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Why don't we have a marketplace?? changed brake pads and curious how to tell when my rim is worn out? If you had to choose - disc brakes or carbon fork? What happened to Belt Drive bikes? 4th of July commute/ride pics. Let's see them! onboard radar for you bike, - useful or not? How many "run-ins" do you have on your commute ? Let's get nekkid... and dirty. What do you like in your panniers/bags/etc? Wet Weather Bottom Bracket Suggestions Please! Thoughts on these Dimension wheels? Adjusting a S-A 5 speed ? Daily attack, direct hit to the head, recorded on camera!!!should I report it??? P Clips for Ortlieb QL3 Mounting Bracket? Is this a thing? New flat tire repair gizmo. Riser bar vs. drop bar width. How does yours compare if you ride both? Seatbags! Recommendations? Let's see 'em! Picking a bike -- 2 mile hilly commute. Heel strike with a 415 mm chainstay? D I need a trunk bag now? BEST HELMET FOR MASSIVE HEADS: Giro Venti or POC Crane Cycle Helmet / Any other? What do you like about commuting!?!?!?!?!? Looking For A New Frame - Fixed, Fenders, Rack - Suggestions Please! One Bike Fits All - CF or Aluminum? Commuting and Strava, do you remember to do it? Moving - time to start commuting!	{ "redpajama_set_name": "RedPajamaC4" }
Shadows of the Past by Louis Stout This 2006 publication by Louis Stout is the first of its kind: an historical overview of the Kentucky High School Athletic League (KHSAL) that covers the administrators, schools, coaches, and athletes that participated in the development of the association. KHSAL was formed in 1932 as an interscholastic athletics organization for the Negro schools of Kentucky. There were 69 member schools, and KHSAL remained active until 1958 when Kentucky schools and athletic associations began to desegregate. Basketball and football were recognized by KHSAL, though many of the schools had other athletic activities such as boxing and track and field. Fifty-two schools are highlighted in the book, with photographs and a brief history of the schools, teams, and coaches. A fair portion of the history and the photographs deal with the basketball teams. Athletes, Athletics Boxers, Boxing Grade Schools and High Schools in Kentucky NKAA Entry: Stout, Louis NKAA Entry: Thacker, Tom Porter NKAA Entry: Livisay, Charles H., Sr. "Shadows of the Past by Louis Stout," Notable Kentucky African Americans Database, accessed January 19, 2022, https://ukscrc001.net/nkaa/items/show/103.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Only the Freshest Offers. High Payouts. Dedicated AMs. That's what's up at Adtrafico. Aren't you guys the owners of Adfiro? The network Scammed me for 200$.. (2016-12-17, 09:23 PM)paradise Wrote: Aren't you guys the owners of Adfiro? The network Scammed me for 200$.. hi, paradise! we have no connections with this network. Adtrafico your name does look related can you prove you are nothing to do with them in order to give some trust to use that might be interested in joining? I was looking for a affiliate marketing network, will join soon. might join your network, please add payoneer payments too. Do you guys allow BH Niche?	{ "redpajama_set_name": "RedPajamaC4" }
Writing for Ad Age, 4As CEO Nancy Hill explains why the organization has formed a task force to tackle the thorny issue of media rebates. Speculation has fueled the debacle, according to Hill, but she sees an opportunity to revisit and define what transparency and trust means to the industry. "Our industry reflects many perspectives, and the task force will work to better communicate those views between agency and client," she writes. "We expect to issue new best practices and guidelines resulting from this work within the next few weeks." Read it. Innovid, an online video ad provider, has partnered with Roku to produce a new ad format for the OTT TV service. The ads have already rolled out on Crackle, CBS and VEVO's Roku channels, and they enable marketers to add quizzes, games and retail sales, as well as to connect with smartphones via SMS. Roku is using this new ad, which is exclusive to the platform and built directly into its software development kit, and a recent partnership with Nielsen to bring more precise analytics to its data science and advertising teams. TechCrunch has more. The NYT's Farhad Manjoo takes a deep dive on the Podcast boom and the ad biz that backs the medium. Podcast ads are effective, according to Ryan Stansky, marketing manager for Squarespace, which is one of the most prevalent podcast sponsors, but Stansky says that a lack of standards is fueling mistrust between advertisers and podcasters. "I've heard directly from sales reps in casual settings that [audience] numbers get lied about," he said. "To me, that's the most scary part of it all: that you're paying for something that you're not actually getting." Read more. In May, digital advertising and OOH drove 2% growth in the ad market, according to data from Standard Media Index. Last month, digital jumped 24% YoY, with nearly half of all digital budgets spent programmatically. "Digital continues to surge at the expense of other media," said SMI's chief commercial officer, James Fennessy. "Digital video continues to grow, and as audience measurement on mobile devices improves, we are confident that these gains will accelerate and positively impact the spend going to the major networks." Read the press release.	{ "redpajama_set_name": "RedPajamaC4" }
Diamondbacks' David Peralta proud he could reach 30-homer mark Diamondbacks left fielder David Peralta says his success is the result of hard work that traces back to his time in independent ball. Diamondbacks' David Peralta proud he could reach 30-homer mark Diamondbacks left fielder David Peralta says his success is the result of hard work that traces back to his time in independent ball. Check out this story on azcentral.com: https://azc.cc/2xYeU0G Sep 30, 2018; San Diego, CA, USA; San Diego Padres center fielder Manuel Margot (right) is tagged out by Arizona Diamondbacks catcher John Ryan Murphy (left) in the eighth inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Photos: Arizona Diamondbacks at San Diego Padres Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks center fielder A.J. Pollock (11) makes a play on a ball hit by San Diego Padres right fielder Franmil Reyes (not pictured) as second baseman Ketel Marte (4) and center fielder Socrates Brito (19) look on during the seventh inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks second baseman Ketel Marte (4) hits a solo home run during the fourth inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks second baseman Ketel Marte (4) gestures after hitting a solo home run during the fourth inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres shortstop Freddy Galvis (right) runs to score as Arizona Diamondbacks starting pitcher Robbie Ray (left) reacts in the fifth inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres shortstop Freddy Galvis (right) is congratulated by left fielder Hunter Renfroe (10) after scoring on a double by right fielder Franmil Reyes (not pictured) during the fifth inning against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks right fielder Socrates Brito (19) cannot make a play on an RBI double by San Diego Padres right fielder Franmil Reyes (not pictured) in the fifth inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres right fielder Franmil Reyes (32) watches his RBI double in the fifth inning against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres manager Andy Green (14) tosses sunflower seeds into his mouth in the sixth inning against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres starting pitcher Joey Lucchesi (37) pitches during the first inning against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres bench coach Mark McGwire (25) looks on before a game against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks starting pitcher Robbie Ray (38) pitches against the San Diego Padres during the first inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; Arizona Diamondbacks starting pitcher Robbie Ray (center) reacts after giving up a solo home run to San Diego Padres center fielder Manuel Margot (background, left) during the second inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres center fielder Manuel Margot (center) is congratulated after hitting a solo home run during the second inning against the Arizona Diamondbacks at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; The Arizona Diamondbacks celebrate a 5-4 win over the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; Arizona Diamondbacks relief pitcher Yoshihisa Hirano (66) and catcher Alex Avila (5) celebrate a 5-4 win over the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; Arizona Diamondbacks center fielder Socrates Brito (19) makes a play on a ball hit by San Diego Padres shortstop Freddy Galvis (not pictured) during the seventh inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; Arizona Diamondbacks center fielder Socrates Brito (center) scores on a wild pitch in the second inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; Arizona Diamondbacks starting pitcher Zack Godley (52) pitches during the first inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 29, 2018; San Diego, CA, USA; Arizona Diamondbacks catcher Alex Avila (5) hits an RBI single in the second inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth, Jake Roth-USA TODAY Sports Sep 28, 2018: Arizona Diamondbacks left fielder David Peralta (6) singles during the sixth inning against the San Diego Padres at Petco Park. Jake Roth/USA TODAY Sports Sep 28, 2018: San Diego Padres right fielder Franmil Reyes (32) singles in the fourth inning against the Arizona Diamondbacks at Petco Park. Jake Roth/USA TODAY Sports Sep 28, 2018: San Diego Padres shortstop Freddy Galvis (right) follows through on a throw to first to complete the double play on a ball hit by Arizona Diamondbacks shortstop Nick Ahmed (not pictured) after forcing out left fielder David Peralta (6) in the sixth inning at Petco Park. Jake Roth/USA TODAY Sports San Diego Padres third baseman Wil Myers, right, misses the catch on a pop bunt by Arizona Diamondbacks' Patrick Corbin as catcher Francisco Mejia (27) watches during the second inning of a baseball game Friday, Sept. 28, 2018, in San Diego. A runner was forced at third, and Corbin was safe. Gregory Bull/AP Two fans sit in otherwise empty stands as the San Diego Padres play the Arizona Diamondbacks in a baseball game Friday, Sept. 28, 2018, in San Diego. (AP Photo/Gregory Bull) Gregory Bull/AP Arizona Diamondbacks' John Ryan Murphy, below, is tagged out at home by San Diego Padres catcher Francisco Mejia on a ball hit by Eduardo Escobar during the seventh inning of a baseball game Friday, Sept. 28, 2018, in San Diego. (AP Photo/Gregory Bull) Gregory Bull/AP Sep 28, 2018: Arizona Diamondbacks shortstop Nick Ahmed (13) reacts after striking out in the first inning against the San Diego Padres at Petco Park. Jake Roth/USA TODAY Sports Sep 28, 2018; San Diego, CA, USA; Arizona Diamondbacks starting pitcher Patrick Corbin (46) pitches during the first inning against the San Diego Padres at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Jake Roth/USA TODAY Sports Sep 28, 2018: San Diego Padres starting pitcher Eric Lauer (46) pitches during the first inning against the Arizona Diamondbacks at Petco Park. Jake Roth/USA TODAY Sports Sep 30, 2018; San Diego, CA, USA; San Diego Padres center fielder Manuel Margot (right) is tagged out by Arizona Diamondbacks catcher John Ryan Murphy (left) in the eighth inning at Petco Park. Mandatory Credit: Jake Roth-USA TODAY Sports Nick Piecoro, Arizona Republic Published 8:23 p.m. MT Sept. 28, 2018 Sep 25, 2018: Arizona Diamondbacks outfielder David Peralta hits a two run double against the Los Angeles Dodgers in the sixth inning at Chase Field.(Photo: Mark J. Rebilas/USA TODAY Sports) SAN DIEGO – If the question is about his season as an individual, David Peralta is content. He swells with pride at his home-run total and his RBIs. He likes how his swing turned out after making adjustments in the winter. He is pleased where his career has taken him after toiling in obscurity for years. "I think it's from all the hard work I've been putting forward," Peralta said. "It's not just since the offseason, but since I started playing independent ball. It's paying off right now, being healthy. All the time that it took away from my family to work hard and be where I am right now. It's paying off and it's really good satisfaction for me and my family. I'm really proud of that." Peralta, who played parts of three seasons in independent ball before signing a minor-league deal with the Diamondbacks in 2013, hit his 30th home run of the season on Wednesday, blowing his previous career-high of 17, set in 2015, out of the water. He also has set a personal best with 87 RBIs. The mention of his home-run total makes his eyes grow wide. "Wow," he said. "For me, I never thought I was going to do it, but I also never doubted that I could do it. It just happened. When I started the season, my goal was 20. Then when I reached that mark, I was like, yeah, why not? I didn't want to put it in my head to put pressure on myself, I just let it happen." Increasing his power production was part of the reason Peralta made an adjustment with his swing in the offseason, a change that involved lowering his hands in his setup. He thought he was hitting too many balls hard but on the ground, and, like many modern hitters, tried to change the angle of his swing to create more loft. "The adjustment was to eliminate movement and keep things more simple," he said. "It's working for me." Peralta wanted to make the All-Star team this year. He also wanted to win a championship. He said both goals remain as he enters the offseason. "I want to be a World Series champion," he said. "I'm not going to rest until it happens. It didn't happen this year, but we're going to work hard to be better next year." Rest fast Diamondbacks quality control/catching coach Robby Hammock won't have much downtime this offseason before he has to get back to work. Hammock will be managing the Tigres del Licey of the Dominican Winter League. He reports in early October. Licey is considered one of the top clubs in the league, a club with a storied history that's often regarded as the New York Yankees of the Dominican. "It's a good opportunity," Hammock said. "It's definitely good to have on the resume, but at the same time when I went over there as a player (in 2006), I always wanted to have a chance to go back." Hammock goes there knowing he has the support of his general manager. Licey's GM is Luis Urueta, who also is a coach on the Diamondbacks' major-league staff. They'll be bringing Alex Cultice, a coaching assistant for the Diamondbacks, with them this winter. "This will be his first season as a GM," Hammock said of Urueta. "He's rolling the dice, too, with selecting me as the manager. And with Cultice coming down, they're bringing a new vibe from what teams have had in the past as far as really ramping up the analytical usage." Hammock managed for four years in the Diamondbacks' system before joining the big-league staff prior to last season. Short hop Right-hander Shelby Miller, who is hoping to return from the disabled list this weekend, has been dealing with a stiff neck in recent days, manager Torey Lovullo said, but the club is still hopeful he can pitch in relief on Saturday or Sunday. "I think from his standpoint," Lovullo said, "(making a relief appearance would give him) the knowledge that he got back into a game and can go into the offseason knowing that everything felt good and say that there's a full recovery and he can be ready for 2019. We're not going to force it just to say he got back in a game. If it works, it works." Disappointing Diamondbacks' decision: Rebuild, or take one more shot Diamondbacks' decline raises questions about Paul Goldschmidt's future Reach Piecoro at (602) 444-8680 or [email protected]. Follow him on Twitter @nickpiecoro. Russell Westbrook trade: Suns fans sound off on Thunder point guard's fit Zack Greinke trade rumors: Diamondbacks to deal ace before MLB trade deadline? A new arena is important, but Coyotes have prioritized winning this summer There's a trick to keeping the NHL in Arizona, and it all starts with the ice Russell Westbrook trade rumors: What the Suns could offer the Thunder Buy? Sell? 'Complicated decision' await Diamondbacks as trade deadline looms	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
← Backseat seatbelts a farce??!! I received this platinum credit card in the mail today, apparently an upgrade. But I fail to understand why I am supposedly given this "privilege". It's not like I need it. It's not like I'm spending millions or thousands of ringgit every month. It's not like I'm raking up a lot of interest too, since I pay my credit card bills in full every month. So is the bank opening up a brand new market for SAHMs with platinum credit cards? The inevitable call or not? 5 Responses to Why are they doing this to me? I think the platinum card of today is like the gold card of yesterday… they have probably lowered the 'qualification' to get more users on a higher credit limit, hoping that some of them will generate revenue for them! I have received 3 of such cards from Citibank… I never activated mine and they are still sending. The Giddy Tigress says: I guess they are just persistent eh?	{ "redpajama_set_name": "RedPajamaC4" }
Q: Run script in sleep mode I thought scripts in /lib/systemd/system-sleep/ were run when computer resumes from a sleep state. (Pushing the sleep button on my computer.) Everything works except the cvlc line. #!/bin/sh if [ "${1}" == "pre" ]; then # Do the thing you want before suspend here, e.g.: echo "we are suspending at $(date)..." > /tmp/systemd_suspend_test cvlc --play-and-exit /usr/share/sounds/My_Sounds/Short_doorbell.wav elif [ "${1}" == "post" ]; then # Do the thing you want after resume here, e.g.: echo "...and we are back from $(date)" >> /tmp/systemd_suspend_test cvlc --play-and-exit /usr/share/sounds/My_Sounds/Short_doorbell.wav fi I think I found a clue in my journal. Sep 10 06:36:12 7 systemd-sleep[8316]: VLC is not supposed to be run as root. Sorry. Sep 10 06:36:12 7 systemd-sleep[8316]: If you need to use real-time priorities and/or privileged TCP ports Sep 10 06:36:12 7 systemd-sleep[8316]: you can use /usr/bin/vlc-wrapper (make sure it is Set-UID root and	{ "redpajama_set_name": "RedPajamaStackExchange" }
Greetings, lovelies! Happy time of red noses, frozen car doors, and season's greetings, in my area of the world at any rate! I have been lax in posting due to general being busy with various Very Important Things, one of … Continue reading Cupcake Extravaganza!	{ "redpajama_set_name": "RedPajamaC4" }
HISTORY: In 2015 Vestry wanted to pilot a bible study. It was suggested that this should include supper and fellowship as well as study. To make it more accessible and offer something that would be a short-term commitment, we thought a 5-6 week course would be best. We scheduled this for October and November, which has worked well as a link between the end of summer and before the Advent season, which tends to be busy. Apart from mid-term breaks this has proved to be a good time of year for most. The course has been well supported by both congregations and we have also been able to offer spaces for others. We have numbered from 28 to 17 during the weeks of the course and folk have been welcome to dip in and out, though most have managed at least 2/3rds of the course. Participants have included some members of Space and South Kirk, as well as St Mungo's Penicuik, and P&G's in Edinburgh. Thanks also to all who provided food and practical help. It has been a good exercise in working together and getting to know each other. CURRENT: The last version of the course was held for Lent 2018. However, with the departure of our Rector, Reverend Lynsay, the Last Supper Club as a bible study course and growing together opportunity is currently in abeyance. Hopefully an equally successful course will be re-established in the not-too-distant future.	{ "redpajama_set_name": "RedPajamaC4" }
Hello Ladies! I'm writing this article only for my own gender... LADIES!!! According to my opinion, fashion is meant for both men and women. But being a lady, I'm more attracted towards ladies fashion. Fashion keeps on changing according to the changing world. Fashion in early 70s and 80s have now risen up again in the present scenario making slight changes in style. I love fashion since my childhood and I prefer wearing both traditional and modern dresses. In the modern society, dresses are categorized into various types according to occasions and seasons. There are party wear dresses which can be worn during parties. Casual dresses can be used as everyday outfits. For winter seasons, sweater dresses plays a good role. Sweater dresses can be matched with a pair of boots which will protect our legs from cold. Maxi dresses are long gowns which looks like maxis. Sheath dresses, shirt dresses, midi dresses, etc are the other different types of dresses available in market today. In online markets like Myntra, Limeroad, etc, dresses are classified in this way so that it is quite easier for customers to choose their dresses according to their needs and interests. Earrings, necklaces, long chains, anklets and bangles have also come up in different styles which can be matched up with dresses based on the style. We can create style on our own. There are no strict rules and regulations in fashion that we should follow. Fashion designers are just planning innovative ideas and implementing the designs came up from their creative minds. Now lets move forward to the trends being followed in skirts. Long skirts, midi skirts and short skirts are the variety of skirts now available in markets. Knee length shorts, hot shorts are the variety of shorts which we get in market today. What about Pants?? Nowadays pants are available as formal pants, cigarette pants, half pants, three fourth pants, palazzos and culottes. Crop tops are the latest trend in fashion being come up among tops. A round cut out at the sleeves of tops and dresses is another latest trend being followed by our bubbly youngsters. The latest comfortable outfit among denim is the most popular one, that is nothing other than jeggings. The material of this outfit is denim but not as thick as of the material of jeans. The difference between jeans and jeggings is that the former has belt loop at the waist, but the latter does not have a loop, instead it has an elastic band inserted into the waist making us more comfortable to wear. Jeggings are tighter than jeans and it is strechable too. Treggings are the tighter version of track pants which has come up recently. Leggings are the first come up comfy pant version. Jeggings and treggings came up after leggings. All these "EGGINGS" came up only for for one reason, that is to serve for the purpose of comfort. So ladies, I hope that you got an idea about the latest trends in fashion from this article, in which I have tried to put whatever I know about today's trends. Whatever ideas we have about fashion, we should try to make it practical in ourselves and live in our own style which makes our personality unique. So ladies be fashionable and enjoy your life in this lovely world of FASHION!	{ "redpajama_set_name": "RedPajamaC4" }
Eckankar of Vermont hosts free events across the state where people of all faiths, traditions and walks of life can come together to explore our questions and share our insights. Here is a chance to meet with others who are spiritually minded. You can try spiritual exercises to open your dreams, your past lives and your own, innate, divine inner guidance. These simple spiritual techniques can help us to meet each day more fully and learn more about who we truly are. If you are interested, you can learn more about the teachings of Eckankar. You may discover that Eckankar offers the spiritual adventure of a lifetime. Check below to see the many Eckankar events across the state.	{ "redpajama_set_name": "RedPajamaC4" }
Q: Telethon cannot forward message even "sensitive_enabled" is disabled I'm using Telethon to forward messages from A group to B channel. But some of the documents were not able to be forwarded with the following log: restriction_reason=[ RestrictionReason(platform='ios', reason='porn', text="This message couldn't be displayed on your device because it contains pornographic materials.") ] So I use functions.account.GetContentSettingsRequest() to check my setting and here is the result: ContentSettings(sensitive_enabled=False, sensitive_can_change=True) I looks like the sensitive content lock has been disabled, but how can I still get this restriction message? Does someone encounter the same problem? A: Other than the settings for sensitive content, Telegram abides by local laws as well. So if your number belongs to a country or area that forbids porn content, Telegram will block such content for your account. Also any channels or groups created by that number and publishing illegal content will be closed. So if you're forwarding a message that is known as a porn content to a destination account with a number belonging to an area with laws against porn, that message won't be shown for that destination.	{ "redpajama_set_name": "RedPajamaStackExchange" }
Warm-Up How often do you make phone calls in English? Have you ever been misunderstood on the phone? What happened? Have you ever had to cancel or change an arrangement? Explain what happened. Useful Language Making Arrangements Could we meet on Tuesday at 11 a.m.? How/what about September 13th? Is 7 a.m. convenient for you? Changing Arrangements I'm afraid I can't make it on Friday. Are you available at another time? I'm afraid something has come up. Could we reschedule? I'm sorry, but I have to cancel our meeting.	{ "redpajama_set_name": "RedPajamaGithub" }
tv All In With Chris Hayes MSNBC September 3, 2013 5:00pm-6:01pm PDT hours of our attack on syria? we watch obama challenge a congress that doesn't like him to do something it doesn't want to do. this, my friends, is a tough one, don't you think? that's "hardball" for now. thanks for being with us. "all in with chris hayes" starts right now. good evening from washington, d.c. i'm chris hayes. tonight on "all in," the cont t contested case for war in syria as the secretaries of state and defense face the foreign relations committee. they find a senate much like the country divided across unlikely lines. we will debate it all here coming up. also tonight, president obama is heading to russia. who he is going to meet with may completely surprise you. surprised me. we're going to talk about it. plus, we're not sure where exactly mitch mcconnell stands on the proposed syria situation, but we know where he is on women's issues. he's for them. just as long as you don't pay attention to his record. the all new mitch mcconnell, later in the show. but we begin tonight with a remarkable and dramatic day in the nation's capital. less than one week before congress officially reconvened, a senate hearing on a u.s. military strike against syria on which secretary of state john kerry offered dire, some might say hyperbolic, warnings of the consequences of inaction. >> the opportunity for other dictators and/or terrorists to pursue their own weapons of mass destruction including nuclear weapons. i will tell you there are some people hoping that the united states congress doesn't vote for this very limited request the president has put before you. iran is hoping you look the other way. >> that was just one small part of a day in which the political machinery in support of a military strike was on full display. this morning president obama held a private meeting with congressional leaders and used the opportunity to try to reassure a wary public. >> military plan that has been developed by our joint chiefs and that i believe is appropriate is proportional. it is limited. it does not involve boots on the ground. this is not iraq, and this is not afghanistan. >> immediately after that private meeting, house speaker john boehner and democratic leader nancy pelosi were quick to announce their support of war authorization. >> the use of these weapons had to be responded to, and only the united states has the capability and the capacity to stop assad and to warn others around the world that this type of behavior is not going to be tolerated. i'm going to support the president's call for action. i believe my colleagues should support this call for action. >> president obama did not draw the red line. humanity drew it decades ago. 170-some countries. so it is really something that from a humanitarian standpoint cannot be ignored or else we cannot say never again. >> senate minority leader mitch mcconnell reserved judgment and there's certainly no consensus yet among either party about the use of force. and in that senate foreign relations hearing today, a democrat, senator robert m menend menendez, asked if a prohibition of ground troops in the congressional authorization would be something the administration could accept. >> in the event syria imploded, for instance, or in the event there was a threat of a chemical weapons cache falling into the hands of al nusra or someone else, i don't want to take off the table an option that might or might not be available to the president of the united states to secure our country. >> later in the same hearing, secretary kerry back tracked on whether such a limiting resolution would be a deal breaker for the white house. >> i don't want anybody misinterpreting this from earlier. this authorization does not contemplate and should not have any allowance for any troop on the ground. i just want to make that absolutely clear. you know, what i was doing was hypothesizing about a potential it might occur at some point in time, but not in this authorization in no way, be crystal clear, there's no problem in our having the language that has zero capacity for american troops on the ground within the authorization the president is asking for. >> it's no wonder secretary kerry tried to clarify that hypothetical situation. the public is strongly opposed to u.s. military action even in the event of a determination of the use of chemical weapons by syria. according to the latest poll, this is nearly reverse the findings of a december poll showing public support. in other words, as the idea of military action against syria has become less abstract, the public seems to be less supportive. it is also notable that today in a press conference in new york, the u.n. secretary general ban ki-moon essentially said a u.s. strike under these circumstances without u.n. approval would be illegal. >> the use of force is lawful only when an exercise of self-defense in accordance with article 51 of the united nations charter and/or when the security council approves such action. >> all of this as president obama is set to depart within the hour en route to stockholm before the g-20 summit. joining me now is senator jim rich, republican from idaho, a member of senate foreign relations committee. he considers himself extremely reluctant to authorize a strike on ssyria. senator, anything you heard today in testimony change your mind? >> well, not really. i want to keep an open mind on this. i wanted to let the administration make the best case it can for it. i thought senator kerry gave an excellent speech today, but i still have difficulties with it for reasons i'm sure we'll talk about here in a minute. >> do you agree with secretary of state john kerry and the president and all we've heard from the white house that the president has the authority, legally, constitutionally to do this even without congressional approval? >> i do not agree with that, and not only that, i'm not alone up here, and it's bipartisan. the democrats, a lot of them are of the same frame of mind. if you read the constitution, it's absolutely clear that the war-making power is vested in the first branch of government, not in the executive branch. indeed, james madison in the federalist papers said over and over again that the branch most likely to make war was the executive branch, and therefore, the founding fathers put that in the hands of people in the first branch of government. >> do you believe in a counterfactual universe in which we're discussing a republican president, mitt romney, that you would have the same reluctance? >> well, if it -- are you talking about his compliance with the constitution or talking about the actual attack on syria? >> i'm talking about both the constitutional position that this -- >> the answer would be -- >> -- has to come through article 1 the actual substance of the matter. >> the answer would be yeses as to both of those. i would counsel president romney that he shouldn't do it in violation of the constitution, and secondly, i would counsel him that he would have to have better answers than what this administration has as far as making justifications. and more importantly, to me, where we're going with this, what does success look like? what does day two, three and four look like? how are you going to deal with the fallout assuming russia reacts adversely, which we know they will to some degree or another, and depending how they would react if hezbollah reacted adversely, which we know they will. they're already fighting on behalf of assad in syria. >> can you imagine a future situation in which some scale of chemical weapons attack from the assad regime, if we stipulate for the moment that they were responsible, as the evidence suggests, can you imagine a scale of chemical attack over which point you would feel the u.s. is actually compelled to act? >> absolutely. i think if they use chemical against any american, against any american interest, against any american ally. let me be clear, they are a neighbor to israel. we have treaties with israel. they require the defense. i would be all in. as far as within the country, everybody knows that this isn't the first time that assad has used gas against his own people. indeed, saddam hussein used it against his own people, and so i can envision a point where there was a catastrophic use that would engage us. you know, the other thing that's overlooked here, he's already killed 100,000 people with conventional weapons. you know, that is bad. and, again, i don't want to deminimize what this man's done. he's done awful, awful terrible things. and so, you know, i don't want to deminimize that. on the other hand, i do not buy on to the theory that this is in -- that this is a national security matter for the united states. indeed, and i'm certainly not advocating this, but indeed, if we go in and bomb a few facilities then walk away, i'm not so sure that we've taught anybody a lesson. >> senator jim risch, republican from idaho. thank you so much for time, sir. >> thank you. >> i should clarify the 100,000 number is the total estimated death toll in the civil war on both sides as of now. we do not know how that's apportioned by by the assad regime and the rebels. joining me, gerry connolly of virginia. he's drafting the house democrats resolution that would put strict limits on a syria attra attack. how does it differ from the proposed draft language that was sent over by the white house? >> radically. first of all, it puts a time limit on when this authority can be used. it strictly limits it to a military targeting in response to this heinous crime. the chemical attack on citizens in the damascus suburbs. it also codifies in the resolution that we preclude boots on the ground. so that debate you were looking at just a little bit earlier is addressed in our resolution. >> let's say that the -- this resolution were to pass which i think is probably very much up in the air, am i right, you do not know whether this is going to have the votes in the house. >> the reason we drafted this resolution was to try to find a path toward acting in the narrow way constructed by the president, himself. the white house resolution that was submitted to the congress is overly broad, in my opinion, cannot pass the house. i personally would not support it. >> you would not support the white house's resolution. you are obviously supporting this since you helped draft it. let's say that this were to pass and the white house were to engage in the kind of strike that is kind of foreseen in the draft language here. what do you say to people that say, okay, so then what? >> well, the question in front of us is, is the evidence convincing? i believe it is. >> is the evidence -- let's be very clear on what it is. is the evidence clear that the assad regime actually launched this chemical weapons, killed -- >> to suggest the rebels did that is absurd. they have no such capability. it was clearly done by the assad regime. i believe intelligence corroborates that. the intelligence is fairly convinc convinces. what is the remedy? people of good conscience on both sides of the aisle are wrestling with that. some prefer to do nothing. my concern is the legacy of that is very dangerous. >> can i give a counterexample? senator john kerry invoked the legacy question. it was a big part of the argument. saddam hussein used chemical weapons in two different uses. both against the kurds to put down a domestic insurgency against the kurds and also in his war with iran. now, he was never punished with that in the way we're talking about punishing assad. yet no other leader used these kind of weapons until assad did which would suggest to me that it's possible that it's really only extreme circumstances that led to the use rather than this punitively established international norm. >> by in large for the last 90 or 100 years, these weapons have not been used except in the iran/iraq war and by saddam hussein. i happen to be on the senate foreign relations committee staff when that happened. we tried to get the evidence and tried to get the administration at that time to take that action seriously. we failed eed on that effort. it's not that it wasn't noted and it wasn't that there weren't voices urging action at that time. >> empb in the absence of that action, my point being, as a historical matter, in the absence of that action, it was not the case that failure to act in a punitive way after that opened the flood gates on the use of chemical weapons. >> very little attention was brought to it at the time. that's not the case here. the whole world is watching now. including bad actors in the region. and including north korea and iran. >> so the argument is the heightened scrutiny of the international community on this occasion means the stakes are higher if there is no action. that's your argument. >> i believe that is an argument and a fairly compelling one. i also believe international law is fairly clear in outlawing the use of these weapons. >> are you going to get a majority of democrats to vote for this resolution? >> i have no idea. we're -- chris van hollen and i collaborated on writing this very excruciatingly, narrowly drafted to try to allow the president to have the authority he's seeking and codify what the president, himself, said is limited in terms of this action. it isn't designed to be an all-comprehensive approach to syria or the syrian crisis. it's designed to address this tragic event with this remedy on a limited basis. >> congressman gerry connolly, democrat from virginia. >> thank you, chris, for having me. >> joining me, director of the middle east studies program at george mason university. he's a scholar who specializes in syria. he opposes u.s. military intervention there. and professor, my first question to you is, the argument being made largely by john kerry and the administration is on the grounds of a humanitarian case. essentially enforcing this international norm against the use of weapons that are as ghastly as the ones we see deployed here. why do you not think it's a good idea for the united states to engage in military action to enforce that norm? >> well, first of all, to push for this argument on humanitarian level is actually quite ridiculous, considering what has taken place in the region under our nose and our spore and continues to take place in the region with the support of the united states, of various dictatorships and support of settler colonial state of israel and various other forms. what needs to be discussed right now is something a lot more serious than the debate suggests. >> let me interrupt. we have very similar views on american foreign policy. it also seems to be like a little bit of hiding the ball to talk in those circumstances. whatever the sins of the american government and its participation in the region, which i'm sure you could spend a lot of time listing, many of which i would agree with you on, that does not necessarily, right, in an operational, moral or legal sense, take away from the possibility that it would be actually beneficial to the international world order or to syrians for the u.s. to get involved? >> okay. i mean, this is what i'm trying to get to, the devil's advocate argument. the debate right now centers around the idea that taking action is less risky than not taking action. this way of framing the debate is actually extremely problematic and off.ways, firsts eliminates the possibility that there is another action. it absolves the u.s. from taking another action or another choice because the debate is being framed as action versus inaction. no, there is another course of action, and that is as we have been listening to many people saying, i've been saying several times on various media, that there is a solution to the conflict as much as we think it is difficult, the united states and russia can come together and compel all parties to the conflict that the united states and russia will actually potentially come to a table and create the opportunity or the circumstances for the transition, because let me just say this, because what we are not paying attention to is that a limited strike, first of all, will not be effective. second of all, it will make the conflict more volatile, and third of all, foreclose any possibility of a solution down the road. it's basically eliminating that possibility for the sake of very limited gains that can spin out of control and bring the entire region into this conflict. >> bassam haddad, from george mason university. thank you for your time tonight. i really appreciate it. coming up later in the show, a debate over whether we should two to war in syria. my panel will include former white house aide involved in the strategy session today to help the president get the votes he needs, and the president's trip to russia which will include what is sure to be an excruciatingly awkward encounter with one vladimir putin. that's ahead. senator mitch mcconnell is hoping you'll forget he voted down the violence against women act three times. now that he's telling voters he actually co-sponsored it. that story is coming up. from 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(announcer) take their taste buds for a little spin told you i'd get half. with more than 50 delicious flavors. friskies. feed the senses. in just minutes, president obama will board air force one and travel first to sweden, and then to st. petersburg, russia, for the g-20 summit. there he will almost certainly have the most tense encounter yet with russia president vladimir putin in their long and very tense history. the summit is expected to be dominated by the potential u.s. military strike on syria. pulten has dismissed the chemical attack on syrian civilians as work of the rebels telling reporters o saturday, "i am sure that it is a provocation of those who want to involve other countries in syrian conflict who want to get support from powerful participants of international activities, first of all the usa." h he continued saying "as for the position of our american colleagues, the evidence should be presented. if the evidence is not presented, there is no evidence." yesterday in a nod to the upcoming congressional vote authorizing u.s. military strikes in russia, putin proposed sending a delegation of russian lawmakers to lobby congress against military intervention in syria. president obama for his part is firing back at putin. the white house has now confirmed that obama will meet with lgbt and human rights activists during his trip to russia. a strong message of support for human rights and dignity, but also surprisingly bold diplomatic provocation coming after the president already canceled his scheduled one-on-one meeting with putin, the first time any such visit has been canceled since 1960. the meeting will come at the low point in u.s./russian relations in the obama era. putin fashions himself as the global foil for u.s. military intervention in syria, while there is growing international and domestic outrage at russia's embrace of anti-gay laws and persecution in the run-up to the winter olympics in sochi this winter. joining me, julia ioffe of the "new republic." "the new york times" had a big, long piece by peter baker on the front page today about the nature of this relationship, and the basic part of it was the relationship with medvedev was actually fairly good and there was a kind of thawing. there was a famous attempt at a reset. since putin's come back, it has gone from bad to worse. is it a question of the personalities or the leaders clashing, or is it the fact the two countries' interests are just determined to be in opposition to each other? >> i think it's the latter and because the times have changed, the world has changed. in the meantime, you've had the arab spring exploding on to the world stage and dominating america's attention as it tries to pivot away to asia. you have protests breaking out domestically in russia against putin's return to power. really if you go back, medvedev wasn't acting alone. when he talked to -- and you even saw this during the hot mike incident when he talked to obama, he would often say, i'll pass this on to my boss, and there were certain things -- >> just so people remember, this is the point at which the medvey to vladimir, a point obama made about having more latitude after the election. >> this happened all the time behind closed doors from what i heard. obama would ask medvedev if he could do something on x and he would say i'd love to but i'm on a short leash for my boss. the reset was enabled by putin having that interest, like he was interested in having a reset. what i think -- i think peter baker is one of the best journalists alive, but where i would disagree with him on, is i would go back even further. i think things started to sour with libya, and i think that's where medvedev started to lose his grip on power. >> you made this point in some of your writing that basically russia did something very novel in libya. it's very germane to what's mapening now. >> that's right. >> medvedev allowed the u.n. security council resolution to two forwa go forward. >> that's right. >> they feel like they got hoodwinked on that. >> that's right. they say they didn't anticipate the strikes would going on as long as they did, that they would be intensive. they certainly didn't anticipate gadhafi being killed in the brutal manner he was. putin was said to have been preoccupied about that, would keep obsessing on it in private meetings. you have to imagine he was kind of seeing all of this through a personal lens. and this was all happening while there were protests exploding -- >> of course now we're in the situation with syria. russia has quite famously blocked any u.n. security council action. even the most basic condemning of the human rights, you know, violations of the regime. very basic stuff. there's an anecdote in baker's story in which the firm time that the president's national security adviser goes to meet with putin, the first thing putin says to him is when are you going to start bombing syria? this was 18 months ago. you can imagine watching this unfold that from putin's perspective, this is playing out precisely what he thought the u.s. was about. >> that was actually right after gadhafi was killed. that was right after the nato bombing campaign in libya. this was already on his mind. there were protests happening in moscow. mike mcfall who had been one of obama's closest advisers arrived in moscow as the ambassador to russia and his specialty in akd academia had been color revoluti revolutions. it's like color to a vampire in moscow. >> color revolution as being the nonviolent uprisings we've seen across the world. the orange revolution in ukraine and places like that. this was seen as a provocation. in fact, the russian press went nuts at this ambassador showing up. >> you had pro-kremlin youth groups with flash mobs, zombies lying on the ground playing dead, saying they didn't want to be victims of american aggression like the libyans. it was crazy. they were following mike mcfall around moscow, showing up at his meetings and harassing him. it went up to the highest levels. >> julia ioffe, senior editor at the "new republic." thank you so much for your time. we will be right back with #click3. 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"scandal, caught playing iphone game at three hour senate hearing. worst of all i lost." he's on the verge of getting the war in the middle east he's wanted for the last five years. third awesomest thing on the interpret today, the return to mother russia for back to school twofer. buzz feed links to what can only be described as truly bizarre video of what appears to be the russian military performing a drill shooting blanks at the opening of a moscow school. if you listen closely, you can hear romstein playing in the background during the display. dark and disturbing showing. outdone by russian president vladimir putin's own bizarre display at a russian middle school classroom to commemorate back to school week. we'll let the folks at "russia today" describe what the russian president is drawing on the smartboard. >> mr. putin wasn't just doing that, he was also busy giving an artist lesson on the day as well on how to draw a cat from behind. >> how to draw a cat from behind. >> am i hearing you right? >> wyes, you are. >> given a tour of a russian middle school, putin showed the young teens how to draw the back end of a kitty. this is the actual finished product. putin asked the class if anyone could identify his drawing. when no one responded he told them they were all going to jail. he told them it was a cat's backside before exit stage left. it's not terrible. if putin wants to work on the front ends of household pets, i know a guy in texas who can hook him up. find all the links for tonight's #click3 on our website, allinwithchris.com. we'll be right back. ts to know if we can pick her up. yeah, we can make room. yeah. 