ in Figure~\ref{mmkb}).
At $\mathrm{lb}$, the Lie algebra restricts to the span of vector fields $\lambda\partial_\lambda,\partial_{z'}$. Hence the fibration takes the form
$$
(y, z', \lambda) \mapsto y.
$$
Similarly at $\mathrm{rb}$ the fibration takes the form
$$
(z, y', \lambda) \mapsto y'.
$$
We let $Z_{\mathrm{lb}} = Z_{\mathrm{rb}} = \partial M$ denote the base of these fibrations.
In the interior of $\MMkb$, the compressed cotangent bundle is canonically isomorphic to the usual cotangent bundle, and hence the canonical symplectic form on $T^*(\MMkb)$ induces a canonical symplectic form $\omega$ on $\Tkbstar \MMkb$. In turn, $\omega$ induces a contact structure at each boundary hypersurface $\bullet$, where $\bullet = \mathrm{bf}, \mathrm{lb}$, or $\mathrm{rb}$. In fact, the contact structure lives on a bundle over $Z_{\bullet}$, denoted $\Nsfstar Z_\bullet$ defined in \cite{HV1}, which we recall here. Here and below we use $\bullet$ to denote one of $\mathrm{bf}, \mathrm{lb}$ or $\mathrm{rb}$.
There is a subbundle of $\Tkb_\bullet \MMkb$ whose fibre at $p \in \bullet$ consists of the span of those vector fields that vanish (as an element of $T_p \MMkb$) at $p$. (This is not the trivial subbundle, since a vector field can vanish as an element of $T_p \MMkb$ while being nonzero as an element of $\Tkb_p \MMkb$; for example, $x^2 \partial_x$ is nonzero as an element of $\Tkb \MMkb$ at $\mathrm{lb}$.)
Dually, we define the annihilator subbundle
$\Tkbstar(F; \bullet)\MMkb$, a subbundle of $\Tkbstar_\bullet \MMkb$. Here the $F$ stands for `fibre'. The quotient
bundle, $\Tkbstar_\bullet \MMkb / \Tkbstar(F; \bullet)\MMkb$, turns out to be the lift of a bundle $\Nsfstar Z_\bullet$ over $Z_\bullet$ to $\bullet$ \cite{HW}. For example, at $\bullet = \mathrm{bf}$, the vector fields vanishing as an element of $T_p \MMkb$, $p \in \mathrm{bf}$, are spanned by all but the last vector field in \eqref{VkbMMkb}, the annihilator subbundle is spanned by $d\lambda/\lambda$, and the quotient bundle is spanned by the remaining elements of \eqref{Tkbstar-basis}. Thus, local coordinates on $\Nscstar Z_\mathrm{bf}$ are $(y, y', \sigma; \nu, \mu, \nu', \mu')$. Similarly, for $\bullet = \mathrm{lb}$, the annihilator subbundle is spanned by $\lambda dz'_i$ and $d\lambda/\lambda$, and the fibres of $\Nscstar Z_{\mathrm{lb}}$ are spanned by
$$
\frac{d\rho}{\rho^2} \, , \ \frac{dy_j}{\rho} \, , \ 1 \leq j \leq n-1,
$$
showing that $(y, \nu, \mu)$ furnish local coordinates on $\Nscstar Z_{\mathrm{lb}}$.
Note that $Z_\mathrm{bf}$ is a manifold with boundary; we denote its two boundary hypersurfaces by $\partial_{\mathrm{lb}} Z_\mathrm{bf}$ and $\partial_{\mathrm{rb}} Z_\mathrm{bf}$. Similarly,
$\Nsfstar Z_\mathrm{bf}$ is a manifold with boundary, with boundary hypersurfaces $\partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$ and $\partial_{\mathrm{rb}} \Nsfstar Z_\mathrm{bf}$. There is a fibration $\phi_{\mathrm{bf}, \mathrm{lb}}$ from $\partial_{\mathrm{lb}} Z_\mathrm{bf}$ to $Z_{\mathrm{lb}}$ given in local coordinates by $(y, y') \mapsto y$. Similarly there is an induced fibration $\phit_{\mathrm{bf}, \mathrm{lb}}$ from $\partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$ to $\Nsfstar Z_{\mathrm{lb}}$ given in local coordinates by $(y, y', \nu, \mu, \nu', \mu') \mapsto (y, \nu, \mu)$. There are of course analogous fibrations at the right boundary $\mathrm{rb}$.
Next we show how $\omega$ induces a contact structure on $\Nsfstar Z_\bullet$. Contracting $\omega$ with $\rho_{\bullet}^2 \partial_{\rho_{\bullet}}$, where $\rho_{\bullet}$ denotes a boundary defining function for $\bullet$, and restricting to $\bullet$ gives a one-form on $\Tkbstar_{\bullet} \MMkb$ that is well-defined up to scalar multiples. It can be checked that it induces a form on $\Nsfstar Z_{\bullet}$ that is nondegenerate in the sense of contact geometry (at least in the interior of $\Nsfstar Z_{\bullet}$), and therefore determines a well-defined contact structure on $\Nsfstar Z_{\bullet}$.
In the case $\bullet = \mathrm{bf}$, we compute that $\omega$ is given by
\begin{equation}\begin{gathered}
\omega = d \Big( \nu \frac{d\rho}{\rho^2} +\nu' \frac{d\rho'}{{\rho'}^2}+ \mu_i \frac{dy_i}{\rho} + \mu'_i \frac{dy'_i}{\rho'} + T \frac{d\lambda}{\lambda} \Big) \\
= d\nu \wedge \frac{d\rho}{\rho^2} +d\nu' \wedge\frac{d\rho'}{{\rho'}^2}
+ d\mu_i \wedge\frac{\lambda dy_i}{\rho} - \mu_i dy_i \wedge\frac{d\rho}{\rho^2} \\ + \
d \mu'_i \wedge\frac{\lambda dy'_i}{\rho'} - \mu'_i dy'_i \wedge\frac{d\rho'}{{\rho'}^2}
+ dT \wedge\frac{d\lambda}{\lambda}.
\end{gathered}\end{equation}
We can use $\rho \partial_\rho + \rho' \partial_{\rho'}$ (where these are lifted from the left and right factors respectively) as a b-normal vector field at $\mathrm{bf}$, and then using $\rho$ as a boundary defining function we obtain
$$
\iota_{\rho(\rho \partial_\rho + \rho' \partial_{\rho'})} \omega =
\mu_i dy_i -d\nu + \sigma (\mu_i' dy_i' - d\nu')
$$
as the contact 1-form on $\Nsfstar Z_{\mathrm{bf}}$. This is precisely the same
contact form that one gets from the manifold $\MMkb$ at a fixed energy level, as was done in \cite{HV2}.
This contact 1-form degenerates at $\partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$: the contact form becomes degenerate in the fibre directions of $\phit_{\mathrm{bf}, \bullet}$ but remains nondegerate in the `base' directions. In fact, over $\partial_{\mathrm{lb}} \Nsfstar Z_{\mathrm{bf}}$, the contact 1-form is the lift of the contact 1-form on $\Nsfstar Z_{\mathrm{lb}}$ (given in local coordinates by $\mu_i dy_i - d\nu$) with respect to this fibration. Moreover, the fibres of $\phit_{\mathrm{bf}, \mathrm{lb}}$ have a natural contact structure given in local coordinates by $\mu'_i dy'_i - d\nu'$. Of course, similar statements are true at the intersection with $\mathrm{rb}$.
This is all explained in more detail in \cite{HV1} and \cite{HW}.
\section{Legendre distributions on the space $\MMkb$}\label{Leg}
\subsection{Legendre submanifolds}\label{sec:legsub}
We recall from \cite{HV1} definitions concerning Legendre submanifolds of $\Nsfstar Z_{\mathrm{bf}}$. Let $n = \dim M$, so that $\dim \Nsfstar Z_{\mathrm{bf}} = 4n-1$. We define a Legendre submanifold $\Lambda$ of $\Nsfstar Z_{\mathrm{bf}}$ to be a smooth submanifold of dimension $2n-1$ such that
\begin{itemize}
\item the contact form vanishes on $\Lambda$.
\item $\Lambda$ is transversal to $\partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$ and $\partial_{\mathrm{rb}} \Nsfstar Z_\mathrm{bf}$, and therefore is a smooth manifold with boundary. The boundary hypersurfaces $\Lambda \cap \partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$ and $\Lambda \cap \partial_{\mathrm{rb}} \Nsfstar Z_\mathrm{bf}$ will be denoted $\partial_{\mathrm{lb}} \Lambda$, respectively $\partial_{\mathrm{rb}} \Lambda$.
\end{itemize}
\begin{remark} As shown in \cite[Section 4]{HW}, this definition is equivalent to the more elaborate definition given in \cite{HV1}, \cite{HV2}.
\end{remark}
We also recall two definitions concerning two Legendre submanifolds that intersect. The first applies away from $\mathrm{lb}$ and $\mathrm{rb}$.
Suppose that
$\Lambda_0$ and $\Lambda$ are two smooth Legendre submanifolds that intersect cleanly in a submanifold of dimension $2n-2$ (disjoint from $\partial_{\mathrm{lb}} \Nsfstar Z_\mathrm{bf}$ and $\partial_{\mathrm{rb}} \Nsfstar Z_\mathrm{bf}$). In that case, each submanifold divides the other into two parts. Let $\Lambda_+$ and $\Lambda_-$ denote the two pieces of $\Lambda_1$. Then both $(\Lambda_0, \Lambda_+)$ and $(\Lambda_0, \Lambda_-)$ are said to form an intersecting pair of Legendre submanifolds.
The second definition concerns two Legendre submanifolds $\Lambda^\sharp$ and $\Lambda$ where $\Lambda^\sharp$ is smooth, and $\Lambda$ is smooth except at $\Lambda^\sharp$ where it has a conic singularity. We say that $(\Lambda, \Lambda^\sharp)$ form an intersecting pair of Legendre submanifolds with conic points if
\begin{itemize}
\item $\Lambda^\sharp$ projects diffeomorphically to the base $\mathrm{bf}$ and does not meet the zero section of $\Nsfstar Z_\mathrm{bf}$ (so that $\spn \Lambda^\sharp = \{ tq \mid q \in \Lambda^\sharp, t \in \RR \}$ is a submanifold of dimension $2n$);
\item the lift $\hat \Lambda$ of $\Lambda$ to the blown-up manifold
\begin{equation}
\big[ \Nsfstar Z_{\mathrm{bf}}; \ \spn \Lambda^\sharp \big]
\label{lambdah}\end{equation}
is a smooth submanifold that meets the boundary hypersurfaces of \eqref{lambdah} (in particular, the lift of $\spn \Lambda^\sharp$) transversally.
\end{itemize}
All this is explained in more detail in \cite{HV1} and \cite{HW}.
In subsequent sections of this paper there are three Legendre submanifolds of particular interest: the boundary (at $\mathrm{bf}$) of the conormal bundle to the diagonal $\Diagb$, which following \cite{HV1}, \cite{HV2} we denote $\Nscstar \Diagb$; the `propagating Legendrian' $L^{\mathrm{bf}}$; and the incoming/outgoing Legendrian $L^\sharp_\pm$. We now define and describe these three submanifolds.
The conormal to the diagonal $\Nscstar \Diagb$ is easy to describe: it is the Legendre submanifold of $\Nsfstar Z_{\mathrm{bf}}$ given in local coordinates $(\sigma, y, y', \nu, \nu', \mu, \mu')$ by $\sigma = 1, y=y', \nu = -\nu', \mu = -\mu'$. Analytically, it is related to pseudodifferential operators on $\MMkb$ of (differential) order $-\infty$: kernels on $\MMksc$ that are smooth and rapidly vanishing at $\mathrm{bf}$ are conormal to $\Nsfstar \Diagb$ when viewed on $\MMkb$.
The incoming/outgoing Legendrian $L^\sharp_\pm$ is also easy to describe in local coordinates: it is given by $\nu = \nu' = \pm 1, \mu = \mu' = 0$. It is clear that this projects diffeomorphically to the base $Z_{\mathrm{bf}}$. Analytically this corresponds to pure incoming/outgoing oscillations $a(y,y',\sigma) e^{\pm i\lambda/x} e^{\pm i\lambda/x'} = a(y,y',\sigma) e^{\pm i/\rho} e^{\pm i/\rho'}$. We write $L^\sharp = L^\sharp_+ \cup L^\sharp_-$.
The propagating Legendrian $L^{\mathrm{bf}}$ is more interesting and geometrically intricate. It is related to the limit at $\partial M$ of geodesic flow on $M$ or, what is the same thing, the Hamilton flow of the symbol of $P - \lambda^2$ at $\mathrm{bf}$. Since this occurs purely at $x=x' = 0$ (where the potential vanishes) and the metric $g$ is asymptotically conic, it is related to geodesic flow on an exact conic metric.
One way to describe $L^{\mathrm{bf}}$ is to start with the intersection of $\Nscstar \Diagb$ and the characteristic variety of $P - \lambda^2$, which is the submanifold $\{ \sigma = 1, y=y', \nu = -\nu', \mu = -\mu'; \nu^2 + |\mu|^2_h = 1 \}$, and take the flowout by the (rescaled) Hamilton vector field associated to the operator $P - \lambda^2$ acting on either the left or the right variables. The Hamilton vector field for this operator vanishes to first order at $\Tkbstar_{\mathrm{bf}} \MMkb$; after dividing by $\rho$, we obtain a nonzero vector field on $\Tkbstar_{\mathrm{bf}} \MMkb$ that descends to a contact vector field on $\Nsfstar Z_{\mathrm{bf}}$. In local coordinates, the symbol of $P - \lambda^2$ acting on the left is
\begin{equation}
\sigma_l(P - \lambda^2) = \nu^2 + h - \lambda^2, \quad h = \sum_{i,j} h^{ij}(y) \mu_i \mu_j,
\label{sigmal}\end{equation}
and the left Hamilton vector field takes the form (after dividing by $\rho$)
\begin{equation}
V_l = -\nu (\sigma \dbyd{}{\sigma} + \mu \dbyd{}{\mu}) + h \dbyd{}{\nu} + \dbyd{h}{\mu_i}\dbyd{}{y_i} - \dbyd{h}{y_i}\dbyd{}{\mu_i},
\label{Vl}\end{equation}
while the symbol of $P - \lambda^2$ acting on the right is
\begin{equation}
\sigma_r(P - \lambda^2) = {\nu'}^2 + h' - \lambda^2, \quad h' = \sum_{i,j} h^{ij}(y') \mu'_i \mu'_j,
\label{sigmar}\end{equation}
and
the right Hamilton vector field takes the form (after dividing by ${\rho'}$)
\begin{equation}
V_r = \nu' (\sigma \dbyd{}{\sigma} - \mu \dbyd{}{\mu}) + h' \dbyd{}{\nu'} + \dbyd{h'}{\mu'_i}\dbyd{}{y'_i} - \dbyd{h'}{y'_i}\dbyd{}{\mu'_i}.
\label{Vr}\end{equation}
Let $L^{\mathrm{bf}}_\pm$ denote the flowout in the positive, resp. negative directions by the vector field $V_l$ from $\Nscstar \Diagb \cap \{ \sigma_l(P - \lambda^2)= 0 \}$.
In \cite{HV1} it was proved
\begin{prop}
(i) Locally near $\Nscstar \Diagb$, the pairs $(\Nscstar \Diagb, L^{\mathrm{bf}}_\pm)$ form an intersecting pair of Legendre submanifolds.
(ii) Locally near $L^\sharp_\pm$, the pair $(L^\mathrm{bf}_\pm, L^\sharp_\pm)$ forms a pair of intersecting Legendre submanifolds with conic points.
\end{prop}
A second way to describe $L^{\mathrm{bf}}$ is directly in terms of geodesic flow on the metric cone with cross section $(\partial M, h)$. Let $g_{\conic}$ be the conic metric
$$
g_{\conic} = dr^2 + r^2 h.
$$
Write $Y = \partial M$.
Then geodesic flow on $(C(Y), g_{\conic})$, the cone over $(Y, h)$, can be written explicitly in terms of geodesic flow on $(Y, h)$ as follows:
Let $(y(s), \eta(s))$, where $s \in [0, \pi]$ is an arc-length parameter (so that $|\eta(s)|_{h(y(s))} = 1$), be a geodesic in $T^* Y$. Then every geodesic $\gamma$ for the exact conic metric $dr^2 + r^2 h$, not hitting the cone tip, is of the form $y = y(s), \mu = \eta(s) \sin s, r = r_0 \csc s, \nu = -\cos s$, $s \in (0, \pi)$, where $r_0 > 0$ is the minimum distance to the cone tip and $-\cot s/r_0 \in (-\infty, \infty)$ is arc length on $C(Y)$.
We define $\gamma^2$ to be the submanifold
\begin{multline}
\gamma^2 = \big\{ (y, y', \sigma = x/x', \mu, \mu', \nu, \nu') \mid y = y(s), y' = y(s'), \mu = \eta(s) \sin s, \\ \mu' = -\eta(s') \sin s', \nu = -\cos s, \nu' = \cos s', \sigma = \sin s'/\sin s, (s, s') \in [0, \pi]^2. \big\}
\label{gamma^2}\end{multline}
Then $\Lbf$ is the union of the $\gamma^2$ over all geodesics of length $\pi$ in $T^*(\partial M)$. The vector fields $V_l$ and $V_r$ are tangent to each leaf $\gamma^2$, and are given in terms of the coordinates $s$ and $s'$ by $V_l = \sin s \partial_s$ and $V_r = \sin s' \partial_{s'}$. Also, the intersection of this leaf with $\Nscstar \Diagb$ is $\{ s = s'\}$, and the conic singularity is at the two off-diagonal corners $s = 0, s' = \pi$ and $s=\pi, s' = 0$, which corresponds to the two different ends of the geodesic. The blowup of the span of $L^\sharp$ that desingularizes these conic singularities corresponds on the leaf $\gamma^2$ to blowing up these two corners.
\subsection{Legendre distributions on $\MMkb$}\label{sect:legdist}
Let $\Lambda \subset \Tscstar_{\mathrm{bf}} \MMb$ be a Legendre submanifold. We define a space of (half-density) functions on $\MMkb$ associated to $\Lambda$. As usual $n$ denotes the dimension of $M$.
Let $\mcA = (\mcA_{\mathrm{bf}_0}, \mcA_{\mathrm{lb}},\mcA_{\mathrm{rb}},\mcA_{\mathrm{zf}})$ be an index family consisting of an index set for each of the hypersurfaces $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{rb}_0, \mathrm{zf}$ of $\MMkb$. Also let $m, r_{\mathrm{lb}}, r_{\mathrm{rb}}$ be real numbers. We shall shortly define the set of Legendre (half-density) distributions $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$. First we give the intuitive idea: for $\lambda > 0$ it is a family of Legendre distributions on $\MMb$, depending conormally on $\lambda$ as $\lambda \to 0$ with respect to the given family. Away from $\mathrm{bf} \cup \mathrm{lb} \cup \mathrm{rb}$ it is polyhomogeneous conormal with respect to the given index family.
