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Contrary to the headline implication in The Times, the Clippers didn't lose to the Thunder because of Donald Sterling; they lost because Kevin Durant and Russell Westbrook outplayed Blake Griffin and Chris Paul when it counted.
Ken Blake
Doc Rivers is my new favorite coach. I was hoping for a candid interview after Game 5 and he did not disappoint with his honest appraisal of his team and the officials. I think it's pretty clear that the NBA wanted the Clippers and the continued discussion of their embarrassing owner off the national stage. Anyone surprised by some of the calls has not been watching the NBA long.
As a Lakers fan I hope another conspiracy theory comes true when the draft lottery is held next week!
Rick Van Kirk
Bill Plaschke's column splendidly characterizes what happened at Game 5 — except for the conclusion. The Clippers were not cursed in that game, they were gamed — gamed by intimidated "homer" officials psychologically programmed to save their skins before an Oklahoma City crowd. The script couldn't have gone any other way, and the referees played their roles accordingly.
Bruce Daniels
Running Springs
I agree with Doc: If that is the result of instant replay, maybe the NBA should just get rid of it.
Larry Weiner
Culver City
Where are they now? It appears that the officials from the USA-USSR finals in the 1972 Olympics are alive and well and officiated Game 5 of the Clippers-Thunder series.
Ian Bardin
Redondo Beach
Enjoyed Doc Rivers' tirade against the officials after Game 5. So, let me get this straight. On the call in question, you agree that the Thunder player was probably fouled, yet, after the foul, the refs botched the out-of-bounds call. Let's put this to a parallel test in the justice system: The criminal robs a house, but is set free because the cops didn't read him his rights?
Gary Engstrom
Mission Viejo
If Jim Healy's iconic radio show were to return to present-day Los Angeles, would one of his signature lines be changed to "Has Leonard Tose gone the Donald Sterling route?"
Doug Thomson
West Los Angeles
Hire power
Mitch Kupchak is quoted as saying the Lakers won't be hiring a coach "any time soon." I don't understand. How many great coaches could be available to run a team as storied as the Lakers, especially in light of other NBA teams making their hires as we speak? Maybe the Lakers know something no one else does, but it seems a sense of urgency is in order. Why did they rush to hire Mike D'Antoni so much that they couldn't wait one day for Phil Jackson's answer whether he would coach the team? It's not like anyone was going to hire D'Antoni away from them.
Richard Karliss
West Hollywood
So you're Mitch Kupchak and you've endured watching your team plummet from World Champions to the Pacific Division cellar in only four years. You've had to deal with a new owner who thinks he knows more about basketball personnel than you do. You're piloting a rudderless ship with no compass to guide your way. So what do you do next? You publicly embarrass the only star your organization still has.
Brian C. Gura
Redondo Beach
So Mitch won't talk to Kobe about a new coach. Is this the same Mitch Kupchak who let Trevor Ariza go, who let Matt Barnes go, and who hired two mediocre coaches to replace an extraordinary coach?
Leonard A. Zivitz
With the fuss about hiring Steve Kerr, one would think he is the second coming of Red Auerbach! The truth is Kerr and my cat are tied on the all-time victory list.
Mark S. Roth
Los Angeles
Attention, Jim Buss. Mike Brown is available!
Jim Davis
Los Angeles
Invisible team
A note to all those Dodgers fans who do not have Time Warner Cable. You're the lucky ones. You don't have to watch Don Mattingly manage.
Ken Krug
El Segundo
The National League West standings at the end of the season should look about same as they did Thursday:
1. San Francisco Giants
2. Colorado Rockies
3. Time Warner Dodgers
4. San Diego Padres
5. Arizona Diamondbacks
Danny Sanchez
Remember: In America greed is good, right? So do me a favor. Stop covering the Dodgers on a daily basis. You don't cover the (pick any non-L.A. team) as we can't see them play on TV either. I am trying to forget the Dodgers, which apparently is OK with Dodgers management, as their game plan is fulfilled — grab the money, and make more money using that money.