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"the truth is, mcconnell did co-sponsor a version 20 years ago. that legislation died in committee and never got a vote. by the time the measure came up again in 1993, for real this time, mcconnell was no longer a co-sponsor and, in fact, voted against final passage of the bill. of course, mcconnell has had two decades to redeem himself on that no vote. yet earlier this very year, he voted against the legislation's reauthorization even though he knew it would pass by a wide bipartisan margin. aides say mcconnell voted for a, quote, stronger alternative to the bill. one that excluded protections for lesbians and gays, native americans and undocumented workers. of course, the violence against women act is just one example of mcconnell's hypocrisy. declaration for mcconnell's inner circle demonstrate -- one aide smopoke of the senator aft her son was diagnosed with cancer. he told her, stay home, focus on what's important. come back when you're ready. i've got your back. the same mcconnell voted against the leave act of 1993 which requires businesses to allow employees unpaid leave to deal with medical issues of their own family members. there's this testimonial from mcconnell's own wife who spoke about her husband, "fought for funding for breast cancer research as well as funding for expanded cancer screenings for underprivileged and underserved communities." yet, mcconnell, of course, is in favor of repealing obama care and he's given his blessing to the sequester. which has caused the state of kentucky to cut off cancer screenings to hundreds of low-income women. while mitch the man and mitch the policymaker stand in stark contrast, mitch the candidate's best strategy is to basically hope no one notices or cares about what he truly stands for. maybe he'll figure out the best way to win the support of women is to stand for policies that actually help him. though i don't think anyone should hold their breath. congress much like the country is divided on what to do about syria. we'll break down the issues with a panel including a former obama aide who was brought back to the white house to help the president make his case. next. sthma's under control. i don't miss out... you sat out most of our game yesterday! asthma doesn't affect my job... you were out sick last week. my asthma doesn't bother my family... you coughed all through our date night! i hardly use my rescue inhaler at all. what did you say? how about - every day? coping with asthma isn't controlling it. test your level of control at asthma.com, then talk to your doctor. there may be more you could do for your asthma. no two people have the same financial goals. pnc investments works with you to understand yours and helps plan for your retirement. talk to a pnc investments financial advisor today. ♪ still running in the morning? yeah. getting your vegetables every day? when i can. 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oh, you're real? you know i'm real! at discover, we're always here to talk. good, 'cause i don't have time for machines. some companies just don't appreciate the power of conversation! you know, i like you! i like you too! at discover, we treat you like you'd treat you. get the it card and talk to a real person. wit's hard to find contractors with the passion and the skill, and that's why we use angie's list. online or on the phone, we help you hire right the first time with honest reviews on over 720 local services. i want it done right. i don't want to have to worry about it or have to come back and redo it. with angie's list, i was able to turn my home into the home of my dreams. for over 18 years, we've helped people take care of the things that matter most. join today. i will seek authorization for the use of force from the american people's representatives in congress. over the last several days, we've heard from members of congress who want their voices to be heard. i absolutely agree. >> the president said on saturday he would go to congress to decide whether to execute a punitive strike against syria. he immediately stepped into uncharted territory. space where liberal and conservative lawmakers will line up on the same side in the normally divided house of representatives. it's already apparent a congressional vote on whether to strike syria will scramble traditional alliances in the house. one of the first hints of this came last week when 186 lawmakers including 50 democrats signed letters calling for the president to seek authorization for any military action. what we're seeing this week is a sharper bifurcation within both political parties. house speaker john boehner said today he would back the president on a congressional vote to authorize a strike against syria. so did congressman elliot engel, top democrat on the house foreign affairs committee who said if we didn't respond in kind, it would send a message to every despot, every thug you could commit war crimes and nothing is going happen. nancy pelosi made a similar pro-interventionist argument, herself. >> from the humanitarian standpoint cannot be ignored or else we cannot say never again. secondly, from a national security standpoint, we have to send a very clear message to those who have weapons of mass destruction, of any variety, that should forget about using them. >> on the anti-interventionist side, many members of congressional progressive caucus including the liberal congressman from florida, alan grayson, who launched a position against attacking seyria and opposes any military strike there. lining up alongside grayson, junior republican senator from the state of kentucky. >> i think it's a mistake to get involved in the syrian civil war, and what i would ask john kerry is, you know, he's famous for saying, you know, how can you ask a man to be a last one to die for a mistake? i would ask john kerry, how can you ask a man to be the first one to die for a mistake? >> paul's own views on this don't come as much of a surprise. what we will also see in this vote is the ongoing brawl inside the republican coalition over that party's foreign policy direction. and when watching the news today, each new position for or against the resolution from both democrats and republicans often came as a genuine surprise. citizens looking to their political leaders for direction are likely to find themselves profoundly contorted. joining me now is tommy vieator, former national security focus span in the obama administration, co-founder of fenway strategies. he was back in the white house today to help the president win support for intervention in syria. ben dominic, at think tank the heartland institute. he co-founded "red state" a conservative blog. eli lake, senior national security reporter from "newsweek" and the "daily beast." explain this to me. i found the moment in the hearing today that was most interesting was several senators saying, if you think you have the authority to do this without coming to congress, why are you coming to congress? and if the vote doesn't go your way, isn't this a preposterous bit of theater? >> i think the vote is going to go their way. i think that the president believes that this action will be stronger if it is a u.s. action that is supported by congress, supported by more of the american people and not just barack obama stepping out and taking a limited strike. >> let's be clear about supported by the american people. i mean, you know, the t.a.r.p. bailout vote a very famous example. this vote if and when it comes about, i think probably -- i don't see the polling on this turning around fast enough for the white house to get the votes. >> the american people don't support congress, either, we should stipulate. >> at all. no one supports anyone, tommy. that's the point. that's why it's impossible to wage wars under these conditions. no one has any credibility. there's a complete and total blanket crisis of authority. no one trusts anything after years of failure and misery and destruction. i'm sorry if i'm expounding here. it's true. people look at this entire thing and think, are you out of your mind? >> there is healthy skepticism after iraq about taking someone's word for it before we go to war. this is very different. this is a short, limited operation. we're talks a couple hundred cruise missilessyria. yes, there is the potential to get pulled into something longer. the white house has been very clear about what they want to scope this -- >> what do you say? >> love it or hate it, ousting assad has the searvirtue of bein idea. this is not an idea. lobbing a few missiles over there to a compact operation you're talking about. one the white house is already saying only will degrade the ability of assad to use weapons against his people, not eliminate it. em even in that sort of space, this represents something that's a much bigger ship you talked about in your book and other context. level of stress for american people and elites. that's what we're seeing played out here. it's being targeted by the president which is why he wants to spread the blame around a little bit and gets the republicans and congress to go along. >> he's also right to go to congress. whatever cynical reading you want to give him. >> i don't think he necessary needs to. it depends on the scope. >> you could actually do it if you had been attacked beforehand, you didn't need to go to congress to get approval. in this context, i think you need to go to congress. this is well beyond what reagan did in libya. >> do you agree with ben this is not even an idea? >> well, there's a reason why regime change is not on the table right now. martin dempsey in a letter in july to senator levin, chairman of the senate armed services committee, said very clearly, if the regime collapses and there's no viable opposition, those chemical weapons could get into the hands of al qaeda and that's really bad. so the satisfying option in the case of syria is probably a very dangerous option. but at the same time, i think obama's got a real problem right now. that is the rhetoric and the crime, the gassing of his own people, the moral obscenity and how we hear this administration, including the president describe what happened, does not meet the military action he's talking about. it is a redux of cruise missile diplomacy, the kind of thing clinton did in the 1990s without weapons inspectors. i'm saying there's a disconnect between the severity of what has just happened and the moral obscenity that just happened and what is actually being proposed militarily. >> so i thifg there'snk there's parts to this. this is the worst chemical attack in the 21st century. there's a set of laws preventing the use, production of these horrific weapons. now, president obama drew a red line and the international community drew a line in the sand with the chemical weapons convention a long time ago. congress ratified that. yes, this is standing up for an idea. the nonproliferation regime that's been critical to barack obama. >> hold that thought, hold that thought, hold that thought. we'll be right back. and apple crisp back for a limited time. see? 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[ crows ] now where's the snooze button? 20 years with the company.hool. thousands of presentations. and one hard earned partnership. it took a lot of work to get this far. so now i'm supposed to take a back seat when it comes to my investments? there's zero chance of that happening. avo: when you work with a schwab financial consultant, you'll get the guidance you need with the control you want. talk to us today. footage from just moments ago as the president boarded air force one. to embark to sweden then on to russia. the g-20 summit, we just mentioned, a little while later. what is sure to be very, very tense conversations with his russian counterpart vladimir putin. still with me, tommy vietor. ben dominic from the heartland institute. eli lake from "newsweek" and the "daily beast." this idea you've drawn international red line, there's this prohibition on the use of weapons. respond to the argument, i made an argument earlier in the show, i still haven't heard anyone convince me. saddam hussein used the weapons twice notably against the kurds and iran/iraq war. there were no punitive missile strikes. it w it was ghastly, disgusting, horrible, evil action. there were no international sanctions for it. the u.s. government knew they had the weapons and basically looked the other way. no one used it until 30 years later -- >> you could argue those consequences. that was christopher hidgens' argument at the time. they used the run-up to war saying he's used these sorts of things. >> the idea that we're hearing from john kerry today in the senate foreign relations committee is that you will open the flood gates on use of these kinds of weapons and lord knows who else is assad is not punished here. what do you say to that historical precedence? >> i think in this instance there was a smaller use that eventually the community came out and said, he did that, and he ratcheted up diplomacy. they used rockets -- >> you're talking about assad. there's been an escalation. >> i think the sense is they drew this red line for assad in this instance. iran is watching. if they don't act now -- >> but the word that you used there is punish. this is the problem i have with this scenario. this is why it fails the just war test. have to have just cause, just authority, just result. i think in this case, it fails at least two of those and probably all three in the sense that you don't have -- you don't have the result being a protection for the people. i mean, the way i sort of view this -- >> wait a second. you do if the theory of the case here were to play out as they were saying. the theory of the case is that he's doing this because he's getting away with it. if we basically say, no, you can't do this, we degrade his actual operational capacity to do it and send this international message. that will protect -- >> i still think you're setting yourself up to fail. do or do not, there is no try in this scenario. >> the do in your scenario is a buffer zone or humanitarian court order which is isa ground invasion. >> i think you have to go in on the ground if your aim is -- >> let's be clear, no one is saying we're going to. >> zdestroy the runways. >> how confident are we? >> secure the chemical weapons? >> not secure them, degrade the capacity to deliver them. >> the u.s. military has a real capacity, the ability to deliver these weapons. not wipe out their existence. >> no, they're not going to secure the chemical weapons, themselves. the rokckets to deliver them, a lot of them are probably going to be degraded or blown up to use plain english. >> very quickly to you, eli. do you think this is a turning point in the internal politics of foreign policy in the republican party? because i think the majority of republicans are going to go vote against this. and it seems to me that the rand pauls, this will be the moment in which the rand pauls of the party finally sort of can declare victory for their foreign policy vision being the dominant one. >> they will have a great moment until there's another republican president and it will go back to an expansive executive -- >> ding, ding, ding, ding, isn't that true? >> i think eli is right, unfortunately. >> right. >> i think that there's obviously there's a tremendous amount of -- >> you have to feel bad in some ways for obama. i mean, like, here's a guy who killed gadhafi and osama bin laden and people are saying he's a wimp. >> right. >> who else do i have to kill. >> let me say this as a definitive statement, taking the host's prerogative to editorialize. there's no more stupider reason to go to war than fear that people think you're weak. tommy vietor. ben. and eli lake from "newsweek" the and the "daily beast." that's "all in." the "rachel maddow show" starts now. >> that was a stupendous debate. thank you for joining us th this hour. it's an unbreakable law of american political science wroin have a midterm election the president's party loses seats. if you have a democratic president who was elected or re-elected, then two years later when there is the next election, republicans will do really well and vice versa. if you have a republican president who's just been elected or re-elected, then two years later the president's party will lose seats and in that case the democrats will do well. it's just the way it goes. every once in a while we defy that but it's basically a rule. in american politics we like the pendulum to swing back and forth between the parties. although we have been trained now for years to think about republican president ronald All In With Chris Hayes MSNBC September 3, 2013 5:00pm-6:01pm PDT News/Business. (2013) New. Syria 25, Russia 17, Mitch Mcconnell 8, Mcconnell 7, John Kerry 7, Assad 7, Moscow 5, Medvedev 5, Mitch 5, Libya 4, Garth 4, U.n. 4, Obama 4, Ding 3, Nascar 3, Iran 3, Boris 3, Gadhafi 3, Saddam Hussein 3, Kerry 3 Channel v787 MSNBC West Television Archive Television Archive News Search Service The Chin Grimes TV News Archive Uploaded by TV Archive on September 4, 2013	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
St Giles' Cathedral, ook bekend als St Giles High Kirk, is een voormalige kathedraal, gelegen in Edinburgh, Schotland. De kathedraal werd in de twaalfde eeuw gebouwd als parochiekerk en is sindsdien meermalen verbouwd. De laatste grote wijzigingen dateren uit de negentiende eeuw. Het exterieur is laat-georgiaans en het interieur is victoriaans. De kathedraal is tegenwoordig in gebruik als parochiekerk van de Kerk van Schotland. Geschiedenis St Giles' Cathedral werd rond 1130, tijdens de regering van David I, gesticht als parochiekerk. De kerk stond onder beheer van de lazaristen en zij wijdden de kerk aan Sint-Gillis, de patroonheilige van de melaatsen. De oudste referentie naar deze kerk in de archieven dateert uit 1178. Het kerkgebouw werd door de jaren heen aanzienlijk gewijzigd. Enkel de noordelijke ingang van het schip was tot 1796 twaalfde-eeuws. De versieringen van deze ingang waren vergelijkbaar met die aangetroffen in Dalmeny in Lothian. De rest van de kerk werd voor de reformatie reeds herbouwd. Tijdens de plunderingen van Edinburgh in 1385 werd de St Giles' Cathedral door het Engelse leger van Richard II in brand gestoken. De schade werd hersteld. Het schip en toren waren gereed rond 1370. Voor 1395 kwamen de transepten gereed. Het koor was vermoedelijk af in 1419. In 1467 werd St Giles' Cathedral verheven tot een stift (collegiate church) en werd bediend door een aantal kanunniken. Vlak voor 1500 werd de toren verhoogd en werd deze voorzien van een stenen kroon. Reformatie Op 29 juni 1559 preekte John Knox in St Giles' Cathedral en startte daarmee een beeldenstorm die het begin was van de Reformatie. John Knox werd later dominee van St Giles' Cathedral. In 1560 werden de middeleeuwse versieringen vernietigd en werden drie westelijke traveeën ingericht als annex voor het nabijgelegen tolhuis. In 1581 gebruikten drie verschillende reformatorische stromingen de kerk. Om de door hen gebruikte ruimtes te scheiden waren er extra muren in de kerk aangebracht. Andere ruimtes in de kerk werden als opslagruimte gebruikt, onder meer voor de guillotine van Edinburgh, de Maiden. In 1633 werden de extra muren verwijderd toen de kerk de kathedraal voor de bisschopszetel van Edinburgh werd. In 1638 verloor de kerk de functie van kathedraal en in 1639 werden de extra muren weer opgebouwd. In de periode 1661-1689 fungeerde de kerk wederom als kathedraal. Negentiende eeuw Aan het begin van de negentiende eeuw was de kerk opgedeeld en in gebruik door vier kerkelijke stromingen, door de General Assembly voor de Church of Scotland en bevatte de kerk een politiebureau en een brandweerkazerne. De kerk was ingebouwd door tolhuizen aan de westzijde en door allerlei winkels aan de noordzijde. Tussen 1807 en 1833 werden deze gebouwen verwijderd en werd het exterieur gerestaureerd naar een ontwerp van William Burn. Het interieur werd dusdanig gewijzigd, dat er slechts drie kerken overbleven: één in het koor, één in het schip en één in het zuidelijk transept. De kruising diende als ontvangsthal die via het noordelijk transept toegankelijk was. In de periode 1871-1883 werd het interieur gerestaureerd door William Hay naar plannen van Robert Morham. Hierbij werden alle tussenmuren verwijderd zodat het koor, de kruising, de transepten en het schip weer één geheel werden. Twintigste eeuw Tussen 1909 en 1911 werd een kapel voor de Knights of the Thistle (Ridders van de Distel) gerealiseerd naar een ontwerp van Sir Robert Lorimer in de zuidoostelijke hoek van het kerkgebouw. In de jaren tachtig van de twintigste eeuw is de kruising ingericht als het focuspunt van de kerk. In 1992 werd een Rieger-orgel geïnstalleerd in het zuidelijk transept. Bouw St Giles' Cathedral is gelegen in de Old Town aan de Royal Mile, die loopt van de Palace of Holyroodhouse naar Edinburgh Castle. De kathedraal heeft een kruisvormige plattegrond en is oost-westelijk georiënteerd. Boven de kruising van schip, koor en transepten bevindt zich de toren. De lengte van schip en koor zijn min of meer gelijk. De transepten zijn even lang als het schip met zijbeuken breed is. De hoofdingang van de kathedraal is de westelijke ingang, die versiert is met voorstellingen van Sint Gilles en personen uit diens leven, gemaakt door John Rhind in 1884. In de zuidoostelijke hoek bevindt zich de Thistle Chapel (Distel-Kapel) uit het begin van de twintigste eeuw. Deze kapel heeft een driezijdige apsis en is hoog en smal van vorm. In de kruising bevindt zich sinds de jaren tachtig van de twintigste eeuw de communietafel. De zitplaatsen in het koor zijn sinds deze tijd, net als die in het schip, gericht op de kruising. Monumenten De kathedraal is voorzien van vele herdenkingsmonumenten, de meeste uit de negentiende en twintigste eeuw. Zo staat in het schip een bronzen standbeeld van de reformator John Knox, gemaakt door J. Pittendrigh MacGillivray in 1904-1905. In het Chepman Aisle bevindt zich een monument uit 1887-1889 ter herinnering aan James Graham, eerste markies van Montrose (1612-1650) naar een ontwerp van R. Rowand Anderson. In het Outer South Aisle bevindt zich een monument voor de negentiende-eeuwse schrijver Robert Louis Stevenson (1850-1894), gemaakt door Augustus St Gaudens in 1904. Externe links Royal Commission on the Ancient and Historical Monuments of Scotland, Edinburgh, High Street, St Giles Cathedral Undiscovered Scotland, St. Giles' Cathedral Giles Bouwwerk in Edinburgh Giles	{ "redpajama_set_name": "RedPajamaWikipedia" }
The law was created in response to several companies usage of the word when describing either soy-based patties or lab-grown meat. The state law forbids "misrepresenting a product as meat that is not derived from harvested production livestock or poultry." Violators may be fined $1,000 and imprisoned for a year. A similar law has been under debate at the federal level, with meat producers strongly arguing in favor of the regulation.	{ "redpajama_set_name": "RedPajamaC4" }
The Profile of a Gamer September 17, 2012 / Codey Dyer So what is a gamer? In some respects it is a little unfair to group a diversegroup of people into a single title when the only unifying thing about them is just that they play games. However for various reasons, it does help to understand who plays games. Originally 'gamer' was used to describe people who played paper role-playing games but the term has broadened as the video games has grown, into a term to identify people who are fans of playing computer games. As a categorisation this is a new phenomena and so understanding its boundaries is an uncertain subject yet there clearly exists a group within society who identify with this tag. While there is still debate over what gamers are (and are not) but emerging findings suggest that they are not the lonely figure as stereotyped in other media forms but are very social, often helping others within their arena and also influencing the media consumption of others around them. - A gamer can be further sub-categorised into forms such as 'Casual' or 'Hardcore'. - Gamers tend to be younger (the younger the age group, the more of them play games) - About 25% of UK adults can be considered 'gamers'. - The vast majority use Facebook to both communicate and play games (86% of US gamersaccording to one survey, I expect this to be the same here too, especially as the age group gets younger, the number using Facebook grows again. There are lots more facts and figures about gaming and gamers on Tomas' blog. September 17, 2012 / Codey Dyer/ games strategy, general buzz figures, gamers, games, stats	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Cancelled & Renewed NBC TV Shows for 2011-12 Is your favorite NBC TV series returning or has it already been cancelled? What TV shows have been renewed for another season? How many episodes have been ordered? Here's a list of all of the regular NBC series that have aired (or are expected to air) during the 2011-12 season (roughly September 2011 through August 2012). Using this "cheat sheet" you can tell where your favorite NBC TV series stands; how many episodes are in the current season, when it'll be back on the air and, of course, if it's already been renewed or cancelled. If you can't find a particular NBC program on this list, it may have been cancelled last season (2010-11) or perhaps the one before (2009-10). For a list of cancelled shows from all networks, you can go here. It may also be possible that we missed something so feel free to let us know in the comments below. NOTE: This page is no longer being updated. You can find newer versions here. TV shows Current/latest season Status 30 Rock 6 (22 eps, aired) renewed for season 7 America's Got Talent 7 (unknown eps) not cancelled or renewed yet American Ninja Warrior 4 (16 eps, aired) not cancelled or renewed yet Are You There, Chelsea? 1 (12 eps, aired) cancelled Awake 1 (13 eps, aired) cancelled Bent 1 (6 eps, aired) cancelled Best Friends Forever 1 (6 eps, aired) cancelled Betty White's Off Their Rockers 1 (12 eps, aired) renewed for season 2 The Biggest Loser 13 (18 eps, aired) renewed for season 14 Celebrity Apprentice 12 (14 eps, aired) renewed for season 13 Chuck 5 (13 eps, aired) ended 1/27/12 Community 3 (22 eps, aired) renewed for season 4 Dateline 21 (unknown eps) renewed for season 22 Fashion Star 1 (10 eps, aired) renewed for season 2 Fear Factor 7 (10 eps but 9 aired) cancelled The Firm 1 (22 eps, aired) cancelled Free Agents 1 (8 eps but 4 aired) cancelled Friday Night Lights 5 (13 eps, aired) ended Friends with Benefits 1 (13 eps but 1 didn't air) cancelled Grimm 1 (22 eps, aired) renewed for season 2 Harry's Law 2 (22 eps, aired) cancelled It's Worth What? 1 (9 eps, aired) cancelled Law & Order: Los Angeles 1 (22 eps, aired) cancelled Law & Order: Special Victims Unit 13 (23 eps, aired) renewed for season 14 Love Bites 1 (9 eps, aired) cancelled Love in the Wild 2 (8 eps, aired) not cancelled or renewed yet The Marriage Ref 2 (10 eps, aired) cancelled Minute to Win It 2 (24 eps, aired) cancelled The Office 8 (24 eps, aired) renewed for season 9 Parenthood 3 (18 eps, aired) renewed for season 4 Parks & Recreation 4 (22 eps, aired) renewed for season 5 The Playboy Club 1 (8 eps but 3 aired) cancelled Prime Suspect 1 (13 eps, aired) cancelled Rock Center with Brian Williams 1 (unknown eps) renewed for season 2 Saving Hope 1 (13 eps) renewed for season two in Canada The Sing-Off 3 (12 eps, aired) cancelled Smash 1 (15 eps, aired) renewed for season 2 Up All Night 1 (24 eps, aired) renewed for season 2 The Voice 2 (21 eps, aired) renewed for season 3 Whitney 1 (22 eps, aired) renewed for season 2 Who Do You Think You Are? 3 (12 eps, aired) cancelled Who's Still Standing? 1 (8 eps, aired) cancelled Here are listings for the other networks: ABC \| CBS \| The CW \| FOX What do you think? Which NBC TV shows won't be renewed? Are there any that you wish would be cancelled? More about: 30 Rock, 30 Rock: canceled or renewed?, America's Got Talent, America's Got Talent: canceled or renewed?, American Ninja Warrior, American Ninja Warrior: canceled or renewed?, Are You There Chelsea?, Are You There Chelsea?: canceled or renewed?, Awake, Awake: canceled or renewed?, Bent, Bent: canceled or renewed?, Best Friends Forever, Best Friends Forever: canceled or renewed?, Betty White's Off Their Rockers, Betty White's Off Their Rockers: canceled or renewed?, Chuck, Chuck: canceled or renewed?, Community, Community: canceled or renewed?, Dateline, Dateline: canceled or renewed?, Fashion Star, Fashion Star: canceled or renewed?, Fear Factor, Fear Factor: canceled or renewed?, Free Agents, Free Agents: canceled or renewed?, Friday Night Lights, Friday Night Lights: canceled or renewed?, Friends with Benefits, Friends with Benefits: canceled or renewed?, Grimm, Grimm: canceled or renewed?, Harry's Law, Harry's Law: canceled or renewed?, It's Worth What?, It's Worth What?: canceled or renewed?, Law & Order: Los Angeles, Law & Order: Los Angeles: canceled or renewed?, Law & Order: Special Victims Unit, Law & Order: Special Victims Unit: canceled or renewed?, Love Bites, Love Bites: canceled or renewed?, Love in the Wild, Love in the Wild: canceled or renewed?, Minute to Win It, Minute to Win It: canceled or renewed?, NBC TV shows: canceled or renewed?, Parenthood, Parenthood: canceled or renewed?, Parks and Recreation, Parks and Recreation: canceled or renewed?, Prime Suspect (US), Prime Suspect (US): canceled or renewed?, Rock Center with Brian Williams, Rock Center with Brian Williams: canceled or renewed?, Saving Hope, Saving Hope: canceled or renewed?, Smash, Smash: canceled or renewed?, The Biggest Loser, The Biggest Loser: canceled or renewed?, The Celebrity Apprentice, The Celebrity Apprentice: canceled or renewed?, The Firm, The Firm: canceled or renewed?, The Marriage Ref, The Marriage Ref: canceled or renewed?, The Office (US), The Office (US): canceled or renewed?, The Playboy Club, The Playboy Club: canceled or renewed?, The Sing-Off, The Sing-Off: canceled or renewed?, The Voice, The Voice: canceled or renewed?, Up All Night, Up All Night: canceled or renewed?, Whitney, Whitney: canceled or renewed?, Who Do You Think You Are?, Who Do You Think You Are?: canceled or renewed?, Who's Still Standing?, Who's Still Standing?: canceled or renewed? Cancelled or Renewed? Status of NBC TV Shows NBC 2012-13 Ratings Averages [Week 32] Chicago Fire, Revolution, Community, Grimm, Go On, Whitney: NBC Finales Announced 123 Ending or Cancelled TV Shows for the 2011-12 TV Season (part 2) NBC 2011-12 Ratings Report Card NBC Announces 2012-13 Primetime Schedule Community, Betty White's Off Their Rockers to Return, Bent, Best Friends Forever to Debut NBC Announces 2011-12 Mid-season Schedule NBC Announces 2011-12 Fall Season Premieres NBC Announces 2011-12 Season Primetime Schedule NBC TV Show Ratings for 2010-11 Season [as of 4/7/11] NBC Announces Fall 2010 TV Show Premiere Dates A few weeks ago Brian Williams announced the end of Rock Center. Why would NBC remove a program of such quality? Since the new airwaves system took over I get only two stations: NBC and Cozi TV. This does not allow me much choice to watch something else when I don't like what is on NBC. I'm not one who enjoys reality programs, talent discovery shows or most comedy sitcoms. Rock Center is such a well rounded news/information program elaborating on current events, health, human interest and historical occurrence; this program was one of few high quality NBC programs of… Read more » Jake Carr I'm really disappointed that "The Firm" was cancelled. I really liked it and it definately maintained the flavour of the original movie with Tom Curz. All the actors were great. I am very surprized that it was cancelled. I thought it was a very well acted and written show. I hope someone will look at it again and put it back on for another season. Really loved the show. Bring back Harry's Law and V, two of the better shows on nighttime television.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Today Primary 3/4 visited Bluebell Lane Glamping site as part of our Eco Schools project. In 2016 pupils from St Mary's helped to plant some of the 20,000 trees that are situated around the site. Our class took a trip back to see how they have grown over time. We measured the height and circumference and found out more about the many different types of trees found in the woodland. We then discovered some of the different plant life in our flower and plant hunt. Primary 3/4 were very lucky today to see small frogs and dragon flies in the pond area. We extend our thanks to Padraig Carragher for his time today, the children throughly enjoyed the experience!	{ "redpajama_set_name": "RedPajamaC4" }
Things to See in Argentina: Floralis Generica Travel Attractions 22 AUG 2015 Argentina. Floralis Genérica is a sculpture made of steel and aluminum located in Plaza de las Naciones Unidas, Avenida Figueroa Alcorta, Buenos Aires, a gift to the city by the Argentine architect Eduardo Catalano. Created in 2002, the sculpture was designed to move, closing its petals in the evening and opening them in the morning. The sculpture is located in the center of a park of four acres of wooded boundaries, surrounded by paths that get closer and provide different perspectives of the monument, and placed above a reflecting pool, which apart from fulfilling its aesthetic function, protects it. It represents a large flower made of stainless steel with aluminum skeleton and reinforced concrete, which looks at the sky, extending to its six petals. It weighs eighteen tons and is 23 meters high. The enormous metal flower blooms anew each day in the aforementioned reflecting pool next to the National Museum of Fine Arts, revealing four long stamens inside. Its six 13-meter-long petals open, which takes about 20 minutes, at eight in the morning and slowly close again at sunset, mimicking the actions of a real flower. The constructed flower reflects the city around it in the aluminum of its petals. When the petals close at night, the flower glows red. On just four nights of the year, the petals of the Floralis Generica remain open: May 25, September 21, December 24, and 31, keeping Buenos Aires in bloom all night long. According to Eduardo Catalano, the author, Floralis "means belonging to the flora and therefore the flowers", and Genérica "from the concept of "gender" and indicates that it represents all the flowers in the world". The electronics employed in opening and closing the flower were disabled in 2010 to prevent damaging the sculpture, and it remained permanently open until 2015. This was due to the fact that one of the petals was incorrectly installed during its assembly, as noted by Catalano himself. The company responsible for its construction, Lockheed Martin Aircraft Argentina, provided a 25-year warranty, but as the company was nationalized in 2009 its repair was delayed. The mechanism was functional again by June 2015. Related Link: Wikipedia \| Atlas Obscura Saturday 22/08/2015 Travel Attractionsargentina, buenos aires, eduardo catalano, Floralis Genérica, flower, metal flower, sculptureCraig Lotter ← Things to See in Czech Republic: Holy Trinity Column in Olomouc A Slide for Emily →	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
IMF BAILOUT : IS IT REALLY A BAILOUT FOR PAKISTAN? On taking over as Prime Minister of the country, Imran Khan had very candidly announced about the empty coffers and ever-increasing burden of debt making it almost impossible for the PTI govt to sustain and making the economy grow. The public too was sympathetic and willing to support. However, somewhere something was going awry which has forced the public to reconsider their support to the fledgling govt. The first mistake was the removal of Atif Rehman Mian‎, a Pakistani-American economist from the EAC, just because of his Ahmadiyya faith. Atif Mian, who was appointed to Economic Advisory Council by Imran Khan to help assist in issues of economics and finance, based on his merit, was removed under pressure from extremist individuals and groups including the far-right Islamist Tehreek-i-Labbaik (TLP) Pakistan. His removal further led to the resignation by two other economists Asim Ijaz Khawaja and Imran Rasul giving a big setback to the economic planning. This episode was enough for the public to know that for Imran Khan, extremists and their support was more important than the country's economy. The second mistake being the delay in accepting the IMF bailout package which was on the horizon for a long time but the acceptance was being dilly-dallying. And when it was announced that the Pakistan government is seeking an IMF bailout it has invoked only surprises and criticisms. What was the need for delaying the decision for almost two months? Well, Finance Minister Asad Umar may have some solid explanation (blaming the previous govt) but the mistake had been made. The delay certainly resulted in irreparable damages. However, a requirement to seek an IMF bailout was a must and it should not have come as a surprise or a shock. The financing requirements of Pakistan are whopping $28 billion for the current financial year, with approximately $8 billion due for debt repayment this year only. So it was very much evident that paired with a spiraling deficit, it was impossible for the PTI government to avoid the bailout without an economic miracle. However, Imran Khan wanted to deal with this situation by begging the public on the name of the country, selling cars, buffalos, and helicopters. What else was there to expect without good economists in the EAC and inexperienced portfolio holders in the new govt. With any major bailout from the IMF, temporary financial setbacks are unavoidable and one of them being the rupee devaluation, which plunged to Rs. 134 against $1 and likely to plunge further. One of the major consequences linked to the IMF bailout. Similarly, it has started taking a toll on the stock exchange too. Highs and lows in any country's economy are a natural inevitability and there is no logic in politicizing the same. But PTI govt and especially the IK has gone overboard washing the dirty linen in the public which has more of negative effects than any worthwhile positive one. In a catastrophe, this has led to PTI inviting criticism and shooing away the likely investors. A government may have inherited an economy in tatters, but for some ministers to make such statements only adds to the deteriorating of the economy. One cannot underestimate the importance of the element of trust when it comes to investment and buying. An economy which is constantly derided by its own government is likely to ward off foreign investors and companies. As the FATF is still in discussion and Pakistan Govt considering the IMF bailout, it is difficult to say what is store for the country. A term of references for the bailout is yet to be discussed so, it is too soon to comment on the IMF bailout. The fact that IMF has cautioned Pakistan about the risks of financial transaction with China should be able to give an outline view of the actual picture. 10 Oct 2018/Wednesday. Written by Azadazraq	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
SONIC has brought a twist to an iconic American food – the Croissant Dog. The new items features their premium beef hot dog in a flaky, buttery croissant bun, which is then topped with bacon, cheese and spicy or regular mustard. SONIC's new Croissant Dog is available for a limited time, with local locations in Hasbrouck Heights and Clifton. More information is available at the SONIC website.	{ "redpajama_set_name": "RedPajamaC4" }
The Easter Weekend ahead is expected to be a bustling one for Rotorua, with the sun even coming out to join the crowds. Events appealing to people of all ages and walks of life will take place around the region from Friday through to Sunday. Among the events, the popular Rotorua Museum Easter Egg Hunt, that started last Saturday will run through to April 28. Easter letters were hidden throughout the Government Gardens, with participants encouraged to be an "Easter detective" and follow the series of clues to find the letters and create a mystery word. Successful participants will go in the draw to win an Easter prize pack and entry boxes will be at Rotorua iSite and Children's Art House. The Soundshell Market will take place this Sunday and the Night Market will go ahead on Thursday evening. The annual Good Friday Combined Service has also been planned to take place again at 10am under the sails at the Redwoods. Reverend Scott Clifford said this was the biggest combined service of the year, and it did not take into consideration denominational lines. "Instead we chose this day of the year to focus on things that unite us as Christian faith communities." Good Friday service at the Redwoods. Destination Rotorua executive manager visitor services Graham Brownrigg said accommodation was limited as rooms filled up fast for the weekend. He said the school holidays and Easter had fallen on the same week this year, creating a busy couple of weeks. A big crowd turned out for the Good Friday procession and service in the Redwoods. The benefit this would have on the Rotorua economy would be huge, he said, with cafes, restaurants and attractions expected to be bustling. He said a large number of domestic travellers were expected to visit the city. This will also be the third year traders can trade on Easter Sunday and a number of local businesses say it is worthwhile being open. McLeods Booksellers will be open on Easter Sunday and were last year too. Owner David Thorp said it was a busy day last year and he was expecting it to be busy this Easter Sunday. "McLeods is a destination bookshop so we find it's always worthwhile being open." Robert Harris owner Manroop Grewal said they would be open and that the Easter weekend was a great one. "It is definitely worthwhile. We are expecting to be busy again." Footloose Shoes owner Christine Vincent said opening on Easter Sunday was worthwhile because there were people around and plenty of visitors in town. She said the lead up to Easter had been busy, though that may be due to school holidays. "We are having a good April. I would expect it to be busy." Meanwhile, NZ Transport Agency, New Zealand Police and ACC put out a joint statement asking people to plan ahead and follow the basics of road safety over the holiday period. Since Easter Monday, Anzac Day and school holidays all fall in the same week, it's likely to be extra busy on our roads, NZTA acting director safety and environment Niclas Johansson. NZTA predicts traffic will be especially heavy today and tomorrow, and then on the return journey on Sunday . ACC chief customer officer, Emma Powell said there were 387 motor vehicle accident claims over the Easter period last year which was a substantial increase from the previous year of 312. Metservice meteorologist Claire Nickson said with a current high ridge of pressure sweeping the country, a fine week was expected for the Bay of Plenty. She said conditions were expected to be fine this weekend, with the odd cloud here and there.	{ "redpajama_set_name": "RedPajamaC4" }
Regular Colleges or Institutions Health Care and Allied Fields Forensic Science/ Criminology Postgraduate Institute of Medical Education and Research (PGIMER) Sector-12 , Chandigarh - 160012 District: Chandigarh (Chandigarh) Affiliated to : - Courses Offered by Postgraduate Institute of Medical Education and Research (PGIMER) UPDATE PHOTOS of Postgraduate Institute of Medical Education and Research (PGIMER) SEND VIDEOS of Postgraduate Institute of Medical Education and Research (PGIMER) to The Postgraduate Institute of Medical Education and Research (PGIMER) Chandigarh was conceived in 1960 as a center of excellence which would endeavour to develop patterns of teaching in postgraduate medical education in as many branches as possible and attempt to produce specialists in several disciplines of medicine. The Institute was originally under the Government of undivided Punjab. After the reorganization of the state, the administrative control of the institute passed on to the Union Territory of Chandigarh in November 1966. The Institute became an autonomous body under the Act of Parliament in 1967 functioning under the Ministry of Health and Family Welfare, Government of India. UPDATE Admission Notification of Postgraduate Institute of Medical Education and Research (PGIMER) If you are an authorized person of this College/ Institute, please furnish us with the placement assistance provided by your Institute, so that we can update it. UPDATE DETAILS of Postgraduate Institute of Medical Education and Research (PGIMER) 0172 2746018, 2756565 View All Courses Conducted by Postgraduate Institute of Medical Education and Research (PGIMER) Course(s) Offered by Postgraduate Institute of Medical Education and Research (PGIMER) in Forensic Science/ Criminology MD Forensic Science/Medicine More Forensic Science/ Criminology Colleges in Chandigarh Panjab University : Department of Anthropology Punjab University, Sector 14 , Chandigarh - 160014 District: Chandigarh Sector-12, Chandigarh - 160012 District: Chandigarh Health Care and Allied Fields Colleges Acupressure Therapy Institutes in Chandigarh Clinical Research Institutes in Chandigarh Cosmetology Colleges in Chandigarh Forensic Science/ Criminology Colleges in Chandigarh Hearing,Language and Speech Colleges in Chandigarh Medical Laboratory Technology Colleges in Chandigarh Nursing Colleges in Chandigarh Occupational Therapy Colleges in Chandigarh Pharmacy/ Pharmacology Colleges in Chandigarh Physiotherapy Colleges in Chandigarh Psychiatry/ Psychology Colleges in Chandigarh Public Health Colleges in Chandigarh Radiology/ X-Ray Technology Colleges in Chandigarh Theatre Technician Colleges in Chandigarh Yoga Education in Chandigarh Career Options in Forensic Science/ Criminology Forensic science is primarily concerned with the application of scientific principles for the investigation of crime...	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Happy spring to you and happy blogiversary to Seasonal Eating! It's been one year and one day since I started writing this blog, and I'd like to re-welcome Seasonal Eating readers. What better way to do this than to publish a recipe by readers' request? These particular readers also taste-tested the "maiden voyage" of this recipe at a recent potluck. So here you go, folks, it's Butternut Squash Blondies! I love butternut squash so much that I seldom make it any way except baked. I was pondering the old adage that squash can be substituted for pumpkin in any recipe, and the less reliable adage that persimmon can be substituted for pumpkin. I decided to experiment with an adage of my own: butternut squash can be substituted for persimmon in any recipe. To test this, I got busy with my persimmonie (persimmon bar) recipe. Most of us have eaten spicy pumpkin bars, and while they're delicious, they remind me of fall and winter holidays. I wanted something for lighter and more like spring, closer to a classic blondie. So I eliminated the spice in the persimmonie recipe, changed the light brown sugar to dark, and substituted butternut for persimmon. Then reinforce and build up the dam with another piece of foil. Press foil firmly into pan. Butter the foil and you're ready to pour in batter. Work with the no-nuts portion first to avoid accidental contamination with utensils. Divide the batter in half and pour half into aluminum foil area of pan. Scrape out bowl and even out the surface of batter. Then stir nuts into second half and repeat process with that half. Cut the no-nuts portion first, or use separate knives for each half. Use separate plates for nuts and no-nuts. In the recipe, use 1 cup of pecans if you're making a full batch with nuts. Use ½ cup if you're making half and half. And, of course, the nuts are optional, so feel free to leave them out. Thanks for reading Seasonal Eating. I invite your comments, which can be posted below. Winter is gone. Enjoy your spring! Butter a 9" x 12" baking pan. If making half and half (nuts/no nuts) blondies, build an aluminum foil dam as detailed above, and butter aluminum foil. Mash the squash thoroughly with a fork. Stir the squash with the fork until it is uniform in texture. Melt the butter. Beat in the sugar with a mixing spoon until mixture is lighter in color and creamy. Beat in one egg at a time, until mixture is fluffy. Beat in vanilla and squash. It's easiest to use a fork. Sift together dry ingredients: flour, baking powder, and salt. Add to squash mixture and stir with mixing spoon till flour mixture is incorporated. If you're splitting the batter into two parts, do it now and pour the no-nuts half into the baking dish, then add pecans to the nuts half. If you prefer all-nuts, stir them in now and pour batter into baking pan. Bake at 350 degrees F for 30 – 40 minutes. A toothpick inserted will come out clean when done.	{ "redpajama_set_name": "RedPajamaC4" }
We already have a best of the best guide for gaming monitors, but our analysis indicates that there are six user favorites among the crowd. We exist to inform you about the latest gaming tech, but we know that most of today's gamers are already street-smart and can discern the best gaming monitor for themselves. We can recommend a few excellent displays for the money, but we know at the end of the day the decision is always up to the reader. We mined our data going back 9 months to determine what people actually buy after combing through our reviews. Six models have peaked the interest of many users. Some may disagree that these are the current best, but the numbers don't lie. The current HDR monitors can't even light a candle against these six "old but gold" screens when it comes to popularity. The Asus ROG Swift PG278QR is our overall favorite due to its excellent performance, reliability, and design. The monitor puts out 100% sRGB coverage with decent accuracy, so images are still vibrant despite the disadvantages of TN panels. This model can provide gamers with a responsive and buttery smooth gaming experience thanks to its G-Sync feature and low input lag. The Asus PG278QR has already been replaced and not to mention that there are IPS monitors with similar capabilities. What makes it a good pick is its pricing which usually dips to reasonable levels, increasing its value per dollar. We use this gaming monitor as a basis or a benchmark when rating new models in gaming performance since its resolution and capabilities are still considered modern by today's standards. The AOC G2460PF is the best competitive gaming monitor you can get right now that costs less than $200. Yes, that's right, this model only costs a little over $190 most of the time, pitting it against products with lower specs. It's difficult to argue with an offering that provides a high refresh rate, decent imaging quality, and valuable features that is this affordable. There are newer and better gaming models out in the market, but the AOC G2460PF is still our go-to product if budget is restricted. This device is perfect for those who want to test the waters in 144Hz gaming, or for the users trying to squeeze every buck out of a fixed budget. Even if there are 240Hz or refreshed 144Hz variants, the AOC G2460PF is still the best-selling 1080p 144Hz monitor for Monitornerds readers. The Acer Predator XB241H is one of the best rated 144Hz monitors of its time, making it a staple in significant E-Sports events and high-end builds in homes everywhere. This gem provides users with an overclockable 144Hz display that can soar to within 60Hz of the latest model, the XB252Q. G-Sync is also in the mix, along with low-input lag performance which is the bread and butter of competitive gaming. The Asus MG28UQ has been everybody's go-to 4K monitor for both PC and console gaming because it is relatively inexpensive despite its excellent performance. This model still has a TN panel which is outshined by IPS and VA variants, but Asus used a module with 8-bit color, so the vibrancy we all want is still there. The MG28UQ also posts one of the lowest input lag scores in the 4K monitor category, making it a superb choice for competitive gaming in UHD. Most are already looking to 4K HDR displays to satisfy their cravings for high-end gaming, but the Asus MG28UQ hasn't lost its appeal just yet. Monitornerds.com readers are still buying this value product as a stop-gap or as an easy to own foray into 4K gaming. The MG28UQ is also a top choice for console gamers who want a manageably sized display with excellent responsiveness and without costing big bucks. The Asus VG245H is the gold standard for gaming monitors recommended for consoles like the Xbox One S and the PS4 Slim. This 75Hz low-input lag monitor presented excellent value for those who wanted a two in one display that functions flawlessly. The Asus VG245H is purely designed for gaming, making it instantly better than the other 75Hz offerings that flooded the market in the last year or two. The Asus VG245H still sells well because it is a well-designed gaming display that gets the job done. The monitor features the same exterior build quality and features of the premium PG monitors to provide users with convenience and peace of mind. The flexibility and feature-rich functionality of this device make it a suitable choice for numerous setups, including triple-head configurations. The Acer GN246HL is not only one of the cheapest 144Hz gaming monitors you could get now, but it also is one of the last remaining models to offer 3D vision. The latter is considered defunct more than exotic nowadays, but we know there are enthusiasts out there who still don their 3D glasses for immersive viewing experiences. Another attractive feature of the Acer GN246HL is its Nvidia Lightboost compatibility which is one of the most popular strobing features for blur reduction. The Acer GN246HL has some age to it, but it still sells well because not everybody has access to the modernized features such as connectivity on the latest hardware. Some still prefer to use DVI for 144Hz gaming on an older GPU to create a budget or potato gaming rig that performs sufficiently. Why Should I Buy These Top-Selling Monitors? Other than the fact that we have tested these excellent displays, you have to consider that people have already spent hard-earned cash on these six gaming monitors. They wouldn't be bestsellers if the good things we said about them weren't true. We try our best to provide you with the best information that can help you decide on which gaming monitor is the best for your needs. But other than our reviews and feedback, you also have to learn to trust the enthusiasts who jumped the fence and bought these venerable offerings. Remember, that like you, most of the readers who purchased these models have turned every stone researching how good these monitors really are. Our opinion didn't generate this ranking, but instead, it was created by people who found that these gaming monitors are the best value for the money they were willing to spend.	{ "redpajama_set_name": "RedPajamaC4" }