We remark that the parametrizations of $\Lambda$ given in the definition below are defined in \cite{HV1} and \cite{HV2}.
\begin{defn}\label{defn:legdist} The space $ I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$ consists of half-densities $u$ on $\MMkb$ that can be written as a finite sum of terms $u = \sum_{j=0}^6 u_j$, where
\begin{itemize}
\item $u_0$ is supported in $\{ \lambda \geq \epsilon \}$ for some $\epsilon > 0$, and $u \otimes |d\lambda/\lambda|^{-1/2}$ is a family of
Legendre distributions in $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}}(\MMb, \lambda \Lambda; \Omegasch)$ with symbol depending smoothly on $\lambda$;
\item $u_1$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf}$ and away from $\mathrm{lb} \cup \mathrm{rb}$, and is given by a finite sum of expressions
\begin{equation}
\rho^{m-k/2+n/2} \lambda^n \int_{\RR^k} e^{i\Psi(y, y', \sigma, v)/\rho} a(\lambda, \rho, y, y', \sigma,v) \, dv \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2}
\label{u1}\end{equation}
where $\sigma = x/x'$, $\Psi$ locally parametrizes $\Lambda$ in the sense of \cite{HV1}, \cite{HV2} and $a$ is polyhomogeneous conormal in $\lambda$, with respect to the index set $\mcA_{\mathrm{bf}_0}$, at $\lambda = 0$ and is smooth in all other variables;
\item $u_2$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf} \cap \mathrm{lb}$, and is given by a finite sum of expressions
\begin{multline}
{\rho'}^{m-(k+k')/2+n/2} \sigma^{r_{\mathrm{lb}} - k/2} \lambda^n \\ \times \int_{\RR^{k+k'}} e^{i\big( \Psi_0(y,v) + \sigma \Psi_1(y, y', \sigma, v, v') \big)/\rho} a(\lambda, \rho', y, y', \sigma, v, v') \, dv \, dv' \, \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2};
\label{u2}\end{multline}
where $\Psi_0 + \sigma \Psi_1$ locally parametrizes $\Lambda$ and $a$ is polyhomogeneous conormal in $\lambda$, with respect to the index set $\mcA_{\mathrm{bf}_0}$, at $\lambda = 0$ and is smooth in all other variables;
\item $u_3$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf} \cap \mathrm{rb}$, and is given by a similar expression to $u_2$ with $(x,y)$ and $(x',y')$ interchanged, and $r_{\mathrm{lb}}$ replaced by $r_{\mathrm{rb}}$;
\item $u_4$ is supported close to $\mathrm{lb} \cap \mathrm{bf}_0$ and away from $\mathrm{bf}$, and is given by a finite sum of expressions of the form
\begin{equation}
\rho^{r_{\mathrm{lb}} - k/2} \lambda^n \int_{\RR^k}
e^{i\Psi_0(y,v) /\rho} a(\rho, x', 1/\rho', y, y', v) \, dv \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2}
\label{u4}\end{equation}
where $\Psi_0$ locally parametrizes $\Lambda_{\mathrm{lb}}$ and $a$ is polyhomogeneous conormal in $(x', 1/\rho')$, with respect to the index sets $(\mcA_{\mathrm{bf}_0}, \mcA_{\mathrm{lb}_0})$ and is smooth in all other variables;
\item $u_5$ is supported close to $\mathrm{rb} \cap \mathrm{bf}_0$ and away from $\mathrm{bf}$, and is given by a similar expression to $u_4$ with $(x,y)$ and $(x',y')$ interchanged, $r_{\mathrm{lb}}$ replaced by $r_{\mathrm{rb}}$, and $\mcA_{\mathrm{lb}_0}$ replaced by $\mcA_{\mathrm{rb}_0}$;
\item $u_6$ is supported away from $\mathrm{bf} \cup \mathrm{lb} \cup \mathrm{rb}$ and is of the form $a \tau$ where $\tau$ is a smooth nonvanishing section of $\Omegakb^{1/2}$ and $a$ is polyhomogeneous with index family $\mcA$ at $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{rb}_0, \mathrm{zf}$.
\end{itemize}
\end{defn}
\begin{remark} Recall that, away near $\mathrm{bf}$, a smooth nonvanishing section of $\Omegakbh$ is given by $\lambda^n |dg dg' d\lambda/\lambda|^{1/2}$; this accounts for the factors of $\lambda^n$ in \eqref{u1}, \eqref{u2} and \eqref{u4}.
\end{remark}
\begin{remark} We have chosen here a different order convention from that used in \cite{HW}. Our convention here has the advantage that if $u \in I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$ then for $\lambda > 0$, $u$ is a smooth family of
Legendre distributions in $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}}(\MMb, \lambda \Lambda; \Omegasch)$ (tensored with $d\lambda/\lambda|^{1/2}$); i.e., the orders do not change. Our orders $m, r_{\mathrm{lb}}, r_{\mathrm{rb}}$ here corresponds to orders $m+1/4, r_{\mathrm{lb}}+1/4, r_{\mathrm{rb}}+1/4$ in \cite{HW}.
\end{remark}
In an analogous way, we can define intersecting Legendrian distributions and distributions associated to intersecting pairs of Legendre submanifolds with conic points on $\MMkb$, based on the definitions given in \cite{HV2} for such distributions on $\MMb$.
\begin{defn}\label{defn:intlegdist} Let $(\Lambda_0, \Lambda_+)$ be an intersecting pair of Legendre submanifolds in $\Nsfstar Z_{\mathrm{bf}}$, which do not meet the left and right boundaries of $\Nsfstar Z_{\mathrm{bf}}$.
The space $ I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, (\Lambda_0, \Lambda_+); \Omegakbh)$ consists of half-density functions $u$ on $\MMkb$ that can be written as a finite sum of terms $u = \sum_{j=0}^3 u_j$, where
\begin{itemize}
\item $u_0$ is supported in $\{ \lambda \geq \epsilon \}$ for some $\epsilon > 0$, and $u \otimes |d\lambda/\lambda|^{-1/2}$ is a family of
Legendre distributions in $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}}(\MMb, (\lambda\Lambda_0, \lambda\Lambda_+); \Omegasch)$ with symbol depending smoothly on $\lambda$;
\item $u_1$ is an element of $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda_0; \Omegakbh)$, microsupported away from $\Lambda_+$;
\item $u_2$ is an element of $I^{m-1/2, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda_+; \Omegakbh)$, microsupported away from $\Lambda_0$;
\item $u_3$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf}$ and away from $\mathrm{lb} \cup \mathrm{rb}$, and is given by a finite sum of expressions
\begin{equation}
\rho^{m-(k+1)/2+n/2} \lambda^n \int_0^\infty ds \int_{\RR^k} e^{i\Psi(y, y', \sigma, v,s)/\rho} a(\lambda, \rho, y, y', \sigma,v,s) \, dv \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2}
\label{u3int}\end{equation}
where $\Psi$ locally parametrizes $(\Lambda_0, \Lambda_+)$ in the sense of \cite{HV1}, \cite{HV2} and $a$ is polyhomogeneous conormal in $\lambda$, with respect to the index set $\mcA_{\mathrm{bf}_0}$, at $\lambda = 0$ and is smooth in all other variables.
\end{itemize}
\end{defn}
\begin{defn}\label{defn:coniclegdist} Let $(\Lambda, \Lambda^\sharp)$ be an pair of intersecting Legendre submanifolds with conic points in $\Nsfstar Z_{\mathrm{bf}}$.
The space $ I^{m, p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, (\Lambda, \Lambda^\sharp); \Omegakbh)$ consists of half-density functions $u$ on $\MMkb$ that can be written as a finite sum of terms $u = \sum_{j=0}^5 u_j$, where
\begin{itemize}
\item $u_0$ is supported in $\{ \lambda \geq \epsilon \}$ for some $\epsilon > 0$, and $u \otimes |d\lambda/\lambda|^{-1/2}$ is a family of
Legendre distributions in $I^{m, p; r_{\mathrm{lb}}, r_{\mathrm{rb}}}(\MMb, ( \lambda\Lambda, \lambda\Lambda^\sharp); \Omegasch)$ with symbol depending smoothly on $\lambda$;
\item $u_1$ is an element of $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$, microsupported away from $\Lambda^\sharp$;
\item $u_2$ is an element of $I^{p, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda^\sharp; \Omegakbh)$, microsupported away from $\Lambda$;
\item $u_3$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf}$, and away from $\mathrm{lb} \cup \mathrm{rb}$, and is given by a finite sum of expressions
\begin{multline}
\lambda^n \int_0^\infty ds \int_{\RR^k} e^{i\Psi(y, y', \sigma, v,s)/\rho} \big( \frac{\rho}{s} \big)^{m-(k+1)/2+n/2} s^{p+n/2-1} \\
\times
a(\lambda, \frac{\rho}{s}, y, y', \sigma,v,s) \, dv \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2}
\label{u3con}\end{multline}
where $\Psi$ locally parametrizes $(\Lambda, \Lambda^\sharp)$ in the sense of \cite{HV1}, \cite{HV2} and $a$ is polyhomogeneous conormal in $\lambda$, with respect to the index set $\mcA_{\mathrm{bf}_0}$, at $\lambda = 0$ and is smooth in all other variables;
\item $u_4$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf} \cap \mathrm{lb}$ and is given by a finite sum of expressions
\begin{multline}
\lambda^n \int_0^\infty ds \int_{\RR^k} e^{i\Psi(y, y', \sigma, v,s)/\rho} \big( \frac{\rho'}{s} \big)^{m-(k+1)/2+n/2} s^{p+n/2-1} \sigma^{r_{\mathrm{rb}}} \\ \times
a(\lambda, \frac{\rho'}{s}, y, y', \sigma,v,s) \, dv \Big| \frac{dg dg' d\lambda}{\lambda}\Big|^{1/2}
\label{u4con}\end{multline}
where $\Psi$ locally parametrizes $(\Lambda, \Lambda^\sharp)$ in the sense of \cite{HV1}, \cite{HV2} and $a$ is polyhomogeneous conormal in $\lambda$, with respect to the index set $\mcA_{\mathrm{bf}_0}$, at $\lambda = 0$ and is smooth in all other variables;
\item $u_5$ is supported close to $\mathrm{bf}_0 \cap \mathrm{bf} \cap \mathrm{rb}$ and is given by a finite sum of expressions analogous to \eqref{u4con}, with $(x,y)$ and $(x',y')$ interchanged, and $r_{\mathrm{lb}}$ replaced by $r_{\mathrm{rb}}$.
\end{itemize}
\end{defn}
\begin{remark} There are typos in the expression \cite[equation (2.23)]{HV2} corresponding to \eqref{u4con}. These have been fixed here. For purposes of comparison, notice that in \cite[equation (2.23)]{HV2}, in the exponent of $x_1$, $N/4 - f_i/2$ vanishes (in the present situation).
\end{remark}
\subsection{The boundary hypersurface $\mathrm{bf}_0$}\label{sec:bfo} The boundary hypersurface $\mathrm{bf}_0$ of $\MMksc$ or $\MMkb$ plays a crucial role in our analysis. This is because it corresponds to the transitional asymptotics between zero energy and positive energy behaviour. Section~\ref{exactcone} is devoted to the analysis of the
model operator induced by $P$ on $\mathrm{bf}_0$, namely the conic Schr\"odinger operator \eqref{conicSchr}. Here we note the geometric structures on $\mathrm{bf}_0 \subset \MMkb$ induced from $\MMkb$. (Unless specifically indicated, we work on $\MMkb$ rather than $\MMksc$ below.)
We first observe that $\mathrm{bf}_0$ is a blown-up version of $\mathrm{ff} \times \mathrm{ff}$, where $\mathrm{ff}$ is the front (blown-up) face of $\Mkb$. The front face $\mathrm{ff}$ is given by $\partial M \times [0, \infty]_r$ where $r = 1/\rho = \lambda/x$. Indeed, the interior of $\mathrm{bf}_0$ admits smooth coordinates $(r, y, r', y')$, where $y, y' \in \partial M$, $r, r' \in (0, \infty)$, and we can easily check that $\mathrm{bf}_0$ is obtained from $\mathrm{ff} \times \mathrm{ff}$ by performing $b$-blowups at the diagonal corners $\{ r = r' = 0 \}$ and $\{ \rho = \rho' = 0 \}$.
Moreover, if we work on $\MMksc$, then the scattering blowup \eqref{scblowup} has the effect of performing the scattering blowup on $\mathrm{bf}_0$, i.e.\ blowing up $\{ \rho = \rho' = 0, y = y' \}$. (Recall that we have already observed in \eqref{exactconicmetric} that the metric $g$ induces an exact conic metric on the front face of $\Mkb$, hence a scattering metric at $\rho = 0$ and conformal to a b-metric at $r=0$.)
Next consider the vector fields $\mathcal{V}_{k,b}(\MMkb)$ restricted to $\mathrm{bf}_0$. First, on the single space, the vector fields $\mathcal{V}_{k,b}(\Mkb)$ restrict to $\mathrm{ff}$ to be scattering vector fields near $\rho = 0$, and b-vector fields near $r=0$. These vector fields on $\mathrm{ff}$ can be lifted to $\mathrm{bf}_0$ via either the left or right stretched projections $\mathrm{bf}_0 \to \mathrm{ff}$, and generate a space of vector fields on $\mathrm{bf}_0$ that coincide with the restriction of $\mathcal{V}_{k,b}(\MMkb)$ to $\mathrm{bf}_0$. In turn, this space of vector fields in $\mathrm{bf}_0$ defines a vector bundle over $\mathrm{bf}_0$ for which such vector fields are the smooth sections.
Its dual bundle ${}^{b,k} T^* \mathrm{bf}_0$ can be identified with the subbundle
of ${}^{k,b}T^*_{\mathrm{bf}_0}\MMkb$ annihilated by the vector field $\lambda \partial_\lambda + x \partial_x + x' \partial_{x'}$. In terms of coordinates \eqref{T}, this bundle is given by $\{ \lambda = 0, T = 0 \}$. As this is a symplectic reduction of the bundle ${}^{k,b} T^* \MMkb$, there is a symplectic form induced on ${}^{b,k} T^* \mathrm{bf}_0$ by the form $\omega$, which, as in Section~\ref{facs}, induces a contact structure on ${}^{b,k} T^*_{\mathrm{bf} \cap \mathrm{bf}_0} \mathrm{bf}_0$, i.e.\ when we restrict to the boundary hypersurface $\mathrm{bf}_0 \cap \mathrm{bf}$.
This restricted bundle is isomorphic (as a bundle and as a contact manifold) to $\Nsfstar Z_{\mathrm{bf}}$. Therefore, we can define Legendre submanifolds, Legendre distributions, etc, for $\mathrm{bf}_0$. However, this is nothing new --- this precisely reproduces the structure described in \cite{HV1} and \cite{HV2} for a manifold with boundary; we could alternatively derive it by treating $\mathrm{ff}$ as a scattering manifold by ignoring the `b'-boundary at $r = 0$, and working locally near the scattering boundary $\rho = 0$, or equivalently working locally near $\mathrm{bf}_0 \cap \mathrm{bf}$.
A consequence of the isomorphism between $\Nsfstar Z_{\mathrm{bf}}$
and ${}^{b,k} T^*_{\mathrm{bf} \cap \mathrm{bf}_0} \mathrm{bf}_0$ is that
Legendre distributions, as defined above, on $\MMkb$ induce Legendre distributions on $\mathrm{bf}_0$, essentially by restriction to $\mathrm{bf}_0$ --- see Proposition~\ref{bfo-rest} for a precise statement.
\subsection{Statement of main results}
The main result of this paper is a rather precise description of the resolvent kernel on the space $\MMksc$.
\begin{theo}\label{mainres} There is an index family $\mcB = (\mcB_{\mathrm{zf}}, \mcB_{\mathrm{bf}_0}, \mcB_{\mathrm{lb}_0}, \mcB_{\mathrm{rb}_0})$ such that the
outgoing resolvent kernel $R(\lambda + i0)$, for $\lambda \leq \lambda_0$, can be represented as the sum of four terms $R_1 + R_2 + R_3 + R_4$, where
\begin{itemize}
\item $R_1 \in \Psi^{-2, (-2, 0, 0), \*}(M, \Omegabht)$ is a pseudodifferential operator of order $-2$ in the calculus of operators defined in \cite{GH1};
\item $R_2 \in I^{m,\mcA}(\MMkb, (\Nscstar\Diagb, L^{\mathrm{bf}}_+); \Omegakbh)$ is an intersecting Legendre distribution on $\MMkb$, microsupported close to $\Nscstar\Diagb$;
\item $R_3 \in I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, (L^{\mathrm{bf}}_+, \Lsharp_+); \Omegakbh)$ is a Legendre distribution on $\MMkb$ associated to the intersecting pair of Legendre submanifolds with conic points $(L^{\mathrm{bf}}_+, \Lsharp_+)$, microsupported away from $\Nscstar\Diagb$;
\item $R_4$ is supported away from $\mathrm{bf}$ and is such that $e^{-i/\rho} e^{-i/\rho'} R_4$ is\footnote{Notice that $e^{i/\rho} = e^{i\lambda r}$ is the usual outgoing oscillation at infinity}
polyhomogeneous conormal on $\MMkb$ with index family $\mcB \cup (\mcB_{\mathrm{lb}}, \mcB_{\mathrm{rb}}, \mcB_{\mathrm{bf}})$, where $\mcB_{\mathrm{lb}} = \mcB_{\mathrm{rb}} = (n-1)/2$ and $\mcB_{\mathrm{bf}} = \emptyset$.
\end{itemize}
We have $m = -1/2$, $p = (n-2)/2$, $r_{\mathrm{lb}} = r_{\mathrm{rb}} = (n-1)/2$, $\min \mcB_{\mathrm{zf}} = 0$, $\min \mcB_{\mathrm{bf}_0} = -2$, $\min \mcB_{\mathrm{lb}_0} = \min \mcB_{\mathrm{rb}_0} = \nu_0 - 1$. Moreover, the leading asymptotics of $R(\lambda + i0)$ at $\mathrm{bf}_0, \mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0$ are given by \eqref{resmodels}.
\end{theo}
There is a corresponding statement about the incoming resolvent, with $L^{\mathrm{bf}}_+$ and $\Lsharp_+$ replaced by $L^{\mathrm{bf}}_-$ and $\Lsharp_-$. Subtracting the incoming from the outgoing resolvent we obtain our result about the spectral measure:
\begin{theo}\label{mainsm} The difference between the outgoing and incoming resolvents is a conormal-Legendre distribution on $\MMkb$ associated to the intersecting pair of Legendre submanifolds with conic points $(L^{\mathrm{bf}}, \Lsharp)$. More precisely, we have
$$
R(\lambda + i0) - R(\lambda - i0) \in I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA'}(\MMkb, (L^{\mathrm{bf}}, \Lsharp); \Omegakbh),$$
where $\mcA'_{\bullet} = \mcA_{\bullet}$ for $\bullet = \mathrm{lb}_0, \mathrm{rb}_0, \mathrm{bf}_0$, but
$$\mcA'_{\mathrm{zf}} \subset \mcA_{\mathrm{zf}} \setminus \{ (\beta, j) \mid \beta < 2\nu_0 \}
$$
and $\mcA'_{\mathrm{zf}} \setminus\{2\nu_0\}\geq \min(2\nu_0+1,2\nu_1)$.
Consequently, the spectral measure \eqref{Stone} of $P_+^{1/2}$ satisfies
$$
dE_{P_+^{1/2}}(\lambda) \in I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA''}(\MMkb, (L^{\mathrm{bf}}, \Lsharp); \Omegakbh) \otimes {|\lambda d\lambda|^{1/2}}$$
where $\mcA''_{\bullet} = \mcA'_{\bullet} + (1,0)$; in particular, the spectral measure vanishes to order $2\nu_0 + 1$ for fixed $z, z' \in M^\circ$. The leading asymptotic of the spectral measure at $\mathrm{zf}$ is given by \eqref{smzf}.
\end{theo}
\section{Symbol calculus for Legendre distributions}\label{sect:symbolcalc}
The symbol calculus follows in a straightforward way from that given for Legendrian distributions on $\MMb$ given in \cite{HV2}. We state the results for $\MMkb$ here without proof. (One reason for stating the results here is to correct some typos in \cite{HV2}; for example, in the exact sequence of Proposition 3.4 of \cite{HV2}, $\rho^{m-{\bf r}}$ should be $\rho^{{\bf r}-m}$, and Proposition 3.5 has a similar typo.)