Kevin Maher
As one of the "70-percenters," I only have one thing to say to last week's letter writer who wrote about Dee Gordon's newfound base-stealing prowess and infield acumen resulting from Maury Will's coaching. Thanks for the Dodger update. I'm just grateful Magic and Guggenheim didn't own the Dodgers in the 1960s; otherwise I'd be saying, Maury who?
Tony Perez
Long Beach
Not only are Time Warner Cable and Dodger management robbing 70% of L.A. from hearing Vin Scully for nine innings, the lack of TV coverage is subjecting fans to Rick Monday's partial sentences and circuitous thoughts on the radio.
Anything more than a routine grounder to short ties Monday's tongue in knots, and confusion is guaranteed when he multitasks and tries calling balls and strikes while telling a rambling story. However, his worst offense is the inability to tell us the score. Rick, it's up there on the scoreboard, which listeners can't see, thanks to TWC and Dodgers management.
Jeff Green
Long Beach
Yasiel Puig hits a home run, flips his bat and the pitcher gets annoyed for being "shown up." In the NBA, players who hit a big shot pound their chest and then dance halfway across the court and their opponent doesn't flinch. Seems like baseball players are a little thin-skinned.
Richard Raffalow
Valley Glen
Yasiel Puig should be lighting candles in gratitude that he's not playing in the era of a Bob Gibson, Steve Carlton or Nolan Ryan, to name just three pitchers who would delight in taking his very swollen head off with their very next pitch, after showing them up.
Bob Jackson
Simi Valley
Still on the job
With all the issues on the Angels' pitching staff since the departure of Bud Black, can someone please help me understand how the pitching coach has avoided the Butcher Block for so many years.
Jim Hebda
Playa del Rey
Holy cow
I can't tell you how disappointed I was when University of Washington running back Bishop Sankey was drafted by the Titans. I thought for sure he'd become a Cardinal, perform a few miracles, then finish his career as a Saint.
Jamie Duckman
Culver City
Good news
With ugliness currently dominating the media, Bill Dwyre's poignant piece on jockey Victor Espinoza was a jolt to the senses. As a result of a past emotional first visit to the City of Hope, Espinoza has been quietly donating 10% of everything he earns to children with cancer at the facility. Had he not won the Kentucky Derby, none of us would be aware of Espinoza's humanity and generosity. Dwyre's article not only gives us that awareness, but the recognition that there is good in the world to offset the evil.
Gary H. Miller
When it comes to owners, California Chrome certainly has it over the Clippers.
Jon White
The Los Angeles Times welcomes expressions of all views. Letters should be brief and become the property of The Times. They may be edited and republished in any format. Each must include a valid mailing address and telephone number. Pseudonyms will not be used.
Mail: Sports Viewpoint
Los Angeles Times
202 W. 1st St.
Los Angeles, CA 90012
Fax: (213) 237-4322


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NEW YORK - APRIL 26: The 2nd Annual National Meningitis gala at the New York Athletic Club on April 26, 2010 in New York City.