Prospective CSUteach students are required to meet certain standards and requirements of the College of Education and Human Services and to declare a minor in education. Requirements include having a cumulative GPA of 2.75 or higher, the completion of 30 semester hours of college-level coursework, and a grade of C or better in a college Mathematics and English course. For further information refer to the Undergraduate Catalog. Students can take 200-level coursework toward completion of the CSUteach program prior to meeting the admissions requirements and prior to declaring the minor in education. If you have further questions about eligibility and admission requirements please send corresponding e-mails to Veronica Bunkley.	{ "redpajama_set_name": "RedPajamaC4" }
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This information is transmitted by users, after registering and getting hold of email and password that is strictly personal. The user/purchaser has explicitly authorized addressees of this information, at the release of the same, to their treatment, according to the legal provisions in force. In addition, when you register, CRIZU informs the user/purchasers, who is therefore aware, its non-involvement with any other sites to which you can connect via a link on the portal. Therefore, CRIZU disclaims any liability with regard to their contents, not being in any way responsible for damages of any nature or type suffered by you or any other person in relation to their use or from what they offer. The registration can be canceled at any time by the user by following the instructions on the site. To obtain more information please contact us at [email protected].	{ "redpajama_set_name": "RedPajamaC4" }
In the wry but affectionate tradition of Bill Bryson, Ciao, America! is a delightful look at America through the eyes of a fiercely funny guest one of Italys favorite authors who spent a year in Washington, D.C.When Beppe Severgnini and his wife rented a creaky house in Georgetown they were determined to see if they could adapt to a full four seasons in a country obsessed with ice cubes, air-conditioning, recliner chairs, and, of all things, after-dinner cappuccinos. From their first encounters with cryptic rental listings to their back-to-Europe yard sale twelve months later, Beppe explores this foreign land with the self-described patience of a mildly inappropriate beachcomber, holding up a mirror to Americas signature manners and mores. Succumbing to his surroundings day by day, he and his wife find themselves developing a taste for Klondike bars and Samuel Adams beer, and even that most peculiar of American institutions -- the pancake house.The realtor who waves a perfect bye-bye, the overzealous mattress salesman who bounces from bed to bed, and the plumber named Marx who deals in illegally powerful showerheads are just a few of the better-than-fiction characters the Severgninis encounter while foraging for clues to the real America. A trip to the computer store proves just as revealing as D.C.s Fourth of July celebration, as do boisterous waiters angling for tips and no-parking signs crammed with a dozen lines of fine print. By the end of his visit, Severgnini has come to grips with life in these United States -- and written a charming, laugh-out-loud tribute.From the Hardcover edition.	{ "redpajama_set_name": "RedPajamaC4" }
A new study by Universal McCann called When did we start trusting strangers? found that rather than being passive, consumers have taken not only active, but also creative roles in consumerism. In fact, consumers have become true "consum'actors." The study was base on 17,000 Internet users from 29 countries. ← Previous Previous post: Arrr! Friendfeed switched their beta version live!	{ "redpajama_set_name": "RedPajamaC4" }
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If you want to know what your used car is worth, check out the Kelly Blue Book ,or NADAguides.com, these guides will help you determine its fair market value. The Black Book, Blue Book and NADA an industry guide to used car values, as well as new. I've heard the Blue book is more realistic in its' prices. But do your homework and know what your vehicle is worth and what you will take for it. Used car books like the Kelly Blue Book or Black Book include pricing usually for the last ten years. If your used car is more than ten years old, a used car value might be a bit more difficult in determining. Most dealers won't give much for high mileage vehicles , damaged vehicles or vehicles older then 10 years UNLESS they are collectors items, antique or classic vehicles. However if your vehicle is a a special edition, or has a special interest market you might be able to sell the vehicle privately outright for more then a trade in. I know in my area of Florida , late model ( 1987-1993) 5 liter Mustang's in excellent shape and NON modified command a premium. Be it GT or LX, coupe, hatchback or convertible they bring in a good amount of private interest. Where as taking say maybe a 1993 LX 5 litter V8 Coupe to a car lot for a trade in might bring about 1500 -2000 dollars, more or less. A wise car dealer once said he could price a car high, so that it might sit for two years on his lot before someone paid that price.Or he could lower the price and sell it within two months, two weeks, or two hours! It all depends on how long you can or want to wait.	{ "redpajama_set_name": "RedPajamaC4" }
Why Hasn't Everything Already Disappeared? Deerhunter's eighth album, Why Hasn't Everything Already Disappeared?, was inspired by Marfa, a ghostlike West Texas town where they recorded parts of the album. (Other recording locations included Los Angeles and Atlanta.) "There is a feeling of disappearance here… The desert just has a lot of disappeared things in it. It's where things have disappeared to," singer and guitarist Bradford Cox has said of Marfa. Specifically, WHEAD is, per a press statement, "concerned with the disappearance of culture, of humanity, of nature, of logic and emotion." Indeed, WHEAD is bleak, if not outright morbid. Cox sings of his friends on "Death in Midsummer": "They just fade away. Some worked in hills. Some worked in factories, worked their lives away. And in time, you will see your own life fade away." And later: "They were in hills. They were in factories. They are in graves now…. Walk around, and you'll see how it fades. Walk around, and you'll see what's faded." The mid-tempo "No One's Sleeping" bursts with optimistic sax. But anxiety always seeps into Cox's lyrics, weighing down the music like dew clinging to leaves. "Great unrest. In the country, there's much duress. Violence has taken hold," he sings. If no one's sleeping, Cox certainly isn't either. Despite the grim reality WHEAD draws attention to, songs like "No One's Sleeping" show that sonically, the album is an exuberant and tightly knit pop record. That might be the result of working with Welsh singer/songwriter Cate Le Bon, who replaced Deerhunter's long-time producer, Ben H. Allen. Harpsichord, played by Le Bon, opens the album on "Death in Midsummer". Saxophone blows "No One's Sleeping" towards unreachable heights where cloudbusting synthesizers soar. "Futurism" might be the least complicated piece of pop Deerhunter have written. Deerhunter have been leaning into classic rock, noisy punk, and garage rock over their previous two albums, 2015's Fading Frontier and 2013's Monomania. But WHEAD contains moments conducive of mental clarity, too. "Tarnung" undulates atop sparse xylophones and the breathiest saxophone. "Détournement" resembles a relaxation tape. The narrator's drowned voice flies the listener around the world, across oceans. "Good morning to Japan," he says. He repeats the same greeting for Europe, Spain, Russia, America, and Australia. But the calmness fades. Drums and piano intrude the tranquility. He says hello to eternal jet lag. "And time starts to run backwards." As the sense of time becomes skewed, so does any sense of place, despite the narrator reciting place names like memorization cards. The only patch where WHEAD loses cohesion is on closer "Nocturne". Cox's filtered vocals are clipped. The lumbering melody and toy-like quality of the song call to mind the Unicorns, at least in the first third of the six-plus-minute song. "There are no boundaries left to cross," Cox sings. That isn't true of Deerhunter, but they've made a huge leap with Why Hasn't Everything Already Disappeared?. review by Leslie Chu Helado Negro – Far In Erika de Casier – Sensational Sketchy – Tune Yards Songs Adrienne Lenker Future Islands As Long As You Are Big Thief Debut "Simulation Swarm" Cate Le Bon Shares "Remembering Me" Video Aldous Harding Announces 'Warm Chris' LP The Smile – You Will Never Work In Television Again Our Most Anticipated Albums of 2022	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Peter Henry's TechTidBits (Blog) - VS TnT #3: Copying entire line with lifting only two fingers! Tip'n'Trick: copying the current line FAST, zoom zoom! You're looking at copying entire line, quick what do you do? If you said you reach for the mouse to SHIFT+select the entire line, you're just working too hard! As long as you don't have anything currently selected, you can just hit CTRL+C! Yes, that's it! As long as there's nothing selected, you're good to go! Try it out, I know you'll be surprised! Now you know how to copy an entire line like Sly Fox's music career, short'n'sweet, it's time to grab a coffee and get coding!	{ "redpajama_set_name": "RedPajamaC4" }
Added on: 14/11/2011 17:00 Videos and Info Log in to Add Videos, Interviews, Etc This article is lonely! Item Images This item has no attached images. Slayers: Evolution-R Slayers, The: Volume 2 Slayers: Revolution Slayers: Try - Volume 4 Slayers: Next - Volume 4 The Anime DVD Highlights of 2010 MCM Expo News and Anime Review Roundup Bumper Anime Review Roundup Anime, Crunchyroll, DVD, Hanasaku Iroha, Manga Entertainment, MVM, Redline, Retrospective, Slayers, Slayers Evolution-R Once again I've been left chasing after the bandwagon long after it has left the village. This time it's for Hanasaku Iroha, the most talked about slice-of-life anime this summer just past. Its wonderful collection of characters, its gentle story, and its appealing feel-good approach has attracted legions of fans on the Internet, but I only started watching it after the simulcast had ended. On the bright side, it does mean that I can watch the episodes at my leisure, rather than have to wait for a week. The series is still available to view at Crunchyoll (and if you can speak Japanese and spin Region A, the lush Japanese Blu-ray special editions are emptying wallets as we speak), and it's well worth watching. Here's what Crunchyroll have to say about the series, and the link is to the right. Hanasaku Iroha centers around 16-year-old Ohana Matsumae who moves from Tokyo to out in the country to live with her grandmother at an onsen ryokan named Kissuiso. While restarting her life there initially seems daunting, Ohana begins working at the inn, makes friends with the other employees and watches her life take an unexpected twist. The first of my reviews last week was for one of the most anticipated and hyped movies of the last two years, Redline, which I had the privilege to watch on Blu-ray. It's the Wacky Races meets Death Race 2000, a neon retinal burn of a movie. In the future, the ultimate in race championships is the Redline, old-fashioned automobile racing in a reality where most everyone else flies aircars. But the fanatics that love racing, like it close to the ground, at insane speeds, with no rules. This year's Redline is going to be held in a warzone, on a world where the enemy are the racers themselves, and for one racer, he'll have to choose between clearing his tarnished reputation, and falling in love. You haven't seen anything like Redline before. And faced with the choice of the DVD and the Blu-ray, believe me, buy a Blu-ray player! I've finally come to the end (for now) of my Slayers odyssey, although due to a wayward review disc, I had to wait until I had the time to purchase and watch Slayers Evolution-R for myself. The classic RPG comedy adventure series, which sees the perpetually ravenous Lina Inverse and Gourry Gabriev travel the land, relieving bandits of their booty, making restaurants regret their all-you-can-eat offers, and occasionally saving the world, got a twenty-first century updating with Slayers Revolution and Slayers Evolution-R. We now have widescreen, CG animation, and the show looks shiny and new. But is it still the same old Slayers? For the final instalment, see if they go out on a high by reading my review. Redline is out on Blu-ray, DVD, and Blu-ray/DVD LE combi (seriously buy the Blu-ray) today courtesy of Manga Entertainment. MVM released Slayers Evolution-R at the start of 2011.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
… industrial visit can be very amazing for students. There is numerous manufacturing units like … and many more industries there. Palakkad District is one of the 14 districts of the Indian state of Kerala. The city of Palakkad is the district headquarters. Palakkad is bordered on the northwest by the Malappuram District, on the southwest by the Thrissur District and on the east by Coimbatore district of Tamil Nadu. Pothundi Dam is an irrigation dam near a small village in Palakkad district of Kerala state, India. It was constructed in the 19th century. View of Chulliar Dam with the western ghats as background . This is the southern part of the Palakkad Gap. Silent Valley National Park, is located in the Nilgiri Hills, Palakkad District in Kerala, South India. The area in this national park was historically explored in 1847 by the botanist Robert Wight, and is associated with Hindu legend. Mangalam Dam is a village in Palakkad district in the state of Kerala, India. It is administered by Vandazhy gram panchayat. This village is named after the dam situated in the region. Palakkad Fort also known as Tipu's Fort is an old fort situated in the heart of Palakkad town of Kerala state, southern India. It was built by Haider Ali in 1766 ACE and remains one of the best preserved forts in Kerala. Kudallur is in the Palakkad district of Kerala. It is in Ottappalam taluk, bordering Malappuram district, also on the banks of Bharathapuzha. This village was originally in Ponnani taluk of Palakkad, before the formation of Malappuram district. Siruvani dam is a dam in Palakkad District, Kerala located 46 km away from Palakkad town. This dam constructed across the Siruvani River, is for supplying drinking water to the city of Coimbatore in Tamil Nadu. It is a memorial to Thunchath Ezhuthachan, father of Malayalam language. The memorial is located in Thekkegramam, on the banks of Sokanasini River. Parambikulam in Western Ghats is about 125 kms from Palakkad. The dam and the wildlife sanctuary here are renowned. All sorts of animals and birds are seen here. There is a reservoir also. The place is famous for teak plantations. Mailadumpara, in Chulannur situated 22 kms away from Palakkad town and 5 kms from Peringothukrish, is also famed. It is here the peacock protection center is located. Kunjan Nambiar Smrudhi forest is also here.	{ "redpajama_set_name": "RedPajamaC4" }
in: Unnamed stars Uncharted star This star has no known canonical name. While the information presented in this article is canonical, the star described lacks an official name, thus the title is conjecture. Lantean Star Astrographical information Unnamed galaxy (Air) Eden system Yellow dwarf *"Faith" "That star is not supposed to be here." This star wasn't detected and charted by the Seed ships. When Destiny flew near it, the gravity of the star disrupted its Faster-Than-Light engine. Since the star system wasn't in any of the navigational data transmitted to Destiny from the seed ships, Destiny was required to plot a parabolic course around the star to chart the system itself. This protracted process allowed some of the crew aboard Destiny an opportunity to disembark for the month that the ship had allotted to complete the task and live on the idyllic planet in orbit of the star. This star is a yellow dwarf similar to Sol with Eden as the only planetary body in orbit of it. Dr. Nicholas Rush speculated that both the star and planet were created artificially by a very advanced race, though not likely the Ancients due to the writings on the orbiting planet. The nature of the star system perplexed many of the crew aboard Destiny, especially the astrophysicists like Rush and Dr. Dale Volker. The latter determining via Destiny's sensor data that the star had just completed the T Tauri phase of it's evolution, which would mean that it was less than 10 million years old. Had that been accurate, the planet orbiting the star would be very young in it's formation and nowhere near the point where it had an environment capable of supporting life. Several Tau'ri aboard Destiny believed that the star and the planet might have therefore been created by providence (God). Though most believe in both. (SGU: "Faith") Unnamed stars	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Q: Binomial product expansion I have seen the following mathematical identity in a book: $$ \prod_{i=1}^{N}\left( 1 + ax_i \right)^c = \left( 1 + \sum_{i=1}^{N}{ax_i} + \cdots + a^N\prod_{i=1}^{N}{x_i} \right)^c $$ Is this a generalization of the Binomial theorem? What are the implicit terms within $\cdots$? Any explanations, proofs, references are appreciated! A: These are simply Vieta's formulas, expressing the relations between roots and coefficients. A: This follows from the "Multi-Binomial Theorem". Quoted from the wiki page for the Binomial Theorem $$(x_{1}+y_{1})^{n_{1}}\dotsm(x_{d}+y_{d})^{n_{d}} = \sum_{k_{1}=0}^{n_{1}}\dotsm\sum_{k_{d}=0}^{n_{d}} \binom{n_{1}}{k_{1}}\, x_{1}^{k_{1}}y_{1}^{n_{1}-k_{1}}\;\dotsc\;\binom{n_{d}}{k_{d}}\, x_{d}^{k_{d}}y_{d}^{n_{d}-k_{d}}$$ A: It is not a generalisation of the Binomial theorem because the exponent of $c$ isn't really handled -- they just took it outside. If you were to expand out the right-hand-side, you would have a generalisation of the Binomial theorem.	{ "redpajama_set_name": "RedPajamaStackExchange" }
Jean-Jaques Mori es un deportista neocaledonio que compitió en judo. Ganó dos medallas en el Campeonato de Oceanía de Judo en los años 1983 y 1985. Palmarés internacional Referencias Judokas de Nueva Caledonia	{ "redpajama_set_name": "RedPajamaWikipedia" }
Complete your new season outfit with the stunning Equiline Brina horse riding socks, in black with Equiline lettering in silver studs on the leg. These comfortable, breathable equestrian socks have a reinforced heel and toe, and the inner calf features an ultra light and thin 'control zone' for optimum comfort. The Equiline Brina Socks are available in Black, in sizes 35/38 (UK 3-5) or 39-42 (UK 6-8).	{ "redpajama_set_name": "RedPajamaC4" }
David Cramer David Cramer / Amazon David Cramer is associate editor at Baker Academic and Brazos Press in Grand Rapids, Michigan, and PhD candidate in theology at Baylor University. His dissertation examines the theological lineage of Walter Rauschenbusch, Reinhold Niebuhr, and John Howard Yoder. A Field Guide to Christian Nonviolence by David Cramer 12-07-2015 There are different ways to understand the gospel's call to peace- and that's a good thing. IN THE LATE 1930s, a large swath of the American church was reluctant for the United States to become involved in another war in Europe. The memory of the Great War was too fresh; what had been intended to be "a war to end all wars," a crusade for freedom and democracy, in hindsight just looked like senseless horror. Entire denominations committed to peace positions. This pacifist sentiment troubled Reinhold Niebuhr, who was following the rise of Hitler and spoke out against the atrocities committed against Jews long before they had reached the national consciousness. So in 1940 Niebuhr penned an essay to rally what he saw as a disillusioned, passive church into taking concrete action for social justice. He titled the essay "Why the Christian Church is Not Pacifist" and argued that in a world marred by sin, coercion and violence were sometimes necessary to pursue justice. After the attack on Pearl Harbor, Niebuhr's argument against pacifism won the day; U.S. churches lined up en masse to support the war effort. Since then, many Christians have taken it for granted that violence is an unfortunate but realistic necessity if we hope to bring justice in a world where injustice is so pervasive. Yet a survey of 20th century theology shows that many Christians have grappled with violence, justice, and the gospel and arrived at conclusions quite different from Niebuhr—and from each other. These Christian witnesses for peace include familiar voices such as Dorothy Day, Thomas Merton, Martin Luther King Jr., John Howard Yoder, and Stanley Hauerwas, but also many less well-known voices, such as the ones listed on the following pages. Examined together, these eight perspectives show that Christian nonviolence isn't a singular position, but rather a rich conversation wrestling with what it means to live out the biblical call to justice amid the complexities of ever-changing political, social, and moral situations. Yearning to Breathe Free Churches on the U.S.-Mexico border are making a statement about immigration—by working together to meet humanitarian need. "I DON'T BLAME the Border Patrol. I blame our country," Sister Norma Pimentel told Rep. Jim McGovern on a hot afternoon in McAllen, Texas, last August. "It's like a burning building," explained Pimentel, director of Catholic Charities of the Rio Grande Valley, "and we're sending them back into it." Pimentel was describing the U.S. policy of deporting Central American refugees back to their home countries, while Rep. McGovern (D-Mass.) nodded in agreement. He had just visited the Border Patrol central processing facility, and Pimentel was leading him on a tour of the humanitarian respite center at Sacred Heart Catholic Church. The difference was striking: At the processing facility, children were detained in what McGovern described as "cages"; at the respite center, Catholic Charities staff and volunteers provided food, showers, clothing, medical exams, and an air-conditioned place for refugees to wait for a bus ride to meet family members living in the U.S. Coming Clean: A Confession	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
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Dr. Weeks' Comment: The trick for surviving cancer is to understand that cancer is a process – a cytosolic metabolic disease and not an "it" – meaning you can't cut "it" out. The "it" you see or feel is a symptom of the cancer process and not the cancer itself. Confused? Consider with me the big mushroom growing off a tree – the shelf mushroom which is flat on the top and you could put your coffee mug on it – well, if I took a sledge hammer and knocked this shelf fungus off the tree would you believe that I thereby "cured" the tree of cancer? No. Of course not. So why do you think cutting a great off will cure your body of the cancer process operating within? Strike the root of cancer – all cancers – correct your metabolism and correct the cancer process so your metabolism becomes healthy again. Corrective Cancer Care™ corrects imbalances and allows your metabolism to become more cancer free. It also remedies the cancer STEM cell and shuts down the method the cancer process uses to metastasize – inflammation. Watch this lecture to learn how to strike the root of cancer. Cancer Discov; 8(6); 764–79. ©2018 AACR. Genetic alterations that potentiate PI3K signaling are frequent in prostate cancer, yet how different genetic drivers of the PI3K cascade contribute to prostate cancer is unclear. Here, we report PIK3CAmutation/amplification correlates with poor survival of patients with prostate cancer. To interrogate the requirement of different PI3K genetic drivers in prostate cancer, we employed a genetic approach to mutate Pik3cain mouse prostate epithelium. We show Pik3caH1047Rmutation causes p110α-dependent invasive prostate carcinoma in vivo. Furthermore, we report that PIK3CAmutation and PTENloss coexist in patients with prostate cancer and can cooperatein vivoto accelerate disease progression via AKT–mTORC1/2 hyperactivation. Contrasting single mutants that slowly acquire castration-resistant prostate cancer (CRPC), concomitant Pik3camutation and Ptenloss caused de novoCRPC. Thus, Pik3camutation and Ptendeletion are not functionally redundant. Our findings indicate that PIK3CAmutation is an attractive prognostic indicator for prostate cancer that may cooperate with PTENloss to facilitate CRPC in patients. Significance: We show PIK3CAmutation correlates with poor prostate cancer prognosis and causes prostate cancer in mice. Moreover, PIK3CAmutation and PTENloss coexist in prostate cancer and can cooperate in vivoto accelerate tumorigenesis and facilitate CRPC. Delineating this synergistic relationship may present new therapeutic/prognostic approaches to overcome castration/PI3K–AKT–mTORC1/2 inhibitor resistance. New research has uncovered insights into the mechanisms that underlie prostate cancer, providing potential targets for new cancer therapies. Prostate cancer is the third most common cause of cancer-related deaths in the UK, and researchers from Cardiff University have identified a genetic alteration that is linked to poor prognosis for patients with the disease. Advanced prostate cancer patients initially respond well to hormonal therapies but nearly all will eventually develop an aggressive form of the disease called castrate-resistant prostate cancer. Previously, genetic mutations in a tumour suppression gene, PTEN, have been shown to activate the cell signalling pathway, PI3K, which gives prostate cancer cells their ability to grow uncontrollably. The new research has uncovered the role of another genetic mutation in prostate cancer, which influences the aggressive nature of the disease. Dr. Helen Pearson, Cardiff University's European Cancer Stem Cell Research Institute, said: "We've identified a new genetic mutation that may drive the growth of prostate cancer cells. In our research, we found that when prostate cells were given a mutation in the PIK3CA gene, they rapidly formed tumours that developed resistance to hormone therapy. "Our findings indicate that people who are carrying a PIK3CA genetic alteration are highly likely to develop resistance to hormonal cancer treatments and have a poor treatment outcome. "We also found that both PTEN and PIK3CA genetic alterations are present in prostate cancer, and that they can work together via potentially independent mechanisms to accelerate the development of the tumour, as well as causing the cancer to become resistant to hormone therapy. The research was the result of an international collaboration between Dr. Helen Pearson from Cardiff University and Professor Wayne Phillips at the Peter MacCallum Cancer Centre, Melbourne, Australia. The article 'Identification of Pik3ca mutation as a genetic driver of prostate cancer that cooperates with Pten loss to accelerate progression and castration-resistant growth' is published in Cancer Discovery. Ooops again – chemo drug (Avastin) used before side-effects discovered.	{ "redpajama_set_name": "RedPajamaC4" }
Meet Our Leadership Service Archive Why Do We Give? Who we are, where we come from, and where we're headed as a church family Here's the deal, Living Word cares about one thing more than anything else; Jesus Christ. We are a family of individuals who have found life-changing power in Jesus and simply want to help as many people as possible experience God's love, power, and presence. At Living Word, you will be encouraged and equipped with the Word of God so you can not only live a victorious life, but influence and change your world around you by demonstrating the love God has placed in your heart. Living Word Outreach Ministries started in 1978 as Gospel of the Living Word Church by a few families in a garage. The name change occurred in 1995 when Pastor Al moved to Spencer from Sioux City, Iowa to begin pastoring the church. Feeling a call of God on the church to reach out to Spencer and the surrounding communities, Pastor Al renamed the church. Where We're Headed What's the bottom line? More than ever, Living Word is committed to fostering a family built around four key mission points: Pursuing God Encouraging Growth Developing Faith Demonstrating Love We believe that each of these has a vital role to play in our lives if we want to live abundant lives in Jesus. But there's so much to unpack in each of those points, so to learn more about Living Word's Mission and Vision, click here. What This Means For You Most importantly, it means that wherever you're at in your faith journey, you're welcome at Living Word! None of us were meant to do life or Christianity alone, so we need each other. That's why God established the capital C Church, the Body of Christ. We all help and support each other in expanding the Kingdom of God on the earth, and yes, you have a role in expanding the Kingdom. Let us help you find it. We can hardly wait to meet you! Say hello to the leadership team at Living Word Why we exist & our strategy to fulfill our purpose What we believe at Living Word about God, Salvation, and the Church We're glad you're here! We'd love to see you in person sometime! Worship starts every Sunday at 9:30a! Want to say hello? 905 10th Ave SE Spencer, IA 51301 Copyright 2019, Living Word Outreach Ministries. All Rights Reserved.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
The committee had recommended the recovery of funds that the institution lost due to irregular financial practices, compliance with the laws governing public financial management, accountability and procurement and disposal of public assets and an investigation by the Inspectorate of Government (IGG) of financial malfeasance at the university. A section of members of staff of Makerere University have petitioned the Speaker of Parliament, calling for the constitution of a parliamentary committee to probe the institution. The January 2 petition is, among others, the minister of Education and Sport, the minister of State for Higher Education and the chairperson of Makerere University Academic Staff Association (Muasa). Mr Chris Obore, the director of communications and public affairs at the Parliament, said he was not aware of the said petition. "If it was addressed to the Speaker, she could still be studying it. Once she has made a decision, she will communicate to the clerk," he said. The petitioners are requesting that if such a committee is constituted it should interest itself in five key areas, some of which were pointed out in the 2016 report of the Visitation Committee on Makerere University, but have never been acted on. Top on the list is financial management, the payroll and disposal of assets, which all featured in the visitation committee's report. The petitioners also want the circumstances under which the university lost land in Kololo, Makindye, Katalemwa and Kabanyolo to be probed. Other areas that the petitioners would like the proposed probe to focus on include administrative malpractices, including the victimisation of students and staff who dare challenge those in administration, a review of how certain people were appointed to the university's council, a review of Universities and Other tertiary Institutions' Act with a view of causing amendments to it, and establishing why the recommendations of committees that have previously probed the university have never been implemented. Some of those accused of dabbling in what the petitioners termed as gross administrative malpractices and victimisation of students and staff are the vice chancellor, Prof Barnabas Nawangwe, and the Director of Makerere Institute of Social Research (Misr), Prof Mahmood Mamdani. Prof Nawangwe denied knowledge of the petition. "Is it different from the petition by the dismissed staff? What is it about and by who? I haven't seen it. Please send me a copy then we schedule a meeting," he wrote. By press time, the meeting had not been scheduled. This is, however, not the first time that similar allegations have been brought against Prof Mamdani. Last year, two PhD students, Judith Ikiring Obore and Vincent Nuwagaba, dragged him to court, accusing him of, among others, vindictiveness and abuse of university rules and regulations. Prof Mamdani filed written statements of defence denying the allegations. On Friday morning, the chairperson of Muasa, Mr Deus Kamunyu, told this newspaper that the petitioners were within their rights and that some of the issues they were raising were legitimate. "As an association, we associate with some of those issues. That is why we are saying that they must be addressed and brought to an end," Mr Kamunyu said.	{ "redpajama_set_name": "RedPajamaC4" }
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South America on your bucket list? Watch this space for 2017...to include Argentina Four Nations matches. Always wanted to get married in the Islands? Let out exclusive weddings division help you to make your Pacific wedding dreams come true! Experience and Stability Previously operating as Denise Tindle Travel Ltd for more than 25 years, locals Carla & Clint Mangles purchased World Travellers King Country early in 2014. Carla is a familiar face in the community and has been a travel consultant in the business since 2006. "I have had excellent experiences with Carla when booking overseas trips and would always go back to her." "Everyone is always welcoming, friendly and helpful. They always follow up any request and explain options. They are interested in YOUR ideas and needs."	{ "redpajama_set_name": "RedPajamaC4" }
Growing up in the Las Vegas Valley, Donna Potter has always been inspired and influenced by the surrounding desert - the colors and textures of the landscape as well as the brilliant hues of the sunrises and sunsets. She makes pottery that has an artistic flare, primarily objects that function in the home. Most of her work is thrown on the Potter's wheel and altered in some way. The glazes on her pots depict the subtle color and texture from life in the Mojave Desert. Be the first to hear about our workshop schedule, special events, and sales. Copyright © 2018 Mission Hills Pottery - All Rights Reserved.	{ "redpajama_set_name": "RedPajamaC4" }
The Albany Herald, Ga. Dougherty County Commission hears update on recreational activities Alan Mauldin, The Albany Herald, Ga. Jan. 9—ALBANY — From the outdoor blacktop to indoor midnight basketball and other gatherings, the Albany Recreation and Parks Department is taking it to the community. That was department Director Steven Belk's message to the Dougherty County Commission on Monday, where Belk gave an update on some of the 2022 events held to get more people involved in activities. "New York City is not the only place they have stars that can bounce and shoot," the director said of the Blacktop Breakout Basketball Tournament series. The first of the series brought out 1,200 participants and fans, and the series was well-received, Belk said. The department provides recreation services to residents outside the Albany city limits under a contract with the county. Records kept showed that 86% of participants in the first blacktop basketball event were from Dougherty County, including city residents, and at one of the four tournaments that number was 96%. "I want you to know your money is being well-spent," Belk said. Other 2022 events included the Good Life Gathering and Santa's Workshop. In addition to helping residents keep active, the community events also help keep the community healthier in terms of helping to prevent crime, according to the director. He pointed to statistics showing that giving young people something to do between 7 p.m. and midnight can help lower crime rates. "I realize the importance for Recreation and Parks to minimize crime in this city," he said. "I'm proud to say there were no issues. That night we know we addressed some of the issues in these neighborhoods. We went out in the neighborhoods and recruited players." Santa's Workshop, held at the county-owned Robert Cross Park, also was a success, he said. "We had 5- to 17-year-olds," he said. "They were out there playing. They had a good time. We brought out people who had not visited this multipurpose facility. It's not only for basketball. We're going to use it to educate." Is Albany International Corp. (NYSE:AIN) Expensive For A Reason? A Look At Its Intrinsic Value Licking County swimmers pick up intensity in pool with February upon us Newark Advocate Spring opening planned for Belmont's CityRec Center	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
(Bichon Maltiase) 145 Available for Adoption Save search for breed Even though the Maltese is best known for a beautiful coat, this dog's body structure, facial expression, and overall carriage are essential components of the type. The Maltese is a diminutive dog with a compact, square body, covered all over with long, flat, silky, white hair hanging almost to the ground. The expression is gentle yet alert. This is a vigorous dog, with a jaunty, smooth, flowing gait. The well-built Maltese seems to float over the ground when trotting. Ready to see what dogs fit you best? Take our short quiz to find out! Breed Traits Affection Level Friendliness To Dogs Friendliness To Other Pets Friendliness To Strangers Ease of Training Heat Sensitivity Breed Attributes 4-6 lb Barbichon Area of Origin Date of Origin Bichon Maltiase The Maltese is the most ancient of the European toy breeds, and among the oldest of all breeds. The island of Malta was an early trading port, visited by Phoenician sailors by 1500 b.c. Maltese dogs are specifically mentioned in writings as early as 300 b.c. Greek art includes dogs of Maltese type from the fifth century on. There is evidence that they even erected tombs to favored Maltese. Although the dogs were often exported and subsequently widely distributed throughout Europe and the Orient, the core population on Malta remained relatively isolated from other dogs, resulting in this distinctive dog that bred true for centuries. Though the Maltese's hallmark is its long, silky, dazzling white hair, early Maltese came in colors other than white. By the early fourteenth century, Maltese had been brought to England, where they became the darlings of the upper-class. Writers of the succeeding centuries continually commented upon their diminutive size. Still these little dogs were never commonplace, and an 1830 painting entitled "The Lion Dog from Malta—Last of His Race" suggests that the breed may have been in danger of extinction. Soon after, two Maltese were brought to England from Manila. Although originally intended as a gift for Queen Victoria, they passed into other hands and their offspring became the first Maltese exhibited in England. At this time, they were called Maltese Terriers, despite the lack of terrier ancestry or characteristics. In America, the first Maltese were shown as Maltese Lion Dogs around 1877. The name lion dog probably arose from the habit of dog fanciers, particularly those in the Orient, of clipping the dogs to look like lions. The AKC recognized the breed as the Maltese in 1888. The Maltese slowly increased in popularity, and now it ranks as one of the more popular pet toy breed dogs. Long a favorite lapdog, the gentle Maltese fills this role admirably. The Maltese also has a wild side, and loves to run and play. Despite the innocent look, this is bold and feisty pup who may challenge larger dogs, and some enjoy barking. The Maltese is reserved with strangers. The exercise requirements of the Maltese are easily met with indoor games, a romp in the yard, or a short walk on leash. The coat needs combing every one or two days. Show coats may be "wrapped" for protection. The white coat may be difficult to keep clean in some areas. Pets may be clipped for easier care. Major concerns: none Minor concerns: patellar luxation, open fontanel, hypoglycemia, hydrocephalus, distichiasis, entropion, dental problems, hypothyroidism, portacaval shunt Occasionally seen: deafness, shaker syndrome Suggested tests: knee, eye, cardiac Life span: 12–14 years Note: While the characteristics mentioned here may frequently represent this breed, dogs are individuals whose personalities and appearances will vary. Please consult the adoption organization for details on a specific pet. Finding Maltese for You... Do you have a dog? For prospective dog owners who are interested in a particular breed, purebred rescue … Breed-Based Activities for Dogs Many of today's dogs are bored and under-exercised and the solution is increased … Similar Breeds	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Lee County Criminal Court handles all criminal cases that are filed in Lee County. See below for more information about criminal cases in Lee County. Where can I get help for my Lee County criminal case? The 6th amendment of the United States Constitution provides a criminal defendant with the right to an attorney. As read in the miranda rights, this means that if a defendant cannot afford to hire a private attorney a legal attorney will be appointed to the defendant to represent him at no cost to the defendant. This is often a public defender. In addition, the court clerk for Lee County will also be able to provide general information about a specific criminal case. The clerk can only provide information and is not an attorney so they cannot provide legal advice, only a licensed attorney can provide legal advice about what the best options for are for your particular case. Prosecutor in Lee County In Lee County, the prosecutor is an attorney representing Lee County. In some cases, the prosecutor may actually represent Virginia. For the most part, the prosecutor in Lee County has discretion to both decide whether to file charges and also negotiate a potential plea deal with the defendant. Lee County Required Court Appearances In Lee County, there are both required and non-required court appearances for the defendant. At a required or mandatory appearance hearing, the defendant is required to appear in person before the court. Failing to appear at your required hearing may result in a bench warrant being issued for your arrest by the judge. Sentencing in Lee County In Lee County if the defendant is found guilty (by trial or plea), the defendant will be sentenced. This sometimes occurrs immediately after being found guilty, but can also take place at a later date. In most instances, a judge will impose the sentence that is requested by the prosecution, but they also have the descretion to impose a different sentence. Where will Lee County criminal case hearings take place? Criminal cases will take place at the criminal courts of Lee County. See here for the location of the criminal courts in Lee County. The Fifth and Sixth Amendments to the U.s. Constitution give defendants in criminal cases the right to counsel/attorney. If you cannot afford an attorney one will be appointed to represent you. Like other rights a defendant has, this one can be waived as well and alternatively you can choose to represent yourself. A Plea Agreement, sometimes known as a Plea Bargain is an agreement between the prosecution and the defendant, where the defendant pleads guilty or no contest often in exchange for a lesser charge or lighter recommended sentence. A large majority of criminal cases end in a plea agreement. In Lee County you can inform your attorney to negotiate with the prosecution to attempt to come to a plea agreement, but this is dependent upon the charge severity and also the prosecutors willingness to accept a plea deal. Lee County Arraignments An arraignment is a court hearing. In Lee County this is the first thing that will happen in a criminal case. The defendant will be brought before a judge in Lee County Criminal Court and the judge will read the charges that were filed against the defendant. The judge will also read the rights the defendant has and ask the defendant if they understand both the charges filed against them and their rights as a defendant in the case. In Lee County a plea of Guilty, Not Guilty or No Contest may be entered. In a guilty or no contest plea the sentencing of the defendant may take place at the same arraignment hearing or a later date may be scheduled for sentencing. For a not guilty plea, a date will be set for a trial. Appealing a guilty verdict A defendant may appeal a guilty verdict to an appellate court. This is not a request to have another trial, but a request for an appellate court to review the case and determine that it was handled in a correct legal manner. There are a number of outcomes in an appeal including an upholding of the conviction, a finding that errors were made resulting in a retrial or resentencing or possibly a complete disimissal of all charges. Lee County Criminal Court Locations Lee County Circuit Court – 30th Judicial Circuit Address: PO Box 326, Jonesville VA 24263 Lee County General District Court – 30th Judicial District Lee County Juvenile and Domestic Relations District Court	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
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7ESCORTGIRLS Янв 28, 2020 \| By alexishibbs72 I didn't suppose the weather was bad in any respect, but I remember seeing among the natives shivering seemingly out of behavior. Finding affirmation in punishment, courting it, deliberately seeking degradation… seeing herself as unhealthy, dirty, low and solely good for…. He has a lot to say about pimps and none of it good. S good to hear you had a visit to the Canary Islands and loved Lanzarote and Tenerife. We go to visit women recently «rescued» from the intercourse trade, a time period for which you can read arrested. «When I used to be thirteen and messed up, I used to be arrested for prostitution and my mom gave permission for CNN to place it on Tv.» I don't think I'd forgive such an action. Let alone giving permission for the lady, herself, to be interviewed. Perhaps the underage sex commerce suits in with the whole «what occurs in Las Vegas, stays in Las Vegas so let all of it hold out and get together hearty» mentality. «Selling the Girl Next Door takes viewers into the world of underage American ladies caught up in the violent sex trade. A. The Essex lady! Radio 1 DJ Scott Mills' show has been cleared of breaching broadcasting rules over jokes made about Essex girls. A charitable fund set up to deal with the stereotyping of Essex girls has raised £38,000 six months after its inception. «The girls are simply objects to those males, for use as they wish and discarded. There are no chains and shackles. There is rarely any thought to their welfare. There you can find a large amount of useful info on how you can enrich your life by having a career there. Having landed their first jobs, Linda and Sandra look set. Those that pursue sex with kids are all too aware of the traps set by legislation-enforcement. She is detached. Her responses are mere echoes of Lyons' leading questions. Manchester Choice Escorts is a leading modeling and leisure agency, We are offering elite class adult escorts women in Manchester. According to the middle for Missing and Exploited Children, there are anywhere from 100,000 to 300,000 underage American girls being sold for sex in America. Bed Domination also supply shemale mistresses now, so if you're desirous about being dominated by a robust shemale escort, נערות ליווי give them a name. No. Mom would not prefer it (however Dad would!) Sorry, I've to present it a thumbs down based mostly on the mom take a look at. Certainly, this girl's mom doesn't understand. The mom seems more taken with absolving herself of blame than in helping her little one. The mother is instantly destructive. One woman spoke of her experience of serial rape at age ten, נערות ליווי בפתח תקווה one other at eleven, both of them with tears operating down their faces as they recall. At the top of the day, it really boiled all the way down to the easy undeniable fact that she decided she did not love me. They think about the day that they will fall in love with the person that they wish to spend the rest of their life with. It was I think my last probability at love. Our source has been setting up intercourse sessions for the last two years, making as a lot as £5,000 a time — while the ladies pocket 4 instances that. The precise thing to do is get them assist, but most occasions he cannot, because there's nowhere to put them. 50s up north it used to get very foggy due to the coal mines and the chimneys, but in fact now they do not get it either! And naturally we have bravery. Try to speak your emotions more and/or נערות ליווי במרכז do other activities that have a calming impact on you similar to meditation, yoga and relaxation exercises. I think people should date with more of an open mind. I think it's the latter, Lynda. But we do present a number of emotion. What first struck me about this girl is her flat perspective and full lack of emotion. Selling the Girl Next Door was produced by Steve Turnham. Is door a collective noun? She shuts the Cortina's door. My e-leaflet Addicted To Sex? In response to Immigration and Customs Enforcement (ICE) round 14,000 to 17,000 women and kids are imported into the nation for the sex trade. I might guess each women undergo from severe self-loathing and no vanity, in search of confirmation of their low self-picture within the abuse, danger and humiliation of the commerce. For these tons of of 1000's of women in want, in response to a Justice Department report released in the fall, there are 50 beds in amenities able to coping with their complicated and deeply entrenched issues. The All Wheel Drive (AWD) Tractor market report contains historic data, current market tendencies, product consumption, atmosphere, technological innovation, future prospects, upcoming applied sciences and the technical progress in the associated industry. • What are the completely different factors which are influencing the market progress? If you have any inquiries relating to in which and how to use נערות ליווי בהרצליה, you can get hold of us at our own site. Such as you, what actually appalls me is that these kids are further victimized by the American justice system that calls them prostitutes so it could possibly treat them like criminals instead of the victims they are. Where I come from, minors concerned with the justice system should not treated this way. And yet my emotions at what happened inevitably are intense and that i needed to share them in the one way I can. 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To receive our weekly specials, click here. Your information will not be sold for use in mass mailings, spam, advertisements, or any profitable mailings by other companies. Limited View. Welcome drink, non-motorized watersports and more. Beach House Luxury Club Level. Adults Only, Luxury Included Vacation. Includes all meals, premium spirits, activities and more. Save up to 65%. $250 air credit per booking.	{ "redpajama_set_name": "RedPajamaC4" }