The principal symbol map is defined on the space $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$ of
Legendre distributions associated to $\Lambda$ and maps to bundle-valued half-densities on $\Lambda \times [0, \lambda_0]$.
Here the bundle in question is the symbol bundle $S^{[m]}(\Lambda)$, pulled back to $\Lambda$ (which we continue to denote $S^{[m]}(\Lambda)$), defined in
\cite{HV2} or \cite{HW} :
\begin{equation}
S^{[m]}(\Lambda) = M(\Lambda) \otimes E \otimes |N^*_{\mathrm{bf}} (\partial \MMkb) |^{m-(2n+1)/4}\label{S[m]defn}
\end{equation}
(where $M(\Lambda)$ is the Maslov bundle, and the other bundles are defined in \cite{HV2} or \cite{HW}). Let $\mcC$ denote the index family for the boundary hypersurfaces of $\Lambda \times [0, \lambda_0)$
that assigns $\mcA_{\mathrm{bf}_0}$ at $\Lambda \times \{ 0 \}$, the one-step index set $r_{\mathrm{lb}} - m$ at $\partial_{\mathrm{lb}} \Lambda \times [0, \lambda_0)$ and the one-step index set $r_{\mathrm{rb}} - m$ at $\partial_{\mathrm{rb}} \Lambda \times [0, \lambda_0)$. Thus $\mcC$ depends on the data $(\mcA, m, r_{\mathrm{lb}}, r_{\mathrm{rb}})$.
Then the principal symbol $\sigma^m(u)$ of $u \in I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$ takes values in the polyhomogeneous space $ \phgc_{\mcC}(\Lambda \times [0, \lambda_0]; S^{[m]}(\Lambda) \otimes \Omegabh)$. It is defined by continuity from the symbol map given in \cite{HV2}.
The following propositions follow straightforwardly from the corresponding results in Section 3 of \cite{HV2}.
\begin{prop}\label{ex} There is an exact sequence
\begin{multline*}
0 \to I^{m+1, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh) \to I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh) \to \\
\phgc_{\mcC}(\Lambda \times [0, \lambda_0], \Omega^\half_b \otimes S^{[m]}(\Lambda)) \to 0.
\end{multline*}
If $u \in I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$,
then $(P - \lambda^2)u \in I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA+2}(\MMkb, \Lambda; \Omegakbh)$ and
$$
\sigma^m((P - \lambda^2)u) = \sigma_l(P - \lambda^2) \sigma^m(u) .
$$
Thus, if $\sigma_l(P - \lambda^2)$ vanishes on $\Lambda$, $(P - \lambda^2)u \in I^{m+1, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA+2}(M, \Lambda;
\Omegakbh)$. The symbol of order $m+1$ of $(P - \lambda^2)u$ in this case is given by
\begin{equation}
\Big( -i \mathcal{L}_{V_l} -i \big(\half + m - \frac{2n+1}{4} \big) \nu + p_{\mathrm{sub}} \Big) \sigma^m(u) \otimes |dx|,
\label{transport}\end{equation}
where $V_l$ is the vector field \eqref{Vl} and $p_{\mathrm{sub}}$ is the boundary subprincipal symbol of $P - \lambda^2$.
\end{prop}
\begin{remark} The boundary subprincipal symbol $p_{\mathrm{sub}}$ is defined in \cite[Section 2.1]{HV2}. Here it is sufficient to note that it is a smooth function on $\Nsfstar Z_{\mathrm{bf}}$ which vanishes on $L^\sharp$.
\end{remark}
In the next proposition, $ \tilde \Lambda = (\Lambda_0, \Lambda_1)$ is a pair of intersecting Legendre submanifolds as in Proposition 3.2 of \cite{HV2}. We are assume that they do not meet $\Tscstar_{\mathrm{lb}}\MMb$ or $\Tscstar_{\mathrm{rb}}\MMb$. Therefore we are left with the order, $m$, at $\Lambda_0$, and the index family $\mcA$. We refer to \cite[Section 3.1, equation (3.8)]{HV2} for the definition of the bundle over $\Lambdat$.
\begin{prop}\label{ex-int} The symbol map on $\Lambdat$ yields an exact sequence
\begin{multline*}
0 \to I^{m+1, \mcA}(\MMkb, \Lambdat; \Omegakbh) \to I^{m,\mcA}(\MMkb, \Lambdat; \Omegakbh) \to \\
\phgc_{\mcA_{\mathrm{bf}_0}}(\Lambdat \times [0, \lambda_0], \Omega^\half_b \otimes S^{[m]}) \to 0.
\end{multline*}
Moreover, if we consider just the symbol map to $\Lambda_1$, there is an exact
sequence
\begin{multline}
0 \to I^{m+1; \mcA}(\MMkb, \Lambdat; \Omegakbh) + I^{m+\half; \mcA}(\MMkb, \Lambda_0; \Omegakbh) \to I^{m;\mcA}(\MMkb, \Lambdat;
\Omegakbh) \\
\to \phgc_{\mcA_{\mathrm{bf}_0}}(\Lambda_1 \times [0, \lambda_0], \Omega^\half \otimes S^{[m]}) \to 0.
\label{ex-int-2}\end{multline}
If $u \in I^{m; \mcA}(\MMkb, \Lambdat; \Omegakbh)$,
then $(P - \lambda^2) u \in I^{m;\mcA}(\MMkb, \Lambdat; \Omegakbh)$ and
$$
\sigma^m((P - \lambda^2)u) = \sigma_l(P - \lambda^2) \sigma^m(u).
$$
Thus, if the symbol of $P - \lambda^2$ vanishes on $\Lambda_1 \times [0, \lambda_0]$, then $(P - \lambda^2)u$ is an element of
$I^{m+1; \mcA}(\MMkb, \Lambdat;
\Omegakbh) + I^{m+1/2;\mcA}(\MMkb, \Lambda_0; \Omegakbh)$. The symbol of order $m+1$ of $(P - \lambda^2)u$ on $\Lambda_1 \times [0, \lambda_0]$
in this case is given by \eqref{transport}.
\end{prop}
In the last of these propositions, $\Lambdat$ is an intersecting pair of Legendre submanifolds $(\Lambda, \Lambdas)$ with conic points, as defined above. Now $\Lambdah$ is a manifold with codimension 2 corners since the blowup \eqref{lambdah} creates a new boundary hypersurface at the intersection with $\Lambda^\sharp$, which we denote $\partial_\sharp \Lambdah$. So $\Lambdah \times [0, \lambda_0]$ has codimension 3 corners. We define the index family $\mcC'$ for $\Lambdah \times [0, \lambda_0]$ to be that
which assigns $\mcA_{\mathrm{bf}_0}$ at $\Lambdah \times \{ 0 \}$, the one-step index set $r_{\mathrm{lb}} - m$ at $\partial_{\mathrm{lb}} \Lambdah \times [0, \lambda_0)$, the one-step index set $r_{\mathrm{rb}} - m$ at $\partial_{\mathrm{rb}} \Lambdah \times [0, \lambda_0)$,
and the one-step index set $p - m$ at $\partial_{\sharp} \Lambdah$.
\begin{prop}\label{ex-conic} There is an exact sequence
\begin{multline}
0 \to I^{m+1,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambdat; \Omegakbh) \to I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambdat; \Omegakbh) \\
\to \phgc_{\mcC'}(\Lambdah \times [0, \lambda_0], \Omega^\half_b \otimes S^{[m]}(\Lambdah))
\to 0.
\end{multline}
If $u \in I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambdat; \Omegakbh)$,
then $(P - \lambda^2)u \in I^{m,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambdat; \Omegakbh)$ and
$$
\sigma^m((P - \lambda^2)u) = \sigma_l(P - \lambda^2) \sigma^m(u).
$$
If the symbol of $P - \lambda^2$ vanishes on $\Lambda$, then $(P - \lambda^2)u \in I^{m+1,p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambdat;
\Omegakbh)$. The symbol of order $m+1$ of $(P - \lambda^2)u$ in this case is given by
\eqref{transport}.
\end{prop}
We next consider the operation of restricting to $\mathrm{bf}_0$. We are mainly interested in this in a neighbourhood of $\mathrm{bf}$, so for simplicity we assume that the index family $\mcA$ is such that the index sets at $\mathrm{lb}_0, \mathrm{rb}_0$ and $\mathrm{zf}$ are empty, i.e.\ the half-densities vanish rapidly at these faces. We also assume for simplicity that the index set $\mcA_{\mathrm{bf}_0}$ satisfies
$$
\mcA_{\mathrm{bf}_0} = (b, 0) \cup \mcA'_{\mathrm{bf}_0}$$
with $\mcA'_{\mathrm{bf}_0} \geq b + \epsilon$ for some $\epsilon > 0$.
Let $\mcA'$ denote $\mcA$ with $\mcA_{\mathrm{bf}_0}'$ substituted for $\mcA_{\mathrm{bf}_0}$. Also recall from Section~\ref{sec:bfo} that a Legendre submanifold
$\Lambda$ for $\MMkb$ induces one, also denoted $\Lambda$, for $\mathrm{bf}_0$. Here $\Lambda$ could be a smooth Legendre submanifold, an intersecting pair of Legendre submanifold, or a Legendre conic pair.
\begin{prop}\label{bfo-rest} Assume that $\mcA$ satisfies the conditions above. Then there is an exact sequence
\begin{multline*}
0 \to I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA'}(\MMkb, \Lambda; \Omegakbh) \to I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh) \to \\
I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \emptyset}(\mathrm{bf}_0, \Lambda; \Omegahbsc) \to 0
\end{multline*}
where the last map on the first line is multiplication by $\lambda^{-b}$ and restriction to $\mathrm{bf}_0$, and the empty set in the exponent of $I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \emptyset}(\mathrm{bf}_0, \Lambda; \Omegakbh)$ indicates rapid vanishing at $\mathrm{lb}_0, \mathrm{rb}_0, \mathrm{zf}$.
\end{prop}
\section{The resolvent for a metric cone}\label{exactcone}
Let $(Y, h)$ be a closed Riemannian manifold of dimension $n-1$, and let $C(Y)$ denote the metric cone over $Y$; that is, the manifold $(0, \infty) \times Y$ with Riemannian metric $\gconic = dr^2 + r^2 h$. This metric is singular at $r=0$, except in the special case that $(Y, h)$ is $S^{n-1}$ with its canonical metric, in which case $C(Y)$ is Euclidean space minus one point, with its standard metric (expressed `in polar coordinates').
In this section we analyze the operator $\Pconic = \Delta_{\conic} + V_0 r^{-2}$ on $C(Y)$, where $V_0$ is a smooth function of $y \in Y$ satisfying
\begin{equation}
\Delta_{Y}+\frac{(n-2)^2}{4}+V_0>0,
\label{posop}\end{equation}
as in \eqref{hyp2}. As is evident from \eqref{Pb}, under this condition $\Pconic$ is a positive operator. Acting initally with domain $C_c^\infty((0, \infty) \times Y)$, it is essentially self-adjoint in dimensions $n \geq 4$; for $n=3$ we use the Friedrichs extension of the corresponding quadratic form.
We construct the resolvent kernel $(\Pconic - (1 + i0))^{-1}$. This problem has been considered previously, e.g.\ in \cite{Callias}, \cite{BS} and \cite{CT}; here we use an essentially microlocal approach based on the theory of Legendre distributions.
\
The operator $\Pconic$ on $C(Y)$ as a differential operator has the form
\begin{equation}
\Pconic = - \partial_r^2 - \frac{n-1}{r} \partial_r + \frac1{r^2} \Delta_Y + \frac{V_0(y)}{r^2} .
\label{conicSchr}\end{equation}
In terms of the variable $x = 1/r$, this reads
$$
-(x^2 \partial_x)^2 + (n-1) x^3 \partial_x + x^2 \Delta_Y + x^2 V_0(y) ,
$$
and is an elliptic scattering differential operator near $x=0$. In the remainder of this section we regard this operator as acting on half-densities, using the flat connection on half-densities that annihilates the Riemannian half-density. Now let
\begin{equation}
\Pbconic = r \, \Pconic \ r
\label{Pb1} \end{equation}
and compute
\begin{equation*}\begin{gathered}
\Big( r \Pconic r \Big) \Big( f |d\gcyl|^{1/2} \Big) \\ =
r^{-n/2} \Big( r^{1 + n/2} \big( - \partial_r^2 - \frac{n-1}{r} \partial_r + \frac1{r^2} \Delta_Y + \frac{V_0(y)}{r^2} \big) r^{1-n/2} \Big) \Big( f |d\gconic|^{1/2} \Big) \\
= \Big( \big( -(r\partial_r)^2 + \Delta_Y + V_0 +(n/2 - 1)^2 \big) f \Big) |d\gcyl|^{1/2}
\end{gathered}\end{equation*}
from which we deduce that, using the connection on the half-density bundle which annihilates the \emph{cylindrical} half-density $|d\gcyl|^{1/2} = |dr/r dh|^{1/2}$,
\begin{equation}
\Pbconic = -(r\partial_r)^2 + \Delta_Y + V_0 +(n/2 - 1)^2 .
\label{Pb}\end{equation}
Hence, after pre- and post-multiplying by $r$, our operator is equivalent to an elliptic b-differential operator $\Pbconic$ endowed with the flat connection that annihilates $|d\gcyl |^{1/2}$. It follows from this formula for $\Pbconic$ that we can separate the $r$ and $y$ variables and express the resolvent kernel $(\Pbconic + k^2r^2)^{-1}$, for $k > 0$, as an infinite sum
\begin{equation}\label{metric-cone-k}
\sum_{j=0}^\infty\Pi_{E_j}(y,y')\Big(I_{\nu_j}(kr)K_{\nu_j}(kr')H(r'-r)+I_{\nu_j}(kr')K_{\nu_j}(kr)H(r-r')\Big) \left|\frac{dr \, dr'}{rr'}\right|^\frac{1}{2}
\end{equation}
where $I_\nu, K_\nu$ are modified Bessel functions (see \cite[Section 4]{GH1}) and $H$ is the Heaviside function. This formula analytically continues to the imaginary axis; setting $k = -i$, and using the formulae
$$
I_\nu (-iz) = e^{-\nu \pi i/2} J_\nu (z), \quad
K_\nu(-iz) = \frac{\pi i}{2} e^{\nu \pi i/2} \Ha^{(1)}_\nu(z),
$$
we see that the kernel of $(\Pconic - (1 + i0)^2)^{-1}$ is
\begin{equation}\label{metric-cone}
\frac{\pi i r r'}{2} \sum_{j=0}^\infty\Pi_{E_j}(y,y')\Big(J_{\nu_j}(r)\Ha^{(1)}_{\nu_j}(r')H(r'-r)+J_{\nu_j}(r')\Ha^{(1)}_{\nu_j}(r)H(r-r')\Big) \left|\frac{dr \, dr'}{rr'}\right|^\frac{1}{2}
\end{equation}
where $\Pi_{E_j}$ is projection on the $j$th eigenspace $E_j$ of the operator $\Delta_Y + V_0 + (n/2 - 1)^2$ (on half-densities) on $Y$ and $\nu_j^2$ is the corresponding eigenvalue; also $J_\nu, \Ha_{\nu}^{(1)}$ are standard Bessel and Hankel functions.
This expression converges only distributionally, and is of very little help in revealing the asymptotic behaviour of the kernel, say as both $r$ and $r'$ tend to $\infty$. For the purposes of this paper, we need very precise information on the kernel in this region. Therefore we give a different construction, based on the construction for scattering metrics in \cite{HV2} and \cite{GH1} together with the construction for b-metrics in \cite{APS}. First we define compactifications of $C(Y)$ and $C(Y)^2$, on which the construction takes place.
\subsection{Compactifications of $C(Y)$ and $C(Y)^2$}\label{sect:coniccomp}
We begin by defining compactifications of $C(Y)$ and $C(Y)^2$.
These constructions are parallel to those in Section~\ref{5.1} for $M \times [0, \lambda_0]$.
Let us compactify $C(Y)$ to $Z = [0, \infty]_r \times Y$, where we use $[0, \infty]_r$ to denote the one-point compactification of $[0, \infty)_r$ with boundary defining function $x = 1/r$ at $r = \infty$. As we have seen, $Z$ is the same as the boundary hypersurface $\mathrm{ff}$ of $\Mkb$.
We denote the boundary hypersurfaces of $Z$ at $r=0$ and $r=\infty$ by $\partial_0 Z$ and $\partial_\infty Z$, respectively. To define the double space, we start from $Z^2$ and perform a `b-blowup';
that is, we blow up the codimension 2 corners of $Z^2$ that meet the diagonal, yielding the b-double product $Z^2_b$:
\begin{equation}
Z^2_b = \big[Z^2; \partial_0 Z \times \partial_0 Z; \partial_\infty Z \times \partial_\infty Z \big].
\label{Z2bdefn}\end{equation}
Let $\Diagb(Z)$ denote the lift of the diagonal submanifold to $Z^2_b$.
We then perform a `scattering blowup' near $r = \infty$. Specifically, we blow up the boundary $\partial_\infty \Diagb(Z)$ of $\Diagb(Z)$ lying over $r = r' = \infty$, obtaining a space we call $\ZZbsc$:
\begin{equation}
\ZZbsc = \big[Z^2; \partial_0 Z \times \partial_0 Z; \partial_\infty Z \times \partial_\infty Z; \partial_\infty \Diagb(Z) \big].
\label{Z2bscdefn}\end{equation}
\begin{figure}[ht!]
\begin{center}
\input{Z2bsc.pstex_t}
\caption{The manifold $Z^2_{b,\mathrm{sc}}$; the dashed line is the lifted diagonal of $Z^2$. The coordinate $r$ vanishes at $\mathrm{zf}$ and $\mathrm{rb}_0$, while $r'$ vanishes at $\mathrm{zf}$ and $\mathrm{lb}_0$. It is canonically isomorphic to the face $\mathrm{bf}_0$ in Figure~\ref{fig:mmksc}.}
\label{Z2bsc}
\end{center}
\end{figure}
If $Y = \partial M$, then $\ZZb$ is canonically diffeomorphic to the boundary hypersurface $\mathrm{bf}_0$ of $\MMkb$, and $\ZZbsc$ is canonically diffeomorphic to the boundary hypersurface $\mathrm{bf}_0$ of $\MMksc$. Accordingly, we label the boundary hypersurfaces of $\ZZb$ and $\ZZbsc$ consistently with those of $\MMkb$ and $\MMksc$: the boundary hypersurfaces of $Z^2$ at $r'=0, r=\infty, r=0, r' = \infty$ will be denoted $\mathrm{lb}_0, \mathrm{lb}, \mathrm{rb}_0, \mathrm{rb}$ respectively,\footnote{This is not a typo; it is really the case that $\mathrm{lb}_0$ corresponds to $r' = 0$ and $\mathrm{rb}_0$ corresponds to $r=0$; see figure.} and the boundary hypersurfaces created by blowing up $\partial_0 Z \times \partial_0 Z$, $\partial_\infty Z \times \partial_\infty Z$, and $ \partial_\infty \Diagb(Z)$ will be denoted by $\mathrm{zf}, \mathrm{bf}$ and (in the case of $\ZZbsc$) $\mathrm{sc}$, respectively. The lift of $\Diagb(Z)$ to $\ZZbsc$ we denote $\Diagbsc(Z)$.
\subsection{Statement of main result for metric cones}
Recall (from Section~\ref{sec:bfo}) that there is a natural identification between
$\Nsfstar Z_{\mathrm{bf}}$ and ${}^{b,k} T^*_{\mathrm{bf} \cap \mathrm{bf}_0} \mathrm{bf}_0$ (where $\mathrm{bf}_0$ here indicates the boundary hypersurface of $\MMkb$) . Also, we noted above that $\mathrm{bf}_0$ is naturally isomorphic to $\ZZb$.