NEW YORK - APRIL 26: The 2nd Annual National Meningitis gala at the New York Athletic Club on April 26, 2010 in New York City. PHOTO CREDIT: © 2010 by Steve Mack | Booking Inquries Contact: Steve Mack | tel: 917.202.4358 | e-mail: email@example.com | PLEASE NOTE: These images are available for licensing through WireImage and Getty Images or call 1-800-IMAGERY. Note: to download original high res files, mouse over the selected photo on the right, and click on the yellow "download photo" icon. To download other sizes, click on the share button above on the right. The, click on "get a link". Once there, click on "copy" corresponding to the size of the image you need. The, paste that link you just copied into a new window of your internet browser. The image will be displayed for you to "save as" to your computer for future use. You may re-name the files as needed or appropriate for your records. Each image file contains the caption information necessary for publication. The same caption information also appears above each photo in the gallery you are viewing. the original files are all 8x10 on the longest side and 300 dpi resolution for printing.Read More
166 / 216

subset: commoncrawl


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0.65 Ct Round 5mm Red Garnet Heart Shape Silver Pendant With 18" Silver Chain
Contact Seller
Product Description
Astrological Sign: Capricorn, AquariusMeaning: Purity, TruthHealing properties of Garnet: The Garnet is known to cleanse and purify when held over the thyroid and spleen. When searching or meditating on past lives the garnet is usually held in the hand or placed on top of the head. The Garnet represents truth and purity and is also well known to be a symbol of love and compassion. Helps with self esteem and security and increases spiritual awareness. It can also help increase the sex drive.Sources of Garnet: Africa, Central Australia (location of the largest garnet ever found), India, Soviet Union, Brazil and the United States.Interesting Facts: The Garnet is known as the stone for a successful business. If your business is not meeting its potential it is said to put 3 or more garnets on your desk.Garnets under your pillow are believed to cure depression. Garnets assist with self-esteem and bring consistency to friendships when worn as jewelry. More so, Garnets are said to protect one on trips.
- Gem Type: Red Garnet
- Total Carat Weight: 0.65
- Cut: Round
- Color: Red
- Clarity:
- Gram Weight: 1.60 grams
- Metal Type:925 Sterling Silver
- Measurements: 3/4 Inch Red Garnet:5.00MM
- Estimated Retail Price: $95.00
- Cut : Round
- Fine/Fashion : Fashion
- Finish : Polished
- Gender : Female
- Jewelry Material : Silver
- Main Stone : Garnet
- Metal Weight (g) : 1.60 grams
- Pearl Dyed : false
- Stone Count : NaN
- Stone Creation Method : natural
- Total Stone Weight (ct) : 0.65
- Weight (g) : 1.60 grams
|Gem Stone King
|Gem Stone King
|Base SKU
Frequently Asked Questions
Shipping Options:
We offer a 30 day Full Refund return policy. Your 100% Satisfaction is our highest priority.
Please keep the following in mind:
* We DO NOT charge a restocking fee for returns
* You have 30 days from the day you receive the item to request a return merchandise authorization (RMA) number
* Please do not ship your item back to us prior to obtaining an RMA number
To obtain a RMA number please send us an email at firstname.lastname@example.com


text:
product description
Related Products:
Misc Makers
3. Single Grit Waterstones
5. Medium Grit Waterstones
7. Natural Waterstones
Sharpening Stones
Sharpening and Maintenance Items
Maker: Misc Makers (click to see more by this maker)
Price: $48.70
Item num: 88049
Item weight: 85.00 oz.Size: 220x70x60mm/8.6"x2-3/4"x2-1/3"
Description: This large Natural Japanese waterstone comes from Kyushu Island, Japan. It includes a mix of grits ranging from 700 - 1000 grit on the Japanese scale. It is well suited for beginning to sharpen knives that have dulled so long as there are no large chips or nicks. It removes metal fairly quickly without leaving an overly deep scratch pattern. I have been using one in my sharpening service and have been very happy with its performance. This stone should be followed by a medium grit stone such as the Aoto Blue Stone (#2500 Grit).
Unlike comparable manmade stones, the natural Amakusa waterstone leaves a shallower scratch which seems a bit easier to polish out on finer stones. Spending a little extra time on the Amakusa reduces time required on finer stones.
Dimensions are approx 8.6" long X 2-3/4" wide X 2-1/3" tall. This is a naturally occurring stone and no two are exactly the same size.
We recommend using a stone holder to keep the stone from slipping while sharpening and to raise the stone above the table's surface.
Availability: In stock. Usually ships in 1-2 business days


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(new versions of linux will open up VIM when you enter VI..which is what we'll be dealing with here)
A win32 version is available Here.
linux help and man files are very informative...but not very helpful if you're new to linux. when i read the vim man file for the first time i could swear i saw things like..."to capitolize the second letter of the forth word in every third line spin your chair around three time then punch the keyboard". so for the longest time i would just install joe or pico
below is all you really need to know to use VI/VIM to view/edit ascii files. of course once you've learned to use it there are many more commands and options that will help you use it well. VIM It is a very powerful tool but being as this is for 'basic survival' we will not be dealling with the advanced stuff.