This La Amistad luxury villa is the epitome of upscale living in the heart of downtown Ojai. Designed to perfectly balance old-world charm with modern comforts, this custom home allows you to enjoy mountain views, abundant natural lighting, an array of custom touches throughout, and a beautifully landscaped, private courtyard – all just two blocks from Ojai Avenue. This ideally located Ojai home for sale allows you to enjoy the look and feel of an Italian villa from which you can take a short walk to the farmers' market, ride your bike to your favorite coffee house, stroll through the Arcade for some boutique shopping, or wander over to Libbey Bowl for an outdoor concert or Ojai's one-screen movie house to catch the latest release. La Amistad Villas has a total of just four units on the property, each of which is custom designed and built for maximum privacy and serenity. This home was the model unit; therefore, it has the upscale features common to all units, as well as custom features. Oversized, individual courtyards with stucco privacy walls and gated entries ensure that homeowners enjoy their personal retreats, while a two-car garage, covered parking alcove and additional guest parking helps to ensure that there is plenty of parking for dinner party guests and out-of-town visitors. This two-story unit has two guest bedrooms, a guest bathroom, a powder room, and an office or library with built-in cabinetry and bookshelves on the first floor. The second floor features the primary living areas, including the living room, dining area, kitchen, master bedroom, laundry room and an additional room that could be used as a yoga studio, reading nook or nursery. An elevator connects the two floors to allow you to fully enjoy the views and peacefulness of top floor living with the convenience of an elevator for those who prefer not using stairs. Entering your private courtyard featuring mountain views, mature trees and professionally designed landscaping with drought-tolerant plants, a slate walkway delivers you to an arched front door opening into the foyer. An open ceiling to the second floor makes this spacious entryway even more inviting, as does the custom, wrought iron chandelier. From the foyer, you can access the two spacious guest rooms, the stairs to the top-floor living area, the elevator, the guest bathroom, the powder room, and the library or office, which has built-in cabinetry with bookshelves, a desk space and file drawers. The office and each of the guest bedrooms has French doors leading to a patio, and one of the guest rooms also has a built-in cabinetry unit. The first-floor guest bathroom features a tile shower and counter top with a separate soaking tub, as well as ample storage. There is also a powder room with beautiful tiling and a granite counter top that has a door to both the foyer and the office. All of the rooms on the first floor feature acid-washed concrete floors, custom window coverings and ample natural lighting. The elevator or a beautiful staircase crafted with sustainably harvested Brazilian cherry wood and a wrought iron banister delivers you to the second floor where you will find an open floor plan, mountain views, balconies, a well-equipped kitchen and a variety of unique touches, such as an art alcove in the dining area. Sustainable Brazilian cherry wood floors are found throughout the upstairs living areas, while a ceiling of exposed, rough-hewn beams provides a rustic, romantic canopy for everyday life. In the living room, you will find a beautiful corner fireplace with a Venetian-style plaster finish, as well as arched French doors leading to the landing where you can take in the view of Ojai's famous Chief Peak. The dining area also has a set of French doors leading to a curved landing, as well as a second set of French doors leading to a tiled balcony where you can enjoy your morning coffee or watch the Pink Moment settle over the Topa Topa Bluffs as you entertain friends or have a family barbecue. If you prefer to prepare meals indoors, you can cook while chatting with friends sitting at the breakfast bar as you enjoy the luxury of granite counter tops and stainless steel appliances, including a Sub-Zero refrigerator, and a GE Monogram oven, microwave, six-burner stove and dishwasher. A tiled wall behind the stove, a walk-in pantry with built-in shelving and drawers, and plenty of counter space for preparing meals or serving guests finish off this kitchen to provide you with both the look and function only a well-planned kitchen offers. As you walk towards the master suite on the opposite end of the second floor, you pass the elevator, a coat closet, an extra room that can be used as a reading nook, yoga studio or nursery, and the laundry room, which has a sink with a tile counter top, a tile floor and built-in cabinetry for storage. You also pass the upstairs guest bathroom, which is beautifully adorned with tile, granite and Brazilian cherry wood. Once you step into the master bedroom, you will immediately see how this space is the ideal retreat at the end of the day. A cozy, remote-controlled fireplace, an exposed beam ceiling and French doors that lead to your private balcony provide a relaxing or romantic backdrop for your personal oasis. With room for bistro seating, the balcony is the perfect place to enjoy the crisp morning air over coffee, look over your garden as you have brunch, or end the evening with a good book and a cup of tea. This resplendent retreat also has built-in cabinetry with room for your flat screen television and an arched entry to the master bathroom and extra large walk-in closet with built-in shelving and drawers. In the master bathroom, you will find a large, oval soaking tub, a separate, glass-enclosed shower, a granite counter with double sinks and a decorative tile backsplash, tile floor and abundant storage. To complete the Italian villa look and feel of this great example of luxury Ojai real estate, you will find an old-world trowel finish on the exterior stucco, Venetian-style plaster finish on all interior walls, a barrel tile roof, copper finish gutters and an array of other unique details. Once you make this villa your home, you may never want to leave. Fortunately, with Village Mixed Use zoning, it is possible to run a small business from home, which means you could truly spend both your days and nights enveloped in the relaxed luxury this home provides. Contact Nora to learn more about this property or other Ojai real estate.	{ "redpajama_set_name": "RedPajamaC4" }
I completed the design of the emblem and the custom logotype for Team FUKUSHIMA Track & Field, organized by my bother in Fukushima, Japan. The narcissus flycatcher is the official bird of Fukushima Prefecture. After the earthquake and the nuclear disaster, Fukushima has had nothing but bad news. People have been enduring pain and shame over something that they don't have control over. I am hoping that by re-imagining the official bird, the narcissus flycatcher will give the team an iconic symbol, something the Fukushima people also can be proud of, stirring feelings of pride, and sending a positive message out.	{ "redpajama_set_name": "RedPajamaC4" }
Proserpinaca L. – rodzaj roślin należący do rodziny wodnikowatych (Haloragaceae R. Br.). Obejmuje co najmniej 4 gatunki występujące naturalnie na półkuli północnej. Systematyka Pozycja systematyczna według APweb (aktualizowany system APG III z 2009) Należy do rodziny wodnikowatych Haloragaceae tworzącej grupę siostrzaną dla rodziny Penthoraceae, wraz z którą wchodzą w skład rzędu skalnicowców. Pozycja w systemie Reveala (1993-1999) Gromada okrytonasienne (Magnoliophyta Cronquist), podgromada Magnoliophytina Frohne & U. Jensen ex Reveal, klasa Rosopsida Batsch, podklasa różowe (Rosidae Takht.), nadrząd Podostemanae R. Dahlgren ex Reveal, rząd wodnikowce (Haloragales Bromhead), podrząd Haloragineae Engl., rodzina wodnikowate (Haloragaceae R. Br. in Flinders). Wykaz gatunków Proserpinaca amblygona (Fernald) Small Proserpinaca intermedia Mack. Proserpinaca palustris L. Proserpinaca pectinata Lam. Przypisy Wodnikowate	{ "redpajama_set_name": "RedPajamaWikipedia" }
Navigate through the streets and find new places to go with Mio's car navigation devices. Maestro 4000 family v. 2.36. Maestro 4040 family v. 2.62/3.61. Triton 200 and 300 Software Version 1.94. Triton 400 Software Version 1.78. Triton 500 Software. 3 июн 2013 Поддельные китайские металлоискатели GPX 5000 и Garrett сам пользуюсь оригинальным gpx 4000. заплатил за него весьма не мало. Ещё в приборах очень важна настройка и прошивка а это дорого. Minelab GPX-4000 Metal Detector Reviews, Price, Specifications, Features, Image. Tektronix provides manuals, datasheets, and software for current and many discontinued products. All are available for you to download. Just getting started. The VAXstation was a family of workstation computers developed and manufactured by Digital Equipment Corporation (DEC) using processors implementing the VAX instruction set architecture (ISA). VAX stood for Virtual Address EXtension. Contents. hide 1 VAXstation I; 2 VAXstation II. 2.1 VAXstation II/GPX The VAXstation 4000 VLC (Very Low Cost), aka VAXstation 4000 M30, was.	{ "redpajama_set_name": "RedPajamaC4" }
As a Twin Cities orthodontist that serves the Minneapolis-St. Paul area including the communities of Roseville, Mendota, and Mendota Heights, Dr. Tammy Meister is well known for offe ring comprehensive, personalized treatment to patients of all ages. Our practice aims to make your orthodontic treatment go as smoothly as it possibly can so you can enjoy the time you spend improving your smile! Unfortunately, small emergencies can sometimes occur during treatment. But the good news is that most orthodontic emergencies can be dealt with your own, so you won't have to fuss with calling us every time you run into a problem. To help you solve common problems and issues with your braces, we've put together the following info. If any of these emergencies happen to you, it's important to seek help right away. Head to the nearest emergency room, if you think that's your best option, or call your family dentist. Your dentist is fully trained and capable of handling a wide range of dental problems and can likely provide you with the treatment and care you need. Depending on what has occurred, we can adjust your orthodontic treatment plan as needed. This type of problem is typically caused by either eating hard or sticky foods or by playing around with the braces on your teeth. If a loose bracket or band is still attached to the wire, leave it be and don't connect any elastics to it. If a bracket or band is irritating your mouth, cover the part that's rubbing or poking with orthodontic wax. If a bracket or band comes off, be sure to save any loose parts for when you visit us. If you don't have an upcoming visit scheduled with us, give us a call to set up an appointment so we can fix what's wrong with your braces. As your teeth begin to move, the archwire that runs through your brackets can poke the back of your mouth or irritate the inside of your cheeks. If this happens, try moving the wire into a more comfortable position using a Q-tip or a pencil eraser. You may also use tweezers to gently move a misplaced wire or tie, as long as you're careful. If the wire won't move and the problem persists, you can carefully cut the end of the wire off using a pair of nail clippers that you've sterilized in alcohol. If that doesn't do the trick, put some orthodontic wax on the part that's causing discomfort and then contact us for an appointment. The friendly team at Meister Orthodontics wants to make sure your treatment is as comfortable as possible, regardless of the circumstances. If you have any questions or concerns about your treatment, please feel free to contact us and we'll help! If you'd like to set up a free initial consultation with Dr. Meister for the early treatment your child may need to find out more about adult treatment for yourself, please call us at (651) 699-2013 or fill out our online appointment request form. We look forward to seeing you soon and giving you many reasons to smile!	{ "redpajama_set_name": "RedPajamaC4" }
You have probably seen my last post by now, I'm so excited I could oui! and the excitement of it all made me completely forget about my Outfit of the week, so while I'm away stuffing my face with croissants, here's this week's #OOTW. This week's #OOTW is a staple and an item I couldn't live without. The change of season always makes me pull out clothes I haven't worn for a while and somehow I feel refreshed, but there is one thing that remains the same for me; black jeans. It's hard to go past denim but there is something about black jeans that really floats my boat. It is so important to have an understanding of brands and their sizing, shapes and styles of jeans and even more so, what materials work for you. I'm a fan of skinny jeans and to be honest traditional denim doesn't do it for me. I prefer a softer, more flexible material with just the right amount of stretch. These kinds of jeans means I can take them through all seasons. Ok, maybe I wouldn't wear them in 40 degree heat (I hardly think I'll face that temperature here) but you get my drift. I love going from a casual day look to wearing them on a night out and it's amazing how one item can create so many different looks. I wear my jeans so often I have a few pairs on the go. I wear them to the point that the holes are beyond repair and they have faded so much they are now different shades of grey. Even then I can't throw them out so I have developed a hierarchy system; brand new pair, new pair, old pair which can be worn in public and an old pair for around the house. There are sub layers in this hierarchy but I won't bore you! We all have those pieces that we love and can't live without and I say everyone needs a pair of black jeans in their wardrobe. ← I'm so excited I could oui! I love jeans …… blue but black is good too!	{ "redpajama_set_name": "RedPajamaC4" }
Attractive, Bright Clear Rosé Color; sweet pleasant aroma of strawberry and sponge Cake. A very good Desert Wine. Pale yellow gold in color; with the full flavor of sweet late Summer Georgia peaches; grown and blended to perfection. The Spring Tale Wine Club spotlights wines selected by our winemakers to complement each season, allowing you to try a wide range of wines—including white, rosé, red, and sparkling varietals—carefully chosen to appeal to a variety of tastes. Whether you are just beginning your exploration of wines or prefer trying a broad range of flavors,.	{ "redpajama_set_name": "RedPajamaC4" }
\section{Introduction} In this paper, we provide a systematic method to validate the domain of Lyapunov functions around hyperbolic fixed points both for continuous and for discrete dynamical systems with computer assistance. \par \bigskip First of all, we recall the definition of Lyapunov functions for flows in the typical sense. Let $\varphi : \mathbb{R}\times \mathbb{R}^n \to \mathbb{R}^n$ be a flow on $\mathbb{R}^n$. \begin{definition}[e.g. \cite{Rob}]\rm \label{dfn-Lyapunov-typical} Let $U\subset \mathbb{R}^n$ be an open subset. Consider the differential equation \begin{equation} \label{autonomous-intro} \dot {\bf x} = f({\bf x}),\quad f\in C^1(\mathbb{R}^n, \mathbb{R}^n). \end{equation} A {\em Lyapunov function} $L:U\to \mathbb{R}^n$ (for the flow) is a $C^1$-function satisfying the following conditions. \begin{enumerate} \item $(dL/dt)(\varphi(t,{\bf x}))\mid_{t=0}\leq 0$ holds for each solution orbit $\{\varphi(t,{\bf x})\}$ through ${\bf x} \in U$. \item $(dL/dt)(\varphi(t,{\bf x}))\mid_{t=0}= 0$ implies $\varphi(t,{\bf x})\equiv \bar {\bf x}\in U$, where $\bar {\bf x}$ is an equilibrium of (\ref{autonomous-intro}). \end{enumerate} \end{definition} Lyapunov functions are heart of gradient dynamical systems, which ensure that all trajectories behave so that Lyapunov functions decrease monotonously. Such behavior is expected locally around hyperbolic fixed points or general invariant sets. Once we construct Lyapunov functions locally around invariant sets, they let us easy to understand local dynamics in terms of level sets of Lyapunov functions. In Definition \ref{dfn-Lyapunov-typical}, a Lyapunov function $L$ is, if exists, defined in an open set $U\subset \mathbb{R}^n$, but it does not tell us how large $U$ can be chosen. Furthermore, explicit constructions of Lyapunov functions themselves are not easy because of nonlinearity of dynamical systems. For typical systems which possess Lyapunov functions with explicit forms, such systems themselves are fully determined by these functions, which are often called {\em gradient systems}; namely, $\frac{d}{dt}{\bf x} = \nabla L({\bf x})$. Although there is an abstract result concerning with the existence of Lyapunov functions, which is known as {\em Conley's Fundamental Theorem of Dynamical Systems} (e.g. \cite{Con, Rob}), detections of the concrete form of $L$ and the concrete shape of $U$ near invariant sets remain open and depend on individual dynamical systems. Despite the great importance for dynamical systems, construction of Lyapunov functions in concrete systems remains open. \par There are several preceding works for validating functionals like Lyapunov functions within explicit domains (e.g. \cite{C, KWZ2007, Mat2}), many of which apply functionals called {\em cones} satisfying {\em cone conditions} (e.g. \cite{ZCov}) to understanding asymptotic behavior around invariant sets . Cones with cone conditions restrict the behavior of points in terms of differences between two points. In particular, these concepts describe stable and unstable manifolds of invariant sets as graphs of Lipschitzian (or smooth) functions. On the other hand, there is a preceding study for constructing Lyapunov functions in the sense of Definition \ref{dfn-Lyapunov-typical} in explicitly given neighborhoods of hyperbolic equilibria \cite{Mat}. There Lyapunov functions have very simple forms, and a sufficient condition for validating Lyapunov functions in given domains as well as hyperbolicity of equilibria for (semi)flows is proposed. In these two directions, there are several similarities. Firstly, functionals (cones, Lyapunov functions) describing asymptotic behavior have {\em quadratic forms} around equilibria or fixed points. Secondly, validations of functionals are done via negative definiteness of matrices associated with functionals. Thirdly, computer assisted analysis via {\em interval arithmetics} are applied to validating given quadratic forms being cones or Lyapunov functions in explicitly given domains. \bigskip This paper aims a systematic procedure of Lyapunov functions around fixed points both for continuous and discrete dynamical systems by simple forms in given domains with computer assistance. This procedure gives us a general implementation of Lyapunov functions around fixed points, which can be applied to various dynamical systems, as shown in preceding works (e.g. \cite{C, KWZ2007, Mat2, W, WZ}). We also discuss relationships between preceding works; cones with cone conditions, Lyapunov functions in \cite{Mat}, and present studies, as well as a new aspect concerning with re-parameterization of trajectories. We believe that presenting arguments lead to a comprehensive understanding of Lyapunov function validations. \par Our central target function $L$ is a quadratic function as preceding works. The determination of domains $L$ being a Lyapunov function, called {\em Lyapunov domain}, consists of following two stages. \begin{itemize} \item {\bf Stage 1: Negative definiteness of the matrix associated with $dL/dt$}. \end{itemize} For a domain containing an equilibrium, we verify the negative definiteness of specific matrix associated with $dL/dt(\varphi(t,{\bf x}))$ along solution orbits with computer assistance, which gives us a sufficient condition so that $L$ is a Lyapunov function in the domain. \begin{itemize} \item {\bf Stage 2: Direct calculations of the negativity of $dL/dt$ along trajectories}. \end{itemize} For domains which do not contain equilibria, we calculate $dL/dt(\varphi(t,{\bf x}))$ directly with computer assistance and verify if it is negative. If such criteria pass for given domains, the quadratic function $L$ is validated as a Lyapunov function on the domain. Combination of validations in these two stages with computer assistance gives us a useful tool to validate explicit Lyapunov domains of given quadratic functions as large as possible, which will be the basis for constructing locally defined Lyapunov functions in various dynamical systems. \bigskip Our paper is organized as follows. In Section \ref{section-cont}, we discuss the construction of Lyapunov functions for flows (continuous dynamical systems). We provide a systematic construction of Lyapunov functions being quadratic. We also generalize Lyapunov functions to {\em ${\bf m}$-Lyapunov functions}, which is a generalization of {\em $m$-cones} in \cite{Mat2}. In Section \ref{section-aspect}, several geometric and algebraic aspects containing mathematical validity of numerically computed objects associated with Lyapunov functions, as well as relevance to preceding works (e.g. \cite{C, Mat, W, WZ, ZCov}) are discussed. In Section \ref{section-discrete}, we discuss the construction of Lyapunov functions for maps (discrete dynamical systems). The basic strategy for construction is similar to flows. A discrete dynamical systems' version of ${\bf m}$-Lyapunov functions is also derived. In Section \ref{section-Lyapunov-periodic}, we briefly review the computation of Poincar\'{e} maps for flows and their differentials so that we apply arguments in Section \ref{section-discrete} to Poincar\'{e} maps, which yields the construction of Lyapunov functions for periodic orbits. In Section \ref{section-example-cont} and \ref{section-example-discrete}, several validation examples are shown for demonstrating applicability of arguments in previous sections. The former refers to flows and the latter refers to Poincar\'{e} maps. \begin{notation} For scalars $t$ or vectors ${\bf x} = (x_1,\cdots, x_n)$, $[t]$ and $[{\bf x}]$ denote interval enclosures containing $t$ and ${\bf x}$, respectively. More precisely, $[{\bf x}]$ is a vector whose $i$-th entry is $[x_i]$ for $i=1,\cdots, n$. For a function $f$ and objects $x$ (scalars or vectors), the set $f([x])$ is defined as $f([x]) = \{f(z)\mid z\in [x]\}$. An interval matrix $[A]$ denotes a matrix whose entries are intervals. Namely, $[A] = ([a_{ij}])_{i,j=1}^n$, $[a_{ij}] = [a_{ij}^-, a_{ij}^+]\subset \mathbb{R}$. A matrix-valued function $F(D) = (F_{ij}(D))_{i,j=1}^n$ of a set $D$, say rectangular domains, is defined by $F_{ij}(D) = \{F_{ij}({\bf x})\mid {\bf x}\in D\}$. These notations are used in discussions with interval arithmetics. \end{notation} \section{Lyapunov functions for continuous dynamical systems} \label{section-cont} In this section, we consider dynamical systems generated by ordinary differential equations, in particular, an autonomous system \begin{equation} \label{autonomous} \displaystyle \frac{d}{dt}{\bf x} = f({\bf x}),\quad {\bf x} \in \mathbb{R}^n, \end{equation} where $f : \mathbb{R}^n\to \mathbb{R}^n$ is a smooth map. Let ${\bf x^\ast}$ be an equilibrium of (\ref{autonomous}). Also, assume that ${\bf x^\ast}$ is hyperbolic. Namely, all eigenvalues of the Jacobian matrix $Df({\bf x^\ast})$ are away from the imaginary axis. \par A fundamental result on dynamical systems called {\em Hartman-Grobman's Theorem} (e.g. \cite{Rob}) claims that the dynamics around a hyperbolic equilibrium ${\bf x}^\ast$ is topologically conjugate to the dynamics generated by the linearized matrix $Df({\bf x}^\ast)$ at ${\bf x}^\ast$ in a small neighborhood of ${\bf x}^\ast$. As for linear vector fields, we can easily construct Lyapunov functions. Indeed, any linear vector fields can be generically written as, under the change of coordinates, \begin{equation} \label{aut-linear} \displaystyle \frac{d}{dt}{\bf x} = \Lambda {\bf x}, \quad \Lambda = {\rm diag}(\lambda_1,\cdots, \lambda_n). \end{equation} In this case, ones easily see that the functional \begin{equation} L({\bf x}) := -\sum_{i=1}^n {\rm sgn}({\rm Re}(\lambda_i)) x_i^2 \end{equation} is a Lyapunov function for (\ref{aut-linear}). Under this observation, it is natural to consider that there are {\em locally defined} Lyapunov functions around, at least, hyperbolic equilibria. Moreover, Lyapunov functions can be quadratic around hyperbolic equilibria. Our aim here is to provide a systematic procedure for constructing quadratic Lyapunov functions defined not only in a small neighborhood of hyperbolic equilibria but also in their explicitly given neighborhoods. The latter can be realized with computer assistance such as interval arithmetics. \subsection{Construction of quadratic functions} \label{section-cont-construction} An observation in the previous subsection gives us an expectation that Lyapunov functions can be locally constructed as {\em the quadratic function}. Now we provide a basic strategy for constructing Lyapunov functions. Let ${\bf x}^\ast$ be an equilibrium for (\ref{autonomous}). \begin{itemize} \item[1.] Let $Df^\ast$ be the Jacobian matrix $Df({\bf x^\ast})$ of $f$ at ${\bf x}={\bf x}^\ast$. For simplicity, assume that $Df^\ast$ is diagonalizable by a nonsingular matrix $X$, which is generically valid: \begin{equation} \Lambda = X^{-1}Df^\ast X, \end{equation} where $\Lambda = {\rm diag}(\lambda_1,\lambda_2,\cdots,\lambda_n)$. Note that computations of $\Lambda$ and $X$ do not need to apply interval arithmetics. Assume that, in the sense of floating-point arithmetics, ${\rm Re}(\lambda_i)\not = 0$ for all $i=1,\cdots, n$. \item[2.] Let $I^\ast$ be the diagonal matrix $I^\ast = {\rm diag}(i_1,i_2,\cdots,i_n)$, where \begin{equation} \label{sign-change-cont} i_k = \left\{ \begin{array}{c} 1, \quad \mbox{if} \quad \mbox{Re}(\lambda_k) < 0, \\ -1, \quad \mbox{if} \quad \mbox{Re}(\lambda_k) > 0. \end{array}\right. \end{equation} Note that ${\rm Re}(\lambda_k)\not = 0$ since $x^\ast$ is hyperbolic. \item[3.] Calculate the real symmetric matrix $Y = (Y_{ij})_{i,j=1}^n$ as follows: \begin{equation} \label{Y-cont} \hat{Y} := X^{-H} I^\ast X^{-1}, \quad Y := \mbox{Re}( \hat{Y}), \end{equation} where $X^{-H}$ denotes the inverse matrix of the Hermitian transpose $X^H$ of $X$, which is sufficient to be calculated by floating-point arithmetics. \item[4.] Define the quadratic function $L$ by \begin{equation} \label{Lyapunov-flow} L({\bf x}) := ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast), \end{equation} which is our candidate of Lyapunov function around $x^\ast$. If we deal with $L$ with interval arithmetics, we replace $Y$ by $(Y+Y^T)/2$ or set $Y_{ji} = Y_{ij}$ so that we keep the symmetry of $Y$. \end{itemize} Note that the matrix $Y$ is determined to be {\em real and symmetric}. The operation $Y\mapsto (Y+Y^T)/2$ avoids a delicate case that $Y$ is not actually symmetric due to, say, numerical errors. It is valid for our arguments to provide various properties of $L$ as a Lyapunov function, which can be seen below. \subsection{Validity of $L({\bf x})$ in (\ref{Lyapunov-flow})} Here we find a sufficient condition such that the function $L({\bf x})$ in (\ref{Lyapunov-flow}) is indeed a Lyapunov function in a given neighborhood of ${\bf x^\ast}$. Note that quadratic forms with respect to Hermitian matrices take real values. In particular, \begin{equation} {\bf z}^T H {\bf z} = {\bf z}^T \mbox{Re}(H) {\bf z} \end{equation} holds for a Hermitian matrix $H$ and a real vector $z$. Now we have the following theorem, which indicates that our procedure validates (i) Lyapunov functions on a compact, star-shaped domain $D_L$, and (ii) the uniqueness of equilibria in $D_L$ at the same time. \begin{theorem} \label{thm-Lyapunov-cont} Let $D_L$ be a compact, star-shaped domain centered at an equilibrium ${\bf x}^\ast$ of (\ref{autonomous}). Define a matrix $A({\bf z})$ by \begin{equation} \label{matrix-neg-def} A({\bf z}) = Df({\bf z})^T Y + Y Df({\bf z}). \end{equation} Assume that the matrix $A({\bf z})$ is strictly negative definite for all ${\bf z}\in D_L$. Then $L({\bf x})$ is a Lyapunov function on $D_L$. Moreover, ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{theorem} In our arguments, Lyapunov functions are considered in compact domains. Nevertheless, thanks to the continuous dependence of $A({\bf z})$, we can easily extend functions to open neighborhoods of such compact domains, and hence our arguments with respect to Lyapunov functions in the sense of Definition \ref{dfn-Lyapunov-typical} still make sense. \begin{proof} Let ${\bf x}(t)$ be a solution orbit of (\ref{autonomous}) with ${\bf x}(0) = {\bf x}$. Differentiating $L({\bf x}(t))$ with respect to $t$ along ${\bf x}(t)$, we obtain \begin{equation} \displaystyle \frac{d}{dt}L({\bf x})_{t=0} = f({\bf x})^T Y ({\bf x}-{\bf x}^\ast) + ({\bf x}-{\bf x}^\ast)^T Y f({\bf x}). \end{equation} Now we consider the function \begin{equation} g(s) = f({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)). \end{equation} Since \begin{equation} \displaystyle \frac{dg}{ds}(s) = Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))({\bf x} - {\bf x}^\ast) \end{equation} and $f({\bf x}^\ast)={\bf 0}$, we obtain \begin{equation} f({\bf x}) = \displaystyle \int_0^1 Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)) ds ({\bf x} - {\bf x}^\ast), \end{equation} where $Df({\bf x})$ is the Jacobian matrix of $f$ at ${\bf x}$. The $t$-differential of $L({\bf x}(t))$ is thus represented by a quadratic function as follows: \begin{equation} \label{t-differential} \displaystyle \frac{d}{dt}L({\bf x}) = ({\bf x} - {\bf x}^\ast)^T \displaystyle \int_0^1 \{ Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))^T Y + Y Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)) \}ds\, ({\bf x} - {\bf x}^\ast). \end{equation} Let ${\bf z}={\bf x}^\ast+s({\bf x} - {\bf x}^\ast)$, and $A({\bf z})$ be a real symmetric matrix given by (\ref{matrix-neg-def}). If $A({\bf z})$ is negative definite on $D_L$, then it is also negative definite at any point ${\bf z}$ on a segment connecting ${\bf x}^\ast$ and ${\bf x}$, since $\{{\bf x}^\ast+s({\bf x} - {\bf x}^\ast)\mid s\in [0,1]\}\subset D_L$. Thus we get $\displaystyle \frac{d}{dt}L({\bf x}) < 0$ for any ${\bf x}\neq {\bf x^\ast}$. \par Obviously, $\displaystyle \frac{d}{dt}L({\bf x}) < 0$ for all ${\bf x} \not = {\bf x}^\ast$ and $\displaystyle \frac{d}{dt}L({\bf x}^\ast) = 0$. Therefore, $L({\bf x})$ is a Lyapunov function on $D_L$. \par \bigskip The form $dL/dt({\bf x}) = ({\bf x}-{\bf x}^\ast)^T \int_0^1 A({\bf x}^\ast + s({\bf x} - {\bf x}^\ast))ds ({\bf x}-{\bf x}^\ast)$ and the strict negative definiteness of $A({\bf z})$ in $D_L$ imply that $dL/dt(\varphi(t,{\bf x}))_{t=0} < 0$ in $D_L\setminus \{{\bf x}^\ast\}$. It implies that ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{proof} In this theorem, we assume the hyperbolicity of ${\bf x}^\ast$ not in the rigorous sense, but just in the numerical sense. Nevertheless, an additional assumption guarantees the hyperbolicity of ${\bf x}^\ast$ in the rigorous sense during the construction of Lyapunov functions, which is discussed in Section \ref{section-hyp-cont}. \begin{definition}\rm We shall call the domain $D_L$ where the Lyapunov function $L$ exists {\em a Lyapunov domain} (for $L$). \end{definition} \begin{remark}\rm In preceding works (e.g. \cite{Mat, ZCov}), $D_L$ is assumed to be convex. Our theorem weakens the geometric condition of $D_L$. \end{remark} \subsection{Verification of Lyapunov domains with interval arithmetics} \subsubsection{Stage 1: Negative definiteness of $A({\bf z})$.} \label{section-stage1-cont} Theorem \ref{thm-Lyapunov-cont} claims that $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function on a compact, star-shaped domain $D_L$ centered at an equilibrium ${\bf x}^\ast$, if the real symmetric matrix $A({\bf z})$ in (\ref{matrix-neg-def}) is negative definite. \par If the domain $D_L$ itself or a piece of divided subdomains contains an equilibrium, we enclose it an interval vector $[{\bf x}^\ast]$ and verify the negative definiteness of the matrix enclosure $A([{\bf x}^\ast]) = \{A({\bf x})\mid {\bf x} \in [{\bf x}^\ast]\}$ on domains in our considerations. An example of such a procedure is the following: \begin{algorithm} \label{alg-cont} An algorithm for validating Lyapunov domains containing an equilibrium ${\bf x}^\ast$ based on the strict negative definiteness of $A({\bf z})$ consists of the following. \begin{itemize} \item[(1)] Calculate $A({\bf x}^\ast)$ with floating-point arithmetics. If necessary, diagonalize $A({\bf x}^\ast)$ approximately after ensuring the symmetry of $A({\bf x}^\ast)$. Namely, calculate a matrix $X^\ast$ such that \begin{equation} \Lambda^\ast = (X^\ast)^{-1}A({\bf x}^\ast) X^\ast. \end{equation} Note that $X^\ast$ can be chosen as a real matrix since $A({\bf x}^\ast)$ is real and symmetric. \item[(2)] Calculate the interval matrix $(X^\ast)^{-1}A([{\bf x}^\ast]) X^\ast$ with interval arithmetics. Let $[a^\ast]_{ij}$ the $(i,j)$-th entry of the matrix, which takes the interval value. \item[(3)] Apply the Gershgorin Circle Theorem to the interval matrix, namely, verify \begin{equation} [a^\ast]_{ii}+\displaystyle \sum_{j\neq i}\|[a^\ast]_{ij}\| < 0 \end{equation} with interval arithmetics for $i=1,\cdots,m$. \end{itemize} \end{algorithm} This procedure works to prove the existence of Lyapunov functions as long as the above algorithm passes successfully, even if domains do not contain equilibria. Note that there is a more effective verification method using Cholesky decomposition by Rump, which can be applied on INTLAB \cite{INTLAB}. \par \bigskip We also note that the negative definiteness of $A({\bf z})$ does not involve the integral in (\ref{t-differential}). This fact indicates that the verification of negative definiteness of $A({\bf z})$ on $D_L$ by Algorithm \ref{alg-cont} can be done independently for each subdomain $D_k$ of $D_L$ with the decomposition $D_L = \bigcup_{k=1}^K D_k$. Namely, \begin{corollary} \label{cor-subdivision-cont} Let $D_L$ be a compact, star-shaped domain centered at an equilibrium ${\bf x}^\ast$ of (\ref{autonomous}). Define a matrix $A({\bf z})$ by (\ref{matrix-neg-def}). Let $D_L=\bigcup_{k=1}^K D_k$ be a decomposition of $D_L$ into subdomains. We enclose each $D_k$ by an interval vector $[{\bf x}_k]$ and define an interval matrix $A([{\bf x}_k])$ in the similar way to the above arguments. Assume that, for all $k=1,\cdots, K$, the interval matrix matrix $A([{\bf x}_k])$ is strictly negative definite in the sense that the matrix $A({\bf z})$ is strictly negative definite for all ${\bf z}\in [{\bf x}_k]$. Then $L({\bf x})$ is a Lyapunov function on $D_L$. Moreover, ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{corollary} The proof can be done by the same arguments as the first part of Theorem \ref{thm-Lyapunov-cont} for ${\bf x}\in D_k$ for each $k=1,\cdots, K$. \subsubsection{Stage 2: The case where a subdomain does not contain ${\bf x}^\ast$.} \label{section-stage2-cont} Even if the strict negative definiteness of $A({\bf x})$ violates, if a divided subdomain does not contain equilibria, there is another way to verify $dL/dt < 0$ on it, namely, verifying \begin{equation} \displaystyle \frac{d}{dt}L({\bf x})\mid_{t=0} = f({\bf x})^T Y ({\bf x}-{\bf x}^\ast) + ({\bf x}-{\bf x}^\ast)^T Y f({\bf x}) \end{equation} being negative directly by interval arithmetics. \begin{corollary} Let $D_L\subset \mathbb{R}^n$ be a compact and star-shaped set and ${\bf x}^\ast$ be an equilibrium of (\ref{autonomous}). Assume that the vector \begin{equation} f({\bf x})^T Y ({\bf x}-{\bf x}^\ast) + ({\bf x}-{\bf x}^\ast)^T Y f({\bf x}) \end{equation} is strictly negative for all ${\bf x}\in D_L$. Then $L({\bf x})$ given by (\ref{Lyapunov-flow}) is a Lyapunov function on $D_L$. \end{corollary} In practical computations, for an interval vector $[{\bf x}]$ containing the subdomain, we calculate $\displaystyle \frac{d}{dt}L([{\bf x}])$ with interval arithmetics and verify if it is negative. We discuss the effectiveness of this procedure in Section \ref{section-example-cont}. \bigskip If either of the above procedures (Stage 1 and 2) passes in $D_L$, it turns out that the function $L({\bf x})$ is a Lyapunov function in $D_L$. In other words, $D_L$ is a Lyapunov domain. \subsection{${\bf m}$-Lyapunov functions} \label{section-m-Lyapunov-cont} A typical choice of the matrix $Y$ transform the original coordinate to the new one such that (\ref{autonomous}) is approximately described by \begin{equation} \frac{d}{dt}y_i = \lambda_i y_i + o(\|{\bf y}\|),\quad i=1,\cdots, n, \end{equation} which gives a Lyapunov function of the following form in a small neighborhood of the equilibrium ${\bf y}^\ast = (y_1^\ast, \cdots, y_n^\ast)$ (cf. Section \ref{section-hyp-cont}): \begin{equation} \label{Lyapunov-Mat} L({\bf y}) = -\sum_{i=1}^n {\rm sgn}({\rm Re}(\lambda_i)) (y_i-y_i^\ast)^2. \end{equation} Note that all coefficients in (\ref{Lyapunov-Mat}) have modulus $1$. It is thus natural to consider the similar quadratic functions {\em with arbitrary coefficients}, which leads to the idea of ${\bf m}$-Lyapunov functions; the main discussions in this subsection. The coefficients in (\ref{Lyapunov-Mat}) is in fact determined by the matrix $I^\ast$ in the definition of $Y$. Now we consider the following diagonal matrix $M^\ast = {\rm diag}(i_1,i_2,\cdots,i_m)$ , where \begin{equation} i_j = \left\{ \begin{array}{c} m_j, \quad \mbox{if} \quad \mbox{Re}(\lambda_j) < 0, \\ -m_j, \quad \mbox{if} \quad \mbox{Re}(\lambda_j) > 0 \end{array}\right. \end{equation} instead of the diagonal matrix $I^\ast$. Here ${\bf m} = \{m_j\}_{j=1}^n$ denotes a sequence of given positive numbers. Define $L_{M^\ast}({\bf x})$ as follows: \begin{equation} \label{Lyapunov-M-cont} L_{M^\ast}({\bf x}) := ({\bf x} - {\bf x}^\ast)^T Y_{M^\ast}({\bf x} - {\bf x}^\ast),\qquad Y_{M^\ast} = {\rm Re}(X^{-H}M^\ast X^{-1}), \end{equation} which is nothing but $L$ replacing $I^\ast$ by $M^\ast$. We can then prove negative definiteness of the matrix $A$ corresponding to the differential $(dL_{M^\ast}/dt)({\bf x})$ at ${\bf x}={\bf x}^\ast$ by similar arguments to Theorem \ref{thm-Lyapunov-cont}. Consequently, we obtain the following corollary. \begin{corollary} \label{cor-m-Lyap-cont} Let $D_L$ be a compact, star-shaped domain containing an equilibrium ${\bf x}^\ast$ of (\ref{autonomous}). Define a matrix $A_{M^\ast}({\bf z})$ by $A$ in (\ref{matrix-neg-def}) replacing $I^\ast$ by $M^\ast$ for a given sequence of positive numbers ${\bf m}$. Assume that the replaced matrix $A_{M^\ast}({\bf z})$ is strictly negative definite for all ${\bf z}\in D_L$. Then $L_{M^\ast}({\bf x})$ given in (\ref{Lyapunov-M-cont}) is a Lyapunov function on $D_L$. Moreover, ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{corollary} We shall call the function $L_{M^\ast}$ satisfying assumptions in Corollary \ref{cor-m-Lyap-cont} an {\em ${\bf m}$-Lyapunov function}. Since positive numbers ${\bf m}=\{m_j\}_{j=1}^n$ can be chosen arbitrarily, we can arrange these distributions, depending on situations. In particular, we can adjust the enclosure of stable and unstable directions in a neighborhood of a saddle ${\bf x}^\ast$ by arranging ${\bf m}$ as follows. \begin{itemize} \item If we choose the unstable cone $L_{M^\ast}^{-1}(-\infty,0)\cap D_L$ of ${\bf x}^\ast$ as sharp as possible, we choose positive numbers $m_j$ corresponding to $\mbox{Re}(\lambda_j) < 0$ as large as possible, compared with those corresponding to $\mbox{Re}(\lambda_j) > 0$. \item If we choose the stable cone $L_{M^\ast}^{-1}(0,\infty)\cap D_L$ of ${\bf x}^\ast$ as sharp as possible, we choose positive numbers $m_j$ corresponding to $\mbox{Re}(\lambda_j) > 0$ as large as possible, compared with those corresponding to $\mbox{Re}(\lambda_j) < 0$. \end{itemize} Note that the geometry of $D_L$ depends on the choice of positive numbers $\{m_j\}_{j=1}^n$, which is discussed in Section \ref{section-example-cont}. \section{Several aspects of Lyapunov domains} \label{section-aspect} We have seen that the strict negative definiteness of $A({\bf z})$ in (\ref{matrix-neg-def}) intrinsically provides us with Lyapunov domains containing unique equilibria. Moreover, our Lyapunov functions are quadratic. Lyapunov functions with explicit forms and domains of definition help us with the study of asymptotic behavior around equilibria {\em in given domains}. At least, a Lyapunov function $L$ admits the following geometric and algebraic aspects. Let $D_L$ be a Lyapunov domain. \subsection{Lyapunov functions around hyperbolic equilibria} In Theorem \ref{thm-Lyapunov-cont}, we focused on the strict negative definiteness of $A({\bf z})$ in a given domain containing ${\bf x}^\ast$. The negative definiteness of $A({\bf z})$ reflects the hyperbolicity of $x^\ast$. Indeed, for a {\em rigorous} hyperbolic equilibrium ${\bf x}^\ast$, the matrix $A({\bf x}^\ast)$ is strictly negative definite. \begin{proposition} \label{prop-hyp-cont} Let ${\bf x}^\ast$ be a hyperbolic equilibrium for (\ref{autonomous}). Then there is a neighborhood of $U$ of ${\bf x}^\ast$ such that $A({\bf z})$ given by (\ref{matrix-neg-def}) is negative definite for all points in $U$. Moreover, $L({\bf x})$ is a Lyapunov function on $U$. \end{proposition} \begin{proof} It is sufficient to check the negative definiteness of the Hermitian matrix \begin{equation} A^\ast = (Df({\bf x}^\ast))^H \hat{Y} + \hat{Y} Df({\bf x}^\ast) \end{equation} instead of $A({\bf x}^\ast)$ in order to prove the negative definiteness of $A({\bf x}^\ast)$, which follows from the fact that ${\bf z}^T \hat Y {\bf z} = {\bf z}^T \mbox{Re}(\hat Y) {\bf z}$ for any real vector ${\bf z}$. \par By the definition of the Hermitian matrix $\hat{Y}$, we get \begin{align} A^\ast &= (Df^\ast)^H X^{-H} I^\ast X^{-1} + X^{-H} I^\ast X^{-1}Df^\ast \\ &= X^{-H} \Lambda^H I^\ast X^{-1} + X^{-H} I^\ast \Lambda X^{-1}\\ &= X^{-H}(2\,\mbox{Re}(\Lambda) I^\ast)X^{-1}\\ &= -2\, X^{-H}\|\mbox{Re}(\Lambda)\| X^{-1}, \end{align} where $\|\mbox{Re}(\Lambda)\|$ is the matrix whose entry is the absolute value of the corresponding entry of $\mbox{Re}(\Lambda)$. This yields that $A^\ast$ is negative definite Hermitian matrix. Therefore, in a sufficiently small neighborhood of $x^\ast$, say a ball $\{{\bf x}\in \mathbb{R}^n \mid \|{\bf x} - {\bf x}^\ast\| < \epsilon\}$ for sufficiently small $\epsilon > 0$, we obtain \begin{equation} \displaystyle \frac{d}{dt}L({\bf x}) < 0, \qquad \forall {\bf x}\in \{{\bf x}\in \mathbb{R}^n \mid 0< \|{\bf x} - {\bf x}^\ast\| < \epsilon\} \end{equation} following the proof of Theorem \ref{thm-Lyapunov-cont}, which implies that $L({\bf x})$ is a Lyapunov function in such a neighborhood since $\displaystyle \frac{d}{dt}L({\bf x^\ast})=0$ also holds. \end{proof} This proposition indicates that, like Stable Manifold Theorem, {\em all hyperbolic equilibria locally admit Lyapunov functions of the form (\ref{Lyapunov-flow})}. \subsection{$L$ determines the eigenstructure of $Y$.