Consequently, the Legendre submanifolds $\Nsfstar \Diagb$, $L_{\pm}$ and $L^\sharp$ introduced in Section~\ref{sec:legsub} induce Legendre submanifolds in ${}^{b,k} T^*_{\bf} \ZZb$. To avoid excessive notation, these Legendre submanifolds of ${}^{b,k} T^*_{\bf} \ZZb$ will be denoted by the same symbols. In terms of these, the main result of this section is
\begin{theo}\label{conic} The kernel of $(\Delta_{\conic} + V_0 r^{-1} - (1 + i0))^{-1}$ is the sum of four terms $R_1 + R_2 + R_3 + R_4$, where
\begin{itemize}
\item
$R_1$ is a pseudodifferential operator on $\ZZbsc$ (in the b-calculus near $\partial_0 \Diagbsc$, and in the scattering calculus near $\partial_\infty \Diagbsc$), supported near $\Diagbsc$ and vanishing to second order at $\mathrm{zf}$;
\item
$R_2 \in I^{-1/2}(\ZZb, (\Nscstar \Diagb, L_+);
\scOh)$ is an intersecting Legendre distribution of order $-1/2$, supported near $\partial_\infty \Diagb$;
\item
$R_3 \in I^{-1/2, p; r_{\mathrm{lb}}, r_{\mathrm{rb}}}(\ZZb, (L_+, L^\sharp); \scOh)$ is a Legendre distribution associated to the intersecting pair of Legendre submanifolds with conic points $(L_+, L^\sharp)$, with $p = (n-2)/2$, $r_{\mathrm{lb}} = r_{\mathrm{rb}} = (n-1)/2$, supported near $\mathrm{bf}$; and
\item $R_4$ is supported away from $\mathrm{bf}$ and is such that $e^{-ir} e^{-ir'} R_4$ is polyhomogeneous conormal on $\ZZb$ vanishing to order $2$ at $\mathrm{zf}$, $n/2$ at $\mathrm{lb}_0$ and $\mathrm{rb}_0$, and $(n-1)/2$ at $\mathrm{lb}$ and $\mathrm{rb}$.
\end{itemize}
\end{theo}
The proof of this theorem will occupy the rest of this section.
\subsection{Parametrix construction}
To construct the kernel of $(\Delta + V_0 r^{-2}- (1 + i0))^{-1}$, we follow the method of \cite{HV2}: we first define a parametrix $\tilde G$ on the space $\ZZbsc$ and show that it gives a good approximation in the sense that
$$
(\Delta + V_0 r^{-2}- 1) \tilde G = \Id + \tilde E
$$
with $\tilde E$ relatively `small'. We then correct $\tilde G$ by a finite rank term to obtain a new parametrix $G$ such that $\Id + E = (\Delta_{\conic} + V_0 r^{-2} -1) G$ is invertible, to obtain $(\Delta + V_0 r^{-2}- (1 + i0))^{-1} = G (\Id + E)^{-1}$. This is all done in a calculus of operators that gives us very good control over the behaviour of the kernel at the boundary of the space $Z^2_{b,\mathrm{sc}}$, allowing us to prove Theorem~\ref{conic}.
To construct $\tilde G$, we use the construction near $\mathrm{sc}$ and $\mathrm{bf}$ from \cite{HV2}, which applies verbatim, as this construction is all local near infinity.
Let us recall that this construction is made in four stages. First, we take an interior parametrix, i.e.\ a distribution $G_1$ conormal to and supported close to $\Diagbsc(Z) \subset \ZZbsc$ whose full symbol is the inverse of the full symbol of $\Delta_{\conic} - 1$. If we apply $\Delta_{\conic} - 1$ to such an interior parametrix we are left with an error term that, in a neighbourhood of $r = r' = \infty$, is smooth and supported close to $\Diagbsc$. If we view the error term on $Z^2_b$, then it is Legendrian with respect to $\Nsfstar \Diagb$ (see Section 4.1 of \cite{HV2}). In the second stage, this error is solved away microlocally with an intersecting Legendre distribution on $Z^2_b$ lying in $I^{-1/2}(\ZZb, (\Nscstar (\partial_\infty \Diagb), L_+), \Omegabsc)$, associated to the conormal bundle of the boundary of $\Delta_b(Z)$ and to the outgoing half of the `propagating Legendrian' $L_+$ described in the previous section. This gives us a parametrix $G_2$ with error te!
rm $E_2$ that is Legendrian with respect to $L_+$ and microsupported away from $\partial_\infty \Nscstar \Diagb$ (see Section 4.2 of \cite{HV2}).
In the third stage, the error $E_3$ is solved away using a Legendrian conic pair associated to $(L, L^\sharp)$, giving a parametrix $G_3$ with error term $E_3$ Legendrian with respect to $L^\sharp$ only; thus, at this stage, the errors at $L$ have been solved away completely (see Sections 4.3 and 4.4 of \cite{HV2}). In the fourth stage, the error term $E_3$ is solved away to infinite order at $\mathrm{bf}$ and at $\mathrm{lb}$ (we recall that we can solve away to infinite order at $\mathrm{lb}$ but not $\mathrm{rb}$ since we apply the operator $\Delta_{\conic} + V_0 r^{-2} - 1$ in the left variables, so we obtain a Taylor series calculation which is easily solved order by order at $\mathrm{lb}$, while at $\mathrm{rb}$ we are left with a global problem which we cannot hope to solve). This yields a parametrix $G_4$ with error term $E$ rapidly vanishing at the boundary of $\ZZbsc$ except at $\mathrm{rb}$ where it has the form $A(r, y, y') (r')^{-(n-1)/2} e^{ir'} |d\gconic d\gconic'|^{1/2}$, where $A = O(r^{-\infty})$ as $r \to \i!
nfty$ (see Section 4.5 of \cite{HV2}).
We take the kernel $\tilde G$ to be equal to $G_4$ in a neighbourhood of $\mathrm{sc} \cup \mathrm{bf} \cup \Diagbsc$ of $\ZZbsc$, and supported away from $\mathrm{lb}_0$ and $\mathrm{rb}_0$. We now need to specify the parametrix near the boundary hypersurfaces $\mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0$.
At $\mathrm{zf}$, where $r = r' = 0$, we use the b-calculus. Any b-pseudodifferential operator on half-densities has a `normal operator', that is, the restriction of the kernel of the operator to the `front face' (here the face $\mathrm{zf}$), which has a natural interpretation as a dilation-invariant operator on a half-cylinder (here $\partial M \times (0, \infty)_\sigma$, where $\sigma = r'/r$). In the present case, we write $\Delta_{\conic} + V_0 r^{-2} - 1 = r^{-1} \big( \Pbconic - r^2 \big) r^{-1}$, so the b-operator of interest is $\Pbconic - r^2$, and its
normal operator is precisely $\Pbconic$, given by \eqref{Pb}, which is manifestly dilation-invariant. In the b-calculus, the normal operator of the inverse of a b-elliptic operator is the inverse of the normal operator \cite{APS}.
We therefore specify that $\tilde G$ vanishes to second order at $\mathrm{zf}$, and the restriction of $(rr')^{-1} \tilde G $ to $\mathrm{zf}$ is equal to $\Pbconic^{-1}$. (We remark that this inverse exists due to assumption \eqref{posop}.) This has a distributional expansion in terms of the eigenfunctions on $\partial M$ as
\begin{equation}\label{metric-cone-zf}
\sum_{j=0}^\infty\Pi_{E_j}(y,y') \frac1{2\nu_j} \Big( (r/r')^{\nu_j} H(r'-r)+(r'/r)^{\nu_j} H(r-r')\Big) \left|\frac{dr dydr'dy'}{rr'}\right|^\frac{1}{2} .
\end{equation}
Thus $\tilde G = (r r') \Pbconic^{-1} + O(\rho_{\mathrm{zf}}^3)$ will be polyhomogeneous conormal at $\mathrm{lb}_0$ and $\mathrm{rb}_0$ with index set
\begin{equation}
\mcA_{\mathrm{lb}_0} = \mcA_{\mathrm{rb}_0} = \{ (\nu_j + 1, 0) \mid j = 0, 1, 2, \dots \}
\label{lborbo}\end{equation}
with $\nu_j$ as in \eqref{metric-cone}; in particular, $\min \mcA_{\mathrm{lb}_0} = \min \mcA_{\mathrm{rb}_0} = \nu_0 + 1$. We also observe that this specification of $\tilde G$ near $\mathrm{zf}$ is compatible with the interior parametrix. This follows
from the fact that the full singularity (modulo $C^\infty$) at the diagonal, both for the interior parametrix and for \eqref{metric-cone-zf}, is uniquely determined by the full symbol of the operator. Explicitly, we can construct a kernel near $\mathrm{zf}$ as follows: we take our interior parametrix, which is supported close to the diagonal, and let $E_{\mathrm{zf}}$ denote the difference between this parametrix (restricted to $\mathrm{zf}$) and \eqref{metric-cone-zf}. As explained above, the difference is $C^\infty$. We extend this $C^\infty$ half-density function in some smooth manner from $\mathrm{zf}$ to $C(Y)$, and add this to our interior parametrix. The result agrees with our specifications both at the diagonal and at $\mathrm{zf}$.
Next we specify what happens at $\mathrm{lb}_0$ and $\mathrm{rb}_0$. To do this, we note that in the expansion \eqref{metric-cone}, the terms are vanishing more and more rapidly at $\mathrm{lb}_0$ and at $\mathrm{rb}_0$ as $j \to \infty$, since
$J_\nu(z) = O(z^{\nu})$ as $z \to 0$. Therefore, we can form a Borel sum at these boundary hypersurfaces. To do this, choose boundary defining functions $\rho_{\mathrm{lb}_0}, \rho_{\mathrm{rb}_0}$ for these boundary hypersurfaces (for example we could take $\rho_{\mathrm{lb}_0} = r'\langle r \rangle/r$, and $\rho_{\mathrm{lb}_0} = r\langle r' \rangle/r'$).
Then we specify that $\tilde G$ is equal to
\begin{equation}
\bigg( \frac{\pi}{2i} (r r') \sum_j \Pi_{E_j}(y,y') \Ha^{(1)}_{\nu_j}(r)J_{\nu_j}(r') \varphi\big( \frac{\rho_{\mathrm{lb}_0}}{ \epsilon_j }\big) + O(\rho_{\mathrm{lb}_0}^\infty) \bigg) \Big|\frac{dr \, dr'}{r r'}\Big|^{1/2}
\label{cone-lbo}\end{equation}
near $\mathrm{lb}_0$, for some $\varphi \in C_c^\infty[0, \infty)$ equal to $1$ near $0$, and some sequence $\epsilon_j$ tending to zero sufficiently fast, and
\begin{equation}
\bigg( \frac{\pi}{2i} (r r') \sum_j \Pi_{E_j}(y,y') \Ha^{(1)}_{\nu_j}(r')J_{\nu_j}(r) \varphi\big( \frac{\rho_{\mathrm{rb}_0}}{ \epsilon_j }\big)+ O(\rho_{\mathrm{rb}_0}^\infty) \bigg) \Big|\frac{dr \, dr'}{r r'}\Big|^{1/2}
\label{cone-rbo}\end{equation}
near $\mathrm{rb}_0$\footnote{Note the confusing fact that $\mathrm{lb}_0$ is the face where $r' = 0$, which $\mathrm{rb}_0$ is the face where $r = 0$!}. (We remark that in these formulae the $\Pi_{E_j}(y,y')$ terms contain half-density factors in the $(y, y')$ variables.)
To check that this is compatible with the behaviour specified at $\mathrm{zf}$, we take the leading behaviour of these expressions at $\mathrm{zf}$. To do this we need the leading behaviour of Bessel and Hankel functions at $r=0$, given by \cite{AS}
\begin{equation}\begin{gathered}
J_\nu(z) = \frac1{\Gamma(\nu + 1)} \big( \frac{z}{2} \big)^\nu + O(z^{\nu + 1}), \\
\Ha^{(1)}_\nu(z) = \frac1{i\pi} \Gamma(\nu) \big( \frac{z}{2} \big)^{-\nu} + O(z^{-\nu + 1}).
\end{gathered}\label{Bessel-asymptotics}\end{equation}
This implies that at the leading behaviour of \eqref{cone-lbo} at $\mathrm{zf}$ is
$$
(rr') \sum_j \Pi_{E_j} \frac1{2\nu_j} \big(\frac{r'}{r} \big)^{\nu_j},
$$
which is equal to \eqref{metric-cone} modulo $O(\rho_{\mathrm{lb}_0}^\infty)$,
and the leading behaviour of \eqref{cone-rbo} at $\mathrm{zf}$ is
$$
(rr') \sum_j \Pi_{E_j} \frac1{2\nu_j} \big(\frac{r}{r'} \big)^{\nu_j},
$$
which is equal to \eqref{metric-cone} modulo $O(\rho_{\mathrm{rb}_0}^\infty)$.
This proves that all our specifications at $\mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0$ are compatible.
We next observe that the asymptotic formulae for Hankel functions for large argument, namely
$$
\Ha_{\nu}^{(1)}(r) = r^{-1/2} e^{ir - i\nu \pi/2 + i\pi/4} h_{\nu}(r), \quad r \geq 1,
$$
where $h_{\nu}(r)$ is a classical symbol of order zero, i.e.\ with an expansion as $r \to \infty$ in nonpositive integral powers of $r$,
implies that, near $\mathrm{lb}_0 \cap \mathrm{lb}$, \eqref{cone-lbo} is of the form $r^{-(n-1)/2} e^{ir}|dg_{\conic} d{\gcyl'}|^{1/2}$ times a polyhomogeneous conormal function with $C^\infty$ index set at $\mathrm{lb}$ and index set $\mcA_{\mathrm{lb}_0}$ at $\mathrm{lb}_0$. A similar statement is valid for \eqref{cone-rbo} near $\mathrm{rb}_0 \cap \mathrm{rb}$.
\begin{remark}\label{summary}
So far, we have found a parametrix $\tilde G$ which is the sum of a number of pieces:
\begin{itemize}
\item a pseudodifferential operator, i.e.\ a kernel conormal at $\Diagbsc$ and supported close to $\Diagbsc$ (this is in the scattering calculus near $\partial_\infty \Diagbsc$ and in the b-calculus near $\partial_0 \Diagbsc$);
\item
an intersecting Legendre distribution supported close to $\partial_\infty \Diagb$;
\item
a conic Legendre pair supported near $\mathrm{bf}$; and
\item
a kernel which is supported away from $\mathrm{bf}$ and is $e^{ir}e^{ir'}$ times a polyhomogeneous conormal half-density, with index sets $\mcA_{\mathrm{lb}_0} = \mcA_{\mathrm{rb}_0}$ at $\mathrm{lb}_0, \mathrm{rb}_0$, and one-step index sets $2$ at $\mathrm{zf}$, $(n-1)/2$ at $\mathrm{lb}, \mathrm{rb}$.
\end{itemize}
In particular, our parametrix $\tilde G$ satisfies the conditions of Theorem~\ref{conic}. It remains to find the correction term and show that it also satisfies the conditions of Theorem~\ref{conic}.
\end{remark}
\subsection{Correction term and true resolvent}\label{correction}
Define $\tilde E = (\Delta_{\conic} + V_0r^{-2} - 1) \tilde G - \Id$. Then $\tilde E$ is $e^{ir}$ times a kernel that is conormal on $\ZZb$ and vanishes to order $1$ at $\mathrm{zf}$, $\infty$ at $\mathrm{rb}_0, \mathrm{lb}_0, \mathrm{lb}$ and $\mathrm{bf}$ and to order $(n-1)/2$ at $\mathrm{rb}$. Thus, $\tilde E$ is a compact operator acting on $\ang{r}^{-l} L^2(Z)$ for any $l > 1/2$. It is not necessarily the case that $\Id + \tilde E$ is invertible on any of these spaces, however. To arrange this, for some (and then, it turns out, every) $l$, we add, following \cite{HV2}, a finite rank term to $\tilde G$, of the form
$$
\sum_{i=1}^N \phi_i \ang{\psi_i, \cdot}.
$$
Here $N$ is the common value of the dimension of the kernel and cokernel of $\Id + \tilde E$ on $\ang{r}^{-l} L^2(Z)$ (where $l$ is a fixed real number $> 1/2$). We choose $\psi_i$ to span the null space of $\Id + \tilde E$ and $\phi_i$ to span a subspace supplementary to the range of $\Id + \tilde E$. Note that, due to the rapid vanishing of the kernel of $\tilde E$ as $r \to \infty$, if $\psi = -\tilde E\psi$, then $\psi$ vanishes rapidly at $r \to \infty$. Also, since $\tilde E$ vanishes to first order at $r = 0$, $\psi$ must vanish to infinite order at $r=0$ also. Hence each $\psi_i \in \CIdot(Z)$.
To choose the $\phi_i$, we prove an analogue of Lemma 6.1 in \cite{HV2}:
\begin{lem} Let $l > 1/2$, and let $\CIdot(Z)$ denote smooth functions on $Z$ vanishing to infinite order at the boundary. Then the image of $\Pconic - 1$ on $\CIdot(Z) + \tilde G (\CIdot(Z))$ is dense in $\ang{r}^{-l} L^2(Z)$.
\end{lem}
\begin{proof}
This is proved in a similar way as Lemma 6.1 in \cite{HV2}. Let $\mathcal{M}$ be the subspace spanned by $(\Pconic - 1)(\CIdot(Z)$ and $(\Pconic - 1)(\tilde G (\CIdot(Z)))$, and let $f$ be a function in
$\ang{r}^{-l} L^2(Z)$ orthogonal (in the inner product on $\ang{r}^{-l} L^2(Z)$) to $\mathcal{M}$. We shall prove that $f=0$.
With $\ang{\cdot, \cdot}$ denoting the inner product on $L^2$, we have
\begin{equation}\begin{gathered}
\ang{ \ang{r}^{l} f, \ang{r}^{l} (\Pconic - 1) u} = 0 \quad \forall \ u \in \CIdot(Z) \\
\implies
\ang{ (\Pconic - 1)(\ang{r}^{2l} f), u} = 0 \quad \forall \ u \in \CIdot(Z)
\end{gathered}\end{equation}
which implies, setting $h = \ang{r}^{2l} f$, that $(\Pconic - 1) h = 0$. Now we apply the same argument setting this time $u = \tilde G v$, where $v \in \CIdot(Z)$, and the operator identity $(\Pconic - 1)\tilde G = \Id + \tilde E$, to deduce that
$ (\Id - \tilde E^*) h = 0$, or equivalently $h = \tilde E^* h$. But $\tilde E^*$ vanishes to order $1$ at $\mathrm{zf}$ and to infinite order at $\mathrm{lb}_0, \mathrm{rb}_0$, which shows that $h(r,y)$ vanishes to infinite order at $r=0$. Similarly, $\tilde E^*$ maps $\ang{r}^{2l} L^2(Z)$ to $r^{-(n-1)/2} e^{-ir} \CI(Z)$ for $r \geq 1$, so we deduce that $h$ has this behaviour for $r \to \infty$. Let $h = r^{-(n-1)/2} e^{-ir} h_0(y) + O(r^{-(n+1)/2})$. Then applying Green's identity to $h$ and its complex conjugate, we find that
$$\begin{gathered}
0 = \int_Z \Big( ((\Pconic - 1)h) \overline{h} - h (\Pconic - 1)\overline{h} \Big)\, r^{n-1} dr dy \\
= \bigg( \lim_{r \to \infty} \int_Y \big( (\partial_r h)\overline{h} - h \partial_r \overline{h} \big) r^{n-1} dy - \lim_{r \to 0} \int_Y \big( (\partial_r h)\overline{h} - h \partial_r \overline{h} \big) r^{n-1} dy \bigg) \\
= -2i \int_Y |h_0(y)|^2 \, dy.