Viewing/Editing files:
if you want to view the contents of a file using vim simply type 'vi filenane' at the prompt. filename being the name of the file you wish to open. If the file is in a directory other than the one you are in the path must be included with the file name. You are now in 'VIEW' mode and no changes can be made.
if you wish to edit this file you'll need to enter 'insert mode' by hitting the 'insert' key on the keyboard. you wll see --INSERT-- appear at the bottom left on your screen. you can now make all the changes you need. use the cursor (arrow) keys on the keyboard to navigate to where you want to make the changes in the document and simply type, delete, whatever.
when you've finished viewing and/or editing you need to return to view mode...this is done by pressing the 'Esc' key. you'll notice --INSERT-- will be gone.
Quitting VI:
so if you find yourself typing in a file you didn't want to be typing in simply enter :qa! and no harm will have been doneCode:if no changes have been made :q and press enter to save changes :wq and press enter quit and not save :qa! and press enter
NOTE: the ':' must be typed along with the letter/s of the command
Creating Files:
The easiest way to creat a new file is simply add the name you want to give the new file as an argument to vi (vi newfilename), enter insert mode, put what you want into the file, switch to view mode (Esc) then save the changes (:wq). a simple ls will show newfile listed there and a 'cat' will show the text you added are in that file.
you can also create a new file by just opening vim, entering insert mode, put in what you want, return to view mode (Esc) then put the name you want to give this file after the write/quit command (:wq newfile).
there is one more feature id like to cover. although its a little beyond survival it can make life allot easier.
if your need to change one string a long .conf or script... while in view mode type the string preceeded by a foward slash (/somestring). as you are typing you'll notice the letters typed are being highlighted at the first location that contains them all. when you get to the full string where you want to make the change, hit enter to be in insert mode at the spot. make your changes then write and quit.
To get help while in insert mode hit <F1>, while in view mode use either F1 or enter :h
ok! let's do a quick exercise.
at the prompt enter 'vi test' (without the quotes). Now hit Insert and type 'this is not a test'. get out of insert mode by pressing 'Esc' the save and quit by entering ':wq' (no quotes...anywhere)
you should be back at the prompt.
now again type vi test. you'll find the text you typed earlier has indeed been saved in the file called test that you created.
now type '/not' hit enter then hit insert. hit del three times then type 'just'. press 'Esc' to leave insert mode, save the changes and exit
a quick 'cat test' should show you your changed sentence.
congrats! your now a vi user. well not a very advanced one but a user just the sam and we got to start somewhere.


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RADWIN 2000 A-Series Software License Key for Capacity Upgrade from 25Mbps to 50Mbps, CAPACITY/P2550/A-Series/25M-50M
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Established in 1997, BSC is a premier reseller of New and Refurbished Data Networking, Voice and Video Communication products. Our specialty is Wireless Networking Systems and Components. We stock thousands of items in our 20,000 square foot warehouse facility.
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This week in Island history
The news of 10 and 15 years ago is from the Jamestown Press. The news of 100 years ago came from the collection of the Newport Historical Society.
100 years ago From the Newport Daily News, Dec. 16, 1909
The movers took advantage of the vacant lot on Howland Avenue in moving the Catholic church, and turned it around so that in going across Narragansett Avenue it will go over the cellar dug there without being turned.
From the Newport Daily News, Dec. 20, 1909
There is another holdup in the moving of the Catholic church. The building was left at the foot of Howland Avenue Saturday night and was to be taken across Narragansett Avenue today, thus obstructing the main thoroughfare on the island for one day, but this morning, when nearly across the street, the telephone company's men, who were to cut the wires, were not on hand and the movers were obliged to stop work for the day.