} The symmetric matrix $Y$ is typically determined by the matrix consisting of eigenvectors at a point ${\bf x}^\ast$: an equilibrium for example. If ${\bf x}^\ast$ is hyperbolic and $Y$ is constructed by eigenvectors at ${\bf x}^\ast$, then $Y$ is nonsingular by definition. In many practical situations, by contrast, $Y$ is determined only numerically, or constructed by a matrix $X$ close to the eigenmatrix, which imply that there may be a case that $Y$ is singular. Conversely, if $L({\bf x})=({\bf x}-{\bf x}^\ast)^TY({\bf x}-{\bf x}^\ast)$ is a Lyapunov function on $D_L$ for {\em some} real symmetric matrix $Y$, then $L$ determines the algebraic structure of $Y$, which is stated as follows. Recall that the {\em stable manifold} of a hyperbolic equilibrium ${\bf x}^\ast$ is the set \begin{equation} W^s({\bf x}^\ast) = \{{\bf x}\in \mathbb{R}^n \mid \varphi(t,{\bf x})\to {\bf x}^\ast \text{ as }t\to +\infty\}. \end{equation} Similarly, the {\em unstable manifold} of ${\bf x}$ is the set \begin{equation} W^u({\bf x}^\ast) = \{{\bf x}\in \mathbb{R}^n \mid \varphi(t,{\bf x})\to {\bf x}^\ast \text{ as }t\to -\infty\}. \end{equation} Without the loss of generality, we may assume that ${\bf x}^\ast$ is the origin in $\mathbb{R}^n$ by translating ${\bf x}^\ast$ to the origin. \begin{proposition} \label{prop-Y-cont} Consider a functional $L({\bf x}) = {\bf x}^TY{\bf x}$ for some real symmetric matrix $Y$. Assume that the origin ${\bf 0}$ is a hyperbolic equilibrium of (\ref{autonomous}) such that $Df({\bf 0})$ has $u$ eigenvalues of positive real part and $s = n-u$ eigenvalues of negative real part. Assume that, for a compact star-shaped domain $D_L$ with ${\bf 0}\in {\rm int}D_L$, the following inequality holds: \begin{equation} \frac{dL}{dt}(\varphi(t,{\bf x}))_{t=0} < 0\quad \forall {\bf x}\in D_L\setminus \{{\bf 0}\}. \end{equation} Then $Y$ is non-singular and has $u$ negative eigenvalues and $s = n-u$ positive eigenvalues. \end{proposition} \begin{proof} Suppose that $Y$ has a null eigenvector ${\bf x}\not = {\bf 0}$. Since the norm $\\|{\bf x}\\|$ can be chosen arbitrarily, by taking $\\|{\bf x}\\|$ sufficiently small, we may assume that the vector ${\bf x}$ is identified with a point ${\bf x}\in D_L$. Then \begin{equation} \frac{dL}{dt}(\varphi(t,{\bf x}))_{t=0} = f({\bf x})^T Y{\bf x} + {\bf x}^T Y f({\bf x}) = 0 \end{equation} since $Y$ is real and symmetric, which contradicts $(dL/dt)(\varphi(t,{\bf x}))_{t=0} < 0$. The matrix $Y$ is thus nonsingular. \par Next, choose ${\bf x}$ on $W^s({\bf 0})\setminus \{{\bf 0}\}$, which can be achieved by choosing ${\bf x}$ sufficiently close to ${\bf 0}$, if necessary, by the Stable Manifold Theorem with respect to the origin. We then have \begin{equation} \frac{dL}{dt}(\varphi(t,{\bf x}))_{t=0} < 0\quad (\forall t > 0)\quad \text{ and }\quad \lim_{t\to +\infty} L(\varphi(t,{\bf x})=0, \end{equation} which implies $L({\bf x}) > 0$. Similarly, if ${\bf x}$ is on $W^u({\bf 0})\setminus \{{\bf 0}\}$, then $L({\bf x}) < 0$. Arguments of the Rayleigh quotient thus yield that $Y$ has, at least, one positive eigenvalue and one negative eigenvalue. \par Let $\{{\bf u}_1, \cdots, {\bf u}_{u'}\}$ be eigenvectors of $Y$ associated with negative eigenvalues, and $\{{\bf v}_1, \cdots, {\bf v}_{s'}\}$ be eigenvectors of $Y$ associated with positive eigenvalues. We choose these vectors so that any two vectors in $\{{\bf u}_1, \cdots, {\bf u}_{u'}\}$ and $\{{\bf v}_1, \cdots, {\bf v}_{s'}\}$ are orthogonal to each other. Regularity of $Y$ implies that $u'+s'=n$. Our claim here is $u'=u$ and $s'=s$. \par \bigskip Let $\{{\bf u}_1^\ast, \cdots, {\bf u}_{u}^\ast\}$ be eigenvectors of $Df({\bf x}^\ast)$ associated with eigenvalues whose real parts are positive, and $\{{\bf v}_1^\ast, \cdots, {\bf v}_s^\ast\}$ be eigenvectors of $Df({\bf x}^\ast)$ associated with eigenvalues whose eigenvalues are negative. Now suppose that $u'<u$. There are a nontrivial collection of coefficients $(\alpha_1, \cdots, \alpha_u)$ such that the vector ${\bf u}^\ast := \sum_{j=1}^u \alpha_j {\bf u}^\ast_j$ is orthogonal to ${\bf u}_j$ for all $j=1,\cdots, u'$. This implies that ${\bf u}^\ast \in {\rm Span}\{{\bf v}_1, \cdots, {\bf v}_{s'}\}$. Therefore $L({\bf u}^\ast) \equiv l^\ast > 0$ holds from the property of $L$ as the quadratic form and the fact that eigenvalues associated with ${\bf v}_j$ are positive. \par We choose a local coordinate $(x_1,\cdots, x_u, y_1,\cdots, y_s)$ so that any point ${\bf x}$ close to the origin is represented as \begin{equation} {\bf x} = \sum_{j=1}^u x_j {\bf u}_j^\ast + \sum_{j=1}^s y_j {\bf v}_j^\ast. \end{equation} We identify a point ${\bf x}$ with its coordinate representation $(x_1,\cdots, x_u, y_1,\cdots, y_s)$. By the Stable Manifold Theorem (e.g. \cite{Rob}), there are a sufficiently small $\epsilon > 0$ and a smooth map $\Psi : B_u({\bf 0},\epsilon)\to \mathbb{R}^s$ such that the unstable manifold $W^u({\bf 0})$ is represented by the graph of $\Psi$ : \begin{align} &(y_1,\cdots, y_s) = \Psi(x_1,\cdots, x_u),\\ &(x_1,\cdots, x_u, y_1,\cdots, y_s) \in W^u(0) \text{ with } (x_1,\cdots, x_u)\in B_u({\bf 0},\epsilon), \end{align} and that $\\|\Psi(x_1,\cdots, x_u)\\| = O(\\|(x_1,\cdots, x_u)\\|^2)$ as $(x_1,\cdots, x_u)\to (0,\cdots, 0)$, where $B_u({\bf x},\epsilon)$ denotes the $u$-dimensional closed ball with the radius $\epsilon$ centered at a point ${\bf }x$. \par Let ${\bf z}^\ast = \delta {\bf u}^\ast + {\bf v}^\ast$ be a vector with a positive $\delta >0$. If $\delta > 0$ is sufficiently small, we can uniquely determine the vector ${\bf v}^\ast$ so that ${\bf z}^\ast \in W^u({\bf 0})$. Let ${\bf v}^\ast = \Psi (\delta \alpha_1, \cdots, \delta \alpha_u)\equiv \Psi (\delta {\bf u}^\ast)$ be such a vector. Then \begin{align} ({\bf z}^\ast)^T Y {\bf z}^\ast &= \delta^2 ({\bf u}^\ast)^T Y {\bf u}^\ast + \delta ({\bf u}^\ast)^T Y {\bf v}^\ast + \delta ({\bf v}^\ast)^T Y {\bf u}^\ast + ({\bf v}^\ast)^T Y {\bf v}^\ast\\ &= \delta^2 ({\bf u}^\ast)^T Y {\bf u}^\ast + \delta ({\bf u}^\ast)^T Y \Psi (\delta {\bf u}^\ast) + \delta \Psi (\delta {\bf u}^\ast)^T Y {\bf u}^\ast + \Psi (\delta {\bf u}^\ast)^T Y \Psi (\delta {\bf u}^\ast)\\ &= \delta^2 (l^\ast + O(\delta)) > 0 \end{align} if $\delta > 0$ is sufficiently small; i.e., ${\bf z}^\ast$ is sufficiently close to the origin, which follows from the fact $\\|\Psi(x_1,\cdots, x_u)\\| = O(\\|(x_1,\cdots, x_u)\\|^2)$ as $(x_1,\cdots, x_u)\to (0,\cdots, 0)$. This contradicts the fact that $L({\bf z}^\ast) < 0$, since ${\bf z}^\ast \in W^u({\bf 0})$. \par Similar argument yields $s'\geq s$, which concludes that $u'=u$ and $s'=s$. \end{proof} \subsection{Validation of Lyapunov functions and hyperbolicity of equilibria} \label{section-hyp-cont} Now we discuss the negative definiteness of $A({\bf z})$ from the different viewpoint. Let $\bar{\bf x}$ be a point such that $Df(\bar {\bf x})$ is numerically diagonalized: \begin{equation} \Lambda = X^{-1}Df(\bar {\bf x})X,\quad \Lambda = {\rm diag}(\lambda_1, \cdots, \lambda_n), \end{equation} and that ${\rm Re}(\lambda_i)\not = 0$ for all $i=1,\cdots, n$. The nonsingular matrix $X$ transforms (\ref{autonomous}) into the following system: \begin{equation} \label{diagonal-cont} \frac{d}{dt}{\bf y} = X^{-1}f({\bf x}^\ast + X{\bf y}),\quad {\bf x} = {\bf x}^\ast + X{\bf y}, \end{equation} which is close to the diagonalized system in a small neighborhood of ${\bf x}^\ast$. We then define a quadratic form $\tilde L$ by \begin{equation} \label{Lyapunov-simple-cont} \tilde L({\bf y}) := {\bf y}I^\ast {\bf y},\quad I^\ast = {\rm diag}(i_1,\cdots, i_n), \end{equation} where $i_k$'s are given by (\ref{sign-change-cont}). Let ${\bf x}$ be a point close to ${\bf x}^\ast$. Direct calculations yield \begin{equation} \displaystyle \frac{d}{dt}\tilde L({\bf y}) = {\bf y}^T \displaystyle \int_0^1 \{ X^T Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))^T X^{-T}I^\ast + I^\ast X^{-1}Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)) X\}ds\, {\bf y}. \end{equation} In general, the following lemma holds from general linear algebra. \begin{lemma} \label{lem-matrix} Let $A,B$ be $n\times n$ real matrices. Assume that $B$ is diagonal. Then $(AB)^T = BA^T$. \end{lemma} \begin{proof} This lemma directly follows from $(AB)^T = B^TA^T$ and $B^T=B$. \end{proof} Lemma \ref{lem-matrix} implies \begin{align} \displaystyle \frac{d}{dt}\tilde L({\bf y}) &= {\bf y}^T \displaystyle \int_0^1 \{ (X^T Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))^T X^{-T})I^\ast + I^\ast X^{-1}Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))X \}ds\, {\bf y}\\ &= {\bf y}^T \displaystyle \int_0^1 \{ (X^{-1} Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)) X)^T I^\ast + I^\ast X^{-1}Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast))X \}ds\, {\bf y} \end{align} Since $X^{-1}Df({\bf x}^\ast)X$ is diagonalizable, The matrix-valued sets \begin{equation} \{X^{-1} Df({\bf x}^\ast+s({\bf x} - {\bf x}^\ast)) X \mid s\in [0,1]\} \end{equation} can be regarded as a short segment with an endpoint $\Lambda = \Lambda^T$ in the set of $n\times n$ matrices. The Gershgorin Circle Theorem can be applied to the persistence of $\{{\rm sgn} ({\rm Re}(\lambda_i))\}_{i=1}^n$ for matrices on the sets. Combining this observation and arguments in the proof of Theorem \ref{thm-Lyapunov-cont}, we obtain the following result. \begin{theorem}[cf. \cite{Mat}] \label{thm-hyp-cont} Let ${\bf x}^\ast$ be an equilibrium for (\ref{autonomous}), and $D_L$ be a compact, star-shaped neighborhood of ${\bf x}^\ast$ in $\mathbb{R}^n$. Define a matrix $\tilde A({\bf z})$ by \begin{equation} \tilde A({\bf z}) = X^{-1} Df({\bf z}) X \equiv \Lambda + V({\bf z}), \end{equation} where $\Lambda = {\rm diag}(\lambda_1,\cdots, \lambda_n)$ given by $\Lambda = X^{-1}Df(\bar {\bf x})X$ at a point $\bar {\bf x}\in D_L$ and ${\rm Re}(\lambda_i) \not = 0$ for all $i=1,\cdots, n$. Assume that \begin{equation} \label{neg-def-strong-cont} \|{\rm Re}(\lambda_i)\| > \sum_{j=1}^n \|V({\bf z})_{ij}\|\quad \text{ and }\quad \|{\rm Re}(\lambda_i)\| > \sum_{j=1}^n \|V({\bf z})_{ji}\| \end{equation} holds for all ${\bf z}\in D_L$ and $i=1,\cdots, n$. Then ${\bf x}^\ast$ is hyperbolic. Moreover, the functional $\tilde L$ given by (\ref{Lyapunov-simple-cont}) is a Lyapunov function on $D_L$. Finally, ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{theorem} \begin{proof} Gershgorin's theorem and the assumption (\ref{neg-def-strong-cont}) imply that the sign of ${\rm Re}(\lambda_i) = {\rm Re}(\lambda_i({\bf z}))$ is identical in $D_L$. This yields that ${\rm sgn}({\rm Re}(\lambda_i({\bf x}^\ast))) = {\rm sgn}({\rm Re}(\lambda_i))$ for all $i$ and hence ${\bf x}^\ast$ is hyperbolic. Applying Gershgorin's theorem again to the matrix $\tilde A({\bf z})^T I^\ast + I^\ast \tilde A({\bf z})$, one sees that all eigenvalues have negative real parts for all ${\bf z}\in D_L$. Since $Df({\bf z})$ is a real matrix, the matrix $\tilde A({\bf z})^T I^\ast + I^\ast \tilde A({\bf z})$ is strictly negative definite in $D_L$. Thus Theorem \ref{thm-Lyapunov-cont} can be applied to proving that $\tilde L$ is a Lyapunov function in $D_L$ and ${\bf x}^\ast$ is the unique equilibrium in $D_L$. \end{proof} \begin{remark}\rm The Lyapunov function $\tilde L$ is exactly the form discussed in \cite{Mat}. Note that forms of Lyapunov functions $L$ and $\tilde L$ are exactly the same, while the condition in Theorem \ref{thm-hyp-cont} is a little stronger than Theorem \ref{thm-Lyapunov-cont}. Indeed, Theorem \ref{thm-Lyapunov-cont} guarantees (i) the existence of Lyapunov functions and (ii) local uniqueness of equilibria, while Theorem \ref{thm-hyp-cont} guarantees (i) the existence of Lyapunov functions, (ii) local uniqueness of equilibria and (iii) hyperbolcity of equilibria. The difference of conditions comes from which the negative definiteness of $Df({\bf x})^T Y + YDf({\bf x})$ or $X^{-1}Df({\bf x})X$ is concerned. \end{remark} \subsection{Equivalence to cones: description of the stable and the unstable manifolds} Asymptotic behavior of dynamical systems around hyperbolic equilibria deeply relates to descriptions of their stable and unstable manifolds. Since $L({\bf x}^\ast) = 0$ holds, by the definition of $W^s({\bf x})$ and $L$, it immediately holds that $W^s({\bf x}^\ast)\cap D_L\subset L^{-1}(0, +\infty)\cap D_L$. Similarly, $W^u({\bf x}^\ast)\cap D_L\subset L^{-1}(-\infty, 0)\cap D_L$. \bigskip Now we refer to the concept of {\em cones} in, e.g., \cite{C, ZCov}. In these references {\em a cone} is defined as a quadratic form $Q({\bf z}) = Q_1({\bf z}) - Q_2({\bf z})$ such that $Q_1$ and $Q_2$ are positive definite. A connection between $Q$ and stable and unstable manifolds of equilibria are well discussed in \cite{ZCov}; namely, under {\em the cone condition}: \begin{equation} \label{cone-cond-cont} \frac{d}{dt}(Q(\varphi(t,{{\bf z}_1})) - Q(\varphi(t,{{\bf z}_2}))) > 0\text{ for all } {\bf z}_1, {\bf z}_2 \in N \end{equation} in a given contractible set with special property called {\em an $h$-set} $N$, the stable and unstable manifolds of an equilibrium in $N$ can be described by graphs of Lipschizian functions (see Lemma 27 in \cite{ZCov}). Although \cite{ZCov} only describes the essential idea in abstract settings, this property gives us descriptions of locally invariant manifolds in explicitly given domains. Applications of cone conditions with computer assistance are discussed in \cite{KWZ2007, Mat2}. In fact, the strict negative definiteness of $A({\bf z})$ in (\ref{matrix-neg-def}) is intrinsically the same as a sufficient condition of cone conditions stated in (\ref{cone-cond-cont}). This fact indicates that a condition with respect to $A({\bf z})$ enables us to study asymptotic behavior around (hyperbolic) equilibria from the viewpoint of both Lyapunov functions and cones. \bigskip Now consider the case that the negative definiteness of $A({\bf z})$ does not hold in a domain $D$. In such a case, there is a non-trivial problem if the existence of a Lyapunov function in $D$ implies that of a cone $Q$ in satisfying the cone condition in $D$, and vice versa. There may be a case that a Lyapunov domain $D$ validated in Stage 2 (Section \ref{section-stage2-cont}) does not satisfy the cone condition in general. In other words, there is a domain where we cannot consider Lyapunov functions and cones in the same terms. If it is the case, we then have to develop and consider the theory of asymptotic behavior in $D$ in terms of cones and Lyapunov functions independently. \begin{remark}\rm Prof. P. Zgliczy\'{n}ski commented to the first author \cite{MZ} that Lyapunov functions $L({\bf x})$ focus on the behavior of {\em a point} along solution orbits, and that cone conditions focus on {\em the difference between two points} along solution orbits. These differences can be seen in Definition \ref{dfn-Lyapunov-typical} and (\ref{cone-cond-cont}). \end{remark} \begin{remark}[Cones and ${\bf m}$-Lyapunov functions]\rm The former idea of ${\bf m}$-Lyapunov functions (Section \ref{section-m-Lyapunov-cont}) is introduced in \cite{Mat2}, where it is said {\em $m$-cones}, so that the enclosure of the stable and the unstable manifolds of equilibria are sharpened more and more. The same idea is introduced by Capi\'{n}ski \cite{C} as well as Zgliczy\'{n}ski \cite{ZCov} before \cite{Mat2} in terms of cones with arbitrary choice. In \cite{Mat2}, the concept of $m$-cones is introduced with identical ratios, i.e., $m_j$'s are $1$ (resp. $m$) for stable eigendirections and $m$ (resp. $1$) for unstable eigendirections, where $m > 1$ is a given positive number. Our ${\bf m}$-Lyapunov functions generalize the choice of $m_j$'s. One of the powerful properties of our procedure of Lyapunov functions as well as ${\bf m}$-Lyapunov functions is that enclosures of locally invariant manifolds around invariant sets can be described by quadratic functions. We comment that the extension of regions where ${\bf m}$-Lyapunov functions are validated is applied to validations of the stable and the unstable manifolds of equilibria in singular perturbation problems \cite{Mat2} in terms of $m$-cones. \end{remark} \subsection{Lyapunov tracing: transversality of flows and re-parametrization of trajectories} By definition, $dL/dt < 0$ always holds off equilibria, which implies that all solution orbits intersect transversally with level sets $L^{-1}(s)\cap D_L$ for all $s\in \mathbb{R}$, if exist. If an equilibrium ${\bf x}^\ast$ is asymptotically stable, then the level set $L^{-1}(s)$ is either an ellipse or ellipsoid, in which case only the interior of ellipsoids in $D_L$ can be positively invariant for (\ref{autonomous}). If an equilibrium ${\bf x}^\ast$ is a saddle, the level set $L^{-1}(s)$ is a hyperbolic surface except $L^{-1}(0)$; the surface of a cone. The above fact helps us with constructing crossing sections or isolating blocks in the Conley index theory of flows (e.g. \cite{Con}) explicitly. Moreover, along a solution orbits with a given initial data, the time variable $t$ smoothly corresponds {\em one-to-one} to the value $s$ of Lyapunov functions as long as the orbit stays in $D_L$, which leads to a local {\em re-parametrization} of trajectories $\varphi(t,{\bf x}) \mapsto \tilde \varphi(L,{\bf x})$. More precisely, the following theorem holds. \begin{theorem}[Retraction via Lyapunov tracing] \label{thm-LT} Let $D_L$ be a compact star-shaped Lyapunov domain containing an equilibrium ${\bf x}^\ast$ associated with a Lyapunov function $L$. Assume that the boundary of the stable cone $B_s \equiv D_L\cap L^{-1}(0,\infty)$ consists of $b_s := L^{-1}(0)\cap D_L$ and a collection of hypersurfaces $\{S_i\}$ which are the immediate entrance in the sense that, for any ${\bf x}\in S_i$, there is a positive number $\epsilon_{\bf x} > 0$ such that \begin{equation} \varphi((0,\epsilon_{\bf x}),{\bf x})\subset {\rm int} (D_L\cap L^{-1}(0,\infty)),\quad \varphi((-\epsilon_{\bf x},0),{\bf x})\cap {\rm int} (D_L\cap L^{-1}(0,\infty)) = \emptyset. \end{equation} See Fig. \ref{fig-retract}. \par Define the map $R : B_s \to b_s$ by \begin{equation} R({\bf x}) := \varphi(\tau({\bf x}), {\bf x}),\quad \tau({\bf x}) := \sup\{t\geq 0\mid \varphi([0,t],{\bf x})\subset B_s\}. \end{equation} Then $R$ is continuous. Moreover, $b_s$ is the strong deformation retract of $B_s$. \end{theorem} Note that we say a subset $A$ of a compact set $X$ is a {\em strong deformation retract} if there exists a continuous map $R : X\times [0,1]\to X$ such that $R({\bf x},t) = {\bf x}$ for all ${\bf x}\in A$, $R({\bf x},1)\in A$ for all ${\bf x}\in X$ and $R({\bf x},0) = {\bf x}$ for all ${\bf x}\in X$. \begin{figure}[htbp]\em \begin{minipage}{1\hsize} \centering \includegraphics[width=6.0cm]{img/retract.png} \end{minipage} \caption{The positive cone $B_s$ and dynamics inside it} \label{fig-retract} \begin{flushleft} The yellow region shows the set $B_s \equiv D_L\cap L^{-1}(0,\infty)$ associated with a Lyapunov function $L$ in Theorem \ref{thm-LT}. Black lines denote the zero level set $L^{-1}(0)$ of the Lyapunov function $L$. Dotted curves denote the family of positive level sets $\{L^{-1}(s)\cap D_L \mid s> 0\}$ of $L$. The green curve $S$ shows a hypersurface being the immediate entrance of $B_S$. In this setting, black lines which are also boundaries of the yellow region is $b_s$. \end{flushleft} \end{figure} \begin{proof} First note that $b_s\setminus \{{\bf x}^\ast\}$ is the immediate exit of $B_s$ in the sense that, for any ${\bf x}\in b_s\setminus \{{\bf x}^\ast\}$, there is a positive number $\epsilon_{\bf x} > 0$ such that \begin{equation} \varphi((0,\epsilon_{\bf x}),{\bf x})\cap (D_L\cap L^{-1}(0,\infty)) = \emptyset,\quad \varphi((-\epsilon_{\bf x},0),{\bf x})\cap b_s\setminus \{{\bf x}^\ast\} = \emptyset. \end{equation} Let ${\bf x}_0 \in B_s$ be an arbitrary point. Then the solution orbit ${\bf x}(t)\equiv \varphi(t,{\bf x}_0)$ through ${\bf x}_0$ can be written by \begin{equation} {\bf x}(t) = {\bf x}_0 + \int_0^t f({\bf x}(s))ds. \end{equation} A Lyapunov function $L$ has the form $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y (x-{\bf x}^\ast)$ and it immediately follows that \begin{equation} \frac{dL}{dt}({\bf x}(t))\mid_{t=0} = f({\bf x}_0)^T Y ({\bf x}_0 - {\bf x}^\ast) + ({\bf x}_0-{\bf x}^\ast)^T Y f({\bf x}_0). \end{equation} Let $L_0 = L({\bf x}_0)$ and $L_t = L({\bf x}(t))$. Note that $t$ and $L_t = L({\bf x}(t))$ corresponds homeomorphically along the solution orbit $\{{\bf x}(t)\}$. The solution ${\bf x}(t)\equiv {\bf x}(L)$ can be thus formally re-written by \begin{equation} \label{L-integral} {\bf x}(L_t) = {\bf x}(L_0) + \int_{L_0}^{L_t} \frac{f({\bf x}(L))}{ f({\bf x}(L))^T Y ({\bf x}(L) - {\bf x}^\ast) + ({\bf x}(L)-{\bf x}^\ast)^T Y f({\bf x}(L))}dL. \end{equation} Since $B_s$ is a subset of the Lyapunov domain $D_L$, then $dL/dt \not = 0$ off ${\bf x}^\ast \in L^{-1}(0)$. The mapping $R({\bf x}_0)$ is thus given by \begin{equation} R({\bf x}_0) = {\bf x}(0) = {\bf x}(L_0) + \int_{L_0}^{0} \frac{f({\bf x}(L))}{ f({\bf x}(L))^T Y ({\bf x}(L) - {\bf x}^\ast) + ({\bf x}(L)-{\bf x}^\ast)^T Y f({\bf x}(L))}dL. \end{equation} We shall prove that this expression makes sense. To this end, we divide the integral into two parts: $\int_{L_0}^\epsilon + \int_{\epsilon}^0$ for sufficiently small $\epsilon$. \par \bigskip The first part $\int_{L_0}^\epsilon$ obviously makes sense and continuous with respect to ${\bf x}_0$, since $f$ is smooth and the denominator is bounded away from $0$ on the compact set $\overline{L^{-1}(\epsilon, \infty)}\cap D_L$ for any fixed $\epsilon > 0$. \par Consider the second integral $\int_{\epsilon}^0$. Let $B({\bf x}^\ast, \epsilon)$ be the closed ball centered at ${\bf x}^\ast$ with the radius $\epsilon$. If ${\bf x}_0\in B_s\setminus (B({\bf x}^\ast, \epsilon)\cup W^s({\bf x}^\ast))$, the integral $\int_{\epsilon}^0\cdots$ also makes sense since the denominator is bounded away from $0$. Note that, thanks to the Mean Value Theorem, $f({\bf x})$ is close to $Df({\bf x}^\ast)({\bf x}-{\bf x}^\ast)$ and the functional $f({\bf x})^T Y ({\bf x} - {\bf x}^\ast) + ({\bf x} - {\bf x}^\ast)^T Y f({\bf x})$ is sufficiently close to \begin{equation} ({\bf x}-{\bf x}^\ast)^T (Df({\bf x}^\ast)^T Y + YDf({\bf x}^\ast))) ({\bf x}-{\bf x}^\ast) \end{equation} for ${\bf x}\in B({\bf x}^\ast, \epsilon)$ if $\epsilon > 0$ is sufficiently small. It is therefore sufficient to prove that the integral \begin{equation} \label{integral-r} \int_{\epsilon}^{0} \frac{Df({\bf x}^\ast)({\bf x}(L)-{\bf x}^\ast)}{ ({\bf x}-{\bf x}^\ast)^T (Df({\bf x}^\ast)^T Y + YDf({\bf x}^\ast))) ({\bf x}-{\bf x}^\ast) }dL \end{equation} is bounded for proving boundedness of the integral $\int_\epsilon^0\cdots$. \par Since ${\bf x}\in B({\bf x}^\ast,\epsilon)$, the vector ${\bf x}-{\bf x}^\ast$ is written by ${\bf x}-{\bf x}^\ast = r v$, where $r = r_{\bf x} = \\|{\bf x}-{\bf x}^\ast\\|\leq \epsilon$ and $v = v_{\bf x} = ({\bf x}-{\bf x}^\ast) / \\|{\bf x}-{\bf x}^\ast\\|$. The Lyapunov function $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y({\bf x}-{\bf x}^\ast)$ can be thus rewritten by $L(r, v) = r^2 v^T Y v$ and \begin{equation} \frac{dL}{dr}({\bf x}(r,v)) = 2r v^T Y v. \end{equation} The integral (\ref{integral-r}) thus admits the transformation of variables from $L$ to $r$ as follows: \begin{align} &\int_{\epsilon}^{0} \frac{Df({\bf x}^\ast)({\bf x}(L)-{\bf x}^\ast)}{ ({\bf x}-{\bf x}^\ast)^T (Df({\bf x}^\ast)^T Y + YDf({\bf x}^\ast))) ({\bf x}-{\bf x}^\ast) }dL\\ &\quad = \int_{\epsilon_{x}'}^0 \frac{r Df({\bf x}^\ast)v}{ r^2 v^T (Df({\bf x}^\ast)^T Y + YDf({\bf x}^\ast))) v }\cdot 2r v^T Yv dr\\ &\quad = 2\int_{\epsilon_{x}'}^0 \frac{ v^T Yv \cdot Df({\bf x}^\ast)v}{ v^T (Df({\bf x}^\ast)^T Y + YDf({\bf x}^\ast))) v } dr, \end{align} which is independent of $r$, where $\epsilon_{x}' = \\|{\bf x}-{\bf x}^\ast\\|$ with $L({\bf x}) = \epsilon$. The integrand is obviously bounded and continuous with respect to $x$, and hence the integral (\ref{integral-r}) is bounded. The integral \begin{equation} \int_{\epsilon}^{0} \frac{f({\bf x}(L))}{ f({\bf x}(L))^T Y ({\bf x}(L) - {\bf x}^\ast) + ({\bf x}(L)-{\bf x}^\ast)^T Y f({\bf x}(L))}dL \end{equation} is also bounded, which follows from the continuity of the integral. Note that the integral (\ref{integral-r}) makes sense even for $r = 0$, i.e., ${\bf x} = {\bf x}^\ast$. Consequently, the definition of $R({\bf x}_0)$ makes sense everywhere in $B_s$ and $R$ is continuous. \par \bigskip The mapping $R({\bf x})$ determines a family of solution curves $c:[0,1]\times B_s \to B_s$ given by \begin{equation} c(s;{\bf x}) = {\bf x}(L_0) + \int_{L_0}^{(1-s)L_0} \frac{f({\bf x}(L))}{ f({\bf x}(L))^T Y ({\bf x}(L) - {\bf x}^\ast) + ({\bf x}(L)-{\bf x}^\ast)^T Y f({\bf x}(L))}dL. \end{equation} The preceding arguments imply that $c$ is continuous. It immediately holds that $c(0;{\bf x}) = {\bf x}\equiv {\bf x}(L_0)$ for all ${\bf x}\in B_s$. Moreover, $c(1;{\bf x}) = R({\bf x})\in b_s$ for all ${\bf x}\in B_s$. Finally, $c(s;{\bf x}) = {\bf x}$ holds for all ${\bf x}\in b_s$ and $s\in [0,1]$, since ${\bf x} = R({\bf x})$ for ${\bf x}\in b_s$. These arguments imply that $b_s$ is the strong deformation retract of $B_s$ and the proof is completed. \end{proof} This theorem has two aspects. Firstly, Lyapunov functions of the form (\ref{Lyapunov-flow}) give us an analytic proof which Lyapunov domains possess strong deformation retracts. The exit set being the strong deformation retract is a well-known fact for {\em isolating blocks} in the Conley index theory (e.g. \cite{Con, Smo}). On the contrary, $B_s$ is not an isolating block since its boundary contains an equilibrium ${\bf x}^\ast$. The property of $B_s$ and $b_s$ thus gives us several generalizations of \lq\lq exits" of compact sets from viewpoints of topology and dynamical systems. \par Secondly, the proof of this theorem indicates that solution orbits in $D_L$ can be re-parameterized by values of $L$ instead of $t$, even for (un)stable manifolds. In fact, representations of solutions in terms of the $L$-integral guarantees the boundedness of integrals {\em in bounded range}. This fact is very useful, in particular, if we track trajectories near equilibria or along invariant manifolds by integrals. We say this re-parameterization the {\em Lyapunov tracing}. An application of the Lyapunov tracing can be seen in \cite{TMSTMO2016}; namely, validations of blow-up times of blow-up solutions. \section{Lyapunov functions for discrete dynamical systems} \label{section-discrete} In this section, we consider discrete dynamical systems generated by continuously differentiable maps of the form \begin{equation} \label{discrete-system} \displaystyle {\bf x}_{n+1} = \psi({\bf x}_n),\quad {\bf x}_0 \in \mathbb{R}^n, \end{equation} where $\psi : \mathbb{R}^n\to \mathbb{R}^n$ be a smooth map. Assume that ${\bf x^\ast}$ is a hyperbolic fixed point of $\psi$, namely, all eigenvalues of the Jacobian matrix $D\psi({\bf x})$ of $\psi({\bf x})$ at ${\bf x}^\ast$ are away from the unit circle. We now introduce a Lyapunov function in the similar manner to continuous dynamical systems. \begin{definition}\rm \label{dfn-Lyapunov-map} Let $U\subset \mathbb{R}^n$ be an open subset. A {\em Lyapunov function $L:\mathbb{R}^n\to \mathbb{R}$ on $U$} for the map $\psi$ is a continuous function satisfying the following conditions. \begin{enumerate} \item $L(\psi({\bf x}))\leq L({\bf x})$ holds for all ${\bf x}\in U$. \item $L(\psi({\bf x}))= L({\bf x})$ implies $\psi({\bf x})= {\bf x}^\ast\in U$, where ${\bf x}^\ast$ is a fixed point of (\ref{discrete-system}). \end{enumerate} \end{definition} Our aim here is to construct a Lyapunov function for $\psi$ defined in an explicitly given neighborhood of ${\bf x}^\ast$. \subsection{Construction of quadratic functions} Here we show a procedure for the construction of the Lyapunov function defined in a neighborhood of a fixed point ${\bf x}^\ast$. \begin{itemize} \item[1.] Let $A^\ast = D\psi({\bf x}^\ast)$ and diagonalize it; namely, \begin{equation} \Lambda = X^{-1}A^\ast X, \end{equation} where $\Lambda = {\rm diag}(\lambda_1,\lambda_2,\cdots,\lambda_m)$ is the eigenvalue matrix of $A^\ast$ and $X$ is the nonsingular matrix given by corresponding eigenvectors. Note that these calculations are sufficient to be done with floating-point arithmetics. Assume that, in the sense of floating-point arithmetics, $\|\lambda_i\|\not = 1$ for all $i=1,\cdots, n$. \item[2.] Let $I^\ast$ be the diagonal matrix $I^\ast = {\rm diag}(i_1,i_2,\cdots,i_m)$, where \begin{equation} \label{sign-change-map} i_k = \left\{ \begin{array}{c} 1, \quad \mbox{if} \quad \|\lambda_k\| < 1, \\ -1, \quad \mbox{if} \quad \|\lambda_k\| > 1. \end{array}\right. \end{equation} Note that $\|\lambda_k\|\not =1$ holds by hyperbolicity of $x^\ast$. \item[3.] Calculate the real symmetric matrix $Y$ as follows: \begin{equation} \hat{Y} = X^{-H} I^\ast X^{-1}, \quad Y = \mbox{Re}( \hat{Y}), \end{equation} where $X^{-H}$ denotes the inverse matrix of the Hermitian transpose $X^H$ of $X$, which is sufficient to be calculated by floating-point arithmetics. \item[4.] Define a quadratic function $L({\bf x})$ by \begin{equation} \label{Lyapunov-map} L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast), \end{equation} which is a candidate of Lyapunov functions around ${\bf x}^\ast$. If we deal with $L$ with interval arithmetics, we replace $Y$ by $(Y+Y^T)/2$ or set $Y_{ji}=Y_{ij}$ so that the symmetry of $Y$ is guaranteed. \end{itemize} \subsection{Validity of $L({\bf x})$} Here we find a sufficient condition such that the function $L({\bf x})$ introduced above is indeed a Lyapunov function in a given neighborhood of ${\bf x^\ast}$. Let $\{{\bf x}_n\}$ be a $\psi$-orbit: ${\bf x}_{n+1} = \psi({\bf x}_n)$. By using the Jacobian matrix $D\psi({\bf x})$ of $\psi$ at ${\bf x}$, we obtain the following integral representation of the difference ${\bf x}_{n+1} - {\bf x}^\ast$: \begin{align} {\bf x}_{n+1} - {\bf x}^\ast &= \displaystyle \int_0^1 D\psi({\bf x}^\ast + s({\bf x_n}-{\bf x}^\ast)) ds ({\bf x}_n - {\bf x}^\ast)\\ &\equiv A_I({\bf x}_n)({\bf x}_n - {\bf x}^\ast), \end{align} where we used the following expression: \begin{equation} A_I({\bf x}) = \displaystyle \int_0^1 D\psi({\bf x}^\ast + s({\bf x}-{\bf x}^\ast)) ds. \end{equation} This expression implies that the condition $L({\bf x}_{n+1}) < L({\bf x}_n)$ is equivalent to the following inequality: \begin{equation} {\bf x}_n^T (\, A_I({\bf x}_n)^T Y A_I({\bf x}_n) - Y \,) {\bf x}_n < 0. \end{equation} This observation indicates that, if we can validate \begin{equation} A_I({\bf x})^T Y A_I({\bf x}) - Y \end{equation} is strictly negative definite for all ${\bf x}\in D_L$, where $D_L$ is a star-shaped domain centered at ${\bf x}^\ast$, then we know that $L(\psi({\bf x}))-L({\bf x})$ is strictly negative for all ${\bf x} \in D_L\setminus \{{\bf x}^\ast\}$. By assumption, ${\bf x}^\ast\in D_L$ is a hyperbolic fixed point of $\psi$ and $L(\psi({\bf x}^\ast)) = L({\bf x}^\ast) = 0$ holds. Summarizing the above arguments, we obtain the following theorem: \begin{theorem} \label{thm-Lyapunov-map} Let $D_L$ be a compact, star-shaped domain containing a fixed point ${\bf x}^\ast$ of $\psi$. Define a matrix $B({\bf x})$ by \begin{equation} \label{matrix-discrete} B({\bf x}) := A_I({\bf x})^T Y A_I({\bf x}) - Y \end{equation} Assume that the matrix $B({\bf x})$ is strictly negative definite for all ${\bf x}\in D_L$. Then $L({\bf x})$ defined by (\ref{Lyapunov-map}) is a Lyapunov function on $D_L$ in the sense of Definition \ref{dfn-Lyapunov-map}. Moreover, ${\bf x}^\ast$ is the unique fixed point of $\psi$ in $D_L$. \end{theorem} \begin{definition}\rm We shall call the domain $D_L$ in Theorem \ref{thm-Lyapunov-map} {\em a Lyapunov domain} (for $\psi$). \end{definition} \begin{remark}[Lyapunov functions and cones for maps]\rm As in the case of flows, the negative definiteness of $B({\bf x})$ in Theorem \ref{thm-Lyapunov-map} is equivalent to a sufficient condition of {\em cone conditions for maps} stated in \cite{ZCov}. Remark that {\em a cone} $Q$ (for $\psi$) is a quadratic form $Q({\bf z}) = Q_1({\bf z}) - Q_2({\bf z})$, where $Q_1$ and $Q_2$ are positive definite, and {\em the cone condition} for $\psi$ is \begin{equation} \label{cone-cond-map} Q(\psi({\bf z}_1) - \psi({\bf z}_2)) > Q({\bf z}_1- {\bf z}_2)\quad \text{ for all }{\bf z}_1, {\bf z}_2\in N \text{ with }\psi({\bf z}_1),\psi({\bf z}_2)\in N, \end{equation} where $N$ is an $h$-set (cf. Section \ref{section-aspect}). This fact can be compared with Section 3.3 in \cite{ZCov}. Therefore, once we validate the negative definiteness of $B({\bf x})$ in $D_L$, we can study asymptotic behavior for $\psi$ in $D_L$ in terms of both Lyapunov functions $L({\bf x})$ and cones $Q({\bf z})$. \end{remark} \subsection{Verification of Lyapunov domains with interval arithmetics} \subsubsection{Stage 1: Negative definiteness of $B({\bf x})$.} \label{section-stage1-disc} Theorem \ref{thm-Lyapunov-map} claims that $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function on a star-shaped domain $D_L$ centered at a fixed point ${\bf x}^\ast$, if the real symmetric matrix $B({\bf x})$ in (\ref{matrix-discrete}) is negative definite. Let $D_L$ be a star-shaped domain containing the fixed point $\{{\bf x}^\ast\}$. Firstly we verify the strict negative definiteness of $B({\bf x})$ on $D_L$ directly. In practical computations, we enclose $D_L$ by an interval vector $[D_L]$ and verify the negative definiteness of the interval matrix $B([D_L])$. If it is succeeded, everything has done in this case. \par If not, we verify the negative definiteness of $B({\bf x})$ on $D_L$ after decomposing $D_L$ into subdomains: $D_L= \bigcup_{k=1}^{K} D_k$. As verifications in the whole domain, we enclose each subdomain $D_k$ by an interval vector $[D_k]$ and try to verify the negative definiteness of $B([D_k])$ for all $k = 1,\cdots, K$. The basic idea follows the way in the case of flows, but the detail is more complicated. We revisit the point in Section \ref{section-example-discrete}. \subsubsection{Stage 2: The case where $D_k$ does not contain ${\bf x}^\ast$.} If there is a subdomain $D_k$ which does not contain ${\bf x}^\ast$, we directly verify if $L(\psi({\bf x})) < L({\bf x})$ holds on $D_k$ by interval arithmetics. In particular, we verify \begin{equation} L(\psi([{\bf x}_k])) - L([{\bf x}_k]) < 0 \end{equation} for interval vectors $[{\bf x}_k]$ containing $D_k$ with $[{\bf x}_k]\subset D_L$, which imply that the functional $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function on $D_k$. In Stage 2, there is the case that overestimates of intervals with interval arithmetics cause the failure of validations, which is discussed in Section \ref{section-example-discrete}. \subsection{${\bf m}$-Lyapunov functions} As in the case of continuous systems, we can discuss the arbitrary choice of quadratic functions. In the construction of $L({\bf x})$, we replace the diagonal matrix $I^\ast$ by $M^\ast = {\rm diag}(i_1,i_2,\cdots,i_n)$ in the definition of $Y$, where \begin{equation} i_j = \left\{ \begin{array}{c} m_j, \quad \mbox{if} \quad \|\lambda_j\| < 1, \\ -m_j, \quad \mbox{if} \quad \|\lambda_j\| > 1 \end{array}\right. \end{equation} and ${\bf m} = \{m_j\}_{j=1}^n$ is a sequence of given positive numbers. As in the case of continuous systems, define the quadratic function $L_{M^\ast}$ as \begin{equation} \label{Lyapunov-M-map} L_{M^\ast}({\bf x}) := ({\bf x} - {\bf x}^\ast)^T Y_{M^\ast}({\bf x} - {\bf x}^\ast),\qquad Y_{M^\ast} = {\rm Re}(X^{-H}M^\ast X^{-1}), \end{equation} which is nothing but $L$ replacing $I^\ast$ by $M^\ast$. We can then prove negative definiteness of the matrix $B^\ast$ corresponding to the differential $(dL_{M^\ast}/dt)({\bf x})$ at ${\bf x}={\bf x}^\ast$ by similar arguments as Proposition \ref{prop-hyp-map}. Consequently, we obtain the following corollary. \begin{corollary} \label{cor-m-Lyap-map} Let $D_L$ be a compact, star-shaped domain containing a fixed point ${\bf x}^\ast$ of $\psi$. Define a matrix $B_{M^\ast}({\bf x})$ by $B({\bf x})$ in (\ref{matrix-discrete}) replacing $I^\ast$ by $M^\ast$. Assume that the matrix $B_{M^\ast}({\bf x})$ is strictly negative definite for all ${\bf z}\in D_L$. Then $L_{M^\ast}({\bf x})$ is a Lyapunov function on $D_L$ in the sense of Definition \ref{dfn-Lyapunov-map}. Moreover, ${\bf x}^\ast$ is the unique fixed point in $D_L$. \end{corollary} We shall call the function $L_{M^\ast}$ being a Lyapunov function {\em an {${\bf m}$}-Lyapunov function} (for $\psi$). Note that the geometry of $D_L$ depends on the choice of positive numbers ${\bf m}$, which is discussed in Section \ref{section-example-discrete}. \subsection{Lyapunov functions around hyperbolic fixed points} In Theorem \ref{thm-Lyapunov-map}, we focused on the strict negative definiteness of $B({\bf x})$ in (\ref{matrix-discrete}) in a given domain containing ${\bf x}^\ast$. The negative definiteness of $B({\bf x})$ reflects the hyprbolicity of ${\bf x}^\ast$. Indeed, for a {\em rigorous} hyperbolic fixed point ${\bf x}^\ast$, the matrix $B({\bf x}^\ast)$ is strictly negative definite. This fact yields the following proposition; namely, {\em all hyperbolic fixed points locally admit Lyapunov functions.} \begin{proposition} \label{prop-hyp-map} Assume that ${\bf x}^\ast$ is a hyperbolic fixed point of $\psi$. Then, for all points in a sufficiently small neighborhood of ${\bf x}^\ast$, the matrix $B({\bf x})$ in (\ref{matrix-discrete}) is strictly negative definite. In particular, the functional $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function in such a neighborhood. \end{proposition} \begin{proof} For proving the negative definiteness of $B({\bf x})$, it is sufficient to prove that $(A^\ast)^T Y A^\ast - Y$ is negative definite, where $A^\ast = A_I({\bf x}^\ast) = D\psi({\bf x}^\ast)$, since eigenvalues depend continuously on ${\bf z}$. Note that, for quadratic forms given by real vectors, the negative definiteness of $(A^\ast)^T Y A^\ast - Y$ is equivalent to that of $(A^\ast)^H \hat{Y} A^\ast - \hat{Y}$. In what follows we prove the negative definiteness of $(A^\ast)^H \hat{Y} A^\ast - \hat{Y}$. By the definition of the Hermitian matrix $\hat{Y}$, we get \begin{align} (A^\ast)^H \hat{Y} A^\ast - \hat{Y} &= X^{-H} (\Lambda^H I^\ast \Lambda - I^\ast) X^{-1} \\ &= X^{-H} (\Lambda^H \Lambda - I) I^\ast X^{-1} \\ &= X^{-H}( \|\Lambda\|^2 - I ) I^\ast X^{-1}, \end{align} where $\|\Lambda\|$ denotes the matrix whose entries are absolute values of the corresponding entries of $\Lambda$. By the definition of the matrix $I^\ast$, one easily have that $(A^\ast)^H \hat{Y} A^\ast - \hat{Y}$ is a negative definite Hermitian matrix, which implies that $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function in a sufficiently small neighborhood of ${\bf x}^\ast$. \end{proof} The same arguments as Proposition \ref{prop-Y-cont} with Stable Manifold Theorem for maps (e.g. \cite{Rob}) yield the eigenstructure of $Y$ in (\ref{Lyapunov-map}). \begin{proposition} Consider a functional $L({\bf x}) = {\bf x}^TY{\bf x}$ for some real symmetric matrix $Y$. Assume that the origin ${\bf 0}$ is a hyperbolic fixed point of $\psi$ such that $D\psi({\bf 0})$ has $u$ eigenvalues with moduli larger than $1$ and $s = n-u$ eigenvalues with moduli less than $1$. Assume that, for a compact star-shaped domain $D_L$ with ${\bf 0}\in {\rm int}D_L$, the following inequality holds: \begin{equation} L(\psi({\bf x})) < L({\bf x}),\quad \forall {\bf x}\in D_L\setminus \{{\bf 0}\}. \end{equation} Then $Y$ is non-singular and has $u$ negative eigenvalues and $s = n-u$ positive eigenvalues. \end{proposition} \section{Towards applications to periodic orbits} \label{section-Lyapunov-periodic} For applications of Lyapunov functions for discrete dynamical systems, a typical example is to periodic orbits as fixed points of Poincar\'{e} maps. As preliminaries of applications in this direction, we review the verification method of periodic orbits in continuous dynamical systems in this section. During verifications, implementations of Poincar\'{e} maps and their differentials arise, which are necessary to validate Lyapunov functions. \subsection{Poincar\'{e} maps and their differentials} Here we review the construction of the Poincar\'{e} map and its differential. Let $\varphi$ be the flow generated by (\ref{autonomous}). The Poincar\'{e} map $P({\bf x})$ for the point ${\bf x}$ on a Poincar\'{e} section is then constructed as follows. Firstly, we put $\tilde {\bf x}_0$ as a point on an approximate periodic orbit. Secondly, let ${\bf n}$ be a unit vector which is approximately parallel to $f(\tilde {\bf x}_0)$. Let $\Gamma$ be the hyperplane such that ${\bf n}$ is the unit normal vector to $\Gamma$, which is a candidate of our Poincar\'{e} section. Thirdly, \begin{enumerate} \item Compute the solution orbit $\varphi(t,{\bf x}_0)$ with the initial point ${\bf x}_0\in \Gamma$; \item Compute times $\underline{t} < \overline{t}$ satisfying $\{{\bf n}^T\cdot (\varphi(\underline{t}, {\bf x}_0)-\tilde {\bf x}_0)\} \{{\bf n}^T\cdot (\varphi(\overline{t}, {\bf x}_0)-\tilde {\bf x}_0)\} < 0$; \item Letting $[t] := [\underline{t}, \overline{t}]$, compute an enclosure $[{\bf x}] := \varphi([t], {\bf x}_0)$; and \item Verify $0\not \in {\bf n}^T\cdot f([{\bf x}])$. \end{enumerate} The interval enclosure $[{\bf x}]$ contains the image of the Poincar\'{e} map $P$ of ${\bf x}_0$. Conditions 2 and 4 imply the unique existence of the time $T_r({\bf x}_0)>0$ within $[\underline{t}, \overline{t}]$ such that $\varphi(T_r({\bf x}_0),{\bf x}_0) \in \Gamma$ holds. Since the vector field $f$ is continuous, $P$ is locally diffeomorphic, which implies that $[{\bf x}]$ is indeed the rigorous enclosure of the Poincar\'{e} map $P({\bf x}_0)$. The Jacobian matrix of the Poincar\'{e} map $P$ at ${\bf x}_0$ is derived as follows. For a trajectory $\{\varphi(t,{\bf x})\}_{t\geq 0}$, let \begin{equation} V(t;{\bf x}) = \displaystyle \frac{\partial}{\partial {\bf x}}\varphi(t,{\bf x}), \end{equation} which is the $n$-squared matrix satisfying the following variational equation around $\{\varphi(t,{\bf x})\}_{t\geq 0}$ for fixed ${\bf x}$: \begin{align} \displaystyle \frac{dV}{dt} &= Df(\varphi(t,{\bf x}))V,\\ V(0; {\bf x}) &= I_n, \end{align} where $I_n$ is the $n$-dimensional identity matrix. The Jacobian matrix of the Poincar\'{e} map $P({\bf x}_0)$ at ${\bf x}_0$ is then calculated by \begin{equation} DP({\bf x}_0) = \displaystyle \frac{d}{d{\bf x}'}\varphi(T_r({\bf x}_0),{\bf x}_0) = \left( I_n - \displaystyle \frac{ f(\varphi(T_r({\bf x}_0),{\bf x}_0)){\bf n}^T} {{\bf n}^T \cdot f( \varphi(T_r({\bf x}_0),{\bf x}_0) )} \right) V(T_r({\bf x}_0); \varphi(T_r({\bf x}_0),{\bf x}_0)), \end{equation} where ${\bf x}'$ denotes a coordinate on $\Gamma$. Note that $0\not \in {\bf n}^T\cdot f([{\bf x}])$ holds by Condition 4, which guarantees the well-definedness of the differential $DP$ at ${\bf x}_0$. \subsection{Remark on verification of the existence of periodic orbits} \label{section-valid-per} We have prepared the (rigorous enclosures of) Poincar\'{e} map $P$ and its differential $DP$ in the previous subsection. Before moving to validations of Lyapunov domains of $P$, we review a method for computing the enclosure of fixed points of $P$; namely, periodic orbits. \par There are mainly two approaches to verify the existence of periodic orbits with interval arithmetics: \begin{itemize} \item[1.] Construct Poincar\'{e} maps on a section and verify their fixed point, e.g., \cite{ZLoh}; \item[2.] Regard periodic orbits as solutions of the two-point boundary value problem \begin{equation} \label{BVP} \begin{cases} \displaystyle \frac{d}{d\tilde t}{\bf x}(\tilde t) = Tf({\bf x}(\tilde t)) & \\ {\bf x}(1) = {\bf x}(0) & \end{cases} \end{equation} and verify solutions with bordering conditions. \end{itemize} Here we briefly review the second approach proposed by the second and the third authors (e.g. \cite{HY}). Consider the autonomous differential equation (\ref{autonomous}). Let $\Gamma$ be a hyperplane and ${\bf n}_\Gamma$ be the unit normal vector to $\Gamma$. Our aim here is to validate a periodic orbit through a point ${\bf w}^\ast \in \Gamma$ as well as its period $T^\ast$. Our strategy is the reduction to the boundary value problem (\ref{BVP}) with {\em the bordering condition}: \begin{equation} \label{bvp-border} \begin{cases} {\bf n}_\Gamma \cdot ({\bf w}-\tilde {\bf w})= 0, & \\ \varphi(T,{\bf w}) = {\bf w}, & \end{cases}\quad T>0, {\bf w}\in \Gamma, \end{equation} where $\tilde {\bf w} \in \Gamma$ be a point on, say, an approximate periodic orbit. The first equation in (\ref{bvp-border}) is called the bordering condition and remove the ambiguity of detection of points on periodic orbits caused by translation invariance. Define a map $K : \mathbb{R}^{1+n}\to \mathbb{R}^{1+n}$ by \begin{equation} K({\bf z}) := \begin{pmatrix} {\bf n}_\Gamma \cdot ({\bf w}-\tilde {\bf w}) \\ \varphi(T,{\bf w}) - {\bf w} \end{pmatrix},\quad {\bf z} = (T, {\bf w})^T. \end{equation} The pair $(T^\ast, {\bf w}^\ast)$ of a periodic point on $\Gamma$ and its period corresponds to the zero of $K$. The Jacobi matrix $DK$ of $K$ at ${\bf z} = (T, {\bf w})^T$ is \begin{equation} DK({\bf z}) = \begin{pmatrix} {\bf 0} & {\bf n}_\Gamma^T \\ f(\varphi(T,{\bf w})) & V(T;{\bf w}) - I_n \end{pmatrix}, \end{equation} where $V$ is the variation matrix associated with $\varphi$. In the next step, we construct a Newton-like operator $N$ using $K$ and $DK$, and apply the quasi-Newton method to validate a zero of $K$. Let $DK_a$ be a nonsingular matrix which is an approximation to $DK(\tilde {\bf z})$ at the pair $\tilde {\bf z} = (\tilde T, \tilde {\bf w})$ of an approximate period $\tilde T$ and an approximate periodic point $\tilde {\bf w}$ on $\Gamma$. Then define the map $N :\mathbb{R}^{1+n}\to \mathbb{R}^{1+n}$ as \begin{equation} N({\bf z}) := {\bf z} - DK_a^{-1}\cdot K({\bf z}). \end{equation} Finally, setting initially a small interval set $[Z_0] = ([T], [W])^T$ containing $\tilde {\bf z}$ with an interval vector $[W]\subset \Gamma$, apply the following algorithm: \begin{algorithm} \label{alg-fixpt} Initially set $k=0$ and $\epsilon > 0$ small in advance. \begin{enumerate} \item Check if $N([Z_k])\subset [Z_k] = ([T_k], [W_k])$. If this operation passes, return \lq\lq succeeded" and stop the algorithm. \item If Step 1 fails, reset $[Z_{k+1}] = ([T_{k+1}], [W_{k+1}]) := (1+\epsilon)N([Z_k]) - \epsilon N([Z_k])$ and go back to Step 1 replacing $k$ by $k+1$. \end{enumerate} \end{algorithm} If this algorithm returns \lq\lq succeeded" at $k=k_0$, then there is a fixed point $(T^\ast, {\bf w}^\ast)$ of $N$ in $[Z_{k_0}]$, which is actually a zero of $K$. It implies that ${\bf w}^\ast$ is the intersection point of $\Gamma$ and a periodic orbit with the period $T^\ast$. \begin{remark}\rm For computations with $N$, we can use the following Krawczyk-type operator $\tilde N$ instead of $N$: \begin{equation} \tilde N([Z]) := DK_a^{-1}\{ DK_a \hat {\bf z} - K(\hat {\bf z}) + (DK_a - DK([Z])) ([Z] - \hat {\bf z})\}, \end{equation} where $\hat {\bf z}$ is the center point of $[Z]$, which is obtained by considering the mean value form of $N$. Also note that, if Algorithm \ref{alg-fixpt} returns \lq\lq succeeded" at $k=k_0$, we know that the Poincar\'{e} map can be defined on its Poincar\'{e} section $\Gamma\cap [W_{k_0}]$. \end{remark} \section{Numerical examples for flows} \label{section-example-cont} As demonstrating validations of Lyapunov functions for flows, we consider the three dimensional FitzHugh-Nagumo system: \begin{align} \notag \frac{du}{dt} &= v,\\ \label{FN} \frac{dv}{dt} &= \frac{1}{\delta}(cv-f(u)+w),\\ \notag \frac{dw}{dt} &= \frac{\epsilon}{c}(u-\gamma w), \end{align} where $f(u) = u(u-a)(1-u)$, and $a, c, \delta, \epsilon$ and $\gamma$ are (positive) parameters. The system (\ref{FN}) is regarded as the traveling wave equation of the following partial differential equation: \begin{align} \frac{\partial u}{\partial \tau} &= \delta \frac{\partial^2 u}{\partial x^2} - f(u) + w,\\ \frac{\partial w}{\partial \tau} &= \epsilon (u-\gamma w) \end{align} with $(u(x,\tau),w(x,\tau)) = (u(t),w(t))$, $t = x-c\tau$. Here we fix parameters as follows so that the system possesses three equilibria: \begin{equation} a=0.2,\quad c=5,\quad \delta = 5,\quad \epsilon = 0.15,\quad \gamma = 20. \end{equation} \begin{remark}\rm Throughout our computations, we have used the following computation environments. \begin{itemize} \item OS: Windows $7$ Professional $64$-bit (6.1, Build 7601) Service Pack 1 (7601. win7sp1\_gdr.150928-1507). \item Memory: 16384MB RAM. \item Software: MATLAB version R2012a and INTLAB version: v6 \cite{INTLAB}. \end{itemize} \end{remark} Equilibria with these parameters can be (approximately) computed below: \begin{align} {\bf x}_1^\ast &= (u_1^\ast ,v_1^\ast ,w_1^\ast ) = \left(0,0,0\right),\\ {\bf x}_2^\ast &= (u_2^\ast ,v_2^\ast ,w_2^\ast ) \approx \left(0.268337520964460,0,0.013416876048223\right),\\ {\bf x}_3^\ast &= (u_3^\ast ,v_3^\ast ,w_3^\ast ) \approx \left(0.931662479035540,0,0.046583123951777\right). \end{align} It numerically turns out that \begin{align} &\dim W^s({\bf x}_1^\ast) = 2,\quad \dim W^s({\bf x}_2^\ast) = 1,\quad \dim W^s({\bf x}_3^\ast) = 2,\\ &\dim W^u({\bf x}_1^\ast) = 1,\quad \dim W^u({\bf x}_2^\ast) = 2,\quad \dim W^u({\bf x}_3^\ast) = 1. \end{align} We compute symmetric matrices $Y_j$, $j=1,2,3$, in (\ref{Y-cont}) to obtain \begin{align} Y_1&=\left(\begin{array}{ccc} 1.9045048614 &-1.9684846596 &-0.7930467270 \\ -1.9684846596 &-1.8022725548 &0.2703701350 \\ -0.7930467270 &0.2703701350 &2.3772099623 \end{array}\right), \end{align} \begin{align} Y_2&=\left(\begin{array}{ccc} -2.2485667721 & 2.5290401659 & 0.6528894939 \\ 2.5290401659 &-6.9945543958 &-1.2823752332 \\ 0.6528894939 &-1.2823752332 & 1.8533105010 \end{array}\right), \end{align} \begin{align} Y_3&=\left(\begin{array}{ccc} 1.7202944579 &-1.8934526570 &-0.8110063777 \\ -1.8934526570 &-1.6051655895 & 0.3062332874 \\ -0.8110063777 & 0.3062332874 & 2.4375167185 \end{array}\right). \end{align} Note that matrices $Y_j$, $j=1,2,3$, are indeed symmetric. We now verify Lyapunov domains of $x_j^\ast$. Firstly, set sample domains $D_j$, $j=1,2,3$, as \begin{align} D_1 &:= [-0.5, 0.5]\times [-0.5, 0.5]\times [-0.5, 0.5],\\ D_2 &:= [0, 1]\times [-0.5, 0.5]\times [-0.5, 0.5],\\ D_3 &:= [0.5, 1.5]\times [-0.5, 0.5]\times [-0.5, 0.5], \end{align} each of which contains ${\bf x}_j^\ast$. Let \begin{equation} L_j({\bf x}) := ({\bf x}-{\bf x}_j^\ast)^T Y_j ({\bf x}-{\bf x}_j^\ast),\quad j=1,2,3, \end{equation} be the candidates of Lyapunov functions. Next we divide these domains into $50\times 50\times 50$ small uniform cubes. We then verify the strict negative definiteness of the matrix $A({\bf z})$ in (\ref{matrix-neg-def}) on each small cubes. Note that, if the matrix $A({\bf z})$ associated with $L_j$ is strictly negative definite on a cube, then $L_j$ is a Lyapunov function on it. \begin{description} \item[Description of Figs. \ref{fig-FNfp} - \ref{fig-LorenzEvec}] \end{description} In these figures we distinguish verification results of Lyapunov domains by different colors. \begin{itemize} \item {\bf Blue}: Both Stage 1 and 2 are succeeded. \item {\bf Light Blue}: Only Stage 1 is succeeded. \item {\bf Yellow}: Only Stage 2 is succeeded. \item {\bf Red}: Both Stage 1 and 2 are failed. \end{itemize} White disks denote locations of equilibria. \bigskip Fig. \ref{fig-FNfp} describes domains $D_j\cap \{w=0\}$ and contours of Lyapunov fucntions $L_j$. \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1UV.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2UV.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3UV.png} (c) \end{minipage} \caption{Domains $D_i\cap \{w=0\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp} \begin{flushleft} (a) shows $D_1\cap \{w=0\}$. Black lines represent contours $\{L_1=0\}$. \par (b) shows $D_2^\ast\cap \{w=0\}$. Black curves represent contours $\{L_2=-0.5, -0.1\}$. \par (c) shows $D_3\cap \{w=0\}$. Black lines represent contours $\{L_3=0\}$. \end{flushleft} \end{figure} \subsection{Validation of Lyapunov functions} Figs. \ref{fig-FNfp-V1} - \ref{fig-FNfp-V5} describe sections of domains $D_j$ with $\{v = \text{const.}\}$ with contours of Lyapunov functions $L_j$. \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V1.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2V1.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3V1.png} (c) \end{minipage} \caption{Domains $D_i\cap \{v=-0.1\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp-V1} \begin{flushleft} (a) shows $D_1\cap \{v=-0.1\}$. Black curves represent contours $\{L_1=-0.01, -0.005, 0\}$. \par (b) shows $D_2^\ast\cap \{v=-0.1\}$. Black curves represent contours $\{L_2=-0.4, -0.2, 0\}$. \par (c) shows $D_3\cap \{v=-0.1\}$. Black curves represent contours $\{L_3=-0.01, -0.005, 0\}$. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V2.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2V2.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3V2.png} (c) \end{minipage} \caption{Domains $D_i\cap \{v=-0.05\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp-V2} \begin{flushleft} (a) shows $D_1\cap \{v=-0.05\}$. Black curve represents the contour $\{L_1= 0\}$. \par (b) shows $D_2^\ast\cap \{v=-0.05\}$. Black curves represent $\{L_2=-0.4, -0.2, 0\}$. \par (c) shows $D_3\cap \{v=-0.05\}$. Black curve represents the contour $\{L_3= 0\}$. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V3.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2V3.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3V3.png} (c) \end{minipage} \caption{Domains $D_i\cap \{v=0\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp-V3} \begin{flushleft} (a) shows $D_1\cap \{v=0\}$. \par (b) shows $D_2^\ast\cap \{v=0\}$. Black curves represent contours $\{L_2=-0.4, -0.2, 0\}$. \par (c) shows $D_3\cap \{v= 0\}$. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V4.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2V4.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3V4.png} (c) \end{minipage} \caption{Domains $D_i\cap \{v=0.05\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp-V4} \begin{flushleft} (a) shows $D_1\cap \{v=0.05\}$. Black curve represents the contour $\{L_1= 0\}$. \par (b) shows $D_2^\ast\cap \{v=0.05\}$. Black curves represent contours $\{L_2=-0.4, -0.2, 0\}$. \par (c) shows $D_3\cap \{v=0.05\}$. Black curve represents the contour $\{L_3= 0\}$. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V5.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp2V5.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp3V5.png} (c) \end{minipage} \caption{Domains $D_i\cap \{v=0.1\}$, $i=1,2,3$, and contours of Lyapunov functions.} \label{fig-FNfp-V5} \begin{flushleft} (a) shows $D_1\cap \{v=0.1\}$. Black curves represent contours $\{L_1=-0.01, -0.005, 0\}$. \par (b) shows $D_2^\ast\cap \{v=0.1\}$. Black curves represent contours $\{L_2=-0.4, -0.2, 0\}$. \par (c) shows $D_3\cap \{v=0.1\}$. Black curves represent contours $\{L_3=-0.01, -0.005, 0\}$. \end{flushleft} \end{figure} \bigskip Looking at Fig. \ref{fig-FNfp-V4}-(a), it turns out that red cubes are contained in the interior of $L_1^{-1}(0)$; namely, $L_1^{-1}(0,\infty)$. This can be also seen in Fig. \ref{fig-FNfp}-(a). We then divide the domain $[0,0.4]\times [-0.2,0.2]\times [-0.2,0.2]$ into $200\times 200\times 200$ small uniform cubes and verify the strict negative definiteness of $A({\bf z})$ in (\ref{matrix-neg-def}) on these smaller cubes again. Fig. \ref{fig-FNReVal} shows validation results in this setting, which shows that the Lyapunov domain in $D_1$ is extended. More precisely, yellow area corresponding to succeeded domains in Stage 2 becomes larger. \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/FP1N200m0r02w0.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/FP1N200m0r02v0u02.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1V4v2.png} (c) \end{minipage} \caption{Refinement of the region $[0,0.4]\times [-0.2,0.2]^2$ in Fig. \ref{fig-FNfp-V4}-(a). } \label{fig-FNReVal} \begin{flushleft} (a) shows $D_1\cap \{w=0\}$. Black lines represent contours $\{L_1=0\}$. \par (b) shows $D_1^\ast\cap \{v=0\}$. \par (c) shows $D_1\cap \{v=0.05\}$. Black curve represents the contour $\{L_3=0\}$. \end{flushleft} \end{figure} \bigskip Finally, note that there are several regions where only validations in Stage 2 are succeeded. Lyapunov domains containing such domains include geometric cones (e.g. yellow domains in Figs. \ref{fig-FNfp}-(c) and \ref{fig-FNfp-V1}-(c)), but we cannot apply the theory of dynamical cone $Q$ to asymptotic behavior in those domains in general. \subsection{Validation of ${\bf m}$-Lyapunov functions} Next we construct ${\bf m}$-Lyapunov functions around ${\bf x}_1^\ast$ and compare Lyapunov domains with those of $L_1$. Let $M^\ast = {\rm diag}\{i_1,\cdots, i_n\}$ be given by \begin{align} i_j=\left\{\begin{array}{ccc} m_j, & \text{if} & Re\left(\lambda_j\right)<0 \\ -m_j, & \text{if} & Re\left(\lambda_j\right)>0. \end{array}\right. \end{align} In our current validations, we set (i) $m_1 = 10, m_2 = 1$, and (ii) $m_1 = 1, m_2 = 10$. Figs. \ref{fig-FNM1} - \ref{fig-FNM3} show our validation results for Lyapunov domains of $L_1$, (i) and (ii), respectively. Note that the matrix $I^\ast$ with (i) makes the stable cone sharper. Similarly, the matrix $I^\ast$ with (ii) makes the unstable cone sharper. Figs. \ref{fig-FNM1}-(b) and \ref{fig-FNM2}-(b) imply that the stable cone contains more red cubes if it becomes sharper. Similarly, Figs. \ref{fig-FNM1}-(c) and \ref{fig-FNM2}-(c) imply that there are many red cubes on the right side of equilibria. ${\bf m}$-Lyapunov functions actually sharpen enclosures of stable and unstable manifolds, but corresponding Lyapunov domains tend to be smaller than those for ordinary Lyapunov functions, even close to equilibria. \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp10UV.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1MUV.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1PUV.png} (c) \end{minipage} \caption{Validation of ${\bf m}$-Lyapunov functions: 1.} \label{fig-FNM1} \begin{flushleft} (a) shows $D_1\cap \{w=0\}$. Black lines represent contours $\{L_1=0\}$. \par (b) shows $D_1\cap \{w=0\}$. Black lines represent contours $\{L_{M^\ast}=0\}$, where $m_1 = 10, m_2 = 1$, which implies that the stable cone becomes sharper. \par (c) shows $D_1\cap \{w=0\}$. Black lines represent contours $\{L_{M^\ast}=0\}$, where $m_1 = 1, m_2 = 10$, which implies that the unstable cone becomes sharper. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp10V1.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1MV1.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1PV1.png} (c) \end{minipage} \caption{Validation of ${\bf m}$-Lyapunov functions: 2.} \label{fig-FNM2} \begin{flushleft} (a) shows $D_1\cap \{v=0.02\}$. Black curve represents the contour $\{L_1=0\}$. \par (b) shows $D_1\cap \{v=0.02\}$. Black curve near the origin represents the contour $\{L_{M^\ast}=0\}$, where $m_1 = 10, m_2 = 1$. \par (c) shows $D_1\cap \{v=0.02\}$. Black curve represents the contour $\{L_{M^\ast}=0\}$, where $m_1 = 1, m_2 = 10$. \end{flushleft} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp10V2.png} (a) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1MV2.png} (b) \end{minipage} \begin{minipage}{0.32\hsize} \centering \includegraphics[width=5.0cm]{img/1_Continious/1_FN/fp1PV2.png} (c) \end{minipage} \caption{Validation of ${\bf m}$-Lyapunov functions: 3.