\end{gathered}$$
This shows that $h_0 = 0$. This implies that actually $h = O(r^{-(n+1)/2})$ as $r \to \infty$, so $h \in L^2(Z)$. But $\Pconic + V_0 r^{-2}$ has a dilation symmetry, so it has no point spectrum. Therefore $h = 0$, which finishes the proof.
\end{proof}
Having established this density result, it follows that we can find $\phi_i$, $i = 1 \dots N$, spanning a space supplementary to the range of $\Id + \tilde E$, each of which is the sum of a function in $\CIdot(Z)$ and one in $\tilde G (\CIdot(Z))$. By the mapping properties of $\tilde G$, such functions are smooth in $(0, \infty)$ and having the form $r^{-(n-1)/2} e^{ir} C^\infty(Z)$ as $r \to \infty$, while polyhomogeneous with index set $\mcA_{\mathrm{lb}_0}$ as $r \to 0$. Thus, when we add this finite rank term to $\tilde G$, it does not change any of properties of $\tilde G$ as listed in Remark~\ref{summary}. Let the resulting kernel be denoted $G$. We then have $(\Pconic - 1)G' = \Id + E$, with $E$ having the same structure as above and with $\Id + E$ invertible on $\ang{r}^{-l} L^2$. Notice that the same $G$ works for all $l > 1/2$.
Let $(\Id + E)^{-1} = \Id + S$. Then, since $E$ is Hilbert-Schmidt on $\ang{r}^{-l} L^2$, and we can write $S = -E + E^2+ ESE$, $S$ is also Hilbert-Schmidt on $\ang{r}^{-l} L^2$. To analyze finer properties of $S$, we introduce the following spaces of operators:
\begin{defn}
Let $\Psi_j^0$, $j = 0, 1, 2, \dots$, be the algebra of operators (acting on half-densities) whose kernels are smooth on $\ZZbsc$, vanishing to order $j$ at $\mathrm{zf}$ and vanishing to infinite order at all other boundary hypersurfaces; thus, we can think of these operators as b-pseudodifferential operators of order $-\infty$, vanishing to order $j$ at $\mathrm{zf}$.
Also, let $\Psi^\infty$ be the algebra of operators (acting on half-densities) whose kernels are smooth on $C(Y)$, and on $\ZZbsc$ are of the form ${r'}^{-(n-1)/2} e^{ir'} \CI(\ZZbsc)$ near $\mathrm{rb}$ and vanish to infinite order at all other boundary hypersurfaces.
\end{defn}
It is straightforward to check the composition properties (the first following from composition properties of the b-calculus)
\begin{equation}\begin{aligned}
\Psi^0_j \circ \Psi^0_k &\subset \Psi^0_{j+k}\\
\Psi^0_j \circ \Psi^\infty &\subset \Psi^\infty \\
\Psi^\infty \circ \Psi^0_j &\subset \Psi^0_k \ \forall \ k, \text{ i.e.\ } \Psi^\infty \circ \Psi^0_j \subset \CIdot(\MMkb) \\
\Psi^\infty \circ \Psi^\infty &\subset \Psi^\infty.
\end{aligned}\label{comp-Psi}\end{equation}
In terms of these algebras, we can write $E \in \Psi^0_1 + \Psi^\infty$.
Iterating the identity $$S = -E + E^2+ ESE,$$ we obtain
\begin{equation}
S = - E + E^2 - E^3 + \dots + E^{4N} + E^{2N} S E^{2N}.
\label{SES}\end{equation}
Applying \eqref{comp-Psi} iteratively, we see that $E^j \in \Psi^0_j + \Psi^\infty$. Therefore, $- E + E^2 - E^3 + \dots + E^{4N} \in \Psi^0_1 + \Psi^\infty$. Next we analyze $E^{2N} S E^{2N}$.
\begin{lem}
The operator $E^{2N} S E^{2N}$ has a kernel of the form
\begin{equation}
\Big( \frac{r}{\ang{r}} \Big)^N \Big( \frac{r'}{\ang{r'}} \Big)^N \ang{r'}^{-(n-1)/2} e^{ir'} C^{N}(Z \times Z)
\label{E2NSE2N}\end{equation}
as a multiple of the half-density $|d\gconic d\gconic'|^{1/2}$. Here $C^N(Z \times Z)$ denotes the space of functions on $Z \times Z$ with $N$ continuous derivatives.
\end{lem}
\begin{proof}
In this proof, all kernels are understood to be multiples of the Riemannian half-density $|d\gconic d\gconic'|^{1/2}$.
First, we know that $S$ is Hilbert-Schmidt on the space
$\ang{r}^{-l} L^2(Z)$, $l > 1/2$, so its kernel is in the space
$$
\ang{r}^{-l} \ang{r'}^{l} L^2(Z \times Z).
$$
However, rearranging the identity $(\Id + E)(\Id + S) = \Id$, we find that
$S = -(E + ES)$. Since the kernel of $E$ vanishes to infinite order as $r \to \infty$, we find that this is true for $S$ as well. In particular, we see that
$$
S \in \ang{r}^{-l} \ang{r'}^{l} L^2(Z \times Z).
$$
Next, we have $E^{2N}(z,z'') \in \Psi^0_{2N} + \Psi^\infty$. If we differentiate this kernel $N$ times, it still vanishes to order $N$ at $\mathrm{zf}$, and to infinite order as $r \to \infty$. Therefore we can say that $E^{2N}$ has a kernel which is of the form
$$
\Big( \frac{r}{\ang{r}} \Big)^N \ang{r}^{-N} C^N \big(Z; \ang{r'}^l L^2(Z') \big);
$$
that is, it is $C^N$ in the first variable, vanishing to order $N$ as $r \to 0$ and infinite order as $r \to \infty$, as a $L^2$ function (weighted by $\ang{r'}^l)$ in the second variable. (The prime on $Z'$ in the formula above indicates the right factor; lack of prime indicates the left factor.)
Equally, we can describe $E^{2N}$ as being in the space
$$
\Big( \frac{r'}{\ang{r'}} \Big)^N \ang{r'}^{-(n-1)/2} C^N \big(Z'; \ang{r}^{-l} L^2(Z) \big);
$$
that is, a $C^N$ function of the second variable, vanishing to order $N$ as $r' \to 0$ and order $(n-1)/2$ as $r' \to \infty$, with values in $L^2$ (weighted by $\ang{r}^{-l})$ in the first variable.
The composition $E^{2N} S E^{2N}$ is therefore, using the descriptions above and applying the Cauchy-Schwartz inequality,
in the space \eqref{E2NSE2N}.
\end{proof}
It follows from the Lemma and \eqref{SES} that $S$ lies in the sum of the spaces $\Psi^0_1 + \Psi^\infty$ and \eqref{E2NSE2N} for every $N$. But the intersection of these spaces is just $\Psi^0_1 + \Psi^\infty$,
so we conclude that $S \in \Psi^0_1 + \Psi^\infty$.
The exact outgoing resolvent kernel on $Z$ is $G' + G'S$.
We need to determine the nature of the correction term $G'S$. Recall that $G'
$ is the sum of a pseudodifferential operator $G_1$ and a distribution $G - G_1$ that is Legendrian at $\mathrm{bf}, \mathrm{lb}, \mathrm{rb}$ and polyhomogeneous at the remaining boundaries. It is not hard to check that
$$
G_1 \circ \Psi^0_1 \subset \Psi^0_1, \quad G_1 \circ \Psi^\infty \subset \Psi^\infty.
$$
Therefore $G_1 \circ S \in \Psi^0_1 + \Psi^\infty$.
The composition of $G - G_1$ with $S$ can be analyzed using Melrose's Pushforward Theorem \cite{cocdmc}. To do this, we view the composition as the result of lifting the kernels of $G - G_1$ and $S$ to the b-`triple space'
\begin{multline*}
\ZZZb = \big[ Z^3; (\partial_0 Z)^3; \partial_0 Z \times \partial_0 Z \times Z; \partial_0 Z \times Z \times \partial_0 Z ; Z \times \partial_0 Z \times \partial_0 Z ; \\ (\partial_\infty Z)^3; \partial_\infty Z \times \partial_\infty Z \times Z; \partial_\infty Z \times Z \times \partial_\infty Z ; Z \times \partial_\infty Z \times \partial_\infty Z \big]
\end{multline*}
in which all of the boundary hypersurfaces of codimension 2 and 3 that meet the diagonal are blown up; see for example \cite[Section 23]{scatmet}. This space has three stretched projections $\pi_L, \pi_C, \pi_R$ to $\MMb$ according as they omit the left, centre or right variable, respectively.
The product of kernels $A$ and $B$ on $\MMb$ can be represented
as
$$
A \circ B = (\pi_C)_* \Big( \pi_R^* A \cdot \pi_L^* B \Big).
$$
Let $A = e^{-ir} (G - G_1)$ and $B = S e^{-ir'} $. Although the kernel of $A$ is Legendrian at some boundary faces, we claim that the product of
$\pi_R^* A$ and $\pi_L^* B$ on $\ZZZb$ is
polyhomogeneous conormal. To see this, notice that the centre variable of $\ZZZb$ is simultaneously the right variable of $A$ and the left variable of $B$. The places where $A$ is Legendrian is at $\mathrm{bf}$ and $\mathrm{rb}$, which is where the right variable of $A$ goes to infinity, but since the kernel of $B$ is rapidly decreasing when the left variable of $B$ goes to infinity, the Legendrian behaviour is killed when these kernels are multiplied on $\ZZZb$.
The pushforward theorem \cite[Theorem 5]{cocdmc} then shows that $e^{-ir} (G - G_1) S e^{-ir'}$ is polyhomogeneous on $\ZZb$ with index sets starting at $1$ at $\mathrm{zf}$, $(n-1)/2$ at $\mathrm{lb}$ and $\mathrm{rb}$, $\infty$ at $\mathrm{bf}$, and $\nu_0$ at $\mathrm{lb}_0$ and $\mathrm{rb}_0$. Therefore $G S$ is a kernel satisfying the conditions of $R_4$ in the statement of Theorem~\ref{conic}. This completes the proof of Theorem~\ref{conic}.
\section{Low energy resolvent construction}\label{lerc}
We now construct the low energy asymptotics of the outgoing resolvent $R(\lambda + i0) = (P - (\lambda + i0)^2)^{-1}$ of $P =\Delta+V$,
for an asymptotically conic manifold $(M,g)$, with $g$ as in
\eqref{metricconic} and with potential function $V$ as in \eqref{hyp2}, \eqref{hyp3}.
It is convenient to split this construction into two parts, the `b'-part and the `scattering' part. To do this we choose a cutoff function $\chi$ such that $\chi(t) = 1$ for $t \leq 1$ and $\chi(t) = 0$ for $t \geq 2$. We then look for two kernels $\Gsc$ and $\Gb$, solving the equations
\begin{equation}
(P - \lambda^2) (\Gsc) = \chi(x/\lambda), \quad
(P - \lambda^2) (\Gb) = 1 - \chi(x/\lambda)
\end{equation}
where the functions on the right hand side act as multiplication operators. We shall continue to use the notation $\rho = x/\lambda$, $\rho' = x'/\lambda$, $\sigma = x/x' = \rho/\rho'$.
\subsection{Construction of $\Gb$}\label{sect:constructionGb}
We start with $\Gb$, which is an approximation to $R(\lambda + i0) (1-\chi(\rho'))$. This is supported away from $\mathrm{bf}$ and $\mathrm{rb}$, see figure \ref{support}. Our ansatz is that $e^{-i/\rho} \Gb$ is conormal at the diagonal $\Diagb$ and polyhomogeneous conormal at the remaining faces. We specify $\Gb$ by giving a certain number of compatible models for $e^{-i/\rho} \Gb$ at each of these faces. We use the boundary defining function $\lambda$ for (the interior of) $\mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0, \mathrm{bf}_0$ and write $(\Gb)^k_\bullet$ for the coefficient of $\lambda^k$ in the expansion of $\Gb$ at these faces. For the leading order coefficient we have $(\Gb)^k_\bullet = \lambda^{-k} \Gb |_{\bullet}$ (note that the operation of restriction of a half-density has the effect of cancelling a factor of $d\lambda/\lambda$).
\begin{figure}[ht!]
\begin{center}
\input{support.pstex_t}
\caption{The support of $G_b$ at the boundary is located on the right of the dashed line.}
\label{support}
\end{center}
\end{figure}
\subsubsection{Terms at $\mathrm{zf}$}
Similarly to the previous section, and following \cite{GH1}, we write $\Delta+V=xP_bx$ for some $b$-elliptic operator in the sense of \cite{APS}
\[P_b=-(x\partial x)^2+\Delta_{\partial M}+(n/2-1)^2+V_0(y) + xW, \quad W\in {\rm Diff}^2_b(M)\]
where $\Delta_{\partial_M}$ denotes the Laplacian on the boundary $\partial M$ equipped with the metric $h(0)$ and ${\rm Diff}^m_b(M)$ denotes
the space of $m$-th order b-differential operators, i.e.\ those obtained from the enveloping algebra of the Lie algebra of smooth vector fields
tangent to $\partial M$. (Here we are writing derivatives with respect to the flat connection annihilating the half-density $|dg_b|^{1/2} = |x^n dg|^{1/2}$.)
The theory of b-elliptic operators given by Melrose \cite[Sec. 5.26]{APS} (see also the discussion in \cite{GH1}) shows that there is a generalized inverse $Q_b$, which is a b-pseudodifferential operator of order $-2$, for the operator $P_b$ on $L^2_b$, such that
\begin{equation*}
P_b Q_b = Q_b P_b = \Id -\Pi_b.
\end{equation*}
where $\Pi_b$ is orthogonal projection on the $L_b^2$ kernel of $P_b$. A zero mode of $P_b$ would be either a zero mode, or a zero-resonance, of $P$. However, assumption \eqref{hyp3} is that $P$ has no resonance nor eigenvalue at $0$. Hence we have
$P_b Q_b = \Id$.
The kernel $Q_b$ is conormal at the b-diagonal $\Delta_{k, \mathrm{sc}} \cap\mathrm{zf}$,
uniformly up to $\mathrm{zf} \cap \mathrm{bf}_0$ (as a multiple of the half-density $|dg_b dg_b'|^{1/2}$), and is polyhomogeneous conormal to the three boundary faces of
$\mathrm{zf}$ (ie. $\mathrm{rb}_0$, $\mathrm{lb}_0$ and $\mathrm{bf}_0$). The index sets giving the exponents and logs in the expansion at the faces are
$\mathcal{E}(Q_b)=(\mathcal{E}_{\mathrm{bf}_0}(Q_b), \mathcal{E}_{\mathrm{rb}_0}(Q_b), \mathcal{E}_{\mathrm{lb}_0}(Q_b))$ where
$\mathcal{E}_{\mathrm{rb}_0}(Q_b)=\mathcal{E}_{\mathrm{lb}_0}(Q_b)$ are a logarithmic extension of the index set
$$
\big\{ \big(\nu_j + k, 0\big) \mid , k\in\mathbb{N}_0, \ \nu_j^2 \in \operatorname{spec} \Delta_{\partial M} + V_0 + (n/2 - 1)^2 \big\}
$$
and \[ \mathcal{E}_{\mathrm{bf}_0}=\mathbb{N}_0\times \{ 0 \}.\]
We set
$({\Gb})_{\mathrm{zf}}^0 = x^{-1} Q_bx^{-1}$.
\subsubsection{Term at $\mathrm{bf}_0$}
As noted above, the face $\mathrm{bf}_0$ of $\MMksc$ is canonically the same as $Z^2_{b,\mathrm{sc}}$ where $Z=(0,\infty)_\rho \times \partial M$.
Following Subsection 3.4 of \cite{GH1}, the operator $P-\lambda^2$ vanishes at order $2$ at $\mathrm{bf}_0$ as a b-differential operator
on $M^2_{k,b}$ and the induced operator at $\mathrm{bf}_0$,
$I_{\mathrm{bf}_0}(\lambda^{-2}(\Delta + V-\lambda^2))$, is given by the operator $\Pconic -1$ acting on the left variable on $Z^2_{b,\mathrm{sc}}$. We therefore set
$({\Gb})_{\mathrm{bf}_0}^{-2}$ to be $1 - \chi(\rho')$ times its inverse constructed in Section \ref{exactcone}:
\begin{equation}\label{bfo}\begin{gathered}
(\Gb)^{-2}_{\mathrm{bf}_0}:= (1 - \chi(\rho')) (\Pconic - (1+i0))^{-1} =
\frac{i\pi (1-\chi(\rho'))}{2\rho\rho'} \\ \times \sum_{j=0}^\infty\Pi_{E_j}(y,y')\Big( J_{\nu_j}(\frac{1}{\rho}) \Ha^{(1)}_{\nu_j}(\frac{1}{\rho'})H(\rho-\rho')+
J_{\nu_j}(\frac{1}{\rho'})\Ha^{(1)}_{\nu_j}(\frac{1}{\rho})H(\rho'-\rho)\Big).
\end{gathered}\end{equation}
This matches with $G_{\mathrm{zf}}^{0}$ at $\mathrm{zf}\cap\mathrm{bf}_0$, since, as shown in the previous section, the operator $\Pconic - 1$ can be written as $\rho \, \Pbconic \, \rho$ where $\Pbconic$ is as in \eqref{Pb}, and the normal operator of $\Pbconic$ (in the sense of the b-calculus) agrees with the normal operator $N(P_b)$ of $P_b$ defined at $\mathrm{zf}$. We have seen that both the normal operators of $x (\Gb)^0_{\mathrm{zf}} x$
and of $\rho^{-1} (\Gb)^{-2}_{\mathrm{bf}_0} \rho^{-1}$ are the inverse of $N(P_b)$, which is precisely the matching conditions for these two models.
\subsubsection{Terms at $\mathrm{rb}_0$ and $\mathrm{lb}_0$}
We take as the leading terms at $\mathrm{rb}_0$ and $\mathrm{lb}_0$, the models given in \cite[Section 4.5]{GH1} with $k$ replaced by $i\lambda$, which amounts to replacing the modified Bessel function $K_{\nu_j}$ in \cite{GH1} by the Hankel function $\Ha_{\nu_j}^{(1)}$. We also have to multiply by $1-\chi(\rho')$ (which only affects $\mathrm{rb}_0$). Therefore we take, for all $\nu_j \leq 1$,
\begin{equation}\begin{gathered}
({\Gb})_{\mathrm{lb}_0}^{\nu_j - 1} = \frac{i \pi}{2} (x' \rho)^{-1} v_j(y,z') \Ha_{\nu_j}^{(1)}(1/\rho) \Big| \frac{d\rho dy}{\rho}dg'_b \Big|^{1/2}, \\
({\Gb})_{\mathrm{rb}_0}^{\nu_j - 1} = \frac{i \pi}{2}(1-\chi(\rho')) (x \rho')^{-1} v_j(z,y') \Ha_{\nu_j}^{(1)}(1/\rho') \Big| \frac{d\rho' dy'}{\rho'}dg_b \Big|^{1/2}
\end{gathered}\label{Gbrbo}\end{equation}
where $v_j(z,y')$ is the unique function on $M \times \partial M$ such that
\begin{equation}
P_b v_j = 0, \quad v_j(x,y,y') = \frac{\Pi_{E_j}(y, y')}{2^{\nu_j} \Gamma(\nu_j + 1)} x^{-\nu_j} + O(x^{-\nu_j - 1} \log x), \quad x \to 0.
\label{vjdefn}\end{equation}
The existence and uniqueness of $v_j$, and the matching of terms \eqref{Gbrbo} with the leading models at $\mathrm{zf}$ and $\mathrm{bf}_0$ is shown in \cite{GH1}.