75 years ago From the Newport Daily News, Dec. 14, 1934
The old ferry boat Mohegan, now owned by Henry H. Brownell of this city (Newport), went ashore on the rocks of Block Island Thursday night and is considered a total loss. The boat, with engines and deck houses removed, was purchased by Mr. Brownell from the Jamestown and Newport Ferry Company last summer. He has been using the hull for storage of fishing gear and his catches, and for sleeping quarters, at Greenport, Long Island. Towed by two small motor boats, the Mohegan was being brought to Newport for the winter…
News has been received from Washington that Conanicut 4-H Club has been selected as the outstanding club on Home Improvement 4-H works in Rhode Island, and has requested that a member of the club be sent to New York to broadcast over the National hookup at 12:30 on Jan. 5, during the "Farm and Home" hour. Miss Elizabeth Chesboro (sic), a prominent member of the club, has been chosen and will leave Jan. 4.
50 years ago From the Newport Daily News, Dec. 14, 1959
Members of Captain Kidd's Pieces of Eight, Sea Horses and Captain Kidd's Treasures 4-H Clubs met at the home of their leader, Mrs. Prescott D. Froberg, on Saturday afternoon. William G. Barber, Eastern Rhode Island County 4-H agent, presented the 4-H charters to the clubs.
From the Newport Daily News, Dec. 16, 1959
Jamestown should and probably will be represented in the future composition of the R.I. Turnpike and Bridge Authority, its chairman, Francis G. Dwyer, said today.
From the Newport Daily News, Dec. 18, 1959
Jamestown Bridge traffic and receipts are increasing, the Bridge Commission was told yesterday. The vehicle count for the first 16 days in December was 3,294, or 24 percent ahead of the same period last year. Receipts were $873.83, or 17 percent, ahead. …The committee ordered 12,000 fishing and map folders, costing about $1,000, for distribution. The commission authorized Christmas lighting at the toll plaza.
25 years ago From the Newport Daily News, Dec. 19, 1984
The 10th annual Christmas pageant will be held Christmas Eve at 5:30 p.m. at Shoreby Hill green.
From the Newport Daily News, Dec. 20, 1984
(photo caption) Artist's rendering shows concrete design for new Jamestown Bridge. Clarke-Fitzpatrick Inc., of Williams Park, N.Y., submitted low bid ($63.9 million) for project using concrete design rather than steel.
15 years ago From the Jamestown Press, Dec. 15, 1994
The new senior Center at the Grange Hall on West Street will be getting a used fire-alarm system worth about $3,500 free of cost to the town. The Town Council voted unanimously Monday to make the donation.
Three options for a bike path from North Main Road to the new ball field at the corner of Eldred Avenue and East Shore Road have been given to the Town Council for consideration.
The dwindling water supply in North Pond reservoir may be augmented within the next few months by water from a nearby well drilled deep into the island's bedrock. Town Council members voted Monday to pay no more than $10,000 to drill a test well just south of the reservoir dam on the pond's east side.
10 years ago From the Jamestown Press, Dec. 16, 1999
Santa Claus will stop by the Jamestown Fire Station to visit with island youngsters tonight beginning at 6 p.m.
Beginning next month, the Jamestown Philomenian Library will start opening for business on Sundays. The first day of the Sunday library hours, from 1 to 5 p.m., will be Jan. 23.
The annual Penguin Plunge, one of Jamestown's biggest events, will go off as usual on New Year's Day, unless the Y2K bug bites us and we are plunged into a state of emergency.


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Stamping plate
Package Content:
1 unit of Stamping Nail Art Image Plate
- Includes 1 large design made up of various sized designs.
- The stainless steel plate measures 6 x 12 cm
- Each plate comes in its own branded protective sleeve.
- The designs are engraved on to the image plate and covered with a protective film which needs to be removed before use.
Warning : kindly handle gently as metal plates may be pointy/sharp on delicate fingers
How to stamp:
1) Remove the blue protective film from intended stamping plate.
2) Apply the Nail Polish of your choice to the design you wish to stamp on a stamping plate template.