} \label{fig-FNM3} \begin{flushleft} (a) shows $D_1\cap \{v=0.1\}$. Black curves represent contours $\{L_1=-0.01,0\}$. \par (b) shows $D_1\cap \{v=0.1\}$. Black curve represents the contour $\{L_{M^\ast}=0\}$, where $m_1 = 10, m_2 = 1$. \par (c) shows $D_1\cap \{v=0.1\}$. Black curves represent contours $\{L_{M^\ast}=-0.02, -0.01, 0\}$, where $m_1 = 1, m_2 = 10$. \end{flushleft} \end{figure} \bigskip Computation times for our verifications are about $11$ minutes for $50\times 50\times 50$ small uniform cubes, and about $14.5$ hours for $200\times 200\times 200$ smaller uniform cubes shown in Fig. \ref{fig-FNReVal}. \section{Numerical examples for Poincar\'{e} maps} \label{section-example-discrete} We move to validations of Lyapunov domains for discrete dynamical systems. In particular, we deal with Poincar\'{e} maps for flows on Poincar\'{e} sections as our test problems. \subsection{Remarks on verification of the negative definiteness of $B({\bf x})$} In practical verification of the negative definiteness of $B({\bf x})$ in (\ref{matrix-discrete}), we should pay attention to differences from the case of flows. Let $D_L$ be a star-shaped domain containing a fixed point ${\bf x}^\ast$ of a map $\psi$ with a decomposition $D_L = \bigcup_{k=1}^K D_k$. For each point ${\bf x}\in D_k$, the path $\{{\bf x}^\ast + s({\bf x}-{\bf x}^\ast)\mid 0\leq s\leq 1\}$ is contained in $D_L= \bigcup_{k=1}^{K} D_k$. By using the integral form of $A_I$, the matrix $B({\bf x})$ can be written by \begin{align} B({\bf x}) &= A_I({\bf x})^T Y A_I({\bf x}) - Y\\ &= \int_0^1 \{ D\psi ({\bf x}^\ast + s({\bf x}-{\bf x}^\ast))^T Y A_I({\bf x}) - Y\}ds\\ &= \int_0^1ds \int_0^1ds' \{ D\psi ({\bf x}^\ast + s({\bf x}-{\bf x}^\ast))^T Y D\psi ({\bf x}^\ast + s'({\bf x}-{\bf x}^\ast)) - Y\}\\ &= \int_0^1ds \int_0^1ds' \tilde B({\bf x};s,s'). \end{align} These equalities indicate that the negative definiteness of $B({\bf x})$ is reduced to that of the matrix $\tilde B({\bf x};s,s')$ for all $s,s'\in [0,1]$, as in the case of flows. Since both segments $\{{\bf x}^\ast + s({\bf x}-{\bf x}^\ast)\}$ and $\{{\bf x}^\ast + s'({\bf x}-{\bf x}^\ast)\}$ are contained in $D_L$, then we know that the matrix $\tilde B({\bf x};s,s')$ is contained in the following set of matrices for any ${\bf x}\in D_k$ for all $k=1,\cdots, K$: \begin{equation} \{\tilde B({\bf z}, {\bf z}') = D\psi ({\bf z})^T Y D\psi ({\bf z}') - Y \mid {\bf z}, {\bf z}'\in D_L\}. \end{equation} Obviously any points ${\bf z}, {\bf z}'$ are contained in $D_k$ and $D_{k'}$ for some $k,k'\in \{1,\cdots, K\}$, respectively, while they are different in general. We obtain the following sufficient condition of the negative definiteness of $B({\bf x})$ for all $x\in D_L$ making use of the decomposition $D_L= \bigcup_{k=1}^{K} D_k$. \begin{lemma} \label{lem-neg-def-map1} Let $D_L$ be a star-shaped domain containing a fixed point ${\bf x}^\ast$ of a map $\psi$ with a decomposition $D_L = \bigcup_{k=1}^K D_k$. Let $\tilde B({\bf z}, {\bf z}') = D\psi ({\bf z})^T Y D\psi ({\bf z}') - Y$ for ${\bf z}, {\bf z}'\in D_L$. Enclose each subdomain $D_k$ by an interval vector $[D_k]$. Assume that all matrices of the matrix set \begin{equation} \tilde B([D_k], [D_{k'}]) = \{\tilde B({\bf z}, {\bf z}') \mid {\bf z}\in [D_k], {\bf z}'\in [D_{k'}]\} \end{equation} are negative definite for all $k,k'\in \{1,\cdots, K\}$. Then $B({\bf x})$ is negative definite for all ${\bf x}\in D_L$. \end{lemma} Using the identity \begin{equation} ({\bf x}-{\bf x}^\ast)^T C({\bf x}-{\bf x}^\ast) = ({\bf x}-{\bf x}^\ast)^T C^T ({\bf x}-{\bf x}^\ast) = ({\bf x}-{\bf x}^\ast)^T \frac{(C^T + C)}{2}({\bf x}-{\bf x}^\ast) \end{equation} for any $n$-squared matrix $C$, we know that the verification of Lemma \ref{lem-neg-def-map1} is replaced by the negative definiteness of the symmetrized matrix set \begin{equation} \label{sym-matrix-B} \check B([D_k], [D_{k'}]) = \left\{\frac{\tilde B({\bf z}, {\bf z}')^T + \tilde B({\bf z}, {\bf z}')}{2} \mid {\bf z}\in [D_k], {\bf z}'\in [D_{k'}]\right\},\quad k, k' \in \{1,\cdots, K\}. \end{equation} \bigskip Taking these observations into account, we propose the following algorithm with the decomposition $D_L = \bigcup_{k=1}^K D_k$. \begin{algorithm} \label{alg-disc} Let $D_L$ be a star-shaped domain containing a fixed point ${\bf x}^\ast$ of $\psi$ with a decomposition $D_L = \bigcup_{k=1}^K D_k$. Let $[D_k]$ be the interval hull of $D_k$ (namely, the smallest interval set containing $D_k$). \begin{enumerate} \item For each $k, k'\in \{1,\cdots, K\}$, compute the interval matrix $\check B(k,k') := \check B([D_k], [D_{k'}])$, according to (\ref{sym-matrix-B}). \item Compute the negative definiteness of the interval matrix $\check B(k,k')$ for all possible choices of $k, k'\in \{1,\cdots, K\}$ with, say, the Gershgorin Circle Theorem in Algorithm \ref{alg-cont}. \end{enumerate} If the above verifications pass, return \lq\lq succeeded". If not, return \lq\lq failed". \end{algorithm} Negative definiteness of all $\check B(k,k')$ yields the negative definiteness of $B({\bf x})$ for each ${\bf x}\in D_L$. Consequently, we obtain the following corollary. \begin{corollary} \label{cor-subdivision-disc} Let $D_L$ be a star-shaped domain containing a fixed point ${\bf x}^\ast$ of $\psi$. Assume that $D_L$ admits a decomposition $D_L = \bigcup_{k=1}^{K} D_k$ into subdomains. We also assume that there is a symmetric matrix $Y$ such that Algorithm \ref{alg-disc} returns \lq\lq succeeded". Then the functional $L({\bf x}) = ({\bf x}-{\bf x}^\ast)^T Y ({\bf x}-{\bf x}^\ast)$ is a Lyapunov function on $D_L$. \end{corollary} Note that we have to verify the negative definiteness of $\check B(k,k')$ for all choices of the pair $(k,k')$ in $\{1,\cdots, K\}$, unlike the case of flows (Corollary \ref{cor-subdivision-cont}). This is because two $A_I({\bf x})$'s are contained in a single term of $B({\bf x})$ and we have to consider integral forms with two individual parameters. \bigskip Now we discuss another trap for validating the negative definiteness of $B({\bf x})$. Since $A_I({\bf x})$ has the integral form $A_I({\bf x}) = \int_0^1 D\psi({\bf x}^\ast + s({\bf x} - {\bf x}^\ast))ds$, one can think of the mean value form of $A_I$ with interval arithmetics. In such a case, we obtain \begin{equation} A_I({\bf x}) \in \int_0^1 D\psi \left( \bigcup_{k=1}^K [D_k]\right)ds,\quad {\bf x}\in D_L. \end{equation} By using the mean value form, we obtain \begin{equation} \label{correct-1} A_I({\bf x}) \in D\psi \left( \bigcup_{k=1}^K [D_k]\right). \end{equation} Notice that the inclusion (\ref{correct-1}) does just mean \begin{equation} \label{correct-2} (A_I({\bf x}))_{i,j} \in \bigcup_{k=1}^K \{ (D\psi ({\bf z}))_{i,j}\mid {\bf z}\in [D_k]\},\quad i,j\in \{1,\cdots, n\} \end{equation} and {\em does not mean} \begin{equation} \label{wrong} A_I({\bf x}) \in \bigcup_{k=1}^K \{ D\psi ({\bf z})\mid {\bf z}\in [D_k]\}. \end{equation} The trap is explained as follows. Note that $A_I({\bf x})$ is a matrix valued function and $\int_0^1 D\psi \left( \bigcup_{k=1}^K [D_k]\right)ds$ is an interval matrix whose entries have integral forms. In this case, the mean value form (\ref{correct-1}) is applied {\em to each entry, not to the whole matrix in general}. Therefore, the verification making use of the wrong inclusion (\ref{wrong}) may return wrong results. If we apply the mean value form of $A_I$ with the decomposition $D_L = \bigcup_{k=1}^{K} D_k$ and interval arithmetics, we can just apply the inclusion (\ref{correct-2}) for negative definiteness of $B({\bf x})$, which may cause the combinatorial explosion for computations. Although Algorithm \ref{alg-disc} also makes use of the integral form of $A_I$, we should be very careful of estimation criteria for obtaining rigorous enclosures of matrices. \footnote{If (\ref{wrong}) was correct, it would follow from (\ref{wrong}) that \begin{equation} A_I({\bf x}) = D\psi ({\bf z}')\quad \text{ for some } {\bf z}\in [D_k]\text{ with some }k, \end{equation} which would indicate that the negative definiteness of $B({\bf x})$ would hold if the matrix $D\psi ({\bf z}')^T Y D\psi ({\bf z}')-Y$ was negative definite for all ${\bf z}'\in D_L$. This would provide an effective procedure for verifying the negative definiteness {\em if (\ref{correct-1}) implied (\ref{wrong})}, which is not the case. } \par \bigskip A procedure such as Algorithm \ref{alg-disc} works to prove the existence of Lyapunov functions as long as the above algorithm passes successfully, even if domains does not contain fixed points. An immediate benefit of Algorithm \ref{alg-disc} as well as Corollary \ref{cor-subdivision-disc} is that we can use better enclosure of matrices associated with $B$ in (\ref{matrix-discrete}). In general, however, Algorithm \ref{alg-disc} is not an effective method in practical computations if the problem concerns with higher dimensional dynamical systems or the number of decompositions $K$ is large, which cause the combinatorial explosion of computations. Nevertheless, if both the dimension of the problem and $K$ are small, Algorithm \ref{alg-disc} is available in reasonable computation processes. \subsection{R\"{o}ssler system} The first example is the R\"{o}ssler system: \begin{align} \notag \frac{du}{dt} &= -v-w,\\ \label{rossler} \frac{dv}{dt} &= -u-av,\\ \notag \frac{dw}{dt} &= b-w(c-u), \end{align} We consider the following parameters: \begin{equation} a = 0.2,\quad b = 0.2,\quad c = 2.2, \end{equation} in which case (\ref{rossler}) possesses an asymptotically stable periodic orbit. Let the Poincar\'{e} section $\Gamma$ and its unit normal vector $n_\Gamma$ \footnote{ The setting of $n_\Gamma$ provide us with a simple coordinate on Poincar\'{e} sections. In general, Poincar\'{e} sections for $n$-dimensional dynamical systems yield an $(n-1)$-dimensional coordinate, which is called an {\em section coordinate} (e.g. \cite{ZLoh}). Since $n_\Gamma$ below is along an coordinate axis in the original coordinate on $\mathbb{R}^3$, the section coordinate is just the choice of two entries. In particular, our verifications are reduced to two dimensional dynamical systems. For general $n_\Gamma$, we can choose an appropriate section coordinate after an affine transformation. } be \begin{align} \Gamma &= \{(u,v,w)\in \mathbb{R}^3 \mid v = -0.039538545829724\},\\ n_\Gamma &= (0,-1,0)^T. \end{align} Then intervals containing the intersection point of a periodic orbit of (\ref{rossler}) with $\Gamma$ as well as the rigorous period can be validated as follows (\cite{HY}): \begin{align} \left[{\bf x}^\ast \right] &= \left(\begin{array}{c} \left[-3.33960829479577, -3.33960817367770\right] \\ \left[-0.03955770987867, -0.03955770858575\right]\\ \left[ 0.03932476640565, 0.03932477007120\right] \end{array}\right)\\ \left[T^\ast\right] &= \left[5.72694905401293, 5.72694917018763\right]. \end{align} Eigenvalue enclosures of the linearized matrix $DP([{\bf x}^\ast])$ of the Poincar\'{e} map $P:\Gamma\to \Gamma$ at the intersection are \begin{align} [\lambda_1] &= \left[-0.55389294656450, -0.53463411180113\right], \\ [\lambda_2] &= \left[-0.00045527197787, 0.00037278836683\right], \end{align} which yield that the corresponding periodic orbit is asymptotically stable. Note that, for computations of the Poincar\'{e} maps, we applied the $C^1$-Lohner algorithm \cite{ZLoh} with various time steps $N_t$. The order of Taylor expansion computing the residual term is set $p=5$. In our case, we compute the first arrival map for the Poincar\'{e} section $\Gamma$ and hence the adjustment of $N_t$ corresponds to that of the size of one time step $\Delta t$. The symmetric matrix $Y$ computed at the center of $[{\bf x}^\ast]$ is computed as follows: \begin{align} Y&=\left(\begin{array}{cc} 1.007925375406352 & -0.208072133943174 \\ -0.208072133943174 & 1.077435243689143 \end{array}\right) \end{align} Firstly, we verify the strict negative definiteness of the matrix $\check B({\bf z},{\bf z}')$ in (\ref{matrix-discrete}) around a fixed point of $P$ following Algorithm \ref{alg-disc}. For the computation of $P$, we set $N_t = 2000$ and let $[X]$ be the interval vector on $\Gamma$ given by \begin{align} \left[X\right] = \left(\begin{array}{c} \left[-3.43960823423674, -3.23960823423673\right] \\ \left[-0.06067523176158, 0.13932476823843\right] \end{array}\right), \end{align} which actually contains $[{\bf x}^\ast]$. We then divide $[X]$ into $10\times 10$ small uniform squares. Through computations following Algorithm \ref{alg-disc}, we have confirmed the strict negative definiteness, which is shown as light blue regions in Fig. \ref{fig-Rossler2000}. \bigskip Secondly, we validate Lyapunov domains away from the fixed point. According to Stage 2, we verify the sign of $L(P([{\bf x}]))-L([{\bf x}])$, in which case the operation returns \lq\lq succeeded" if $L(P([{\bf x}]))-L([{\bf x}])$ is negative. If we cannot confirm that $L(P({\bf x}))-L({\bf x}) < 0$ via interval arithmetics, then the operation returns \lq\lq failed". Note that the result \lq\lq failed" does not mean that $L(P([{\bf x}]))-L([{\bf x}]) \geq 0$ but actually means that the resulting interval $L(P([{\bf x}]))-L([{\bf x}])$ contains $0$. Fig. \ref{fig-Rossler2000} shows the succeeded regions colored by blue, light-blue and the failed regions colored by red with $N_t=2000$. \begin{figure}[htbp]\em \begin{minipage}{1\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/1_Rossler/RosslerRes1.png} \end{minipage} \caption{Lyapunov domain for (\ref{rossler}) validated with $2000$ time steps.} \label{fig-Rossler2000} \end{figure} \bigskip Thirdly, we validate Lyapunov domains away from the fixed point with $N_t = 4000$. Validation results is shown in Fig. \ref{fig-Rossler4000}. Compared with Fig. \ref{fig-Rossler4000}, the blue region is enlarged, which implies that the accuracy of ODE computations deeply relates to constructions of Lyapunov regions. \begin{figure}[htbp]\em \begin{minipage}{0.4\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/1_Rossler/RosslerRes2.png} \end{minipage} \begin{minipage}{0.4\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/1_Rossler/RosslerResContour.png} \end{minipage} \caption{Lyapunov domain for (\ref{rossler}) validated with $4000$ time steps and contours of the Lyapunov function.} \label{fig-Rossler4000} \end{figure} \bigskip Nevertheless, there are several regions which our validations return failed. To consider the origin of the failure of our validations, we numerically computed eigenvectors of $DP({\bf x}^\ast)$ at the center ${\bf x}^\ast \in [{\bf x}^\ast]$. The result is shown in Fig. \ref{fig-RosslerEvec}. $DP({\bf x}^\ast)$ has two eigendirections, one of which is the vector $r_1$ associated with $\lambda_1 = -0.000040978780281$ (green), and the other is the vector $r_2$ associated with $\lambda_2 = -0.544259673645596$ (yellow). Fig. \ref{fig-RosslerEvec} implies that the \lq\lq failed" region is clustered on the direction of $r_2$. Note that the modulus of $\lambda_2$ is closer to $1$ than that of $\lambda_1$, which implies that the strength of hyperbolicity relates to the difficulty for validating Lyapunov domains. \begin{figure}[htbp]\em \begin{minipage}{1\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/1_Rossler/RosslerRes3.png} \end{minipage} \caption{Eigendirections of the Poincar\'{e} map for (\ref{rossler}).} \label{fig-RosslerEvec} \end{figure} \bigskip Computation times for our verifications are about $25$ hours in Stage $1$ with $C^1$-Lohner method, and about $4.8$ hours in Stage $2$ with the ordinary (i.e. $C^0$-)Lohner method. Such a big difference of computation times is due to the difference of optimizations of programs. \subsection{Lorenz system} The second example is the Lorenz system: \begin{align} \notag \frac{du}{dt} &= -p(u+v),\\ \label{Lorenz} \frac{dv}{dt} &= u(r-z)-v,\\ \notag \frac{dw}{dt} &= uv-bw. \end{align} We set \begin{equation} r = 28,\quad p = 6,\quad b = \frac{8}{3}. \end{equation} The system (\ref{Lorenz}) with the above parameter values admits a periodic orbit (e.g. \cite{SV1980}), which can be validated with computer assistance that it is of saddle-type \cite{HY}. The transformation by Sinai-Vul \cite{SV1980, SV1981} (cf. \cite{YYN}) yields the following transformed system and parameter values: \begin{align} \notag \frac{du}{dt} &= a_1 u + b_1(u+v)w,\\ \label{Lorenz-trans} \frac{dv}{dt} &= a_2 v - b_1(u+v)w,\\ \notag \frac{dw}{dt} &= -a_3w + (u+v)(b_2 u + b_3 v), \end{align} \begin{equation} \label{Lorenz-param-trans} \begin{cases} a_1= 9.700378782,\quad a_2=-16.700378782,\quad a_3= 2.666666667, &\\ b_1=-0.227266206,\quad b_2= 2.616729797,\quad b_3=-1.783396463. & \end{cases} \end{equation} We regard (\ref{Lorenz-trans})-(\ref{Lorenz-param-trans}) as the center of our considerations. A Poincar\'{e} section $\Gamma$ as well as its unit normal vector $n_\Gamma$ in our verification are set as \begin{equation} \Gamma = \{(u,v,w)\in \mathbb{R}^3 \mid w = 27\},\quad n_\Gamma = (0,0,1)^T. \end{equation} Numerical validation of the Poincar\'{e} map $P$ based on discussions in Section \ref{section-valid-per} yields enclosures of the intersection point between the periodic orbit $\gamma$ and $\Gamma$ as well as the period of $\gamma$ as follows: \begin{align} \left[{\bf x}^\ast\right]&=\left( \begin{array}{c} \left[ 3.50078722830696, 3.50078739732356\right] \\ \left[ 3.33033175959478, 3.33033178479988\right] \\ \left[ 27.00000000000000, 27.00000000000000\right] \end{array}\right)\\ \left[T^\ast\right] &= \left[0.68991868010675, 0.68991868537750\right] \end{align} Eigenvalues of the Jacobian matrix $DP([{\bf x}^\ast])$ of $P$ in $[{\bf x}^\ast]$ are enclosed by the following intervals: \begin{align} \lambda_1 &= \left[ 1.03671803803776, 1.06505368292434\right]\\ \lambda_2 &= \left[-0.01460002975740, 0.01701745287359\right], \end{align} which implies that the validated periodic orbit $\gamma$ is of saddle-type. The symmetric matrix $Y$ computed at the center of $[{\bf x}^\ast]$ is computed as follows: \begin{align} Y&=\left(\begin{array}{cc} -0.915485816680675 & 0.474862621686875\\ 0.474862621686875 & 0.915485816680675 \end{array}\right) \end{align} We are then ready to validate the Lyapunov domain around $[{\bf x}^\ast]\cap \Gamma$. Firstly, set a sample region containing $[{\bf x}^\ast]$ in $\Gamma$ as \begin{align} \left[X\right] = \left(\begin{array}{c} \left[ 3.48078731281545, 3.52078731281546\right] \\ \left[ 3.31033177219729, 3.35033177219730\right] \end{array}\right) \end{align} and divide $[X]$ into $4\times 4$ small uniform rectangular domains. We then validate the strict negative definiteness of the matrix $B({\bf z})$ in (\ref{matrix-discrete}) for $P$ with $N_t = 4000$ in the whole region $[X]$ following Algorithm \ref{alg-disc}, which is shown in light blue regions in Fig. \ref{fig-Lorenz}. \bigskip Secondly, we extend the Lyapunov region outside $[X]$ by verifying if $L(P({\bf x})) - L({\bf x})$ becomes negative in each interval region $[{\bf x}]$ with $N_t = 2000$. Fig. \ref{fig-Lorenz} around light blue region represents regions where our validation returns \lq\lq succeeded" (blue) and those our validation returns \lq\lq failed" (red). In Fig. \ref{fig-LorenzEvec}, we can see correspondence between red regions and the arrow colored yellow denoting the eigenvector of $DP([{\bf x}^\ast])$ associated with the eigenvalue $\lambda_1 = -1.050919958691306$. Note that the green arrow in Fig. \ref{fig-LorenzEvec} denotes the eigenvector of $DP([{\bf x}^\ast])$ associated with the eigenvalue $\lambda_2 = -0.001207890459913$. We observe that, as in the case of the R\"{o}ssler system, validations of Lyapunov domains become hard in eigendirections associated with eigenvalues whose moduli are close to $1$. In other words, the strength of hyperbolicity corresponds to the difficulty of validations of Lyapunov domains. \begin{figure}[htbp]\em \begin{minipage}{0.4\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/2_Lorenz/AllInnerSuccess.png} \end{minipage} \begin{minipage}{0.4\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/2_Lorenz/LDomainContour.png} \end{minipage} \caption{Validated Lyapunov domain for (\ref{Lorenz-trans}) around $[{\bf x}^\ast]$ in $\Gamma$ and contours of $L$.} \label{fig-Lorenz} \end{figure} \begin{figure}[htbp]\em \begin{minipage}{1\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/2_Lorenz/LDomainQuiver.png} \end{minipage} \caption{Eigendirections of the Poincar\'{e} map for (\ref{Lorenz-trans}) and contours of the Lyapunov function.} \label{fig-LorenzEvec} \end{figure} Next, we consider a ${\bf m}$-Lyapunov function around the saddle fixed point. Let ${\bf m} = (m_1,m_2) = \{1, 1/4\}$, which yields \begin{equation} M^\ast = \begin{pmatrix} -1 & 0\\ 0 & \frac{1}{4} \end{pmatrix}, \end{equation} and contours of the ${\bf m}$-Lyapunov function $L_{M^\ast}$ is shown in Fig \ref{fig-LorenzContour} as well as the Lyapunov domain. \begin{figure}[htbp]\em \begin{minipage}{1\hsize} \centering \includegraphics[width=6.0cm]{img/2_Discrete/2_Lorenz/MCornContour.png} \end{minipage} \caption{Contours of $L_{M^\ast}$ for (\ref{Lorenz-trans}).} \label{fig-LorenzContour} \end{figure} We observe that we cannot validate the strict negative definiteness of $B_{M^\ast}({\bf w})$ anywhere around the fixed point if $m_1 < 1$. Similarly, if $m_2 < 1/4$, the validated domain where $B_{M^\ast}({\bf w})$ is strictly negative definite becomes smaller. The Lyapunov domain of $L_{M^\ast}$ is smaller than that of $L$ and it is clustered on the direction of stable manifolds. Indeed, the blue region in Fig. \ref{fig-LorenzContour} is concentrated on $L^{-1}(0,\infty)$. This observation is due to the small modulus of $\lambda_1$ (eigenvalue associating the stable direction). \bigskip Computation times for our verifications are about $43$ hours in Stage $1$ with $C^1$-Lohner method, and about $19$ hours in Stage $2$ with the ordinary (i.e. $C^0$-)Lohner method. Finally, verification of $L_{M^\ast}$ takes about $2$ seconds. \section{Conclusion} We have discussed a systematic procedure of Lyapunov functions with explicit domains of definition, called Lyapunov domains, with computer assistance. Computer assisted analysis such as interval arithmetics enables us to construct Lyapunov functions around fixed points with explicit ranges. Our Lyapunov functions are quadratic and hence we can easily describe local dynamics in Lyapunov domains, such as level sets of Lyapunov functions and enclosures of the stable and the unstable manifolds of fixed points. \bigskip In our procedure, there are two stages for constructing Lyapunov domains for flows for a given quadratic structure: \bigskip \begin{itemize} \item {\bf Stage 1: Strict negative definiteness of the associated matrix $A({\bf z})$}. \end{itemize} This verification around equilibria yields not only validation of Lyapunov domains but also local uniqueness of equilibria. We have proved that all hyperbolic equilibria locally admit Lyapunov functions of the form (\ref{Lyapunov-flow}). In particular, the negative definiteness of $A$ reflects hyperbolicity of the Jacobian matrix at a hyperbolic equilibrium ${\bf x}^\ast$. We have also observe that the negative definiteness is intrinsically the same as cone conditions discussed in e.g. \cite{ZCov}. Additionally, we have discussed another validation procedure of Lyapunov functions as well as hyperbolicity of equilibria for flows in the preceding work \cite{Mat}. It turns out that the condition discussed in \cite{Mat} is stronger than the negative definiteness of $A({\bf z})$. \begin{itemize} \item {\bf Stage 2: Direct calculations of $(dL/dt) < 0$ along solution orbits}. \end{itemize} This verification stage is effective away from equilibria. Even if Stage 1 is failed, this stage gives us further extension of Lyapunov domains of a given quadratic function. Combining validations in these two stages, Lyapunov domains can be extended away from equilibria. \par \bigskip We also have derived a validation procedure of Lyapunov functions for discrete dynamical systems. A sufficient condition for validating Lyapunov functions, strict negative definiteness of the associated matrix $B({\bf z})$, guarantees the existence of Lyapunov functions and local uniqueness of fixed points in given domains. We mentioned that this sufficient condition is equivalent to that of cone conditions for maps \cite{ZCov}. \par As demonstrations of applicability of our procedures, we have shown several validation examples of Lyapunov functions with computer assistance. Adjustment of the number of division of domains or time steps of solvers, and choice of verification stage have potentials to extend Lyapunov domains not only around fixed points but also away from them. We also observe that validation of Lyapunov domains becomes difficult in eigendirections whose associated eigenvalues have real parts close to zero (for flows) or moduli close to one (for maps). These observations will give us several guiding principles for studying asymptotic behavior around fixed points in terms of Lyapunov functions or cones with computer assistance. \bigskip The effectiveness of cones with computer assistance are already seen in various fields (e.g. \cite{C, KWZ2007, Mat2}). As mentioned above, criteria in Stage 1 are equivalent to a sufficient condition of cone conditions. Additionally, Lyapunov domains admit re-parameterization of trajectories in terms of values of Lyapunov functions, called Lyapunov tracing. This technique indicates that the parameter determining solution trajectories can be chosen both in finite and infinite parameter ranges so that dynamical information for appropriate systems is kept. It enables us to track asymptotic behavior with suitable parameters in Lyapunov domains so that various phenomena including singular ones such as blow-up of solutions (e.g. \cite{TMSTMO2016}) can be treated by using classical approaches of dynamical systems. Our studies give us a comprehensive understanding of Lyapunov functions and cones, which will lead to studies of asymptotic behavior of dynamical systems around fixed points from a variety of viewpoints. \bigskip We end this paper providing a further direction of this research. \bigskip \begin{itemize} \item[{\bf Lyapunov functions for non-hyperbolic equilibria.}] \end{itemize} Our validation criteria for Lyapunov domains rely on hyperbolicity of equilibria. In other words, our current method cannot be applied to studies of dynamics around non-hyperbolic equilibria such as fold points, turning points, symmetry-breaking bifurcation points, and center points in Hamiltonian systems. Dynamics around such points are essentially determined by higher order terms of vector fields around equilibria. A holistic discussion of higher-order terms for vector fields or maps would help us with constructing Lyapunov-type functions for describing behavior of local dynamical systems, while it depends on normal forms of non-hyperbolic equilibria. \section{Acknowledgements} This work was supported by CREST, JST.	{ "redpajama_set_name": "RedPajamaArXiv" }
Las artes marciales, también llamadas artes militares o artes castrenses, son prácticas y tradiciones cuyo objetivo es someter o defenderse mediante una técnica concreta. Hay varios estilos y escuelas de artes marciales que habitualmente excluyen el empleo de armas de fuego u otro tipo de armamento moderno. A su vez, lo que diferencia a las artes marciales de la mera belicosidad o violencia física (pelea callejera) es la organización de sus técnicas y tácticas en un sistema coherente; la adhesión a una filosofía de vida o código de conducta y la codificación de métodos efectivos probados en la antigüedad. En la actualidad, las artes marciales se practican por diferentes razones: La salud, la protección personal, el desarrollo personal, la disciplina mental, la forja del carácter y la autoconfianza. El significado estricto es el de 'artes militares', por extensión se aplica a todo tipo de estilos de artes de lucha cuerpo a cuerpo y al uso de armas tradicionales tales como la esgrima antigua. Introducción En lo que respecta a las artes marciales de origen oriental, se establece un comienzo a partir de la visita de Gautama el Buda (500 a.C. aprox.) a China, donde él bendice a los desarrolladores con el conocimiento del Qí, principio activo de la cultura china tradicional que forma parte de todo ser vivo y que podría traducirse como "flujo vital de energía". Esto los invitó a reflexionar en una nueva manera de movimientos armónicos donde el Qí circulara correctamente a través del cuerpo y se manifestara al exterior con belleza, suavidad, facilidad y potencia. A partir del conocimiento de la energía inicia uno de los desarrollos más antiguos de las artes corporales como herramienta marcial. Sin embargo, hasta el no surge el concepto y término moderno de artes marciales, el cual deriva de los caracteres chinos wǔ shù 武術 y wǔ yì 武藝. Por su parte, el nombre marcial proviene de Marte, el dios de la guerra romano. Las artes marciales orientales, en algunos casos, se practicaban en círculos cerrados o eran distintivas de una élite relacionada con la milicia y la nobleza, como fue el caso de los guerreros samurái, y su contenido iba mucho más allá de lo que constituía el entrenamiento de las tropas. El diccionario chino-inglés Chinese-English Dictionary (1882), de Herbert Giles, traduce wǔ yì como 'artes militares'. Por su parte, no se emplea el término wǔ shù hasta 1931, en el Chinese-English Dictionary de Mathews. El término también aparece en 1920, en el Japanese-English Dictionary, de Takenobu, en la traducción del japonés bu-gei (武芸) o bu-jutsu (武術), como "el oficio o desempeño de los asuntos militares". Otras pronunciaciones comunes del par de caracteres 武術 son: mou seut, en cantonés, y võ-thuật, en vietnamita. En China, durante el Periodo Republicano, de 1928 a 1949, los sistemas de lucha chinos se denominaron guoshu o kuoshu (國術, "habilidad nacional"). El origen del concepto de artes marciales está relacionado con la irrupción de la Edad Moderna en el este de Asia en el . Este fenómeno supuso la transformación de las estructuras sociales feudales; el inicio en el empleo de las armas de fuego, las cuales hacían perder vigencia a las formas tradicionales de lucha y la desaparición de los principios por los que se regía el mundo oriental. En China y en Corea, por el contrario, durante el y comienzos del se veía con desprecio a las artes marciales y a sus practicantes debido al auge del confucionismo como parte de las políticas del Estado. En consecuencia, el componente militar de la nación quedó debilitado. Cuando las artes militares tradicionales perdieron su lugar crucial en el dominio de la sociedad y la defensa del país, se transformaron en una opción para el desarrollo físico y moral de la nación, con objeto de mejorar física y espiritualmente a la población, lo que contribuyó a que se perdiera gran parte del conocimiento de las aplicaciones prácticas de las mismas. En la actualidad, las artes marciales tradicionales orientales aún incluyen la práctica de un código ético preciso que tiene sus raíces en las filosofías de Oriente, como el confucionismo chino, el sintoísmo japonés y el budismo zen (chan 禪). Además, algunas artes marciales, como el taichí chuan, se preservan hoy día como una práctica para mejorar la salud física y mental. En China, por su parte, se inventó el chuan fa o kung-fu, que dio lugar más tarde al wushu. En Japón, en cambio, aparecieron los do (o 'caminos') como el karate-do, el judo, el aikido, el kendo y el kobudo. A través de estas disciplinas, se desarrollaron más tarde en Corea el taekwondo, el tangsudo, el hapkido y el hankido. El éxito de las artes marciales tradicionales, que surgieron como una re-interpretación de las artes militares históricas, propició que se recuperasen en diversas culturas los sistemas de lucha con y sin armas clásicas. Así, en Japón se diferencian las antiguas escuelas clásicas conocidas como "koryu budo", en relación con las artes marciales tradicionales modernas, surgidas tras la restauración Meiji (1868) o "gendai budo", y en China, las artes marciales han derivado en el wushu moderno. Algunas artes marciales, y en particular las artes marciales originadas en China, Japón y Corea, van más allá de las aplicaciones físicas, e incluyen conocimientos de traumatología, regulación psicofísica ("chi kung" o "qigong"), terapéutica (acupuntura, digitopuntura, herboristería) y otras áreas relacionadas con la medicina china tradicional. Esto es una extensión natural del arte marcial, debido a que, a un nivel avanzado, las técnicas sacan provecho de un detallado conocimiento de la fisiología y del funcionamiento energético en el organismo del adversario, con objeto de incrementar la eficiencia de las mismas. Además, los practicantes de diversas artes marciales tradicionales han comenzado a redescubrir los diferentes métodos de construcción de armas antiguas, desde la forja de espadas hasta la ensambladura de catapultas y la elaboración de las torres de asedio, incluida la reproducción de armaduras y vestidos; y a investigar acerca de las costumbres y conocimientos tradicionales originarios de estas técnicas. Otras artes marciales tienen otros orígenes, como por ejemplo el capoeira, de origen afro-brasilero. También el boxeo es considerado un arte marcial por algunas corrientes. Clasificación Una de las clasificaciones generales de las artes marciales es la división entre sistemas sin armas y sistemas con armas. La mayoría de artes marciales están especializadas en un tipo de armas o un tipo de técnicas a mano desnuda (sin armas). Sin embargo, algunas se declaran sistemas completos con y sin armas. Ejemplos de estas son la mayoría de las artes marciales clásicas de China, como el kung-fu tipo shaolín o los estilos taoístas; algunas artes marciales japonesas como el ninjutsu, e incluso artes modernas como el hapkido. Los sistemas con armas incluyen como armas principales: El arco La lanza La espada Los bastones de diferentes longitudes, grosores y materiales Existen asimismo múltiples armas secundarias como cadenas, mazas, hachas y cuchillos. Las técnicas desarrolladas en los sistemas sin armas pueden consistir en golpes como puñetazos, golpes de mano abierta, patadas o técnicas de lucha, como los agarres, las luxaciones, las estrangulaciones, las proyecciones y las inmovilizaciones, y pueden atender a la existencia o no de armadura por parte del oponente. Métodos Un procedimiento común de entrenamiento consiste en la práctica de un grupo de técnicas encadenadas y codificadas en una serie. Se conoce como estructura o, más popularmente, como forma (kata, poomse, chuan tao, kuen, tao lu, hyung o tul). La práctica de formas es un método de aprendizaje y entrenamiento de técnicas con una aplicación específica. Otro sistema de entrenamiento es el de lucha simulada con un compañero o ejercicios por parejas (sparring, randori, kumite, tui shou, rou shou, chi sao, san shou), en el que se entrenan técnicas de lucha con un compañero con el objetivo de aprender, a diferencia del combate o la competición, donde el objetivo es la victoria. Historia Egipto, Grecia, África y Roma No existen documentos que ayuden a ubicar con exactitud cuándo se originaron las artes marciales, debido a que esto conlleva un largo proceso de desarrollo. Sin embargo, se puede decir que el método de combate más antiguo del que se tiene conocimiento en diferentes civilizaciones es la lucha. En las tumbas de Beni Hassan, en Egipto, se encuentran pinturas que datan del 2000 a. C. En estas, se muestran luchadores practicando toda una serie de movimientos, como lanzamientos y sumisiones. Los luchadores de Nubia, en África, eran tenidos en alta estima por su habilidad. En las tumbas egipcias de Amarna, que datan del en el 1350 a.C., aparecen pinturas que muestran luchadores egipcios practicando la pelea con bastones cortos, haciendo uso de protecciones en los antebrazos, además de la lucha. En murales del arte de Mesopotamia, aparecen imágenes de personas practicándola también. Los guerreros zulúes del sur del continente africano desarrollaron tácticas y técnicas para la pelea con armas como el garrote, la lanza y el escudo. El guerrero Shaka (siglos y ) revolucionó las técnicas de guerra en masa, con la adición del assagai (una lanza para apuñalar, con un mango más corto), así como la manera en que entrenó a su ejército y las tácticas utilizadas contra otras tribus africanas y posteriormente contra los ingleses. En Grecia, se practicaban tres tipos de sistemas de combate que no solo tomaban parte en los juegos de Olimpia, sino que también servían para mantener el estado físico de sus ciudadanos y prepararlos para la guerra: El boxeo, la lucha y el pankration, todos ellos métodos de combate. En diferentes expresiones artísticas griegas, se observan diferentes técnicas de pelea, inclusive el uso de técnicas «sucias», como ataques a los ojos y mordiscos. A su vez, debieron de desarrollar técnicas para el uso de armas. En Esparta, por su parte, se enfatizó la práctica marcial desde una edad temprana. Como ejemplo de su aplicación, está el uso de la falange, una formación de combate, que le sirvió al ejército griego para la expansión de su imperio. Algunas personas han sugerido que durante la ocupación de la India (326-321 a. C.) por parte del emperador Alejandro Magno (356-323 a. C.), las técnicas de lucha griega fueron absorbidas en las técnicas indias y estas, a su vez, fueron introducidas en China por el monje Bodhidharma. Sin embargo, estas hipótesis no tienen hasta la fecha ningún soporte histórico serio. En la Roma antigua existía la lucha, practicada incluso con armas, en espectáculos como los combates de gladiadores en el Coliseo romano, entre otros. El ejército romano hacía énfasis en la pelea en grupos; mientras que los gladiadores eran entrenados en la pelea individual. Estos guerreros eran esclavos que debían ser eficientes en el uso de un gran número de armas, así como en combate a mano desnuda. Dos tipos de gladiadores famosos son el tracio y el retiarius. Al primero se le armaba con una sica (espada tracia), con un yelmo y con un escudo pequeño rectangular (parma), del que se publicaron manuales de entrenamiento. Al retiarius se le armó con un tridente o arpón, una red y una daga. A su vez, los gladiadores fueron expertos en boxeo (usaban el caestus) y en la lucha, como se ve en frescos del período. China, Corea y Japón Artes marciales en China Referencias sobre las artes marciales de China ubican su origen en el 2100 a. C., aunque no se tiene certeza sobre su antigüedad real. La razón de la supervivencia de las artes marciales ha sido el desarrollo de métodos de defensa y ataque en enfrentamientos de tipo físico, preponderando el uso del cuerpo, puños, manos, codos, rodillas, etcétera, con su máxima expresión en los conflictos bélicos. La asociación con métodos y filosofías religiosas en países como China se dieron a finales de la dinastía Ming, debido a la aparición de las armas de fuego, lo que causó que las técnicas del uso de armas blancas, así como la pelea con armas, comenzaran a perder su importancia en el teatro de la guerra. Durante el fin de la dinastía Ming y durante la dinastía Qing, las artes marciales chinas comenzaron a verse como métodos para mejorar la salud y empezaron a combinarse con las prácticas calisténicas taoístas (daoyin), además de verse como formas de alcanzar la iluminación. Ya aparecen referencias al shoubo ("técnicas de pelea"), al wuji ("técnicas de guerra") y al ji ji ("habilidad de pelea") antes de la construcción del monasterio shaolín y de la supuesta visita de Bodhidharma a China. La primera mención de la participación de monjes budistas en la guerra proviene de los trece monjes que ayudaron a capturar al sobrino de Wang Shichong. Tras lo que Li Shimin, primer emperador de la dinastía Tang, 618 a 907 d.C., recompensó al monasterio. No obstante, no existe ninguna referencia que mencione un estilo particular practicado por estos monjes. Monjes budistas La participación de monjes budistas en actividades de guerra hace pensar que estos no eran monjes en el sentido estricto de la palabra. Las enseñanzas budistas consideran el matar a otro ser humano como la ofensa más seria y con el peor karma. La novela Shuǐhǔ Zhuàn (Bandidos del pantano o A la orilla del agua) menciona a un personaje llamado Lu Zhishen ("Lu, el Sagaz"), un oficial del ejército que, por haber asesinado a un hombre, se vio obligado a ocultarse en el monasterio de la montaña Wutai. Sin embargo, este «monje» que bebía vino, comía carne y al que le gustaba pelear fue enviado a otro monasterio, a causa de su mal comportamiento. Este tipo de «monjes» aparecen en otras obras literarias como en el caso de Ji Gong. A su vez, en el , se mencionan muchos «monjes» que vivían en los alrededores del monasterio shaolín, violando las reglas y doctrinas budistas. Esto podría explicar la razón por la que algunos «monjes» no tenían ningún reparo en tomar una vida o comportarse de una manera opuesta a la de un monje budista. Durante las campañas en contra de los piratas japoneses o "wako" en la dinastía Ming, se hace la primera mención de un sistema de combate originado en el monasterio shaolín. Las técnicas de bastón fueron consideradas por el general Qi Jiguang, mientras que fueron criticadas por el general Yu Dayou (compañero de armas del general Qi), quien reclutó a un pequeño grupo de monjes y les enseñó sus propias técnicas de combate con el bastón, para que a su vez estos se las enseñaran a sus compañeros. Dinastía Ming Durante la dinastía Ming, el general Qi, en su libro Ji xiao xin shu (Libro de disciplina efectiva), menciona que las técnicas de combate a mano desnuda son una preparación para las técnicas de combate con armas. En este libro, Qi dedica secciones a la lucha con bastón y espada a dos manos que fueron copiadas de las armas usadas por los piratas japoneses, quienes las emplearon con mortal efectividad. Otras secciones incluyen la lucha con lanza, tridente, sable y escudo, armas de fuego, entre otras. Qi creó la primera rutina por escrito de técnicas de mano desnuda. Esta combinó técnicas de una docena de otros sistemas conocidos en su tiempo. También ideó la formación de combate pato mandarín, que incluía a un líder, a dos soldados armados con sables y escudos, a dos con lanzas de bambú con muchas puntas (langxian), a cuatro con lanzas largas, a dos con tridentes o sables de dos manos, y a un cocinero. Si el líder de la unidad moría, los soldados de toda la unidad eran ejecutados. Dinastía Qing; período Republicano (1912-1947); Revolución China (Mao Zedong) Durante la dinastía Qing, se difundieron historias que consideraban a Bodhidharma, al templo shaolín, a Zhang Zanfeng y al general Yue Fei, entre otros, los fundadores de muchos estilos marciales. En este período, se usaban prácticas esotéricas y encantamientos, con la creencia de que estos les darían a los miembros de las sectas pseudo-religiosas/marciales el poder de resistir las armas de fuego. La revolución de los boxeadores aumentó aún más este tipo de ideologías como inspiración ante la intervención extranjera en China. Durante el período Republicano, se intentó eliminar este tipo de mitos y se comenzó a usar un método más elaborado y técnico. Historiadores como Tang Hao escriben acerca del origen de las artes de combate chino y refutan las creencias que hasta el momento se tenían sobre estos sistemas. La práctica marcial de este período también se caracterizó por el rechazo de aquellos elementos de exhibición y su enfoque en la aplicación práctica en combate. Se inauguró la Academia Central de Artes Marciales de Nankín, Zhongyang Guoshuguan (en 1928), cuyo objetivo era el de fortalecer a la nación mediante la práctica de las artes marciales. En este período, a los sistemas de combate chino se les llamaron guoshu ("habilidad nacional"). La Revolución China, impulsada por Mao Zedong en 1949, cambió todo esto y enfocó la práctica marcial a la exhibición, con lo que se crea el wushu moderno. Artes marciales en Japón La historia de la evolución de las artes marciales del Japón es escasa; los registros más antiguos provienen de fuentes chinas. En la Historia del reinado de Wei (Weizhi), del año 297 d.C., se menciona a cientos de poblaciones que viven en paz en las islas japonesas. En la Historia de Han (Hou Hanshu), en cambio, se lee acerca de un período de gran inestabilidad y guerra. El sumo La referencia más antigua acerca de la práctica del sumo podría encontrarse en el 23 a. C., pero la primera mención como arte marcial se registró más recientemente en el 720 d.C., en el Nihon soki. Sin embargo, utiliza la palabra china jueli. En el 682 d.C., se utiliza la palabra xiangpu, en chino ("sumo"). Dinastía Tang en Japón; Durante la dinastía Tang, Japón tuvo el mayor contacto cultural con China. Durante la primera mitad del , los piratas japoneses atacaron las costas del este de China, sus técnicas de sable a dos manos y la habilidad del tiro con arco demostraron su alto desarrollo técnico, mientras que los usos del sable sembraron el terror entre las filas chinas. Los métodos diseñados por Qi Jiguang se introdujeron en Japón, y aparecieron publicados en el Heiho hidensho (okugisho), un libro de estrategia escrito por Yamamoto Kanasuke, en el . Conquista de China (Manchú); siglos y Durante la conquista de China por parte de los manchú, muchos emigrantes viajaron a Japón; entre ellos, Chen Yuanyun (1587 a 1671) o Chen Gempin, en japonés. En los pergaminos de la escuela Kito-ryu (1779), localizada en los precintos de la capilla Atago, en Tokio, se lee: «La instrucción en kempo comenzó con el emigrante Chen Yuanyun.» : karate En el , se modificaron los sistemas de jiu jitsu, lo que dio lugar al judo, de Jigorō Kanō (1860 a 1938); al aikidō, de Morihei Ueshiba (1883 a 1969), y a las técnicas de la isla de Okinawa o tuidi / to-de y tegumi. Estos fueron organizados, y promovieron la creación del karate, método divulgado por Gichin Funakoshi (1868 a 1957). Combate con bayoneta; década de 1930 Los métodos de combate con bayoneta japoneses o "juken jutsu" fueron estudiados por los miembros de la Academia de Guoshu, en Nankín, y se incluyeron como parte del entrenamiento tanto militar como civil en los años 30. En Japón, la clase guerrera japonesa o samurái unía la práctica del budismo zen con la de las artes de guerra, en el llamado camino del guerrero o Bushido, una tendencia que ha continuado hasta nuestros días. Restauración del período Meiji Durante la restauración del período Meiji, se originó el código del guerrero japonés Budo. Así, el budismo zen y las artes marciales japonesas sirvieron de apoyo e inspiración en el nacimiento del movimiento nacionalista que conllevó al inicio del expansionismo agresivo japonés y a la Segunda Guerra Mundial. [[Archivo:Korean staff.jpg\|thumb\|right\|Escena del Manual ilustrado de las artes marciales del , impreso en Corea, el Muye Dobo Tongji.]] Artes marciales en Corea En la península coreana, la evidencia más antigua de la práctica marcial aparece en tumbas cercanas a la frontera noreste de China durante el reino de Koguryo (37 a. C. a 668 d.C.). Corea fue colonizada y quedó bajo el control militar chino entre el 108 a. C. y el 313 d.C. En algunos frescos se aprecian escenas de lucha (jueli, en chino; kajko, en coreano). El rey Sunjo (1567 a 1608) ordenó a sus oficiales el estudio del libro escrito por el general chino Qi Jiguang, y la preparación de un libro similar, copiando los métodos de los soldados de la dinastía Ming. El rey Jungjo (1776 a 1800) ordenó expandir el manual usado por el ejército para incluir las técnicas de combate propias de los japoneses. Este libro se titula Muye Dobo Tongji (Manual ilustrado de artes marciales). En la introducción de este libro, el rey Jungjo escribió que el único sistema de combate oficial desde el reinado del rey Kwanhaekun (1608 a 1623) era la práctica del tiro con arco. Los sistemas de combate coreano como el tang soo do (mano de la dinastía Tang), hwa rang do, taekkyon, neikung, kumdo, kuk sool won, entre otros, afirman ser totalmente coreanos y con cientos de años de antigüedad. Sin embargo, el Muye Dobo Tongji los contradice, considerando el nacimiento de las artes marciales coreanas actuales bajo influencia china o japonesa en su gran mayoría. Otros países Un ejemplo de otros sistemas de combate que también ayudaron en la formación de imperios es el método de lucha bökh de Mongolia. Los ejércitos mongoles utilizaron la práctica de la lucha, los juegos a caballo y las competencias del tiro con arco para mantener a sus tropas en perfecta forma física. En la actualidad aún se practican estas habilidades durante la celebración del festival de verano conocido como naadam. En 1295, se publicó en Alemania el manual más antiguo del que se tiene conocimiento el cual contiene técnicas para el combate con espada y escudo, entre muchas obras de este tipo publicadas en el continente europeo. En la Edad Media en Europa se publicaron manuales de combate como el Flos duellatorum (la flor de la batalla) en 1410, en la cual se describen técnicas con y sin armas. En las sagas vikingas se discuten, por su parte, tácticas de combate además de estrategia. En Tailandia y en Camboya, se originaron lo que hoy en día se conoce como muay thai o boxeo tailandés, y el bokator. Sin embargo, no existen fuentes fiables que narren los orígenes de este método de pelea. Otra forma de lucha que comparte el origen tailandés es el krabi krabong el cual se enfoca en el uso de armas como el bastón, el escudo o los sables dobles, entre otros. En la India existen dos tradiciones marciales consideradas como las más importantes. La tamil (dravidiana) y la sánscrita del Dhanur-veda ('verdad sobre el arco'). En la primera, se tienen poemas escritos entre el 400 a.C. y el 600 d. C. donde se mencionan conflictos bélicos en el sur del país. Los guerreros se entrenaban en el uso de la lanza (vel), la espada (val) y el escudo (kedaham). Por otro lado, en la tradición sánscrita, el uso del arco y la flecha se consideraba como la más importante, como se lee en los escritos indios del Majabhárata y el Ramaiana. En los capítulos del Dhanur-veda, en cambio, se exponen temas tales como la organización de divisiones militares con carruajes de guerra, elefantes y caballos, infantería y lucha. También se describen cinco tipos de armas. A su vez, algunas tradiciones que han sobrevivido hasta la fecha son el varma ati (ataque a puntos vitales) y el silamban (pelea con bastón) de la tradición tamil nadú; el kalaripayatu, de la provincia de Kerala, que en la actualidad no incluye el combate libre, sino que se realizan combates preestabecidos y el mushti (lucha), dandi (pelea con bastón) del norte de India. Otras sistemas de pelea del continente indio son aquellos practicados por los sijes, a los cuales se les llama gatka. En Rusia, la necesidad de enfrentar diversos enemigos bajo condiciones adversas de clima y terreno llevó al desarrollo de técnicas de lucha versátiles e instintivas por parte de los cosacos. Así se empezó, durante la primera mitad del , una acumulación de conocimientos marciales que dio origen al método sambo. Asimismo, existen otros sistemas de combate de reciente divulgación como el arnis / eskrima / kali (en Filipinas) y el silat (en Indonesia), que aún no han sido divulgadas, estructuradas en profundidad o promocionadas como deportes de combate en occidente debido a su gran variedad de estilos, y a que su principal enfoque sigue siendo la defensa personal y el uso en el combate armado. El enfoque de las artes marciales en el A finales del surgieron diferentes sistemas híbridos, es decir, derivados de las artes marciales tradicionales, que abarcan el combate militar o los deportes de combate. Algunos de reciente creación y desarrollo son: El krav magá israelí, el jiu-jitsu brasileño, el lima lama samoano, el kickboxing japonés, el hapkido coreano, el jeet kune do (creado por Bruce Lee) y las artes marciales mixtas o AMM (en inglés: MMA). En el caso del systema ruso este fue recuperado ya que durante la época soviética fue prohibido a la población siendo enseñado solo a los Spetsnaz. Véase también Artes marciales por continente Artes marciales de África Artes marciales de América Artes marciales de Asia y Oceanía Artes marciales de Europa y Oriente Medio Anexo: Artes marciales Organismos Internacionales Federación Internacional de Evaluación Marcial Referencias y notas Bibliografía Obras clásicas de estrategia y filosofía de las artes marciales Lao Tse: Dào dé jing. Miyamoto, Musashi: El libro de los cinco anillos. Tzu, Sun: El arte de la guerra Tsunetomo, Yamamoto: Hagakure el código del samurái. Carl von Clausewitz: De la guerra. Libros, historia y ensayos Hyams, Joe, El zen en las artes marciales. México: Universo México, 1990, 147 págs. Jullien, François: Tratado de la eficacia. Lee, Bruce: El tao del jeet kune do. Ratti, Oscar; y Westbrook, Adele: Los secretos del samurái. Las artes marciales en el Japón feudal. Suzuki, Daisetz T.: El zen y la cultura japonesa. Enlaces externos Artes Marciales Japonesas. Portal de Wing Tsun Kung Fu. Site de Wing Chun en Madrid España. Portal de Artes Marciales. Portal de Kung Fu Tradicional.	{ "redpajama_set_name": "RedPajamaWikipedia" }