\subsubsection{Terms at $\mathrm{lb}$}\label{termsatlb}
Let $\tau$ be the half-density in \eqref{lblbo}.
Near $\mathrm{lb}$, we choose $G$ such that $e^{-i/\rho}G$ is polyhomogeneous. More precisely, we choose $G$
of the form $a e^{i/\rho} \rho^{(n-1)/2} |\tau|^{1/2}$
where $a$ is polyhomogeneous, with index sets
$\mathcal{F}_{\mathrm{bf}_0} = \mathcal{E}_{\mathrm{bf}_0}(Q_b) - 2, \mathcal{F}_{\mathrm{lb}_0} = \mathcal{E}_{\mathrm{lb}_0}(Q_b) - 1$ at $\mathrm{bf}_0, \mathrm{lb}_0$ and with the $C^\infty$ index set $0$ at $\mathrm{lb}$, and with leading behaviour at $\mathrm{bf}_0$ and at $\mathrm{lb}_0$ chosen to match the models already specified at those boundary hypersurfaces. This is possible since the models at adjacent faces $\mathrm{bf}_0$ and $\mathrm{lb}_0$ are both of the form $e^{i/\rho}$ times a polyhomogeneous half-density; for $\mathrm{bf}_0$ this follows from the Legendrian description of the kernel in Section~\ref{exactcone}, while for $\mathrm{lb}_0$ it follows from standard asymptotics of Hankel functions as their
argument tends to infinity, as observed above Remark~\ref{summary}.
A standard computation in scattering theory (see \cite[(4.30) -- (4.31)]{HV2} for example) shows that if we apply $(P - \lambda^2)$ to a kernel of the form $$\tilde a e^{i/\rho} \rho^{(n-1)/2 + k} |\tau|^{1/2},$$ with $\tilde a$ polyhomogeneous and with index set $0$ at $\mathrm{lb}$, the result is a kernel of the form $$\lambda^2 b e^{i/\rho} \rho^{(n-1)/2+ k + 1} |\tau|^{1/2},$$ where $b \, |_{\mathrm{lb}} = -2ik a \, |_{\mathrm{lb}}$. Using this iteratively, we can solve away the error term at $\mathrm{lb}$ to infinite order. In fact, applying this with $k=0$ shows that the result of applying $P - \lambda^2$ to $$a e^{i/\rho} \rho^{(n-1)/2} |\tau|^{1/2}$$ with $a$ is as above vanishes to $3$ orders better at $\mathrm{lb}_0$ and $\mathrm{bf}_0$, and $2$ orders better at $\mathrm{lb}$. (We gain three orders at $\mathrm{lb}_0$ and $\mathrm{bf}_0$ since the operator itself vanishes to second order, and the leading models at these faces are killed by the corresponding induced operator, which leads to a gain of an additional order.) This error term c!
an be solved away iteratively at $\mathrm{lb}$ with terms of the form
$$\tilde a e^{i/\rho} \rho^{(n+1)/2 + k} |\tau|^{1/2}, \quad k = 2, 3, \dots
$$
and where $\tilde a$ vanishes $1$ order better at $\mathrm{bf}_0$ and one order better at $\mathrm{lb}_0$ compared to $a$, i.e.\ the correction terms do not affect the leading models at $\mathrm{bf}_0$ and $\mathrm{lb}_0$ at all. In this way we can remove the error term at $\mathrm{lb}$ completely, i.e.\ so that it vanishes to infinite order there.
We conclude that we can construct a kernel $\Gb$ such that
$$
(P - \lambda^2) (\Gb) - (1 - \chi(\rho)) = E_b \in \phgc_{\mcE}(\MMkb; \Omega_{k,b}^{1/2}(\MMkb)),
$$
such that $\min \mcE_{\mathrm{zf}} = 1$, $\min \mcE_{\mathrm{bf}_0} = 1$, $\min \mcE_{\mathrm{lb}_0} = \nu_0 + 2$, $\min \mcE_{\mathrm{rb}_0} = \nu_0$, $\mcE_{\mathrm{lb}} = \emptyset$, and vanishing in a neighbourhood of $\mathrm{bf}, \mathrm{rb}$.
\subsection{Construction of $\Gsc$}
This is supported away from $\mathrm{lb}_0 \cup \mathrm{zf}$. Initially, we work in a smaller region, which is supported close to $\mathrm{bf}$ --- say in the region where $\rho, \rho' < \epsilon$. In these coordinates, the metric can be written
$$
g =
\lambda^{-2} (d\rho^2/\rho^4 + h(\lambda \rho)/\rho^2) \equiv \lambda^{-2} dg_\lambda.
$$
Our operator $P - \lambda^2$ can be written in the $(\rho, y)$ coordinates as $\lambda^{2} (\Delta_\lambda +V_0 \rho^2 + \lambda \rho^3 W - 1)$ in the $\rho$ coordinates, where $\Delta_\lambda$ is the Laplacian with respect to the metric $g_\lambda$. Thus, our equation $(P - \lambda^2) G = \Id$ is equivalent to
$$
(\Delta_\lambda +V_0 \rho^2 + \lambda \rho^3 W - 1) G = \lambda^{-2} \Id.
$$
Since this operator has coefficients depending smoothly on $\lambda$ down to $\lambda = 0$ in this region, we can perform the first part of the parametrix construction in \cite{HV2} (that part in Section 4)
uniformly in $\lambda$, obtaining a Legendre distribution polyhomogeneous in $\lambda$ with index set $-2$ at $\mathrm{bf}_0$. We give just a sketch of this construction here, referring to \cite{HV2} for full details.
\subsubsection{Pseudodifferential term}
We begin by choosing a pseudodifferential operator $\Gsc_1 \in \Psi^{-2, (-2, 0,0); *}(M; \Omegakbh)$, in the calculus defined in \cite{GH1},
that solves away the singularity along the diagonal, in the equation
$$
(P - \lambda^2) G_1 =\chi(\rho').
$$
See Section 4.1 of \cite{HV2} and Section 3.1 of \cite{GH1}.
\subsubsection{Intersecting Legendre term}
Next we consider the error term $\Esc_1 = (P - \lambda^2) \Gsc_1$. On the space $\MMkb$, it is a Legendre distribution associated to $\Nscstar \Diagb$. We can solve this away (using Proposition~\ref{ex-int} in place of Proposition 3.2 from \cite{HV2}) by adding to $\Gsc_1$ an intersecting Legendre distribution $$\Gsc_2 \in I^{-1/2, \infty, \infty; \mcB}(\MMkb, (\Nscstar \Diagb, L^{\mathrm{bf}}); \Omegab),$$ obtaining a parametrix $\Gsc_2$ with an error term $E_2 \in I^{-1/2, \infty, \infty; \mcE}(\MMkb, L^{\mathrm{bf}}; \Omegab)$ that is Legendre with respect to $L^{\mathrm{bf}}_+$, microsupported away from $\Nscstar \Diagb$, and supported away from $\mathrm{lb}$ and $\mathrm{rb}$. Here, $\mcB_{\mathrm{bf}_0} = -2$, but $\mathcal{E}_{\mathrm{bf}_0} = 0$ (we gain two orders at $\mathrm{bf}_0$ because the operator $P - \lambda^2$ vanishes to second order there).
See Section 4.2 of \cite{HV2}.
\subsubsection{Conic Legendre term}
We can solve away the error term $\Esc_2$ by adding to $\Gsc_2$ a Legendre distribution in the space $I^{m, p ; r_{\mathrm{lb}} , r_{\mathrm{rb}} ; \mcA}(\MMkb, (L^{\mathrm{bf}}, L^\sharp)$, with $m=-1/2$, $p = (n-2)/2$, $r_{\mathrm{lb}} = r_{\mathrm{rb}} = (n-1)/2$, associated to the conic pair of Legendre submanifolds $(L^{\mathrm{bf}}, L^\sharp)$ (using Proposition~\ref{ex-conic} in place of Proposition 3.5 from \cite{HV2}). We then obtain a parametrix $\Gsc_3$ with error term $\Esc_3$ Legendre with respect to $L^\sharp$ only: $\Esc_3 \in I^{p , r_{\mathrm{lb}} + 2 , r_{\mathrm{rb}} \mathcal{E}; \mathcal{B}}(\MMkb, L^\sharp; \Omegab)$. See Sections 4.3 and 4.4 of \cite{HV2}.
\subsubsection{Correction at $\mathrm{bf}_0$}
Now we make a step that is absent from the argument in \cite{HV2}; we correct
the leading behaviour at $\mathrm{bf}_0$ to the exact conic resolvent. We observe that the pseudodifferential singularities of the parametrix constructed above as well as those at $\Nsfstar \Diagb$ and at the propagating Legendrian $L^{\mathrm{bf}}_+$ are uniquely determined. By contrast, the singularities at $L^\sharp$ are not uniquely determined (although the \emph{singularities} of the symbol on $L^\sharp$ where $L^\sharp$ meets $L^{\mathrm{bf}}_+$ are determined --- this subtle point is explained in \cite{MZ}). Thus, the difference
$$
F_{\mathrm{bf}_0}^{-2} := (\Gsc_3)_{\mathrm{bf}_0}^{-2} - (\Pconic - (1 + i0)^2)^{-1},
$$
is Legendre with respect to $L^\sharp$ only. (To clarify the notation in this expression, the superscripts $-2$ are the coefficients of $\lambda^{-2}$ at $\mathrm{bf}_0$, while the superscript $-1$ is a power.) By Proposition~\ref{bfo-rest}, this is the boundary value of a term $F \in I^{p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, L^\sharp_+; \Omegakbh(\MMkb))$. Let $\Gsc_4 = \Gsc_3 + F$.
Now the error term $\Esc_4 = (P - \lambda^2) (\Gsc_4)$ is better: it vanishes to order $1$ at $\mathrm{bf}_0$, i.e.\ we may now take $\mathcal{E}_{\mathrm{bf}_0} = 1$.
\subsubsection{Leading terms at $\mathrm{rb}_0$}
To match with $(\Gsc_4)^{-2}_{\mathrm{bf}_0}$, we define $(\Gsc)^{\rho}_{\nu_j - 1}$, for all $j$ such that $\nu_j \leq 1$, to be given by the second line of \eqref{Gbrbo}, with the factor $1 - \chi(\rho')$ replaced by $\chi(\rho')$.
\subsubsection{Solving away outgoing errors at $\mathrm{bf}$ and $\mathrm{lb}$}
We now solve away all outgoing errors at $\mathrm{bf}$ and $\mathrm{lb}$ as in Section 4.5 of \cite{HV2} and Section~\ref{termsatlb} above, by adding to $\Gsc_4$ a suitable Legendre distribution associated to the outgoing Legendrian $L^\sharp$, obtaining $\Gsc_5$. Since the error term $\Esc_4$ already vanishes to order $1$ at $\mathrm{bf}_0$, the correction terms will be at order $-1$ at $\mathrm{bf}_0$ and therefore do not affect the leading behaviour of $\Gsc_4$ at $\mathrm{bf}_0$ (which are at order $-2$) at all. The new error term $\Esc_5$ is such that $e^{-i/\rho'} \Esc_5$ is polyhomogeneous on $\MMkb$ and vanishes to order order $1$ at $\mathrm{bf}_0$, order $\infty$ at $\mathrm{lb}$ and $\mathrm{bf}$, order $\nu_0$ at $\mathrm{rb}_0$ and $(n-1)/2$ at $\mathrm{rb}$.
\subsection{Correction term and true resolvent}
Let our parametrix $G$ be given by $G = \Gb + \Gsc_5$. Then the error term $E = (P - \lambda^2) G - \Id$ is such that $e^{-i/\rho'} E \in \mathcal{A}_{\mathcal{E}}(\MMkb; \Omegakbh(\MMkb))$ is polyhomogeneous on $\MMkb$ such that $\min \mathcal{E}_{\mathrm{zf}} = 1$,
$\min \mathcal{E}_{\mathrm{bf}_0} = 1$, $\min \mathcal{E}_{\mathrm{lb}_0} = \nu_0 + 2$,
$\min \mathcal{E}_{\mathrm{rb}_0} = \nu_0$,
$\min \mathcal{E}_{\mathrm{rb}} = (n-1)/2$, and $\mathcal{E}_{\mathrm{bf}} = \mathcal{E}_{\mathrm{lb}} = \emptyset$.
If we express this in terms of a half-density of the form $|dg_b dg_b' d\lambda/\lambda|^{1/2}$, which lifts to $\MMkb$ to be a smooth nonvanishing b-half-density, then the orders of vanishing are
as above except at $\mathrm{rb}$, where it changes to $-1/2$.
(Note: by changing to a b-half-density the order of vanishing is reduced by $n/2$ at $\mathrm{lb}$ and $\mathrm{rb}$, and by $n$ at $\mathrm{bf}$; however, because we already have infinite order vanishing at $\mathrm{lb}$ and $\mathrm{bf}$, only the change at $\mathrm{rb}$ is visible.) Since b-half-densities are square-integrable precisely when the order of vanishing is positive, it follows that the error term $E$ is Hilbert-Schmidt on $x^l L^2(M)$ for every $l > 1/2$ and each $\lambda > 0$, with the Hilbert-Schmidt norm tending to zero as $\lambda \to 0$. In particular, it is compact, and invertible for sufficiently small $\lambda$.
Consequently the true resolvent $R(\lambda) = (P - (\lambda + i0)^2)^{-1}$ is given by $G(\Id + E)^{-1}$.
We next analyze the structure of the correction term. Define $S$ (for sufficiently small $\lambda$) by
\begin{equation}
(\Id + E)^{-1} = \Id + S;
\label{Sdefn}\end{equation}
then the correction term is $GS$.
Let us define $E_{\phg}$ to be the kernel $E$ conjugated by $e^{i/\rho}$: $E_{\phg} = e^{i/\rho} E e^{-i/\rho'}$.
Also let $S_{\phg} = e^{i/\rho} S e^{-i/\rho'}$.
We have, for any $N$,
$$
S = \sum_{j=1}^{2N} (-1)^j E^j + E^N S E^N \implies S_{\phg} = \sum_{j=1}^{2N} (-1)^j E_{\phg}^j + E_{\phg}^N S_{\phg} E_{\phg}^N.
$$
By the results of \cite{GH1},
$E_{\phg}^j$ is polyhomogeneous conormal with index family $\mcE^{(j)}$ where index family $\mcE^{(j+1)}$ is given at $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{rb}_0, \mathrm{zf}$ inductively by
\begin{equation}\begin{aligned}
(\mathcal{E}^{(j)}_{\mathrm{lb}_0}+\mathcal{E}_{\mathrm{zf}})&\bar{\cup}(\mathcal{E}^{(j)}_{\mathrm{bf}_0}+\mathcal{E}_{\mathrm{lb}_0}) \text{ at } \mathrm{lb}_0, \\
(\mathcal{E}^{(j)}_{\mathrm{rb}_0}+\mathcal{E}_{\mathrm{bf}_0})&\bar{\cup}(\mathcal{E}^{(j)}_{\mathrm{zf}}+\mathcal{E}_{\mathrm{rb}_0}) \text{ at } \mathrm{rb}_0, \\
(\mathcal{E}^{(j)}_{\mathrm{bf}_0}+\mathcal{E}_{\mathrm{bf}_0})&\bar{\cup}(\mathcal{E}^{(j)}_{\mathrm{lb}_0}+\mathcal{E}_{\mathrm{rb}_0}) \text{ at } \mathrm{bf}_0, \text{ and } \\
(\mathcal{E}^{(j)}_{\mathrm{zf}}+\mathcal{E}_{\mathrm{zf}})&\bar{\cup}(\mathcal{E}^{(j)}_{\mathrm{rb}_0}+\mathcal{E}_{\mathrm{lb}_0}) \text{ at } \mathrm{zf}.
\end{aligned}\label{Ejformulae}\end{equation}
From \eqref{Ejformulae} it is straightforward to prove by
induction that
\begin{equation}\begin{gathered}
\min \mathcal{E}^{(j)}_{\mathrm{lb}_0} \geq \nu_0 + 2 + j, \quad
\min \mathcal{E}^{(j)}_{\mathrm{bf}_0} \geq 1+j, \\
\min \mathcal{E}^{(j)}_{\mathrm{rb}_0} \geq \nu_0+j, \quad
\mathcal{E}^{(j)}_{\mathrm{zf}} \geq j, \\
\mathcal{E}^{(j)}_{\mathrm{bf}} = \mathcal{E}^{(j)}_{\mathrm{lb}} = \emptyset, \quad \mathcal{E}^{(j)}_{\mathrm{rb}} = (n-1)/2.
\end{gathered}\label{Ejinduction}\end{equation}
It follows that the index family $\Ebar$ defined by $\Ebar_\bullet = \cup_j \mathcal{E}^{(j)}_\bullet$ is well-defined. We show
\begin{lem} The kernel $S_{\phg}$ is polyhomogeneous on $\MMkb$ with index family $\Ebar$.
\end{lem}
\begin{proof} Let $Q_N$ be the differential operator
$$
Q_N = \chi(\rho') \prod_{j=0}^{N-1} \big(\rho'\frac{d}{d\rho'} - \frac{n-1}{2} - j \big) , \quad \rho' = \frac{x'}{\lambda},
$$
where $\chi(\rho')$ is a smooth function equal to $1$ for $\rho' \leq 1$ and $0$ for $\rho' \geq 2$.
This operator has the property that it maps a function of $\rho'$ of the form
${\rho'}^{(n-1)/2} \CI(\rho')$ into a function of the form ${\rho'}^{(n-1)/2 + N} \CI(\rho')$, that is, it kills the first $N$ terms of the expansion of a function in
${\rho'}^{(n-1)/2} \CI(\rho')$ at $\rho' = 0$.
Using the definition of polyhomogeneous conormality given in \cite{cocdmc}, it is enough to show, for every positive integer $N$, that $S_{\phg}$ can be written as a sum $S_{\phg, N, 1} + S_{\phg, N, 2}$, where $S_{\phg, N, 1} \in \mathcal{A}_{\Ebar}(\MMkb; \Omegakbh)$, and $Q_N S_{\phg, N, 2}$ is conormal (as opposed to polyhomogeneous conormal) on $\MMkb$ with respect to a multiweight $\frak{r} = \frak{r}_N$, all of whose entries tend to infinity with $N$.
To do this, we write
\begin{equation}
S_{\phg} = \sum_{j=1}^{2N} (-1)^j E_{\phg}^j + E_{\phg}^{N} S_{\phg} E_{\phg}^{N} := S_{\phg, N, 1} + S_{\phg, N, 2}.