3) Remove the excess nail polish with Scraper using a 45 degree angle.
4) Roll the Stamper over the selected design being careful not to use too much pressure.
5) Transfer the design by rolling the Stamper over your nail.
6) Apply a top coat for a longer lasting result.
7) Lastly you may clean the stamping plates with nail polish remover.
Note: Recommended to use small stamper to transfer small designs (1.5-2cm) and bigger stamper(2.7cm) for big designs
Additional products need to be purchased separately for example a Nail Art Stamper, Scraper and Nail Varnish.


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Changing pot laws prompt child-endangerment review
DENVER (AP) — Marijuana's changing legal status is complicating matters in family law courts.
The drug remains illegal federally, but its growing acceptance is making it more complicated to resolve custody and child-endangerment disputes that involve marijuana.
No data exist to show how often pot use comes up in custody disputes, or how often child-welfare workers intervene in homes where marijuana is used.
But law enforcement and marijuana activists agree that the drug is increasingly popping up in family law. A pot plant in the basement may not bring criminal charges in many states. But the same plant can become a piece of evidence in child custody or abuse cases.
Colorado lawmakers earlier this year considered updating child-endangerment statutes. But the efforts were abandoned as too complicated.
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|Monrovia, Md.
|High School:
2011: Enters his sophomore season looking to build on the outstanding success he obtained as a freshman ... is a smooth player with outstanding skill ... possesses great vision, which allows him to set up teammates in positive scoring positions ... will be a key component to York's overall success this season.
2010: Played in all 16 Spartans contests during his rookie campaign ... made a significant splash in his first season, totaling 35 points ... distributed a team-best 26 assists, which proved the highest single-season total in the history of the program ... scored nine goals on the year ... tallied one game-winning goal ... scored two man-advantage goals ... picked up 30 groundballs ... caused five turnovers.
Personal: is a business management major ... is the son of Dave and Christy Lowe ... was born on July 30, 1991 ... was the 2009 men's lacrosse Frederick Gazzette Player of the Year ... was a first-team all-area selection ... names his brothers, Chris and Mike, as the people he most admires ... hobbies include lifting, Netflix, playing Super Smash Brothers, chilling with friends, and relaxing ... favorite athlete is Connor Martin ... chose York because of the great athletic facility and the small class sizes ... most significant athletic achievement was reaching the Maryland 3A State Championship game ... favorite athletic moment while at York was a come behind victory against Marymount in 2010 ... after graduation he plans to attend business school.


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Our Furry Friends
In 2012, we introduced you to hundreds of beautiful homes, and the lovely, stylish, and warm people who inhabit them. But sometimes, it was the non-human occupants who really stole the show. From puppies to kitties to some more unusual companions, here are some of our favorite pets of 2012.
Click on the homeowner's name to see more of their home (and their pets)!
1. Jamie's Boston terrier Penelope
2. Isabelle's Airedale
3. Chad's sleepy dog Dutch
4. Michael's fluffy pup
5. Michelle's chocolate Lab Beau
6. One of RJ and Francis' adorable Shih Tzus
7. Apartment Therapy contributor Liana's pup Luna
8. Bert & David's Pug Sophie
9. Samuel's Corgi Denver
10. Matt & Ben's adorable white pup
11. Knoxy's pup Edie
12. Erin & Rob's adorably grumpy bulldog Brother Bear
13. Sam & Anne's Vizla pup Indiana
14. Wendy's Boston terrier Oscar
15. Wendy & Gavin's two pugs Olive and Bear
Cats & Other Critters:
1. Shannon's cat Messi
2. Joseph & Brad's cat Olivia
3. Apartment Therapy Contributor Adrienne's cat Angus
4. Jennifer's feline sidekick Capone
5. One of Shiva Rose's pet bunnies
6. Rustam's feline roommate
7. Clytie & Claudia's cozy cat
8. Amber's black and white cat Pigeon
9. In the barnyard at Lauren & Paul's Enchanted Urban Farmhouse
10. One of the inhabitants of Jules & Henry's 'Modern Menagerie' Loft
(Images: See linked posts for full image credits)


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VATICAN CITY — Catholic cosmophiles will want to know about a special Mass being celebrated in Rome's Basilica of St. Mary of the Angels and Martyrs this Sunday to mark the 445th anniversary of the birth of Galileo Galilei. It's just one of a number of initiatives the Vatican is involved in to commemorate the International Year of Astronomy.