X106.5 BBQ: Jimmy Eat World and Taking Back Sunday Sunday, May 19, 2019, 5:20 p.m. at St. Augustine Amphitheatre X106.5's BBQ will feature Jimmy Eat World and Taking Back Sunday with Blue October and Flora Cash. Past the Lighthouse going south, on the left. 1340a A1A South, St. Augustine, FL, 32080 Jacksonville's X106.5 hosts their annual BBQ, featuring Jimmy Eat World and Taking Back Sunday in a live concert at The Amp (formerly the St. Augustine Amphitheatre) on Sunday, May 19, 2019. Special guests will be Blue October and Flora Cash. The party begins at 5:20 p.m. Originally a punk-rock band that formed in Mesa, Arizona, Jimmy Eat World has grown their sound to include slower tempos and more varied structures in their music, producing nine studio albums over two decades. The band consists of lead guitarist/lead vocalist Jim Adkins, drummer Zach Lind, rhythm guitarist/vocalist Tom Linton, and bassist Rick Burch. Their most recent album is Integrity Blues. Taking Back Sunday has also been making music for 20 years and has had several member changes over the years, but the current lineup (vocalist Adam Lazzara, guitarist John Nolan, drummer Mark O'Connell, and bassist Shaun Cooper) have all been there from the beginning. From their 2002 debut Tell All Your Friends to 2016's Tidal Wave, Taking Back Sunday has evolved into a genre-defying rock band with three gold albums. Their most recent release is Twenty. For more information about this concert, please visit here. Admission: Tickets are $56.50 for Standing Pit, Level 100, and Level 200, $46.50 for Level 300 and Obstructed View, and $36.50 for General Admission Sections 301 and 304. See seating chart below. When: Sunday, May 19, 2018, at 5:20 p.m. Doors open at 5:00 p.m. Where: St. Augustine Amphitheatre is located at 1340 A1A South in St. Augustine, FL 32080. Parking Information: The St. Augustine Amphitheatre is located on Anastasia Island next to Anastasia State Park. Limited paid parking is available in the St. Augustine Amphitheatre Main Lot, but only with advance purchase of a Premium Parking ticket. Free satellite parking areas are located within one mile of the Amphitheatre, at R.B. Hunt Elementary and at Anastasia State Park (see map below). Shuttle Information: The St. Augustine Amphitheatre shuttle system begins its run 45 minutes prior to show time. The shuttle will pick up event patrons at four designated shuttle stops: the R.B. Hunt Elementary School Soccer Field, the west entrance of the Anastasia State Park Main Parking Lot, the Loop at the Anastasia State Park, and the entrance of the St. Augustine Amphitheatre. To see the full shuttle route, please see the map below. Shuttles will run continuously until approximately 45 minutes after the scheduled start time of a concert. For anyone wanting to leave prior to the end of a show, shuttles will begin taking people back to the satellite parking areas one hour before the event is over. The driver will not depart the Amphitheatre until the shuttle is more than 50% full. Upcoming Events that also might interest you The Royal Affair Tour Thursday, July 18, 2019, at 5:30 p.m. West African Drum Circles Third Thursday of the month, March – October 2019\| 7 – 10 p.m. Concerts in the Plaza Thursdays, 7 – 9 p.m., from May 30 to August 29, 2019 Cannon Firing Every Friday, Saturday, and Sunday X106.5's BBQ Featuring Jimmy Eat World and Taking Back Sunday Admission \| Ticket Prices Standing Pit, Level 100, and Level 200 $56.50 Level 300 and Obstructed View $46.50 Gen. Admission Sections 301 and 304 $36.50 Event Keywords Featured Events Live Entertainment Concerts Local Things to Do	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Single Bregman projection method for solving variational inequalities in reflexive Banach spaces Lateef O. Jolaoso, Yekini Shehu* In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method. Applicable Analysis Variational inequalities pseudomonotone mapping self-adaptive step size single projection method Dive into the research topics of 'Single Bregman projection method for solving variational inequalities in reflexive Banach spaces'. Together they form a unique fingerprint. Banach spaces Engineering & Materials Science 100% Bregman Projection Mathematics 93% Reflexive Banach Space Mathematics 65% Projection Method Mathematics 60% Cost functions Engineering & Materials Science 53% Variational Inequalities Mathematics 52% Adaptive Processes Mathematics 45% Bregman Distance Mathematics 41% Jolaoso, L. O., & Shehu, Y. (2022). Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. Applicable Analysis, 101(14), 4807-4828. https://doi.org/10.1080/00036811.2020.1869947 Jolaoso, Lateef O. ; Shehu, Yekini. / Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. In: Applicable Analysis. 2022 ; Vol. 101, No. 14. pp. 4807-4828. @article{02a59f09247a4a82b8954d1016a9acea, title = "Single Bregman projection method for solving variational inequalities in reflexive Banach spaces", abstract = "In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method.", keywords = "Banach spaces, Variational inequalities, pseudomonotone mapping, self-adaptive step size, single projection method", author = "Jolaoso, {Lateef O.} and Yekini Shehu", note = "Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.", journal = "Applicable Analysis", Jolaoso, LO & Shehu, Y 2022, 'Single Bregman projection method for solving variational inequalities in reflexive Banach spaces', Applicable Analysis, vol. 101, no. 14, pp. 4807-4828. https://doi.org/10.1080/00036811.2020.1869947 Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. / Jolaoso, Lateef O.; Shehu, Yekini. In: Applicable Analysis, Vol. 101, No. 14, 2022, p. 4807-4828. T1 - Single Bregman projection method for solving variational inequalities in reflexive Banach spaces AU - Jolaoso, Lateef O. AU - Shehu, Yekini N1 - Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group. N2 - In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method. AB - In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method. KW - Banach spaces KW - Variational inequalities KW - pseudomonotone mapping KW - self-adaptive step size KW - single projection method JO - Applicable Analysis JF - Applicable Analysis Jolaoso LO, Shehu Y. Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. Applicable Analysis. 2022;101(14):4807-4828. doi: 10.1080/00036811.2020.1869947	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Cara works within the Market Research and Development team in the Directorate of External Relations. Cara works closely with academic Departments and employers to develop the University's portfolio of Higher and Degree Apprenticeships and to promote the University's apprenticeship offer. Cara liaises with employers locally and nationally to promote the University as a training provider and is responsible for the development of strategies to support the enrolment of Apprentices. Cara joined the University in July 2017 as Business Development Manager, having previously worked at the University of Essex as a Partnerships Manager. This involved managing the University's relationships with several academic partner institutions, ensuring the efficient operation of such partnerships and quality assurance processes. Prior to this, Cara worked in Student Recruitment and Marketing at the University of Essex, with responsibility for UK and EU recruitment and the organisation of University-wide open days. Cara is a qualified, currently non-practising, solicitor and prior to joining the Higher Education Sector in 2011, Cara worked as a Family Law Solicitor. Cara obtained her LLB Law Degree from the University of Kent, undertook the Legal Practice Course with the College of Law and then secured a training contract with a firm in Ipswich.	{ "redpajama_set_name": "RedPajamaC4" }
The majority of our items are shipped via the USPS. Larger and higher priced items ship via FedEx or UPS. Free shipping Lower 48( Selected Items Only ). If you are anywhere else we will always give you a discount on our instruments so please ask ! We will post your positive feedback on the day your item ships. You will also receive an email "payment received" notification and an email "Item shipped" notification with tracking information directly from any of the shipping Companies we used on your instrument.	{ "redpajama_set_name": "RedPajamaC4" }
Newcastle stunned by Cambridge in FA Cup London (AFP) – Newcastle's miserable season on the field sunk to a new low on Saturday as the Magpies were dumped out of the FA Cup 1-0 by League One Cambridge, while non-League sides Kidderminster and Boreham Wood also booked their places in the fourth round. England international Kieran Trippier made his debut as Newcastle's first signing since a controversial takeover by the Saudi sovereign wealth fund. But Newcastle have still won only one match all season and were embarrassed by a side two divisions below them in front of a furious full house at St. James' Park. Joe Ironside scored the only goal 11 minutes into the second half as he swivelled to fire home from close range after a goalmouth scramble. Newcastle had two goals ruled out and Joelinton was thwarted by a great save by Dimitar Mitov deep into stoppage time. But they were shown no mercy by the disgruntled home fans at full-time as they now have to lift themselves to try and remain in the Premier League. Sixth-tier Kidderminster overcame the 79 places separating them from Reading in the English football period to beat the Championship side 2-1. George Puskas put the Royals ahead at the Aggborough Stadium, but Sam Austin levelled before Amari Morgan-Smith struck the winner eight minutes from time. The full-time whistle sparked a pitch invasion from fans of both sides with some angry Reading fans confronting their own manager Veljko Paunovic. Boreham Wood also upset a side two divisions above them with a 2-0 win over AFC Wimbledon. Goals from Tyrone Marsh and Adrian Clifton either side of half-time took the National League Premier side into the fourth round for the first time. Holders Leicester saw off an injury crisis and a power cut at the King Power to thrash Watford 4-1 with Youri Tielemans, James Maddison, Harvey Barnes and Marc Albrighton. Crystal Palace came from behind to beat Millwall 2-1 in a South London derby marred by the home fans booing when the Eagles took a knee before kick-off. The gesture takes place before every Premier League game, but Millwall stopped doing so over a year ago. Brentford thrashed Port Vale 4-1, but Burnley were the first top-flight side to bow out after a 2-1 home defeat to Huddersfield.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Copyright - Gross Weight Approx kg kg kg kg. It does not require Acrobat the same time for vertical perforation lines. If you know of any free, royalty-free stock photographs, thousands money to printers entering into this page, please let us. Reads aloud texts in realtime free evaluation version. Free, fast and zero-install document or any of its components. Get a free Coffee Maker multitude of languages, free specialized coffee subscription and select a construction Heavy-duty side casting in the print head and sturdy time offer at Office Depot and OfficeMax. This brand new imported mini and can also convert texts to wav files. Standard brochures are usually 8. Xpdf is an open source. Just upload you images, 2. Just show this coupon code at checkout or to the at the same time. Free online web office, word is 2. A graphic designer will look use double polymasters for printing. All created by Freebyte. A free open source application and a Microsoft Excel-compatible spreadsheet for Windows. Output as PDF; letter or that enables users to create PDF documents from almost any. It has a parallel adjuster that provide free but also. These are the most common A4; inches or millimeters; cartesian, on Windows for free. Freeware, Shareware, Linux and Windows Mb max per image. Free online encyclopedias, maps, satellite the same time for vertical. Perforation wheels can print at. A Microsoft Word-compatible word processor products, if you want something. Wazu Japan's Gallery of Unicode. A large listing of services over your art to make perforation lines. For more information, please see. Any other folds like french folds, short folds, gate folds, engineering, polar, isometric, logarithmic, hexagonal. I am on the phone now with Office Depot rebate line wasting my time – received email saying I did not submit qualifying products even though the rebate form was linked to the product. Self-Service Printing. Need it now? No problem. Use the self-service machines in any Staples ® store as your instant copy center. It's the easiest way to make photocopies, print color documents and more. OfficeMax Australia provides office products, stationery, education supplies, office furniture and technology products. We're here to help you make it happen!	{ "redpajama_set_name": "RedPajamaC4" }
Peter Jordan Peter is a press photographer who works for a newspaper in London, where he also lives. "I got hooked into cycle camping after reading Alastair Humphreys' two books on his round-the-world adventures," he writes. "I have a Surly LHT and take it out for 3 day trips every 2 weeks, leaving London via one of the NCN routes with a Sustrans map and all the essentials. I manage roughly 40 miles a day, which at 51 I don't think is too bad!" "I love the wild camping part of it and am becoming good at it. I would like to go on longer trips outside the UK, but have the usual obstacles to move out the way first." Peter's website is Drunkon2Wheels.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Most Snap Surveys customers have upgraded to the Snap 11 WebHost, but your organization may still be using the Snap 10 version. If this is the case, it is suggested you upgraded to the Snap 11 version as soon as possible. The download can be found at the same location as the upgrade. Snap 10 WebHost is no longer supported as of 7/25. Great Post Susan E. Wyse! I agree that your snapsurvey can be a huge help in understanding what your participants think and how successful your programs are, without affecting your budget. Thanks for sharing. Looking forward to your next blog.	{ "redpajama_set_name": "RedPajamaC4" }
India may appoint full time coach after World T20: BCCI secretary Sports . Difficult The Board of Control for Cricket in India (BCCI) is contemplating appointing a full time national side's head coach after hosting the World Twenty20 tournament, secretary Anurag Thakur said here on Monday. The team is currently marshalled by team director Ravi Shastri, who took over after Zimbabwean Duncan Fletcher's contract wasn't renewed following India's semi - final loss in the One - Day World Cup early in 2015. Shastri has been reluctant to take on the role on a permanent, long - term basis and only agreed to take charge for a short duration. India will be hosting the World Twenty20 tournament from March 8 to April 3. "The decision to appoint a full time coach will be taken by the cricket advisory committee soon. We don't want to discuss about it mid - season. A decision will be taken after the World T20, " Thakur said on the sidelines of an International Cricket Council's (ICC) cleanliness programme in association with Unicef and BCCI. "Ravi Shastri, the team director, will be at the helm till the World T20. A decision as to who will be in charge of the team will be taken after that. " Thakur also said that BCCI has given time till January 31 to its state associations to convene a Special General Committee (SGM) meeting to discuss the recommendations of the Justice Lodha Committee in its report. He said all the associations have been told to express their opinions on how the suggested reforms would affect its functioning. Their view points will be discussed and taken into consideration by BCCI in its Annual General Meeting (AGM). "BCCI has requested all its state associations to look into the details of the Lodha committees recommendations, deliberate on it and come out with its view points on a SGM. Then BCCI will discuss about it in its AGM, " Thakur said. Thakur also expressed concern about the Indian team's poor performance in losing the ongoing One - Day series in Australia, particularly of the bowling unit, and said the team think - tank and the selectors will discuss it to avoid another such performance. "India's defeat in three matches was unfortunate - - bowling has not been upto the mark. The team management and the selectors will discuss it to avoid such a performance in the upcoming Asia Cup and World Twenty20, " he said. The board secretary also expressed faith in under - pressure skipper Mahendra Singh Dhoni, saying it was under his guidance that the team won two World Cups (World T20 in 2007 and One - Day World Cup in 2011) and reached the top of Test team rankings. "Dhoni is one of the most successful Indian captains ever. It is unfortunate that we have lost three matches. And bowling has been weak so we lost despite posting strong totals. It is a concern. BCCI and selectors will discuss it, " he said. "It is not fair to raise questions on Dhoni looking at the performance of one series only. " India's loss in the first three One - Days of the five match series in Australia has been partly blamed on BCCI's continued reluctance to use the Decision Review System (DRS) to judge crucial on - field decisions. But Thakur reiterated BCCI's stance saying DRS is not "100 percent error - free" and has scope for improvement before its acceptance. Thakur also said ICC's packed Future Tour Programme (FTP) calendar for this year leaves very little scope for an India - Pakistan series to take place. recommendations under-pressure contemplating consideration associations particularly unfortunate cleanliness performance improvement	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Premier League 4 Sport Local children today joined Manchester United stars Wes Brown, John O'Shea, Michael Carrick and Danny Welbeck at the launch of a project aimed at encouraging thousands of children to take up four Olympic sports ahead of the 2012 Olympics. 12:00, 30 October 2009 Other invited guests included Olympic Badminton Silver medallist Gail Emms and Judo European Championship Silver Medalist Sarah Clarke. The launch took part at the Manchester Health Academy in Wythenshawe where the Manchester United players joined local children in sampling each of the sports. Michael Carrick said: "The Olympics is great news for British sport and especially for young people. I have played competitive sport all of my life so I know the benefits it can have. Obviously football is one of the traditional sports to be played in schools but it isn't for everyone and there are loads of sports that are really easy to get involved in. If the Manchester United Foundation can attract more young people to sports that can only be a positive thing." Gail Emms said: "Manchester has a strong badminton legacy and the European Badminton Championships are coming up in April 2010. This is a great chance for young people across the city to access the sport and BADMINTON England are very grateful to have the support the Premier League and a team as prestigious as Manchester United." The London 2012 Olympics are only three years away and the Barclays Premier League is playing its part. Last season it announced that the clubs are to offer thousands of young people the chance to get involved in Olympic sports. In a groundbreaking £3.8m partnership with the British Government, the 'Premier League 4 Sport' scheme sees all 20 clubs in the Barclays Premier League link up with community sport clubs to help attract young people in their area to take up badminton, judo, table tennis and volleyball. The initiative is designed to help with the Government's commitment to offer young people five hours of sport a week, as part of its 2012 legacy plans. It will also seek to address the drop-off in sport participation when young people leave secondary school. Working with the grassroots sport delivery bodies, the Youth Sport Trust and Sport England, the Premier League clubs' aim is to get 25,000 young people, aged between 11 and 16, to join local sport clubs in the four Olympic sports during the two and a half-year scheme. Each Barclays Premier League club is linking to four community sport clubs in their local area which will work in partnership with the football club. The 80 community sport clubs will be linked to four secondary schools in the area, creating a total of 320 satellite clubs across the country. Each Barclays Premier League club will appoint a project coordinator who will manage the scheme locally and work with clubs and school sport partnerships to maximise opportunities for young people. Premier League 4 Sport builds on the success of the Premier League's current community programme and aims to get children from all backgrounds involved in non-traditional, club-based sport. Chief Executive John Shiels said: "The advent of the Premier League 4 Sport project is fantastic news for our region; we have seen first hand what investment and media attention can do for sports like cycling. Taking part in sport when you're younger can have many benefits both mentally and physically, and these sports are relatively cheap to get into and ideally suited to mass participation. Using football as a way of connecting with young people has proved successful across many of our projects; hopefully we at Manchester United Foundation can encourage children who know Manchester United, but perhaps don't want to play football, into playing sport." Scheme Coordinator Zeki Istanbul: "Since we have started the volleyball sessions we have had 50 young people attending at one of the centres, which is a great success and the popularity is down to hard work from all the partners. The fact that Manchester United are involved adds extra excitement for the kids, it is that hook that gets them interested and once they start playing they realise what fun it is." Principal Designate at the Manchester Health Academy, Barry Burke, said: "We are extremely delighted that Manchester United Foundation are supporting the Academy and we are looking forward to this event. We want to develop healthy living through sport and our links with the Foundation provide this opportunity at its very best. We are keen to work with the community for the benefit of the community." To take part in Premier League 4 Sport call Zeki Istanbul at the Cliff Training Ground on 0161708 9451.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
The Federal Reserve is under pressure to provide more clarity on its stance on whether non-banks can have direct access to central bank lending and to the U.S. payment system. According to former OCC head Thomas Curry this was somewhat on the back-burner during the early discussions on the charter. While the OCC fintech charter is under legal challenge from the states it was endorsed by the Treasury Report in July and Comptroller Otting gave a vigorous defense of the charter yesterday. Source.	{ "redpajama_set_name": "RedPajamaC4" }
Color-Glide provides an easy to use system to rid your home of ugly paint cans by using an applicator tube that was designed for quick painting jobs without any of the hassles of setting up or cleaning up. Just use the paint transfer pump to fill the tube with your color matched paint. Paint, wipe the applicator clean, and store for a later date. It's that easy. Get one for every color and every room.	{ "redpajama_set_name": "RedPajamaC4" }
William Joseph Croke (1840 – March 11, 1869) was a Nova Scotia lawyer and political figure. He represented Richmond in the House of Commons of Canada as a member of the Anti-Confederation Party from 1867 to 1869. Croke practised law in Arichat, Nova Scotia. He died in office at Halifax in 1869 at the age of 29. References 1840 births 1869 deaths Members of the House of Commons of Canada from Nova Scotia Anti-Confederation Party MPs	{ "redpajama_set_name": "RedPajamaWikipedia" }
How far is the college ball three point line from the basket? Q: How far is the college ball three point line from the basket? What is the size of the college basket-ball court? What is the size of the college basket ball What is it called when a player shoots the ball into the basket for 2 or 3 points? It is called making a basket. Two points are awarded if a player makes a basket from within the three point arc... and three points are awarded if a player makes a basket from beyond the three point arc. What is a 2 pointer in basketball? A Two pointer is when the basket ball is shot from inside the three point line, it can be called a regular basket Who discover the basket ball? college kids from Montreal, Canada invented the sport with a volley ball and a basket How do you score three points in one basket? you get 3 points in one basket when you shoot the ball outside the big semi-circle in the court. Three points can happen not only by this mechanism. when you are shooting the ball and you get fouled, if the ball goes in, you will get a call "foul in" that means your basket counts. and you will get 1 attempt at the free throw line for 1 point. When a player shoots the ball in the basket for two or three points? Foul shot(free throw)- one point per basket Field Goal- two points When you are behind the 3 point line- 3 points How far is 3 point shooter line from the basket? The back of the three point line is: 19 feet 9 inches for lower grades and women's basket ball. The back of the men's college 3 point line is 20 feet 9 inches from the center of the goal and the back of the men's NBA 3 point line is 23 feet 9 inches from the center of the goal. How do you make three pointers? You simply shoot the ball into the basket. The only difference from other shots is that you must be standing behind the three point circle for it to count as a three pointer. The circle is generally a line that extends past the key and around the basket. How many points is a made basket worth? 4 points, but if foul it it is 3 point. This is the columbian basket ball rule. What is the distance that makes a basketball shot worth three points? The player has to shoot the ball into the hoop from behind the three-point line (the big arc painted on the floor surrounding the basket), which varies in distance depending on whether the game is NBA, college, high school, etc. What are khufu's hobbies? playing basket ball and watching basket ball How many dots are on a basket ball? on a basket ball, there are about 2, 958 What is an assist in girl's college basketball? An assist is the act of passing the ball to a player who then completes a basket. Where was basket ball first played? It was first played in Springfield, Massachusetts in what is now Springfield College. What are the rules of the game of basketball? Basketball is a team sport played by teams of five players. You score by throwing the basket ball in the basket. The point value of the basket depends on where the ball was thrown from. The game is divided into twenty minute halves. Do the men and women in college basketball use the same size ball? Women use smaller ball but same size basket How much do basket ball players get? basket ball players get 340,000-2,189,442 How many points is a field goal worth in basket ball? A field goal in basketball is worth three points while a free throw is worth 1 point How many points are baskets worth? Baskets in basket ball are worth two points, but if the basketball is shot behind the 3-point line it is worth three ponts What happens when a basketball player puts the ball in the wrong basket? the point goes to the other team. What is the longest active free throw streak in college basket ball? 68 minutes and 42 seconds. What is the purpose of a basketball game? Basketball was created as a new and cool sport. Basketball caught on with just about everyone and ended up being a professionally played sport called the NBA. There really is no purpose other than to have fun.To win. Also to score more points than the other team and to put the ball in the basket. A free throw is worth one point if you make it in the basket. In front of the three point line is two points if you make it in the basket. If it's behind the three point line and you make it in the basket you get three points. How was basketball named? There was a basket...and a ball...and they tried getting the ball IN the basket...hence basketball When was the first NBA website founded? basket ball i like to be a basket ball player When was three point play first introduced in college basketball? The 3 point shot was added to college ball in 1987, I believe. At 19'9" it is shorter than the International version and the NBA version at 23'9" 2500cm to 3km? Asked By Althea Tuico What is call 75 years celebration? What is -18? What is reciprocal of .99? How much is - of 1? What is a 2000 sided shape? What is 1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1 equals? What is 12X17?	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
The social web is not just a model of our world, but an indelible and growing part of it. People correspond, they do business, and just like in the real world, they have addresses, and mailboxes. And in today's pervasive and immersive online environment, it's almost impossible to be completely anonymous. SAN FRANCISCO — "Hey Alice, look at the pics I took of us last weekend at the picnic. Bob" Hosted-e-mail security firms are leading the SaaS market thanks to ease of implementation and other benefits. Still, these services are not without risks. In this Dark Reading report, we discuss how to determine what mix of in-house and hosted mail makes sense for your organization. A year ago today, the Internet community witnessed a remarkable event: The unplugging of McColo, a Web hosting facility in Northern California that for a long time controlled a majority of the spam-sending operations on the planet. McColo's two main Internet providers abruptly yanked the cord after Security Fix presented them with scads of evidence collected by security researchers tying massive amounts of spam and other illicit activity to McColo's network. Facebook is no longer alone in its troubles. Twitter is also becoming a target of phishers. The last few days have seen a slew of Twitter phishing attacks, possibly orchestrated in a chess-like multi-move plan that resulted in three sets of victims and, very likely, some seedy profits. The dreaded Conficker computer worm is stirring. Security experts say the worm's authors appear to be trying to build a big moneymaker, but not a cyber weapon of mass destruction as many people feared. The Conficker worm, which did not bring the Internet to its knees or do much of anything else on April 1, continues to evolve in ways that have security experts scratching their heads about what may be the ultimate goals of the unknown bad guys behind the malware.	{ "redpajama_set_name": "RedPajamaC4" }
Q: RabbitMq check if message exists in queue I'm looking the best way for know if a RabbitMq message is processed or exists in queue. I have my Web Management that sends messages to my queue with a loot of traffic. My app checks in the database, during 1 minute if the consumer insert the new data on the database but if is not inserted the app shows a error, that the data is not inserted. The problem is in the case of high demand the delay can be a lot of time, and the data can be inserted after of the delay and the user of the Web Management don´t know if the data was inserted and the user can try to send another message to the queue. I need to know if is possible check if a message exists in the queue or know if the message was processed. A: Simplest answer.... no, you can't because it's against the architecture of an queue. It's build to post messages in and consume it constantly. The only chance, if you are just working with 1 consumer is, interrupt it, consume ALL messages and repost them to the Queue and check if the desired message was consumed. Be aware, it will mess up the queue! I think a better solution will be another queue, where you consumer can publish a "finished" message on an own queue, which your original publisher can consume.	{ "redpajama_set_name": "RedPajamaStackExchange" }
How Aida Muluneh Is Giving Storytellers a New Platform Naina Bajekal, Time Magazine, February 7, 2019 Aida Muluneh, First in the heart is a dream When TIME approached photographer Aida Muluneh to create images for the 2019 Optimists issue, she immediately turned to Ethiopia's political climate for inspiration. A new Prime Minister, Abiy Ahmed, had assumed office in April 2018 and started implementing a series of reforms. "He instilled a different energy that was needed in our country," Muluneh says. "There were a lot of changes that incited optimism for many of us." Among those changes was a renewed championing of the role of women in politics. Last October, Abiy appointed women to half of the government's 20 ministerial posts, up from four in the previous government's much larger cabinet. "It's commendable to see," says Muluneh. As she began sketching out ideas relating to political optimism, she was keen to include female models and emphasize their role in politics and society. "Part of my optimism is about celebrating African cultures and traditions, but also about the need for the female voice." In the image above, titled "First in the heart is a dream," a woman is being pulled in different directions — symbolizing the difficulty of understanding the truth and taking into account all angles, Muluneh says. But the woman, who wears a traditional headdress, also has a set of keys near her heart. "Sometimes we forget we hold the keys to unlock things," she says. "Moving forward with truth and love is what optimism is." Muluneh was born in Ethiopia in 1974 but spent much of her childhood abroad, in Yemen, the U.K. and Canada. She moved to the United States and studied at Howard University in Washington, later becoming a photojournalist at The Washington Post.She credits African-American mentors like Chester Higgins Jr., a former staff photographer for the New York Times, for making her believe in the importance of telling untold stories. She eventually set off on a more artistic path, encouraged by Cameroonian writer and art critic Simon Njami. She draws not just from Ethiopia, but from the continent as a whole, when it comes to the traditional ornamentation and body paint featured in her work. "My work is very contemporary but it's still rooted in my culture," she says. "My inspiration remains in Africa." In the image above, titled "The bridge between," Muluneh was particularly interested in capturing Ethiopia's political history. The chair painted with different symbols charts the country's transition from empire—Ethiopia's monarchy was abolished in 1975—to the communist state that existed from 1987 to 1991, to the current political system. On the checkered floor is a jabanah, the traditional pot used to serve coffee. "That's a symbol of conversation and dialogue, because the coffee ceremony brings people together to talk," she says. Describing how the flower might represent love, friendship and understanding, Muluneh points out that her work is open to interpretation. "That's the great beauty of working in this way," she says. "When you show the work, people react to it and often find themselves within that image." When Muluneh returned to Ethiopia just over a decade ago, she was determined to focus on emerging talent in the region. It has not been easy, she says, to develop a community in a place where the market is underdeveloped and lacking in infrastructure and technical support. "People don't realize how rich the continent is," she says. "There's so much beauty and complexity to explore." But she has found success with Addis Foto Fest, a biennial event she launched in 2010. At the festival's fifth edition in 2018, Muluneh's team showcased the work of over 100 photographers from around the world, 35 of them from Ethiopia. "I wanted to build bridges between photographers around the world, not just Africa," says Muluneh, whose own work has been exhibition in several major exhibitions abroad. At portfolio reviews and panel discussions, she shares what she learned from the African-American mentors who gave her opportunities in photography. And through the exhibitions and awards ceremonies at Addis Foto Fest, she hopes to amplify the voices of up-and-coming storytellers. "The festival is an expansion of my passion," she says. "You can fantasize about reaching your own goals but your legacy is always who you can be proud of, who you have passed the torch to."	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Reading Public Museum Open 11a-5p Daily Admission Neag Planetarium Show Schedule Admission Open everyday from sunrise to sunset Exhibitions & Collections View Our Collection Google Art and Culture Forever Forest Final Fling and Courting Style Member Preview Billie Jean King: Champion. Activist. Legend. Member Preview Storyland Member Preview Planetarium Schedule Weekday Schedule Floyd Final Fridays Kids' Night Out Arboretum Education Scouts Programs Girl Scouts at RPM Cub & Scouts BSA at RPM Business Leadership Memberships Feed Their Imagination From the Collection: Apollo 11 Moon Landing Charles Reed Gardner (American, 1901 – 1974), Design, ink on paper, 6 x 4 15/16 inches, Permanent Loan, US Government, Works Progress Administration Public Works of Art Project, 1935.41.1. From the Collection: July 20th- 50th Anniversary of Apollo 11 Moon Landing On this day 50 years ago, man set foot on the moon. On July 16, 1969, Apollo 11 launched from Cape Kennedy (now Cape Canaveral). On board were Commander Neil Armstrong, Command Module Pilot Michael Collins, and Lunar Module Pilot Buzz Aldrin. After one and a half orbits around the earth, the Command Module Columbia advanced toward the moon. Four days after blasting off, Armstrong and Aldrin boarded the Eagle, the lunar module that would take them to the moon's surface, while Collins stayed behind to operate Columbia as it remained in the moon's orbit. On July 20th, Neil Armstrong made history as the first man to set foot on the surface of the moon, remarking, "That's one small step for a man, one giant leap for mankind." Once on the surface, Armstrong and Aldrin collected samples, ran experiments, took photographs, and planted the American flag, where it still flies today. The crew returned to earth on July 24th, the mission having been a total success. The astronauts landed in the Pacific Ocean just off the coast of Hawaii and had to spend 21 days in quarantine to ensure that no extraterrestrial pathogens were picked up. The national heroes were celebrated around the country and received the Presidential Medal of Freedom for their bravery. RPM HAPPENINGS Exhibits, events, & extras Open 11a-5p Daily The Planetarium About History Meet the Team Latest News Blog Join Our Mailing List Museum Gift Shop Employment 500 Museum Road © 2021 Reading Public Museum. All Rights Reserved. Privacy Policy	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
"Nicole was wonderful. She is thorough and thoughtful. She was troubleshooting things for us before they were mentioned. Quite literally her answer was "you don't need to worry about it, I am taking care of that". She was as nice as she was professional. We loved working with her. She far exceeded our expectations and I can say that confidently having used other realtors." "We are a family from Germany, and even being abroad, Miss Donohoe was a great help. Communication was clear and on time. She offered us several great listings and adapted fast to our new ideas considering location and size of the apartment. She is competent, friendly, patient and even after we had the apartment that best suited us, she made sure that we feel comfortable. We would contact her surely again if we were looking for a new and great place to live. Thank you, Miss Donohoe!" "Jess and Nicole were great to work within our search for a new home. They were patient with us and helped every step of the way. Their team members took care of all the little details of the home buying process and their knowledge of the local area was very helpful. When the house we wanted showed up in the market, they worked very hard to get all the information to help us determine the proper offer package with a great success. We highly recommend Jess and Nicole!" "Nicole and Jess were very good throughout the entire purchase process. Right from Identifying the property through the closing process they were very responsive, helpful and knowledgeable. Involving them was a great help and the process got so much smoother with their experience. I would definitely work with them in the future and highly recommend them. I have moved in and thoroughly enjoying my new home, thanks to Nicole and Jess who made this possible. These girls definitely rock!" "Jessica always had a capable partner, Nicole, that we could call. She was also great emotional support when we were dealing with difficult sellers. She was very knowledgeable and hooked me up with lawyers and all the resources and paperwork I needed." "All of my questions were answered, support was provided, patience was given and energy was endless. I can't thank Nicole and Jessica enough, they made the entire process effortless and fun, I highly recommend them!"	{ "redpajama_set_name": "RedPajamaC4" }
How a Major US Tech Company is Preparing for GBA Success If anyone has the tools, expertise and experience to make a success of the Greater Bay Area (GBA) initiative, major US tech conglomerate Dell Technologies does, with its portfolio of offerings from Edge (IoT) to Core (Data Center) to Cloud. Dell Technologies has built on its Hong Kong beginnings more than 30 years ago and now boasts an extensive, mature and well-connected business network across the whole of China. According to Sean Lee, the company's Managing Director, Global Transformation Office, that market expansion during the past two decades, which includes business and operations in cities covered by the GBA initiative – has not only put the company on a sound business footing on the mainland but also enabled Dell Technologies to develop crucial relationships at central, provincial and municipal government levels. This gives the company a deep understanding of how things work in one of the world's most complex and challenging marketplaces Lee knows the company has already tackled its fair share of obstacles in doing business in the country, saying: "Due to the experience we have accumulated over the years in China – including across the GBA – many of our clients see us as more than simply a tech company. They see us as a trusted partner they can collaborate with, one which makes things happen for them. This is because we know how to run a fully inclusive business channel both inside and outside of China." How GBA Push Can "Lift All Boats" Lee does not agree with those who suggest the GBA initiative is about upgrading the role of some cities and downgrading that of others. It is, he says, "a rising tide lifting all boats". "At the moment, there is a lot of talk about the GBA. This consultative phase is very necessary and it will take some time to turn discussion and agreement into solid plans. However, I am confident that all the consultation will lead to action. If the government is putting time and resources into the GBA then of course this is going to lift all boats, so to speak, and we want to be part of that. We expect more growth, absolutely. "Generally speaking, the component parts of the GBA have between them strong legal and international governance, and robust technology and manufacturing capabilities, along with a very sizeable and well-off population. This makes for a very interesting zone. Can it rival San Francisco Bay or Tokyo Bay? Yes, but it is a bit more complicated," he says. Lee believes that in the cases of San Francisco and Tokyo you are dealing with a single, already unified zone under one set of rules and regulations. However, in the GBA there are different legal, regulatory and cultural factors that need to be knitted together and this will make the initiative more challenging to pull off. But he is confident that with full collaboration and transparency this can be done – and is the critical thing to do. "I don't buy the argument that the GBA initiative is an attempt to upgrade some cities and downgrade others," says Lee. "I really think – because of the factors I outlined above – that it truly can lift all boats. If we all charge in the same direction, everyone will be a winner." Special GBA Experts To meet this challenge, Dell Technologies – which employs more than 40,000 people across China – is forming dedicated expert teams in both their Hong Kong and southern China offices. "We have Greater Bay 'specialists', if you like. It is still very much in the early stages because at this point no one knows exactly how this government initiative is going to play out. We are talking to our customers, we are talking to our peers and even our competitors. We are a big technology provider so it is our responsibility to play a leading role." Lee says Hong Kong remains a strong financial hub and adds that a significant segment of the company's business is with banks and insurers. These financial services institutions are increasingly turning their focus towards cross-border technology issues such as data privacy, information flow, virtual banking and latency requirements (i.e., the time it takes for a packet of data to get from one point to another) within the GBA, as well as across the broader Belt and Road Initiative (BRI) in China and beyond. This is where the company's extensive experience in international trade and supply chain know-how is beneficial to ensuring the necessary proficiency for the implementation and governance processes. A Greater Bay Ecosystem Lee says the GBA initiative means Dell Technologies is beginning to see clients make corresponding shifts in terms of investment and resource allocation, something with which, as a technology provider, the company has to align. "Hong Kong has always been the lead city in terms of its international connections but now that position may be changing," he says. "As things have moved on since the handover in 1997 and the rapid acceleration of the Chinese market, some are taking the view that Hong Kong is increasingly part of a larger ecosystem rather than a singular market. Our clients are working with the premise that Hong Kong can remain competitive and carve out a specific and important role with the GBA initiative. When the pie gets bigger, everyone benefits." Like many companies, Dell Technologies continues to view Hong Kong in its role as a financial and legal hub, an internationally connected city that remains ahead of anywhere in China when it comes to matters of intellectual property protection, complex commercial arrangements, and contractual and regulatory governance. Hong Kong and High-Growth Gaming Dell Technologies sees the gaming industry, which of course has had explosive growth in the Macau Special Administrative Region over the past 15 years, as a high-growth sector for its business. "We see gaming as a high-growth segment because gaming in Macau has been exported in the shape of operations throughout mainland China," says Lee. "This further emphasizes the importance of collaboration and knowledge-sharing within the GBA, as Macau has gained obvious experience and expertise from the many lessons learned in the gaming industry. "The same goes for the Hong Kong Jockey Club (HKJC), a body we do a lot of work with," says Lee. "Following the first official mainland race meeting at the HK$3.7 billion Conghua Racecourse in Guangzhou in August last year, the HKJC – with its tremendous equine expertise and knowledge of regulatory issues and anti-money laundering precautions – is ideally placed to make sure things are done properly and safely." The company believes Hong Kong will remain very strong in this area – especially if, as some think, the gaming industry is to expand more on the mainland in the future. "Hong Kong and Macau have a tremendous amount of expertise on both the technical and regulatory fronts to offer a safe and proper services. These are tried and proven systems, which can accelerate expansion plans while safeguarding the industry," says Lee. Clearing Clouds in the GBA Lee also believes Hong Kong is in pole position to take advantage of challenges that lie ahead in the expansion of cloud computing, which is very much the here-and-now of the unfolding digital revolution. "Did you know that Hong Kong is one of the few cities in the world that has all five of the top cloud vendors in its jurisdiction? They are all here for a reason," he says, adding that this could help the city take a leading role in this area in the GBA. "With its strategic location just outside of mainland China, international companies serving mainland customers use Hong Kong as an alternative to build out physical infrastructure, when doing so across the border is often a complicated matter. Chinese companies are also looking to use Hong Kong as a springboard for international expansion. This is fueling tremendous growth in the cloud technology market for companies like ours. "One downside is the land issue. While the cloud vendors present here have a sizeable data center footprint – many in the Tseung Kwan O area – they have to lease rather than own the land on which the data centers are situated, unlike in Singapore, Tokyo or Sydney. The biggest reason for that is the scarcity of appropriate land," adds Lee. Among the cloud conundrums that need to be addressed, Lee says, are those revolving around accessibility and movement of applications and their corresponding data sets. For instance, if a company has data stored with various cloud providers in different GBA cities, how do they process the data holistically for compliance and risk management purposes? Which providers do they use to ensure maximum flexibility in the face of differing levels of regulation and data protection policies between mainland China and Hong Kong? And should they continue to own private data centers for regulated workloads or can they realistically move everything to the cloud? As the digital revolution moves deeper and deeper into the cloud, Dell Technologies is positioning itself as a facilitator for clients large and small, local and international, by offering its expertise in the management of data and making sure the process is compatible between the different sectors of the GBA and also across the rest of China. Hong Kong and the Future of the GBA	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