\label{SEt}\end{equation}
Clearly, $S_{\phg, N, 1}$ is polyhomogeneous conormal with respect to the index set $\Ebar$. We claim that $Q_N S_{\phg, N, 2}$ is conormal with respect to multiweights\footnote{Note that the rate of decay of $E_{\phg}^N S_{\phg} E_{\phg}^N$ is $N + O(1)$ at all boundary hypersurfaces except for $\mathrm{rb}$, as $N \to \infty$, so the purpose of $Q_N$ is to force an improvement of the rate of decay at $\mathrm{rb}$.} $r_{\mathrm{lb}_0} = r_{\mathrm{rb}_0} = r_{\mathrm{bf}_0} = r_{\mathrm{zf}} = r_{\mathrm{lb}} = r_{\mathrm{rb}} = N$, $r_{\mathrm{bf}} = 2N$.\footnote{It would actually be true with $r_{\mathrm{lb}_0} = \nu_0 + N + 2$, $r_{\mathrm{rb}_0} = \nu_0 + N$, $r_{\mathrm{bf}_0} = 1 + N$, $r_{\mathrm{zf}} = N$, $r_{\mathrm{bf}} = r_{\mathrm{lb}} = \infty$, $r_{\mathrm{rb}} = (n-1)/2 + N$ but it is sufficient, and easier, to show the weaker claim.} We can take
$$
\Big( r_{\mathrm{lb}_0} r_{\mathrm{rb}_0} r_{\mathrm{bf}_0} r_{\mathrm{zf}} r_{\mathrm{lb}} r_{\mathrm{rb}} \Big)^N \rho_{\mathrm{bf}}^{2N} = \lambda^N \langle \frac{x}{\lambda} \rangle ^N \langle \frac{x'}{\lambda} \rangle ^N,
$$
To show the conormality of $Q_N S_{\phg, N, 2}$ with respect to these multiweights, we consider $m$ vector fields $W_1, \dots, W_m$ on $\MMkb$, tangent to the boundary, where $m \in \mathbb{N}$ is arbitrary. We must show that
\begin{multline}
W_1 \dots W_m \big( Q_N S_{\phg, N, 2} \big) \in \Big( r_{\mathrm{lb}_0} r_{\mathrm{rb}_0} r_{\mathrm{bf}_0} r_{\mathrm{zf}} r_{\mathrm{lb}} r_{\mathrm{rb}} \Big)^N \rho_{\mathrm{bf}}^{2N} L^\infty(\MMkb) \\ =\lambda^N \langle \frac{x}{\lambda} \rangle ^N \langle \frac{x'}{\lambda} \rangle ^N L^\infty(\MMkb).
\label{tobeproved}\end{multline}
We next observe that vector fields on $\MMkb$ tangent to the boundary are generated, over $\CI(\MMkb)$, by b-vector fields on $M$, lifted to $\MMkb$ by either the left or the right projection, and by $\lambda \partial_\lambda$. So it is sufficient to prove \eqref{tobeproved} when the $W_i$ are generating vector fields as just described. Notice that, writing $S_{\phg, N, 2} = E_{\phg}^{N} S_{\phg} E_{\phg}^{N}$, the $W_i$ lifted from $M$ by the left, resp. right, factor act on the left, resp. right, factor of $E_{\phg}^{N}$. Notice also that the operator $Q_N$ acts only on the right factor of $E_{\phg}^{N}$ and increases the order of vanishing at $\mathrm{rb}$ to order $(n-1)/2 + N$. However, the vector field $\lambda \partial_\lambda$ acts on all three factors of $S_{\phg, N, 2}$, including the middle factor $S_{\phg}$.
We have already seen that $S_{\phg}$ is, for each fixed $\lambda > 0$, a Hilbert-Schmidt operator on $x^l L^2(M)$, $l > 1/2$, with uniformly bounded Hilbert-Schmidt norm. The same is true for $(\lambda \partial_\lambda)^j S_{\phg}$ for every $j$. In fact, using the identity
$$
(\Id + E_{\phg}) (\Id + S_{\phg}) = \Id \implies E_{\phg} + E_{\phg}S_{\phg} + S_{\phg} = 0,
$$
we compute
$$
\lambda \partial_\lambda S_{\phg} = - (\Id + S_{\phg}) \Big( \lambda \partial_\lambda E_{\phg} \Big) (\Id + S_{\phg}) ,
$$
from which it follows (using the polyhomogeneity of $E_{\phg}$) that
$\lambda \partial_\lambda S_{\phg}$ is Hilbert-Schmidt on $x^l L^2(M)$, $l > 1/2$, with uniformly bounded Hilbert-Schmidt norm. Proceeding inductively we can deduce this for $(\lambda \partial_\lambda)^j S_{\phg}$ for every $j$.
Now we write $z, z', w, w'$ for points in $M$, with $x(z), x(w)$, etc, denoting the corresponding boundary defining functions, and express the kernel of $Q_N S_{\phg, N, 2}$ as
\begin{multline*}
Q_N S_{\phg, N, 2}(\lambda, z, z') =
\int\limits_{M \times M} \Big( x(w)^{l} E_{\phg}^{N}(\lambda, z, w) \big( x(w')^{-l} (Q_N)_{z'} E_{\phg}^{N}(\lambda, w', z') \big) \Big) \\ \times \Big( x(w)^{-l} x(w')^{l} S_{\phg}(\lambda, w, w') \Big) \, dg(w) \, dg(w'), \quad l > \frac1{2}.
\end{multline*}
We then apply the vector fields $W_i$ (assumed without loss of generality to be either b-vector fields on $M$ lifted from the left or right factors, or the vector field $\lambda \partial_\lambda$) to
this expression, and multiply by the factors
\begin{equation}
\lambda^{-N} \langle \frac{x}{\lambda} \rangle ^{-N} \langle \frac{x'}{\lambda} \rangle ^{-N}
\label{rhofactors}\end{equation}
from \eqref{tobeproved}. Using Cauchy-Schwarz (taking advantage of the Hilbert-Schmidt property of kernels $x(w)^{-l} x(w')^{l} S_{\phg}(\lambda, w, w')$, etc), and using the conormality of $E_{\phg}^N$ to absorb the factors from \eqref{rhofactors}, we see that \eqref{tobeproved} is satisfied.
\end{proof}
Now we analyze $GS$. We have
\begin{equation}
e^{-i/\rho} GS e^{-i/\rho'} = \Big( e^{-i/\rho} G e^{-i/\rho} \Big) S_{\phg}.
\label{GScomp}\end{equation}
Note that $e^{-i/\rho} G e^{-i/\rho} $ is not polyhomogeneous at $\mathrm{bf}$ (that is, as both $\rho$ and $\rho'$ tend to zero), but is at all other boundary hypersurfaces. However, after composing with $S_{\phg}$, this non-polyhomogeneity is killed by the rapid decrease of the kernel of $S_{\phg}$ at $\mathrm{bf}$ and $\mathrm{lb}$, i.e.\ as its left $\rho$ variable tends to zero (just as in the discussion in the last paragraph of Section~\ref{exactcone}). Hence we can apply \cite[Proposition 2.10]{GH1} to the composition \eqref{GScomp}. We find that
$e^{-i/\rho} GS e^{-i/\rho'}$ is polyhomogeneous and vanishes to order
(at least) $1$ at $\mathrm{zf}$ and $\mathrm{bf}_0$, order $\nu_0 + 1$ at $\mathrm{lb}_0$ and $\mathrm{rb}_0$, $(n-1)/2$ at $\mathrm{lb}$ and $\mathrm{rb}$ and $n-1$ at $\mathrm{bf}$.
In particular, this correction term vanishes to one order higher than $G$ at $\mathrm{bf}_0, \mathrm{zf}, \mathrm{lb}_0, \mathrm{rb}_0$. Therefore, writing $R_{\bullet}^k$ for the coefficient of $\lambda^k$ in the expansion of the resolvent at $\bullet$, we have, with $v_0$ given by \eqref{vjdefn},
\begin{equation}\begin{aligned}
R_{\mathrm{bf}_0}^{-2} &= G_{\mathrm{bf}_0}^{-2} = \big(P_{\conic} - (1 + i0)^2\big)^{-1}; \\
R_{\mathrm{zf}}^0 &= G_{\mathrm{zf}}^{-1} = (x x')^{-1} P_b^{-1}; \\
R_{\mathrm{lb}_0}^{\nu_0 - 1} &= G_{\mathrm{lb}_0}^{\nu_0 - 1} = \frac{i \pi}{2} (x' \rho)^{-1} v_0(y,z') \Ha_{\nu_0}^{(1)}(1/\rho) \Big| \frac{d\rho dy}{\rho}dg'_b \Big|^{1/2}, \\
R_{\mathrm{rb}_0}^{\nu_0 - 1} &= G_{\mathrm{rb}_0}^{\nu_0 - 1} =\frac{i \pi}{2}(x \rho')^{-1} v_0(z,y') \Ha_{\nu_0}^{(1)}(1/\rho') \Big| \frac{d\rho' dy'}{\rho'}dg_b \Big|^{1/2}.
\end{aligned}\label{resmodels}\end{equation}
\section{Spectral measure}
In this section we study the spectral measure $dE_{P_+^{1/2}}(\lambda)$ of the operator $P_+^{1/2}$ and prove Theorem~\ref{mainsm}. The spectral measure is related to the resolvents $R(\lambda \pm i0)$ by
\begin{equation}
dE_{P_+^{1/2}}(\lambda) = \frac{d}{d\lambda} E_{P_+^{1/2}}(\lambda) \, d\lambda = \frac{\lambda}{\pi i} \Big( R(\lambda + i0) - R(\lambda - i0) \Big) \, d\lambda, \quad \lambda > 0.
\label{subtraction}\end{equation}
The resolvent kernel $R(\lambda \pm i0)$ is invariant under involution, i.e.\ $R(\lambda \pm i0)(z,z') = R(\lambda \pm i0)(z',z)$, and the formal adjoint of $R(\lambda + i0)$ is $R(\lambda - i0)$, i.e.\
$$
R(\lambda - i0)(z,z') = \overline{R(\lambda + i0)(z', z)}.
$$
It follows that the spectral measure can be expressed
\begin{equation}
dE_{P_+^{1/2}}(\lambda)(z,z') = \frac{2\lambda}{\pi} \Im \big( R(\lambda + i0)(z,z') \big) \, d\lambda, \quad \lambda > 0.
\label{smim}\end{equation}
We now discuss cancellations that occur when the two resolvent kernels are subtracted.
\subsection{Behaviour at diagonal}\label{behavdiag}
The diagonal singularity of the resolvent kernel is completely determined by the full symbol of $P$. Consequently, the diagonal
singularity cancels in the expression \eqref{subtraction}, and the spectral measure is smooth across the diagonal. Another way to see this is that the spectral measure satisfies an elliptic equation $(P - \lambda^2) dE(\lambda) = 0$, so it cannot have any local singularities.
Moreover, the difference between the outgoing ``$R_2$" piece and the incoming ``$R_2$" piece (in the terminology of Theorem~\ref{mainres}), which are intersecting Legendre distributions associated to $(\Nsfstar \Diagb, L^{\mathrm{bf}}_+)$ and $(\Nsfstar \Diagb, L^{\mathrm{bf}}_-)$ respectively, is a Legendrian associated to the propagating Legendrian $L^{\mathrm{bf}}$ alone. This is because the left Hamilton vector field \eqref{Vl} is nonzero at $L^{\mathrm{bf}} \cap \Nsfstar \Diagb$, and tangent to $L^{\mathrm{bf}}$. Since Legendrian regularity propagates on $L^{\mathrm{bf}}$ along the Hamilton vector field, the spectral measure is Legendre across $\Nsfstar \Diagb$, i.e.\ it is a Legendre distribution on $\MMkb$ associated to the intersecting pair of Legendre submanifolds with conic points $(L^{\mathrm{bf}}, L^\sharp_+ \cup L^\sharp_-)$.
\subsection{Leading asymptotics at $\mathrm{bf}_0, \mathrm{lb}_0,\mathrm{rb}_0$}
We start by giving the leading asymptotics of the spectral measure at the boundary hypersurfaces $\mathrm{bf}_0, \mathrm{lb}_0,\mathrm{rb}_0$.
At $\mathrm{bf}_0$ (and also at $\mathrm{lb}_0,\mathrm{rb}_0$) we have already determined the leading asymptotic of the outgoing resolvent --- see \eqref{resmodels}. Since the imaginary part of $i \Ha_{\nu}^{(1)}(r)$ is $J_{\nu}(r)$, we see from \eqref{smim} that the leading asymptotic of the spectral measure $dE_{P_+^{1/2}}(\lambda)$ at $\mathrm{bf}_0$ is at order $-1$, and is given by ${\rm Im}(G_{\mathrm{bf}_0}^{-2})$, that is
\begin{equation}\label{sbfo}
(dE)_{\mathrm{bf}_0}^{-1} = dE_{\Pconic^{1/2}}(1) =
r r' \sum_{j=0}^\infty\Pi_{E_j}(y,y')J_{\nu_j}(r)J_{\nu_j}(r') \left|\frac{dr \, dr'}{rr'}\right|^\frac{1}{2} .
\end{equation}
Similarly, at $\mathrm{lb}_0$, $2/\pi$ times the imaginary part of the resolvent kernel yields, as the leading asymptotic of the spectral measure at $\mathrm{lb}_0$,
\begin{equation}\label{slbo}
(dE)_{\mathrm{lb}_0}^{\nu_0} = (x' \rho)^{-1} v_0(y,z') J_{\nu_j}(1/\rho) \Big| \frac{d\rho dy}{\rho}dg'_b \Big|^{1/2},
\end{equation}
where $v_0$ is as in \eqref{vjdefn}. The $\mathrm{rb}_0$ leading asymptotic has the same form by symmetry of the resolvent kernel.
\begin{equation}\label{srbo}
(dE)_{\mathrm{rb}_0}^{\nu_0} = (x \rho')^{-1} v_0(y',z) J_{\nu_j}(1/\rho') \Big| \frac{d\rho' dy'}{\rho'}dg_b \Big|^{1/2}.
\end{equation}
\subsection{Expansion at $\mathrm{zf}$}\label{exp}
We will show that the expansion of the resolvent kernel at $\mathrm{zf}$ is real up to the term at order $\lambda^{2\nu_0}$.
An immediate consequence is a determination of the rate of vanishing of the spectral measure at $\mathrm{zf}$:
\begin{prop}\label{cancellation} The spectral measure $dE_{P_+^{1/2}}(\lambda)$ for the operator $P_+^{1/2}$ vanishes to order $2\nu_0 + 1$ at $\mathrm{zf}$. More particularly, it has expansion at $\mathrm{zf}$ of the form
\[dE_{P_+^{1/2}}(\lambda)= \Big(\lambda^{2\nu_0+1} w(z) w(z') |dg dg'|^{1/2} + O(\lambda^{\min(2\nu_0+2,2\nu_1+1)}) \Big)d\lambda \]
where $w$ is a solution of $P w = 0$, and $ w \sim x^{n/2 - 1 - \nu_0} W(y)$ as $x\to 0$ for some smooth function $W$ on $\partial M$.
\end{prop}
\begin{proof}
We first show that we may choose the parametrix $G$ so that its expansion at $\mathrm{zf}$ up to order $\lambda^{2\nu_0}$ is real. This is certainly true for the pseudodifferential part of $G$; indeed, the real part of any pseudodifferential parametrix is also a pseudodifferential parametrix, since $P$ has real coefficients.
Now consider the expansion of ${\rm Im}(G_{\mathrm{bf}_0}^{-2})$ at the face $\mathrm{zf}$.
\begin{comment}
The Bessel function $J_{\nu}(r)$ is a real function, while the Hankel function $\Ha_{\nu}^{(1)}$ has an expansion at $r=0$
of the form
\[\begin{gathered}
\Ha^{(1)}_\nu(r)\sim
r^{-\nu}\sum_{j=0}^\infty b_j(\nu)r^{2j}+r^{\nu}\sum_{j=0}^\infty c_j(\nu)r^{2j} \quad {\rm if \ }\nu\notin \mathbb{N} \\
\Ha^{(1)}_\nu(r)\sim r^{-\nu}\sum_{j=0}^{\nu-1} b'_j(\nu)r^{2j}+r^{\nu}\sum_{j=0}^\infty c'_j(\nu)r^{2j} +\log(r)
r^{\nu}\sum_{j=0}^\infty d_j'(\nu)r^{2j} \quad {\rm if \ }\nu\in \mathbb{N}
\end{gathered}\]
for some (explicit) constants $b_j(\nu),b_j'(\nu),c_j(\nu),c_j'(\nu),d'_j(\nu)$, where the $b_j$, $b_j'$ and $d_j'$ are pure imaginary.
Therefore we see from \eqref{bfo} that $G_{\mathrm{bf}_0}^{-2}$ has an expansion at $\mathrm{zf}$ of the form
\[G_{\mathrm{bf}_0}^{-2}\sim (rr') \sum_{j=0}^{\lfloor \nu_0 \rfloor} (rr')^j Q_{2j}(y,y', r/r')+ r^{2\nu_0 + 2} \log r Q'(y, y',r/r') +
O(r^{2\nu_0 + 2})
\]
where $Q_{2j}(y,y', r/r')$, $Q'$ are real conormal (to the diagonal) distributions on $\mathrm{bf}_0\cap\mathrm{zf}$ and $Q' = 0$ unless $\nu_0 \in \mathbb{N}$.
\end{comment}
We see from the expansion of modified Bessel functions $J_{\nu}(z)$ at $z=0$ and \eqref{sbfo}
that the imaginary part of $G_{\mathrm{bf}_0}^{-2}$ has index set $\mathcal{Z}$ at $\mathrm{zf}$
of the form $\mathcal{Z}=\cup_{\nu_j\leq \nu_0+1/2}(2\nu_j+2) \cup \mathcal{Z}'$ where $\mathcal{Z}'\geq 2\nu_0+3$ and has no log terms; in particular if
$\partial M=S^{n-1}$ and $V_0=0$, one has $\mathcal{Z}=n+\mathbb{N}_0$.
Similarly, we see from \eqref{srbo} and \eqref{slbo} that $G_{\mathrm{lb}_0}^{\nu_0 - 1}$ and $G_{\mathrm{rb}_0}^{\nu_0 - 1}$ have a real expansion at $\mathrm{zf}$ up to order $\nu_0 + 1$ and their imaginary part has index set at $\mathrm{zf}$ of the form $\mathcal{Y}=\cup_{\nu_j\leq \nu_0+1}(\nu_j+1)\cup \mathcal{Y}'$
where $\mathcal{Y}'\geq \nu_0+2$ is an index set with no log terms and $\mathcal{Y}=n/2+\mathbb{N}_0$ if $\partial M=S^{n-1}$ and $V_0=0$. Also, $G_{\mathrm{zf}}^0$ is real, and the higher order terms $G_{\mathrm{zf}}^\alpha$, for $\alpha > 0$, can be chosen arbitrarily provided that they are compatible with terms specified at $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{rb}_0$.
It follows that we may choose $G$ so that the expansion at $\mathrm{zf}$ is real up to order $\lambda^{2\nu_0}$ (in the sense that $\lambda^{2\nu_0}$ is the first non-real term occurring), actually with imaginary part having index set at $\mathrm{zf}$
of the form $X=\cup_{\nu_j\leq \nu_0+1/2}2\nu_0\cup \mathcal{X}'$ where $\mathcal{X}'\geq 2\nu_0+1$ has no log terms and
$\mathcal{X}=n-2+\mathbb{N}_0$ if $\partial M=S^{n-1}$ and $V_0=0$. We will choose $G$ so that its imaginary part has expansion at $\mathrm{zf}$
\begin{equation}\label{imG}
{\rm Im}(G)=\lambda^{2\nu_0}A(z,z')+O(\lambda^{\min(2\nu_0+2,2\nu_1)})
\end{equation}
for some smooth kernel $A$ on $\mathrm{zf}$ satisfying $PA=0$, which can be done as long as the expansion
matches with the imaginary parts of $G^{\nu_0-1}_{\mathrm{rb}_0},G^{\nu_0-1}_{\mathrm{lb}_0},G_{\mathrm{bf}_0}^{-2}$ at $\mathrm{rb}_0,\mathrm{lb}_0,\mathrm{bf}_0$.