Archbishop Gianfranco Ravasi, president of the Pontifical Council for Culture, will preside over the Mass, which starts at noon.
Members of the Switzerland-based World Federation of Scientists have been invited to attend and a number of Chinese scientists will be present, according to the federation's press release.
The Chinese participants are also going to present a bronze statue, presumably of Galileo. Another special guest will be the Russian explorer of the North Pole, Arthur Chilingarov.
After the Mass, people can visit a special exhibit in the basilica, which was the last one constructed by Michelangelo. It was built between 1563 and 1566 amid the ancient ruins of the Baths of Diocletian.
The show will feature Galileo's major discoveries and inventions such as a re-creation of the pendulum and the inclined plane. There will also be photographic display panels and film footage of interesting events and experiments. For example, visitors can watch a video of U.S. astronaut David Scott conduct Galileo's famous objects-fall-at-the same-rate experiment.
Galileo discovered that all objects released together fall at the same rate regardless of mass, like the 10-pound weight and the one-pound weight he reportedly sent careening down off the Leaning Tower of Pisa. Commander of the Apollo XV mission to the moon, David Scott, dropped a feather and a hammer at the same time on the moon and, because there is no air resistance on the moon, they hit the ground at the same time.
Did you know that the Basilica of St. Mary of the Angels also houses a famous meridian calendar?
Cardinal William Keeler (who is the titular cardinal of the basilica) and the Archdiocese of Baltimore helped find donors and collect funds for the restoration of the basilica's glass dome in 2001. The dome's lantern has stained-glass panels, prisms and blown-glass spheres that reveal the seasons and the time of day by the way sunlight enters and falls on the basilica floor.
Sunlight is diffused over a circle on the floor during the spring and autumn and concentrated on one-half of the circle during the summer and winter.
Another Rome meridian? St. Peter's Square and the obelisk. Read this great article by Vatican astronomer Jesuit Brother Guy Consolmagno to find out more!


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INGLEWOOD, Calif. (April 4, 2012)— A stakes winner each of the last two years at Betfair Hollywood Park, Smiling Tiger continued to prepare for his 5-year-old debut Wednesday morning.
The multiple graded stakes winning sprinter worked five furlongs over Cushion Track in 59 seconds, the best of 28 works at the distance.
Owned by Alan Klein and Phil Lebherz and trained by Jeff Bonde, Smiling Tiger won the Grade III Lazaro S. Barerra Memorial Stakes during the 2010 Spring/Summer meet before capturing the Grade I Ancient Title during the Oak Tree/Hollywood Park meet later that year.
In 2011, the son of Hold That Tiger won another Grade I locally, easily taking the Triple Bend Handicap in gate-to-wire fashion. Among his victims that day was eventual Breeders' Cup Sprint winner and Eclipse champion Amazombie.
Out of the Cahill Road mare Shandra Smiles, Smiling Tiger, who could surface in races like the $100,000 Los Angeles Handicap (May 28) and a defense of his title in the Triple Bend (June 30) during the Spring/Summer meet, has won eight of 18 and banked $1,214,353.
Copyright © 2009-2012, Hollywood Park. All rights reserved. Site design by Love Has No logic Design Group


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Finding Milwaukee spa deals is so easy it may be the best kept secret in your local area! Whether you are seeking a day of relaxation for yourself or looking for a perfect gift for that special friend, relative, or significant other in your life, Milwaukee spa coupons are there to make sure you can find what you're looking for at a fraction of the normal price.