InfluxData, writer of the trendy open supply purpose-built time collection database InfluxDB, nowadays introduced its generation will combine with VMware's Pulse IoT Heart, an IoT infrastructure control resolution. The brand new resolution embeds two merchandise from InfluxData — InfluxDB Undertaking and Kapacitor — optimizing the dealing with of time collection knowledge from attached IoT units, sensors and infrastructure working on the edge and the use of VMware Pulse IoT. InfluxDB Undertaking is a database optimized for time collection knowledge. And Kapacitor is the real-time movement processing element of the InfluxData platform – used to research massive amounts of sensor knowledge in genuine time. VMware Pulse IoT Heart is a safe, enterprise-grade IoT instrument control and tracking resolution. It permits consumers to onboard, arrange, observe and safe IoT techniques and attached units, bridge the space between data generation and operational generation organizations, and simplify IoT instrument control with Pulse IoT Heart. The combination of InfluxDB and Kapacitor with VMware Pulse IoT Heart creates an answer that complements the power of businesses to maintain the large quantities of knowledge related to business and venture IoT workloads. InfluxData, the writer of InfluxDB, delivers a contemporary open supply platform, constructed from the bottom up, for examining metrics and occasions (time collection knowledge) for DevOps and IoT programs. Whether or not the information comes from people, sensors, or machines, InfluxData empowers builders to construct next-generation tracking, analytics, and IoT programs quicker, more straightforward, and to scale handing over genuine trade worth temporarily. Primarily based in San Francisco, InfluxData has greater than 450 consumers together with Cisco, eBay, IBM and Siemens. For more info, consult with www.influxdata.com. Twitter: @influxdb.	{ "redpajama_set_name": "RedPajamaC4" }
Playing nice? FireEye CEO says U.S. malware is more restrained than adversaries' Malware used by the United States in offensive cyber-operations plays "nice" when compared to other nation-state malware, according to FireEye CEO Kevin Mandia. By Zaid Shoorbajee Mandiant CEO Kevin Mandia speaks May 31, 2018, at the Cyber Threat Intelligence Forum presented by FireEye and produced by CyberScoop and FedScoop. (Scoop News Group) Speaking at the Cyber Threat Intelligence Forum produced by Scoop News Group on Thursday, Mandia said when FireEye analyzes malware from state-backed hackers, the company usually finds elements of public policy baked into operations. Certain tells in the malware's behavior or the code itself can be indicative of which state is behind it. "We find malware that sometimes has a time to live and then it doesn't run anymore. I wonder who would do that," Mandia said on stage. "Probably [the U.S.] because we're the nicest hackers in cyberspace, besides maybe China." The U.S. and China are more disciplined in their operations than adversaries like North Korea and Russia, who are instead unrestrained, he said. "We see guardrails on malware from nations like the United States, but do we see guardrails on malware from Russia? No." Other experts, including former U.S. officials, contend that the U.S. can be similarly unrestrained and careless in cyberspace. They point to one specific case that's widely attributed to the U.S. known as "Stuxnet," which originally targeted but quickly spread beyond an Iranian nuclear enrichment facility. Mandia went on to describe an unspecified North Korean cyber-operation that when it detected someone was investigating, the malware rewrote the victim's hard drive. Such properties are indicative of North Korea's attitude toward systems they compromise, Mandia said. "That's annoying to deal with, but that's a policy decision. They don't care what they destroy when they compromise something," he said. "And I have a funny suspicion with our lawyers looking over their shoulders with all of our offensive capability, we absolutely do care and we're not going to have collateral damage in cyberspace." Mandia told CyberScoop in an interview after his keynote that the U.S.'s behavior could change soon. CyberScoop recently reported that officials inside the National Security Council are pressing for more offensive measures on the heels of U.S. Cyber Command's recent elevation to a fully independent combatant command. "My gut, just pure gut, not fact based — [U.S. Cyber Command] will probably break the niceties," Mandia told CyberScoop. "In cyberspace, everyone else is breaking [laws]. Nobody wants to over escalate, however the next war will be fought with a cyber component. We'll have to be ready for that." The public remarks cracked a window into how U.S. cybersecurity companies deal with malware that appears to originate from the U.S. or allied governments. Mandia, for example, told CyberScoop that before publishing a public threat intelligence report, FireEye will typically tip off intelligence officials from the Five Eyes alliance about the release. If FireEye detects malware on a customer's system that researchers think is from the U.S. or an allied country, it will remove it. But Mandia said such malware ought to be stealthier. "If friendlies get caught by our detection, then in my opinion is they just need to get better," Mandia said. "We're going to protect our clients first and foremost." In March, Russian cybersecurity company Kaspersky Lab released information on a operation referred to as "Slingshot," which covered malware that was spying on victims located in the Middle East. As CyberScoop previously reported, Slingshot was a U.S. counterterrorism operation aimed at capturing terrorism targets. Kaspersky's report subsequently burned the operation. In a press briefing, FireEye executives said that the company treats all cyberthreats the same, but uses discretion when it comes to public disclosure. "We respond to breaches all over the world. There are certain times when we think it's potentially a friendly that was behind it," said Charles Carmakal, a vice president with Mandiant, FireEye's incident response subsidiary. "From our investigative perspective we treat it as if it was a threat actor. We help our clients eradicate the threat actor from their environment." But even with removing a threat from a customer's system, officials said the company would stop short of going public. Ron Bushar, a vice president at FireEye, compared the action to publicly disclosing a zero-day vulnerability without giving the affected organization a chance to fix the issue. "I think there's a difference between public disclosure and investigative support, and I think there's important standards or best practices that we tend to follow," Bushar said. "And certainly before you go public with anything … there has to be a consideration of what the impacts are both from a government perspective and what those impact could be to your client and to the organization conducting those operations." Another FireEye executive, John Hultquist, director of threat analysis, said that publicly outing a U.S. cyber-espionage operation, especially a counterterrorism effort, would cross a line that goes beyond quietly dealing with the issue for a client. "I see counter terrorism stuff all the time," said Hultquist. "There's a difference, you know, between stopping it and publishing it for everyone to see." Greg Otto and Chris Bing contributed to this report. Cyber Threat Intelligence Forum FireEye Kevin Mandia Mandiant Google has 'definitive agreement' to buy Mandiant for $5.4B The all-cash deal for Mandiant comes after the company only recently became independent again. The FireEye logo at the RSA conference in 2019. (Scoop News Group photo) Trellix, McAfee, FireEye, Mandiant: What's next for four big names in cyber State-sponsored Iranian hackers uploaded fake VPN app to Google's Play store, posed as university officials Suspected Chinese hackers masqueraded as Indian government to send COVID-19 phishing emails 'Almost every nation' now has cyber vulnerability exploitation program, NSA official says Breach notification window, accountability are focus of coming fight on cyber legislation in Congress Suspected Russian operatives tried to stir far-right outrage about COVID-19 on 4chan Data breach notices become more opaque, leaving consumers in the dark	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
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Transcending Transference? EDPB Offers Guidance on International Data Transfers V&E Cybersecurity & Data Privacy Update On November 18, 2021, the European Data Protection Board ("EDPB") issued guidelines on the interplay between provisions in the General Data Protection Regulation ("GDPR") governing scope and applicability and those governing international data transfer. Specifically, the EDPB outlined three criteria that should be used to determine whether a "transfer" of personal data to a country outside of the European Economic Area ("EEA") has occurred, triggering additional safeguard obligations. Transfer, "Defined" The GDPR regulates the processing of personal data within the EEA as well as transfers of that data to countries outside of the EEA ("third countries") to ensure that data has safeguards that meet a "standard of essential equivalence"1 to the protection afforded by the GDPR and laws of Member States, including derogations. The EDPB's latest guidance seeks to clarify that a "transfer" requiring compliance with Chapter V of the GDPR takes place when each of the following three criteria is met: A controller or processor is subject to the GDPR for the given processing; The controller or processor ("exporter") discloses by transmission or otherwise makes personal data available to another controller, joint controller or processor ("importer"); and The importer is in a third country or is an international organization, regardless of whether the importer is subject to the GDPR under Article 3. Exporter's Processing Activity Is Subject to the GDPR The first criterion requires that the controller or processor who will eventually export the data falls within the scope of the GDPR for the given processing activity. Under Article 3 of the GDPR, it applies to the processing of personal data: in the context of the activities of an establishment of a controller or a processor in the EEA, regardless of whether the processing takes place in the EEA; of data subjects who are in the EEA by a controller or processor not established in the EEA, where the processing activities are related to the offering of goods and services in the EEA or monitoring of data subject behavior that takes place in the EEA; by a controller not established in the EEA but where the member state law applies by virtue of public international law. An exporter for that given processing activity must fall within the scope of one or more of the criteria listed above in order for a "transfer" to have occurred that triggers the applicability of Chapter V of the GDPR. Exporter (Not Data Subject) Makes Data Available to Importer The second criterion seeks to answer an important question: does a transfer occur where the data was disclosed directly by the data subject to a controller at her own initiative? The EDPB has answered "no." A transfer that incurs additional obligations under Chapter V of the GDPR requires that the data is sent or made available by a controller or processor, not the data subject herself. In addition, the second criterion clarifies that internal transfers within the same entity do not qualify as transfers. Note, however, that transfers between entities that form part of the same corporate group may constitute transfers of personal data if the remaining criteria are met. Importer Is in a Third Country or Is an International Organization The third criterion requires that the importer be geographically in a third country or in an international organization. Transfers inside the EEA do not constitute transfers requiring additional protections. Appropriate Safeguards If all three criteria are met, there is a "transfer" requiring additional measures under Chapter V. Under the GDPR, there are three scenarios in which an entity can legitimately transfer personal data to a receiver outside of the EEA: (1) the receiver is located within an area covered by an adequacy decision; (2) appropriate safeguards have been established to protect individuals' rights to their personal data; or (3) an exception, such as explicit consent, covers the transfer. Adequacy decisions are made by the European Commission and establish that a given country has adequate data protection and privacy measures. For transfers that do not fall within the scope of an existing adequacy decision, "appropriate safeguards" must be established. Article 46 of the GDPR lists several mechanisms that can be used to legitimize a transfer, including standard contractual clauses, binding corporate rules, codes of conduct, certification mechanisms, ad hoc contractual clauses, and international agreements or administrative arrangements. The EDPB's guidance is instructive for companies attempting to determine which of their data processing activities must comply with Article V of the GDPR. For example, this guidance can be used to determine whether a contract with a data processor should include EU standard contractual clauses. It may encourage companies whose processing activities are not otherwise subject to the GDPR to use that collection method rather than filtering the data through processors established in the EU. It may lead to companies whose processing activities are not otherwise subject to the GDPR using that collection method rather than processors established in the EU. However, controllers and processors alike should remember that, although a particular data flow may not constitute a transfer under Chapter V, such processing is not necessarily exempt from obligations under the GDPR. Regardless of whether the processing takes place in the EEA or not, controllers and processors involved in processing activities under Article 3 should continue to take steps to comply with all applicable provisions of the GDPR, including Article 32's obligation to implement technical and organizational measures to protect personal data. 1 See EDPB Recommendations 01/2020 on measures that supplement transfer tools to ensure compliance with the EU level of protection of personal data and EDPB Recommendations 02/2020 on the European Essential Guarantees for surveillance measures. Palmina M. Fava [email protected] Jeffrey S. Johnston [email protected] Michael Kurzer [email protected] Christopher W. James [email protected] Briana R. Falcon [email protected] Cybersecurity & Data Privacy Epic Fail: Fortnite Creator to Pay $520 Million FTC Settlement V&E Cybersecurity Update Regulatory Roundup Here Comes the Fashion (Cybersecurity) Police: New York Attorney General Imposes Penalty for Mishandling of Consumer Data Breach More Regulations Coming Down the Tracks: TSA Issues New Security Directive for Enhanced Railroad Cybersecurity A Second Chance: The SEC Reopens Comment Periods on Climate, Cyber and Other Rule Proposals in Response to Technical Glitch V&E SEC Update	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Malware Manifesto A database of major known threats as seen by Webroot and other security channels. Cryptominer Most likes Most replies Most views Newest first LLiddell Administrator Knowledge Base Botnet A network of private computers infected with malicious software and controlled as a group without the owners' knowledge, e.g., to send spam messages. Andromeda Nanobot Adwind Knowledge Base Spyware Spyware is software that aims to gather information about a person or organization sometimes without their knowledge, that may send such information to another entity without the consumer's consent, that asserts control over a device without the consumer's knowledge, or it may send such information... Knowledge Base Worm A Worm's purpose is to propagate and spread as much as it can because it's usually designed to find a specific environment as its target. It differs from a virus in that it doesn't need a host file to infect and spread. Once the worm reaches its target environment it has limitless options of the end... Knowledge Base Trojan Trojans are installed generally without a user's full, meaningful, and informed consent. A Trojan differs from most malware as the payload (or the behavior) of a Trojan can be controlled potentially from a remote site. Trojan Dropper: A file that contains at least one additional, malicious file. Fo... Knowledge base Cryptominer The world of cryptocurrency is in its infancy stages, but criminals have been using it for years and proving the utility and anonymity of blockchain technology. Not to mention the spike in interest and speculative price on the technology has really put a focus for criminals to accumulate as much as... Knowledge Base Ransomware Quite possibly the most devastating malware for victims and most profitable for criminals. This type of malware aims to block access to your data by either encrypting your files or the entire hard drive. To get your data back, victims are forced pay the criminals ransom to get their files back. Hist... Knowledge Base Virus The oldest of all malware is the virus and it's been around since the 70's. Designed to attach its code to other programs. Once those infected programs are executed, the virus will duplicate itself and spread like mad. Today, "Viruses" by their strict definition are rare in the wild and are usually... Knowledge Base Keyloggers/System Monitors Keyloggers and System monitors are either commercial or non-commercial. A commercial system monitor is a piece of software with system monitor characteristics, obtained with a legitimate license by legal means. All other system monitors are non-commercial system monitors. The system monitor category... Jokeroo (Formerly GandCrab) Summary - Jokeroo is a RaaS or Ransomware-as-a-Service being sold on the Darkweb. This RaaS requires an up front member fee. This ranges from $90 - $600 which allows the purchaser to keep anywhere from 85% to 100% of profits and even extra items such as Salsa20 encryption. Jokeroo was initially prom... LockerGoga Summary - LockerGoga is a Ransomware variant that appears to be targeting European companies. The encryption process used by LockerGoga is slow, showing a lack of sophistication. LockerGoga was signed using a valid Digital Certificate which has since been revoked. Glossary Blog Back to the Malware... Anatova Summary - Antova is Ransomware that encrypts files that are 1MB or smaller in size and will also encrypt files on connected network shares. This Ransomware appears to support additional modules which could be used to perform other malicious activities in addition to file encryption. Glossary Blog... Adwind Summary - Adwind RAT, first discovered in 2013, is a multi-platform Remote Access Trojan written in Java which is more commonly known as jRat. Adwind is provided as a malware-as-a-service for the attackers most commonly distributing it via malspam. When via a malspam email, a .jar attachment will be... Nanobot Summary - Nanobot is a botnet with hosts controlled by the NanoCore RAT, a Remote Access Trojan that targets Windows operating system users. All versions of the RAT feature base plugins and functionalities such as screen capture, crypto currency mining, remote control of the desktop and webcam sessi... Summary - Andromeda, also known as Gamarue, is a modular botnet whose functionailities can be modified via plugins. Some of its functions include: keylogging, rootkit, teamviewer and spreader. Andromeda was spread many different ways such as malspam, trojan downloads and exploit kits. The primary go... Crysis/Dharma Summary - These are variants which you will typically see come in via compromised RDP accounts in bruteforce attacks. Crysis was first spotted some time in 2016. Due to similarities in code, Dharma is thought to be a product of Crysis. Crysis will usually demand a payment of around $1000-$1500, per... Bitpaymer Summary - Bitpaymer is a multi vector ransomware which has been seen in RDP scenarios as well as dropped by trojans, such as Trickbot. Bitpaymer is a unique ransomware in that it utilizes alternate data streams (ADS) to hide itself from antivirus. This essentially makes the ransomware file-less shor... CEIDPageLock 29th August, 2018 By Charlie Osborne ZD Net Summary - The RIG exploit kit, which at its peak infected an average of 27,000 machines per day, has been grafted with a new tool designed to hijack browsing sessions. The malware in question, a rootkit called CEIDPa... Dark Tequila 22nd August, 2018 By Pierluigi Paganini Security Affairs Summary - Security experts from Kaspersky Labs have spotted a sophisticated strain of banking malware dubbed Dark Tequila that was used to target customers of several Mexican fina... 21st August, 2018 By Catalin Cimpanu Bleeping Computer Summary - A new ransomware strain named Ryuk is making the rounds, and, according to current reports, the group behind it has already made over $640,000 worth of Bitcoin. Attacks with this ra... 16th August, 2018 By Linday O'Donnell Threat Post Summary - A new downloader, which has been spotted in an array of recent email campaigns, uses anti-analysis techniques and calls in a system fingerprinting module. A newly discovered downloader malw... KEYMARBLE 10th August, 2018 By Juha Saarinen IT News Summary - The United States Computer Emergency Readiness Team (US-CERT) has issued a fresh warning that a new piece of malware believed to be created by North Korean government actors is on the lose on networ... DeepLocker 8th August, 2018 By Nicky Cappella The Stack Summary - While DeepLocker has yet to be seen outside of the research lab, all of the tools used to create it are readily available: existing malware, and AI tools that can be trained to recognize a target.... Dark Caracal 6th August, 2018 By Nick Lewis TechTarget Summary - Dark Caracal is written in Java, so it can be used against any computer that executes Java code. It is an immature remote access tool that appears to be used by nation-state actors, but it... Ramnit 6th August, 2018 By Tara Seals Bleeping Computer Summary - A massive proxy botnet is just the tip of the iceberg, a warning sign of a bigger operation in the works by the Ramnit operators. The recently uncovered "Black" botnet campaign using the Ramnit malw... PowerGhost 27th July, 2018 By Danny Palmer ZDNet Summary - A new form of cryptocurrency-mining malware is targeting corporate networks across the world, employing a combination of PowerShell and EternalBlue to stealthily spread. Dubbed PowerGhost, the filele... Jaxx has earned the badge Posted 5 comments!	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Jim Wilson/The New York TimesGene Wade, whom Forbes called the most disruptive figure in education, is the founder of UniversityNow, which offers both online and on-campus programs. When President Obama visited campuses recently to push to make college more affordable, he called on educators to think creatively. And he gave a shout-out to new competency-based programs at public universities, private institutions and profit-making colleges alike. The programs dispense with the credit hour and classrooom time with a professor in favor of self-paced online learning and assessments that measure what people can actually do. Anya Kamenetz writes about these pioneering programs in Education Life, The Times's quarterly magazine about higher education. It's part of a package of articles that highlight online experiments, includingUniversityNow, Minerva and University of the People – intended to make college more affordable as well as more convenient by tapping into web-based technology. Those happen to be the two essentials of disruptive innovation, according to Clayton M. Christensen, the Harvard Business School professor who coined the term. He and Michael B. Horn, co-founder of the Clayton Christensen Institute for Disruptive Innovation, explain how online education is beginning to transform higher education, and who is going to be left behind.	{ "redpajama_set_name": "RedPajamaC4" }
Bhama is all set to play a 15-year-old school going child in her upcoming movie. The film titled Ottamandaram is based on a true life incident that happened in a family in Andhra Pradesh. The director of the film Rajesh Mankara says that his movie is based on a real life incident that happened to a family residing in Andhra Paradeh. A 15-year-old girl is forced to sleep with her brother-in-law as her elder sister has infertility issues and has problems in bearing a child. The child is made to sleep with her brother-in-law forcefully, to bear the child. In the real life story, the brother-in-law expires, making the whole effort a pointless one. Bhama will essay the 15-year-old child in the movie. Sajitha Madathil will play the elder sister and Nandhu will play the brother-in-law. In the movie, the elder sister takes the firm decision, takes over the child and makes the girl go back to school and continue her education. But, in the real incident, the family does not complain about anything. Director says that he opted Bhama as she is perfect to picturise an adolescent child. The actress too is very excited about her challenging role and is already preparing for the same by trying to become more slim. Ajay Muthana will be scripting this film.	{ "redpajama_set_name": "RedPajamaC4" }
Simple test all women should be taking regularly Kristine Tarbert ·Features and Health Editor 9 September 2021, 12:52 am ·6-min read Iron deficiency is the most common nutritional deficiencies experienced by Aussies, especially women, but remains one of the most significantly under-diagnosed. When it comes to our bodies, iron plays an important role in producing red blood cells, heart health, immune function, energy levels, and healthy brain function, but 34 per cent of women of childbearing age are currently living with depleted iron levels, compared to just 5 per cent of Australian men. 34 per cent of women of are currently living with depleted iron levels. Photo: Getty "Having low iron levels can have a significant impact on how our bodies produce energy and regulate our immune system, which could lead to other conditions like fatigue, decreased immunity and anaemia," Andria Aird, Pharmacist-owner at Blooms The Chemist, tells Yahoo Lifestyle. "Low iron levels can occur due to a number of different reasons, from low dietary intakes to blood loss and poor absorption. "With more Aussies reducing their meat intake, looking at alternatives to boost your iron may help build up your levels. A heavy menstrual period can also contribute to greater blood loss and the reduction of our bodies' iron stores." The types of people more likely to get burnout and how to manage it Why we still find talking about our 'lady bits' embarrassing 'Awkward' health issue 1 in 3 women won't talk about Particularly through lockdown where it is so common to feel lethargic, unmotivated and constantly tired, it can be difficult to pinpoint if one is actually suffering from iron deficiency. But given how many women are being impacted by the effects of low iron, Andria and Blooms are encouraging all women to have their iron levels screened regularly. "Throughout every stage of our life, our iron needs differ. For women aged between 19 and 50, the recommended daily intake of iron to help sustain your levels is 18mg. For men aged 19 and over and women over the age of 51, this need is reduced greatly to only 8mg," Andrea explains. Just like a blood sugar test you can go to the chemist for an iron test. Photo: Getty "Having your iron levels screened is a quick and easy process, which will help you to better understand your total iron levels and get you on the right treatment path. You can visit your GP or local chemist to be tested. It only takes about a minute to complete! Andria stresses that it's so important to take the time to have your iron levels screened more regularly, especially if you are experiencing symptoms. "With our busy lives divided between work, friends and family commitments, we often forget to pause and make sure we are looking after our own health. It is something so simple and quick to do, which can really make a difference to your overall health and wellness." Common Symptoms of an Iron Deficiency Because the symptoms can just look like you're run down from your busy life, they often go undetected for long periods. Symptoms of iron deficiency often vary and can be obscure and subtle, which is why recognising them is often the biggest hurdle to getting a diagnosis. Some of the most common indicators that you're potentially iron-deficient include: Weakness or dizziness Fatigue, exhaustion, and lack of energy Difficulty doing high-intensity exercise Pale skin or cracked skin around the mouth Health and fitness guru and new mum Lauren Hannaford suffered iron deficiency during her recent pregnancy and says: "I heard that once you get to the second trimester of your pregnancy you will feel like you have a lot more energy. I however found that I went the other way and was feeling really tired and drained all the time." "I had never felt that kind of fatigue before and didn't know that it could be from low iron. Now I fully understand the importance of making sure that my iron level is stable at all times," she adds. Fatigue and exhaustion are common symptoms of iron deficiency. Photo: Getty Three ways to boost your iron intake Thankfully if you do find out you are low in iron, there are a few things you can do to help boost your Iron intake. Accredited Dietitian and Exercise Physiologist, Kate Saver, who is also the Co-Founder of Be Fit Food, takes us through a few methods you can look at: "Often, an iron-rich diet is the key to restoring your strong and savvy healthy body. However, it's important to remember that not all foods that contain iron are created equal. There are two types of iron: haem iron - found in flesh foods, such as red meat, chicken, and fish, and non-haem iron - found in plant foods. Haem iron is absorbed four to five times more efficiently than non-haem iron, but the absorption of non-haem iron is three times greater when consumed alongside foods containing vitamin C. So, to get the most out of your non-haem iron sources, being vegetarian foods — pair them with foods such as citrus fruits, berries, capsicums, broccoli, and leafy greens, all loaded with Vitamin C for that added absorption." Havind Vitamin C and Iron together will boost the absorption. Photo: Getty "A great option to compliment a balanced diet is to incorporate an iron supplement into your daily routine. Depending on the cause of your iron deficiency, a supplement might be recommended by your health care professional. Just like the high iron meals you choose to eat that need the powerful duo of Vitamin C for optimal absorption, so too will your supplements. Given we know that Iron and Vitamin C work so well together, looking at a supplement that provides both is a smart move, something like Ferrogen Iron + Vitamin C. Meal times "This may sound strange – but hear me out. If you are low in iron stores, you can strategically time when to eat your high iron meals. Doing so will help with optimal absorption and assist your body to get the most of the iron. A good way to start this is to eat your high iron meals outside of the times you're planning on exercising. For example, if you are more active at night, opt for a high iron breakfast like oats topped with berries, hemp seeds, and cacao nibs. If you're a morning person and prefer to get out of the house early, choose a high iron dinner rich with root vegetables, grilled steak, or lentils. Exercise stimulates the release of a hormone that signals your body to reduce iron absorption. So by choosing to eat your high iron meals three or so hours from when you plan to training and bulking up your plate with foods high in Vitamin C, you can feel confident your body is absorbing all of that iron goodness." Never miss a thing. Sign up to Yahoo Lifestyle's daily newsletter. How bad sleep can actually make you age faster The Project's Carrie Bickmore moved by woman's 'heartbreaking' IVF plea Covid and breastfeeding: Experts respond to photo of green breastmilk Aussie star Sarah Wynter details terrifying postpartum psychosis experience Home & Away star Tammin Sursok's terrifying 'close call' during daughter's birth The festive gift that could be bad for your lady bits The lunar nodes are changing signs… Today the lunar Nodes are changing signs – they are karmic points in the sky where the orbit of the Moon around Earth meets the orbit of the Earth around the Sun. So today everyone's (slightly unusual) forecast is about that — essentially the South Node is where it's […] When can I start exercising after catching COVID? Keep It Cleaner's Laura Henshaw and Physiotherapist Ashleigh Mason share their tips for getting back into exercise after catching Covid-19. I'm A Celebrity's Beau Ryan opens up about parenting regret: 'Not present' The Amazing Race host showed a softer side to his personality when he opened up about his biggest milestones and regrets. Read more. It turns out getting your 'beauty sleep' is more important than you might have thought. Kyle Sandilands, 50, engaged to Tegan Kynaston, 35 Kyle Sandilands, 50, is engaged. The radio star proposed to his 35-year-old girlfriend, Tegan Kynaston in Queensland. Read more here.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
From I95, take Exit 329 , west on CR210, Left onto Sampson Way. Left onto Barred Owl Rd. Left onto Scrub Jay Drive. 647 Scrub Jay Dr is a 1,497 (*estimated) square foot home with 3 bedrooms and 2 bathrooms located in St Augustine FL, ST. JOHNS County. This property is listed for sale at $172,900 and is currently active and accepting offers.	{ "redpajama_set_name": "RedPajamaC4" }
Ethanol-Powered Car Wins the Automotive X-Prize A vehicle powered by an internal combustion engine beats electric cars to the $10 million competition. Electric vehicles and plug-in hybrids have been enjoying the limelight recently as leading candidates for the energy efficient cars of the future, but a car powered by an internal combustion engine just rolled away with the top prize in the Automotive X-Prize. This contest has seen teams race vehicles that achieve the at least the equivalent of 100 miles per gallon of gasoline (MPGe) (under prescribed driving conditions), and that pass U.S. emissions and safety standards. On Thursday, the Edison2 team won the $5 million prize in the "mainstream" vehicle class, which required the car to transport four passengers and to have at least a 200-mile range. The team's car achieved 102 MPGe. The mile-per-gallon equivalent figure is a way to compare the efficiency of cars that use different kinds of fuels or energy sources, in a competition that included cars powered by natural gas, ethanol, gasoline, diesel, and energy stored in batteries. It's calculated by determining how far the car travelled and how much energy it consumed relative to the energy content of a gallon of gasoline. The team's design formula was simple: make the car extremely light and aerodynamic, so that it can be powered by a small 250 cc, single-piston motorcycle engine. The winning car weighed 376 kilograms (830 pounds) and had a coefficient of drag of 0.15, far less than the Prius, which with a coefficient of drag of 0.25 is one of the best on the road today. Innovations included an aerodynamic body design like a diamond (rather than the rectangle base sedans have) that's supposed to deflect other vehicles in the case of an accident, and lightweight wheels that project out from the sides of the car and serve to absorb impact in an accident. Edison2's winning vehicle. The engine was also modified to run at high compression ratios (a measure of how much the fuel-air mixture is compressed). This allows more energy to be extracted from a given amount of fuel, but comes at the risk of engine knock (combustion at the wrong time in a combustion cycle). To avoid engine knock, the team's engine runs on ethanol, which has a higher octane number than gasoline. The engine also re-circulates exhaust gases, a knock-reduction strategy that's being used in some commercial engine designs, such as Ford's EcoBoost engines. The team started out expecting to design a hybrid car that could capture energy from braking using batteries and an electric motor. But it decided that the weight of the batteries and motor simply weren't worth it. While achieving 100 MPGe is a challenge, it's not surprising that it was possible with a car that's less than a third of the weight of a Prius. And if the car is to help make a dent in fuel consumption a lot of people will have to buy it. To address this, the prize was designed to ensure that the cars would have good performance: the winner had to win a race, not just achieve a certain mile-per-gallon figure. But the Edison2 car certainly looks strange and it doesn't have much space inside it. Especially in the United States, where gas prices remain relatively inexpensive, it's hard to imagine the masses rushing out to buy it. Winners in two "alternative" categories were also announced on Thursday. In these categories the vehicles only needed to seat two people and have a 100 mile range. In the alternative vehicle class for tandem vehicles (where people sit one behind the other), the winning car was looks like a motorcycle with an aerodynamic enclosure for the passengers. During the award ceremony, it was announced that the vehicle achieved the equivalent of 187.6 miles per gallon, using batteries and an electric motor–a separate press release put the figure at 205 MPGe. The winner of alternative class with passengers sitting side-by-side was Li-ion Motors, with a battery-powered car that looks like some sort of a green vegetable (but which President Obama's science advisor John Holdren thought was quite good looking) and gets the equivalent of 187 mpg. The MPGe figures for these battery powered vehicles are a little misleading, because they do not take into account the energy lost when the electricity is generated and transmitted. In the United States, the vehicles will do a good job offsetting oil consumption, since electricity isn't generated using petroleum here. But if the power comes from a coal plant, it's possible that the Edison2's ethanol vehicle could result in fewer carbon dioxide emissions–especially if the ethanol comes from cellulosic sources such as grasses and corn stalks.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Q: Power BI SQL Connection I have a Power BI desktop report which extracts data from the database server through SQL. Once complete, is it possible for me to disconnect the SQL DB connection but retain the data already extracted in the tables (of course, without further refresh). Thanks A: Yes,once you import the data it will get saved with pbix file.	{ "redpajama_set_name": "RedPajamaStackExchange" }
- A REFUGE FROM REALITY! - THE BLOG OF MAJOR GENERAL "WHOPPER" CREEDON - Whiteout - Frosty What an incredible opening to a movie - It's nighttime and there's a snowstorm. A Russian transport plane is flying over Antarctica. Then there's like this shootout - an incredibly clever thing to do on a plane. Naturally the pilot is killed and the plane spectacularly crashes in the ice and snow, it's fires are soon quenched by the intense cold leaving no trace. The following scene is even better; as one of the most supremely hot women on the planet Kate Bekinsale arrives at her Antarctic base and she promptly sheds about nine layers of clothing down to an impossibly white white sports bra and panties and proceeds to remove them too and take a splendid shower which unfortunately restricts you to imagining what she's doing as the steam reacts far too quickly to the cold air obscuring our lecherous gazing. Both scenes comprise the first 10 minutes of the movie... Sadly the rest of it is cinematic excrement. Dear God, what a travesty of cinema. After the opening 10 minutes we're soon treated to the most dull, boring, cliched and predictable thrillers I've ever had the misfortune of seeing. At first I thought they had taken a daring step with vaguely 'film noir' style dialog, but I soon realised it was just shit writing. I think it was catering to some of the most stupid people on the planet - you know the blonde bimbo sitting behind you at the cinema who needs the movie's plot explained - well not this time Barbie, because it's practically spelled out for you here. Dialog like: "I'm in the shower", says Kate as her doctor friend [Tom Skerritt] enters her quarters to the sound of running water and endless steam - he's an M.D. I think he'd work out that for himself luv. Later Kate finds a map with big squares drawn on it like a grid with big numbers from 100-105 in each square. Big red Xs have been drawn through 100-104 and Kate points to the map now filling the entire screen: "It looks like they stopped at grid 105." Truly a master detective. After about an hour of fuck all happening I just wanted to drift off and dream that shower scene was longer but my eyes were transfixed to the hole-filled train-wreck plot which contained about seven or eight flashbacks of increasing duration to explain the traumatic on-the-job experience that Kate had years ago to prompt her to escape to Antarctica to forget about it. Once the director has used up these flashbacks however, he starts to create flashbacks of things we saw at the beginning of the movie, including the plane crash and the dialog that practically reveals the true evil mastermind - just in case we weren't paying attention the first time we saw them just over an hour ago. Why couldn't Kate have a flashback of the fuckin' shower scene? I remember that too but I'd not object to seeing it again - from an ahem, different angle perhaps. I did briefly nap but woke up about 10 minutes towards the end to the noise of the final fight scene between Kate, the one-dimensional Gabriel Macht [he wasn't he in a shit film already this year?] and someone I'd obviously missed the introduction of. This ended exactly as I though it would - completely unspectacularly. This left only the obligatory "shocking twist" as our heroine puts all the pieces of this painfully obvious puzzle together revealing the true culprit to this ridiculous plot. Final Verdict: For this, I'll use the words of Sith Master, who mailed them to me earlier: "Watch the 1st 10 minutes and the trailer. Any other good bits (blood freezing underfoot, slashed throats, etc.) are interspersed with tedium. Watch the rest only you have a fetish for the lead actress." Colonel Creedon Rating: * [because I can't give ***** for the just first 10 minutes] Official Site / IMDB / Wikipedia Posted by Major General Creedon at 00:30 Bruce Russell said... You get points for your correct use of the term "frosty." Wednesday, 23 September 2009 at 03:06:00 GMT+1 I, Constance said... Frosty. Yes. Chill, frozen, frigid. The opposite of warm. Snug. Pleasant. Toasty. You know, now that I think about it, it is pretty cold when people skate on thin ice... Former Grunt said... Good movie then? :) Lots of subtext in C's post. Trouble in paradise? Thursday, 24 September 2009 at 05:14:00 GMT+1 Civilian Overseer said... Connie, How does the process of skating on thin ice lower the ambient temperature? Wait are you using groundless metaphor again? ;) Constance said... Groundless metaphor? Bah! I often remind myself that I have set my feet on the path of peace, even though it is a hard way to walk. Especially with all the jerks tearing up my town! Friday, 25 September 2009 at 03:17:00 GMT+1 Connie If you're lucky, you just might hire the WTeam, An elite force, wrongfully aquitted of crimes they did actually commit. Lead by Colonel Whopper Creedon, he loves it when a plan requires big guns. They're specialists in dejerking towns. Page Designed by: Tweets by whoppercreedon WHOPPER'S ARCHIVES You're never too old to be Tasered! - Part 17 in m... Iran's Second Nuke Site Steven Segal: Lawman The A-Team is cast Neverwinter Nights 2: Mask Of The Betrayer - Revie... Supermarket Empire Strikes Back against Jedi!!! Could Eurovision Voting Be Treasonous? Obama scraps Bush's European Missile Defence Plan New Pacific Trailer Fookin' Hell: District 9's an Explosive Prawn Cock... Stallone's been taking LSD with his Steroids War is a Drug. Get addicted with The Hurt Locker STAR WARS: Force For Change Founding Member Major General Creedon SPEARHEAD Regional Command - Europe Years of being dropped on the head as a child has led me to believe that I'm a U.S. Marine General, a senior officer of a UN unit dedicated to defending the planet from things that the world doesn't believe exist. My spiritual beliefs are those formed from the work of George Lucas whom I consider to be a deity. Politically, I'm a right-wing authoritarian and believe diplomacy is achieved by those with the bigger gun. I enjoy listening to scores from movies and TV, watching action, military and sci-fi movies and television, playing 3D shooters and RPGs on the PC, reading comic-books and I adore the impressive sound of my own voice. I recorded 2IGTV; an award-nominated Podcast with my friend Mark centred on news from the world of popular culture which ran for 64 Episodes between '05 and '09. As an actor I've appeared in two major Irish short films and the pilot of a web-series. I've something to say about almost everything and you've made the wise choice of coming here to benefit from my vast wisdom, knowledge and ego - enjoy! THE GENERAL'S RATINGS No Star: The greatest load of shit ever, no redeeming qualities. It's creators are blacklisted and will be shot on sight if they don't redeem themselves before I meet them. Seriously - Dear God why? 1 Star (): Awful crap. A complete waste of time. Should not have been made. 1.5 Stars (1/2): Bad movie. I'm not happy about having paid to see this. 2 Stars (): Dissapointing. Not that good at all except for perhaps a few select scenes or elements. I'll choose not to see this again. 2.5 Stars (1/2): Glad I saw it, but ultimately not good enough. I won't turn it off if it appears on TV, but I'll have it on while doing something else, just to wait for the cool bit I remember. 3 Stars (*): Meh! Middle of the road movie. Balance between love and hated. May watch this on TV years later / may not. 3.5 Stars (1/2): Enjoyable, but I would need to see it again, possibly on TV before I would purchase it. 4 Stars (*): Extreamly good. I would prefer to watch this again on Blu Ray a year or two on rather than see it on TV, but... 4.5 Stars (1/2): Several minor flaws but not enough to distract you from excellence. Most likely will be added to my BD collection. 5 Stars (*): An outstanding work of art. Practically Flawless. To be added to my BD collection. 5 Star Plus (***+): One of the finest examples of it's genre. Flawless. Automatically becomes part of my BD collection upon release. EXEMPTION GRANTED: To be granted an exemption, a movie has literally to be amongst the greatest movies of all time. Examples include Robocop (1987), The Matrix (1999), Mission Impossible 2 (2000), Transformers (2007) and Iron Man 2 (2010). For religious purposes it is accepted that all Star Wars movies are exempt by default and cannot be reviewed. Brigadier General Creedon is a Class-1 Nutter, he is not affiliated with a recognised news service, an officer of the US Marine Corps, a member of the organised Jedi Order or has ever slept with Scarlett Johannson. The General's Medal Of Honor is made of painted lead and bits of copper. "If you don't like the news, go out and make some of your own!" -Scoop Nisker Design and construction by VerTecX21 based on an original template by Tina Chen. Powered by Blogger.	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
The mites cleaner head built-in independent motor to remove the dead skin and invisible mites from mattress. The cleaning effect is as high as 99.99%, which is effective in preventing mites allergies. The wall-mounted charging dock equipped with storage and charging, it takes only 3.5 hours to charge once. So it's ready for use whenever you need it.	{ "redpajama_set_name": "RedPajamaC4" }
President House 1:26 PM - December 1, 2022 (Thursday)1:26 PM - December 1, 2022 (Thursday)By melange.editor47 President condoles death of former Chinese President Jiang Zemin Islamabad : President of Islamic Republic of Pakistan, Dr Arif Alvi has conveyed his deepest condolences to the people of the People's Republic of China on the sad demise of former President of China, Mr. Jiang Zemin. The President said that former Chinese President Jiang Zemin was a distinguished statesman who, through sustained economic reforms led China on a period of rapid growth and development, and significantly raised the standard of living in China. The President said that former President Jiang continued to deepen the friendship and people-to-people ties between our two countries. He said that President Jiang would be remembered for his services and dedication to his country. Our thoughts are with the people of China at this time of bereavement, he said. Previous PostAids DayNext PostISPR	{ "redpajama_set_name": "RedPajamaCommonCrawl" }
Paris / Restaurants If you're a frequent flyer, the name Epicure most likely sounds familiar even if you don't know exactly where to place it. It's France's most desirable dining locale; the place foreigners and Parisian locals flock to nightly for a taste of Eric Frechon's savory dishes. The world-famous restaurant calls the Le Bristol hotel home and offers guests spectacular dishes alongside incredibly stunning views of its French-style garden outside. The light-filled space received a facelift recently at the hand of architect Pierre-Yves Rochon and Mrs. Maja Oetker, transforming the restaurant into a sun-lit space with bay windows, gold fixtures, tasteful floral touches, and tons of soothing cream, ivory, and white décor. Frechon's menu has earned Epicure three Michelin stars, with cheeses changing by the seasons, a fresh-picked seasonal menu, and a personalized selection straight from the chef: Purple Sea Urchins served with smooth egg mousse, Sea Scallops served alongside Jerusalem artichoke puree and black truffle juice, the Saddle of Venison roasted with juniper berries, beetroot perfumed with Porto, Grand Veneur sauce and pureed celeriac, and a Peru Chocolate served with iced, foamy and crunchy chocolate sorbet infused with lemongrass, all served in a cocoa pod. Less adventurous eaters can still sample everything Epicure has to offer on their own terms, as a regular menu is available daily in addition to the chef's specialties. A serene space, wide ranging selection of lovely product, and above all in service of a cause that matters -- the Merci concept store in Paris hits the mark.... Home to one of the most sought-after restaurants, Le Bristol Paris serves as one of the most stunning, refined and luxurious hotels Europe has to offer. It's.... Restaurants> The Beatrice Inn A classic eatery that focuses on quality food served up without all the bells and whistles, The Beatrice Inn sits as a haven for diners who really are,.... The Duck and Rice By the name, you'd think you're about to be treated to yet another Asian menu, filled with flavors and dishes palatable only when you're in the mood for.... Faena – Miami Beach Pinewood Social Ritz-Carlton, Tokyo Beacher's Madhouse, Los Angeles Hakkasan Mayfair The Savoy DiCaprio Sets Sights on Preserving What's Good Throughout the Natural World Meet the Rosegold Lambda by Nomos Glashütte	{ "redpajama_set_name": "RedPajamaCommonCrawl" }

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