To determine the kernel $A(z,z')$ on $\mathrm{zf}$, we note that the eigenvalue $\nu_0^2$ for
$\Delta_{\partial M} + V_0 + (n/2 - 1)^2$ is simple, and the eigenfunction does not change sign, so there is a unique positive normalized eigenfunction $W(y) |dh|^{1/2}$ for this eigenvalue. Therefore, using Melrose's b-calculus as outlined in \cite[Section 2.1]{GH1}, there is a unique half-density $\tilde w |dg_b|^{1/2}$ such that $P_b \tilde w = 0$ and $\tilde w(x, y) = x^{-\nu_0} W(y) + O(x^{-\nu_0 + \epsilon})$ as $x \to 0$ for some $\epsilon > 0$; moreover, this is the only solution to $P_b u = 0$ (up to scaling) in the space $x^{-\nu_0 - \epsilon} L^2_b$, if $\epsilon > 0$ is sufficiently small, and we have $v_0(z, y') = \tilde w(z) W(y)$. We then set
$$
A(z,z') = (xx')^{-1} \tilde w(z) \tilde w(z') |dg_b dg_b'|^{1/2}.
$$
and from the expansion of \eqref{sbfo}, \eqref{srbo}, \eqref{slbo} at $\mathrm{zf}$, we see that the expansion of $\lambda^{2\nu_0}A(z,z')$
matches with the asymptotic of \eqref{sbfo}, \eqref{srbo}, \eqref{slbo} at $\mathrm{zf}$. Moreover, if $\nu_1\geq \nu_0+1$,
the expansion of \eqref{sbfo}, \eqref{srbo}, \eqref{slbo} at $\mathrm{zf}$ involve no power of $\lambda$ between $\lambda^{2\nu_0}$ and
$\lambda^{\min(2\nu_0+2,2\nu_1)}$, therefore $G$ can be chosen so that ${\rm Im}(G)$ satisfies \eqref{imG}.
Since $P$ has real coefficients, the error term $E=(P-\lambda^2)G-\Id$ has the same property as $G$, i.e.\
it has a real expansion at $\mathrm{zf}$ in powers of $\lambda$ up to $\lambda^{2\nu_0}$, and since $PA=0$,
the expansion at $\mathrm{zf}$ of $(P-\lambda^2){\rm Im}(G)={\rm Im}(E)$ is actually of order $\min(2\nu_0+2,2\nu_1)$.
We next claim that the same is true for the powers $E^j$. To see this,
we use \eqref{Ejformulae} to show inductively that the expansion at $\mathrm{zf}$ is real to order $\min(2\nu_0+2,2\nu_1)$, since the terms at $\mathrm{lb}_0$ and $\mathrm{rb}_0$ do not affect the expansion at $\mathrm{zf}$ until order $2\nu_0 + 2$.
Since $S$ in \eqref{Sdefn} is given by a finite sum of the form $\sum_{j=1}^{2N} (-1)^j E^j$ up to a term that vanishes to high order $\sim N$ at $\mathrm{zf}$, the same property holds true for $S$. By the same arguments, $GE^j$ has a real kernel up to order $\min(2\nu_0+1,2\nu_1)$.
Finally we show, using exactly the same method as for the powers $E^j$, that the composition $GS$ has a real expansion at $\mathrm{zf}$ in powers of $\lambda$ up to $\lambda^{2\nu_0}$, and since $GS \sim G\sum_{j\geq 1}(-1)^jE^j$ (as an expansion at $\mathrm{zf}$), we see that the resolvent $R(\lambda)$ itself has the property that it has a real expansion at $\mathrm{zf}$ up to order $2\nu_0$ with the leading term of $dE_{P_+^{1/2}}(\lambda)$
given by (transforming back to the original scattering metric $g$)
\begin{equation}
(dE)_{\mathrm{zf}}^{2\nu_0+1} = w(z) w(z') |dg dg'|^{1/2},
\label{smzf}\end{equation}
where $w |dg|^{1/2} := x^{-1} \tilde w |dg_b|^{1/2}$ satisfies $P w = 0$, and $ w = x^{n/2 - 1 - \nu_0} W(y) + O(x^{n/2 - 1 - \nu_0 + \epsilon})$, $x \to 0.$ For example, if the potential function $V$ vanishes, then $W$ is constant, $\nu_0 = (n/2 - 1)$, and $ w$ is just a constant function.
Moreover the next asymptotic term in the expansion of $dE_{P_+^{1/2}}(\lambda)$ is at order $\min(2\nu_0+1,2\nu_1)$.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{mainsm}] Theorem~\ref{mainsm} follows directly from Theorem~\ref{mainres} and the cancellations proved in Section~\ref{behavdiag} and Proposition~\ref{cancellation}.
\end{proof}
\begin{comment}
\subsection{Leading asymptotics at $\mathrm{bf}_0, \mathrm{lb}_0, \mathrm{zf}$}
We conclude by giving the leading asymptotics of the spectral measure at the boundary hypersurfaces $\mathrm{bf}_0, \mathrm{lb}_0$ and $\mathrm{zf}$. At $\mathrm{bf}_0$ (and also at $\mathrm{lb}_0$) we have already determined the leading asymptotic of the outgoing resolvent --- see \eqref{resmodels}. Since the imaginary part of $i \Ha_{\nu}^{(1)}(r)$ is $J_{\nu}(r)$, we see from \eqref{smim} that the leading asymptotic of the spectral measure $dE_{P_+^{1/2}}(\lambda)$ at $\mathrm{bf}_0$ is at order $-1$, and is given by
\begin{equation}
S_{\mathrm{bf}_0}^{-1} = dE_{(\Pconic)^{1/2}}(1) =
r r' \sum_{j=0}^\infty\Pi_{E_j}(y,y')J_{\nu_j}(r)J_{\nu_j}(r') \left|\frac{dr \, dr'}{rr'}\right|^\frac{1}{2} .
\end{equation}
Similarly, at $\mathrm{lb}_0$, $2/\pi$ times the imaginary part of the resolvent kernel yields, as the leading asymptotic of the spectral measure at $\mathrm{lb}_0$,
\begin{equation}
S_{\mathrm{lb}_0}^{\nu_0} = (x' \rho)^{-1} v_0(y,z') J_{\nu_j}(1/\rho) \Big| \frac{d\rho dy}{\rho}dg'_b \Big|^{1/2},
\end{equation}
where $v_0$ is as in \eqref{vjdefn}.
The leading asymptotic $S_{\mathrm{zf}}^{2\nu_0+1}$ at $\mathrm{zf}$ satisfies
\begin{itemize}
\item
$(xx') S_{\mathrm{zf}}^{2\nu_0+1}$ is annihilated by $P_b$ in both the left or the right variables, and
\item
$S_{\mathrm{zf}}^{2\nu_0+1}$ matches with the asymptotics at $\mathrm{bf}_0$ and $\mathrm{lb}_0$ above.
\end{itemize}
To determine $S_{\mathrm{zf}}^{2\nu_0+1}$, we note that the eigenvalue $\nu_0^2$ for
$\Delta_{\partial M} + V_0 + (n/2 - 1)^2$ is simple, and the eigenfunction does not change sign, so there is a unique positive normalized eigenfunction $W(y) |dh|^{1/2}$ for this eigenvalue. Therefore, using Melrose's b-calculus as outlined in \cite[Section 2.1]{GH1}, there is a unique half-density $w |dg_b|^{1/2}$ such that $P_b w = 0$ and $w(x, y) = x^{-\nu_0} W(y) + O(x^{-\nu_0 + \epsilon})$ as $x \to 0$ for some $\epsilon > 0$; moreover, this is the only solution to $P_b u = 0$ (up to scaling) in the space $x^{-\nu_0 - \epsilon} L^2_b$, if $\epsilon > 0$ is sufficiently small, and we have $v_0(z, y') = w(z) W(y)$. It follows from this that $S_{\mathrm{zf}}^{2\nu_0+1}$ is determined uniquely by the two conditions above, and we have
$$
S_{\mathrm{zf}}^{2\nu_0+1} = (xx')^{-1} w(z) w(z') |dg_b dg_b'|^{1/2}.
$$
Transforming back to the original scattering metric $g$, we can write
\begin{equation}
S_{\mathrm{zf}}^{2\nu_0+1} = \tilde w(z) \tilde w(z') |dg dg'|^{1/2},
\label{smzf}\end{equation}
where $P \tilde w = 0$, and $\tilde w = x^{n/2 - 1 - \nu_0} W(y) + O(x^{n/2 - 1 - \nu_0 + \epsilon})$, $x \to 0.$ For example, if the potential function $V$ vanishes, then $W$ is constant, $\nu_0 = (n/2 - 1)$, and $\tilde w$ is just a constant function.
\end{comment}
\begin{proof}[Proof of Corollaries~\ref{cor:waves} and \ref{propagators}]
Using the spectral measure, we write
\begin{equation}
\operatorname{1\negthinspace l}_{(0, \infty)}(P) \chi(P)F_t(\sqrt{P})=\int_{\mathbb{R}^+} \chi(\lambda^2)F_t(\lambda)dE_{P_+^{1/2}}(\lambda)
\label{F_t(P)}\end{equation}
with $F_t(\lambda)=e^{it\lambda^2}$, $\cos(t\lambda)$ or $\sin(t\lambda)/\lambda$. Then the leading asymptotic of the kernel $\chi(P)F_t(\sqrt{P})(z,z')$
as $t\to \infty$ for $z,z'\in M^0$ is straightforward by using Theorem \ref{mainth}: the leading term
$\lambda^{2\nu_0+1} w(z) w(z')$ of $dE_{P_+^{1/2}}(\lambda)$ at $\lambda=0$
produces the leading term in \eqref{waveexp1} or \eqref{propexp} as $t\to \infty$, while the error $O(\lambda^{\min(2\nu_0+2,2\nu_1+1)}))$
contributes at most an error term in \eqref{waveexp1} or \eqref{propexp} as $t\to \infty$, by using the fact that $dE_{P_+^{1/2}}(\lambda;z,z')$ is smooth in $z,z'$ and
polyhomogeneous conormal at $\lambda=0$. Moreover,
putting $F_t(\lambda) = e^{-i\lambda t}$, and using \cite[Example 7.1.17]{Ho}, we find that
$$
\int_0^\infty \chi(\lambda) e^{\pm it\lambda} \lambda ^{2\nu_0 + 1} \, d\lambda = \Gamma(2\nu_0 + 2) e^{\pm i \pi (\nu_0 + 1)} t^{-2(\nu_0 + 1)} + O(t^{-\infty}), \quad t \to \infty,
$$
which gives the constants in \eqref{waveexp1}.
\end{proof}
\begin{remark}\label{manyends} If we do not assume that the boundary $\partial M$ is connected, then our analysis works much as above. However, if $\partial M$ has more than one component, the lowest eigenvalue $\nu_0$ of the operator $\Delta_{\partial M} + V_0 + (n/2 - 1)^2$ need not be simple, and the leading asymptotic $(dE)_{\mathrm{zf}}^{2\nu_0+1}$ would then have rank equal to the multiplicity of $\nu_0$. Similarly, the expansion \eqref{propexp} of the propagator as $t \to \infty$ would have rank equal to the multiplicity of $\nu_0$.
\end{remark}
\section{Index of Notation}
\begin{tabbing}
\bf{Notation} \hskip 25pt \= \bf{Description/definition of notation} \hskip 60pt \= \bf{Reference} \\
\> \> \\
$(M^\circ, g)$ \> asymptotically conic manifold \> Section~\ref{sect:Geometricsetting}\\
$M$ \> compactification of $M^\circ$ to manifold with boundary \> Section~\ref{sect:Geometricsetting} \\
$x$; $r$ \> $x$ is a boundary defining function on $M$, $x = 1/r$ \> Section~\ref{sect:Geometricsetting} \\
$g$ \> scattering metric on $M^\circ$ \> Section~\ref{sect:Geometricsetting} \\
$h(x)$ \> family of metrics on $\partial M$ \> Section~\ref{sect:Geometricsetting} \\
$V$ \> potential function on $M$ \> Section~\ref{sect:Geometricsetting} \\
$V_0$ \> leading asymptotic of $V$ at $\partial M$, equal to $x^{-2} V |_{\partial M}$ \> Section~\ref{sect:Geometricsetting} \\
$\Delta_g$ \> positive Laplacian on $(M, g)$ \> Section~\ref{sect:Geometricsetting} \\
$\Delta_{\partial M}$ \> positive Laplacian with respect to $h(0)$ on $L^2(\partial M)$ \> Section~\ref{sect:Geometricsetting} \\
$\nu_j^2$ \> eigenvalue of $\Delta_{\partial M} + (n-2)^2/4 + V_0$ on $L^2(\partial M)$ \> Section~\ref{sect:Geometricsetting} \\
$P$ \> $\Delta_g + V$ \> Section~\ref{sect:Geometricsetting} \\
$P_+$ \> positive spectral part of $P$, $\operatorname{1\negthinspace l}_{(0, \infty)}(P) \circ P$ \> Section~\ref{sect:Geometricsetting} \\
$R(\sigma)$ \> $(P - \sigma^2)^{-1}, \ \Im \sigma > 0$ \> Section~\ref{sect:Geometricsetting} \\
$R(\lambda + i0)$ \> boundary value of $R(\sigma)$ for $\Re \sigma = \lambda \in \RR$, $\Im \sigma \downarrow 0$ \> \\
$[X; Y]$ \> real blowup of a manifold with corners $X$ at $Y$ \> Section~\ref{5.1} \\
$\MMkb$ \> blowup of $[0,1] \times M \times M$ \> Section~\ref{5.1} \\
$\MMksc$ \> further blowup of $\MMkb$ \> Section~\ref{5.1} \\
$\mathrm{zf}$, $\mathrm{lb}$, $\mathrm{rb}$, $\mathrm{bf}$, \> boundary hypersurfaces of $\MMkb$ \> Section~\ref{5.1} \\
$\mathrm{lb}_0$, $\mathrm{rb}_0$, $\mathrm{bf}_0$ \> \> \\
$\Delta_{k,b}$ \> closed lifted diagonal in $\MMkb$ \> Section~\ref{5.1} \\
$E$, $\mathcal{E}$ \> index set, index family \> Section~\ref{sect:phg} \\
$E_1 + E_2$, $E_1 \extunion E_2$ \> \ \ Addition and extended union of index sets \> Section~\ref{sect:phg} \\
Integral, one-step \> \ \ Properties of index sets \> Section~\ref{sect:phg} \\
$\min E$ \> minimal exponent in an index set \> Section~\ref{sect:phg} \\
$\Vb(M), \Vsc(M)$ \> b-vector fields, resp. scattering vector fields on $M$ \> Section~\ref{sect:compcotbundle} \\
$\rho$ \> $x/\lambda$ \> Section~\ref{sect:compcotbundle} \\
$\mathcal{V}_{k,b}(\Mkb)$ \> certain Lie algebra of vector fields on $\Mkb$ \> Section~\ref{sect:compcotbundle} \\
$\mathcal{V}_{k,b}(\MMkb)$ \> analogous Lie algebra of vector fields of $\MMkb$ \> Section~\ref{sect:compcotbundle} \\
$\Tkb \Mkb$ \> compressed tangent bundle of $\Mkb$ \> Section~\ref{sect:compcotbundle} \\
$\Tkb \MMkb $ \> compressed tangent bundle of $\MMkb$ \> Section~\ref{sect:compcotbundle} \\
$\Tkbstar \Mkb $ \> compressed cotangent bundle of $\Mkb$ \> Section~\ref{sect:compcotbundle} \\
$\Tkbstar \MMkb $ \> compressed cotangent bundle of $\MMkb$ \> Section~\ref{sect:compcotbundle} \\
$\nu, \mu, \nu', \mu', T$ \> coordinates on the fibres of $\Tkbstar \MMkb$ \> Section~\ref{sect:compcotbundle} \\
$\Omegakb(\MMkb)$ \> compressed density bundle of $\MMkb$ \> Section~\ref{sect:densities} \\
$\sigma$ \> $x/x'$ \> Section~\ref{facs} \\
$Z_\bullet$ \> base of fibration on boundary hypersurface $\bullet $ of $\MMkb$ \> Section~\ref{facs} \\
$\Nsfstar Z_\bullet$ \> bundle over $Z_\bullet$, admitting contact structure \> Section~\ref{facs} \\
$L$, $\Lambda$ \> Legendre submanifold \> Section~\ref{sec:legsub} \\
$(\Lambda_0, \Lambda_1)$ \> intersecting pair of Legendre submanifolds \> Section~\ref{sec:legsub} \\
$(\Lambda, \Lambda^\sharp)$ \> conic Legendre pair \> Section~\ref{sec:legsub} \\
$\hat \Lambda$ \> blowup of $\Lambda$ to $[\Nscstar Z_{\mathrm{bf}}; \textrm{span} \Lambda^\sharp]$ \> \eqref{lambdah} \\
$\Nscstar \Diagb$ \> boundary of the conormal bundle to the diagonal \> Section~\ref{sec:legsub} \\
$\Lbf$ \> propagating Legendrian \> Section~\ref{sec:legsub} \\
$L^\sharp_\mp$ \> incoming/outgoing Legendrian \> Section~\ref{sec:legsub} \\
$\sigma_l(P - \lambda^2)$ \> symbol of $P - \lambda^2$ acting in the left factor \> Section~\ref{sec:legsub} \\
$\sigma_r(P - \lambda^2)$ \> symbol of $P - \lambda^2$ acting in the right factor \> Section~\ref{sec:legsub} \\
$V_l$ \> Hamilton vector field of $\sigma_l(P - \lambda^2)$ \> Section~\ref{sec:legsub} \\
$V_r$ \> Hamilton vector field of $\sigma_r(P - \lambda^2)$ \> Section~\ref{sec:legsub} \\
$ I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, \Lambda; \Omegakbh)$ \> \> \\ \> space of Legendre distributions
\> Defn~\ref{defn:legdist} \\
$ I^{m, r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, (\Lambda_0, \Lambda_+); \Omegakbh)$ \> \> \\ \> space of intersecting Legendre distributions \> Defn~\ref{defn:intlegdist} \\
$ I^{m, p; r_{\mathrm{lb}}, r_{\mathrm{rb}}; \mcA}(\MMkb, (\Lambda, \Lambda^\sharp); \Omegakbh)$ \> \> \\ \> space of distributions assoc. to Legendre conic pair \> Defn~\ref{defn:coniclegdist} \\
$S^{[m]}(\Lambda)$ \> line bundle over $\Lambda$ \> \eqref{S[m]defn} \\
$\mathcal{L}_{V_l}$ \> Lie derivative of $V_l$ on half-densities \> Section~\ref{sect:symbolcalc} \\
$g_{\conic}$ \> $dr^2 + r^2 h$ on $(0, \infty) \times Y$ \> Section~\ref{exactcone} \\
$P_{\conic}$ \> homogeneous Schr\"odinger operator on metric cone \> \eqref{conicSchr} \\
$P_{b, \conic}$ \> $r P_{\conic} r$ \> \eqref{Pb} \\
$\gcyl$; $|d\gcyl|$ \> $r^{-2} g_{\conic}$; $|dr/r dh|$ \> Section~\ref{exactcone} \\
$Z$ \> $(0, \infty) \times Y$ \> Section~\ref{sect:coniccomp} \\
$Z^2_b$ \> b-double space of $Z$ \> \eqref{Z2bdefn} \\
$Z^2_{b, \mathrm{sc}}$ \> further blowup of $Z^2_b$ \> \eqref{Z2bscdefn} \\
$g_b$; $|dg_b|$ \> $r^{-2} g$; $r^{-n} |dg|$ \> Section~\ref{sect:constructionGb} \\
$T_\bullet^k$ \> coefficient of $\lambda^k$ in expansion of $T$ at $\bullet$ \> Section~\ref{sect:constructionGb} \\
\end{tabbing}
| {
"redpajama_set_name": "RedPajamaArXiv"
} |
Shihan Lowe with over 35 years of martial art experience is certified in Dai-Lchi Karate-Do Int. He is licensed by the national Karate Federation, and with over 30 years of teaching experience he has had the pleasure of training national and international champions.
His self defense based classes, aid in weight reduction, offer cardio training, and improve daily energy levels. | {
"redpajama_set_name": "RedPajamaC4"
} |
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