So what services do spas offer that might be included in Milwaukee spa deals? First of all, spas specialize in different areas. An express spa is likely to have shorter services that you can enjoy briefly before heading back to work, school, or the kids. These spas are meant to give short, intensive bursts of refreshment.
Milwaukee spa discounts on express spas will likely include coupons for rapid manicures, basic pedicures, and express facials.
A rapid manicure is a stripped down version of a full manicure. Treating the hands with moisturizer, shaping the nails, and applying a quick drying coat of polish to make them shine is all that you need some days to feel your best. The same is true for a basic pedicure. After a brief hot water soak, your feet will be exfoliated and massaged with lotion. Polish is applied quickly and then you can be on your way with happy toes! Also, an express facial will give you a quick cleanse and exfoliation to bring out your best complexion. Milwaukee spa deals will get you the best price on these quick, revitalizing services.
Standard day spas are more time consuming, but their services are definitely worth the planning and time! Try a relaxing hour long massage or hot stone service. The Swedish modality of massage is the most relaxing and more popular of all spa massage services. However hot stone massage is also a great way to get a deep, warming penetration to all your muscles. Both of these techniques help improve your overall comfort and sense of well being.
Full spas also offer body waxing for almost every area of the body. Legs can be made silky smooth by removing all hair with wax. This will also leave the skin satiny smooth and feeling great. Hot wax not only removes hair, it also helps to reduce the overall growth of hair in the areas waxed over time.
Check out all the great spa services available to you today!


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|« 2009 (v61)
|2011 (v63) »
| On the Asymptotic Behavior of Complete Kähler Metrics of Positive Ricci Curvature
Anchouche, Boudjemâa
Let $( X,g) $ be a complete noncompact Kähler manifold, of dimension $n\geq2,$ with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that $X$ can be compactified, i.e., $X$ is biholomorphic to a quasi-projective variety$.$ The aim of this paper is to prove that the $L^{2}$ holomorphic sections of the line bundle $K_{X}^{-q}$ and the volume form of the metric $g$ have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kähler metric $g$ and of the Fubini--Study metric induced on $X$. In the case of $\dim_{\mathbb{C} }X=2,$ we establish a relation between the number of components of the divisor $D$ and the dimension of the groups $H^{i}( \overline{X}, \Omega_{\overline{X}}^{1}( \log D) )$.
| Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential
Bouchekif, Mohammed; Nasri, Yasmina
In this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of $\mathbb{R}^N$. By variational methods we study the existence results.
| Branching Rules for Ramified Principal Series Representations of $\mathrm{GL}(3)$ over a $p$-adic Field
Campbell, Peter S.; Nevins, Monica
We decompose the restriction of ramified principal series representations of the $p$-adic group $\mathrm{GL}(3,\mathrm{k})$ to its maximal compact subgroup $K=\mathrm{GL}(3,R)$. Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in $K$. We establish several irreducibility results and illustrate the decomposition with some examples.
| An Algebraic Approach to Weakly Symmetric Finsler Spaces
Deng, Shaoqiang
In this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann--Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions $2$ and $3$. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. This means that reversible non-Berwaldian Finsler spaces with vanishing S-curvature may exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces.
| Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces
Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre
We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in $L^{p}$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.
| The Langlands Correspondence on the Generic Irreducible Constituents of Principal Series
Kuo, Wentang
Let $G$ be a connected semisimple split group over a $p$-adic field. We establish the explicit link between principal nilpotent orbits and the irreducible constituents of principal series in terms of $L$-group objects.
| Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues
Li, Chi-Kwong; Poon, Yiu-Tung
Let $A$ and $B$ be $n\times n$ complex Hermitian (or real symmetric) matrices with eigenvalues $a_1 \ge \dots \ge a_n$ and $b_1 \ge \dots \ge b_n$. All possible inertia values, ranks, and multiple eigenvalues of $A + B$ are determined. Extension of the results to the sum of $k$ matrices with $k > 2$ and connections of the results to other subjects such as algebraic combinatorics are also discussed.
| Some Applications of the Perturbation Determinant in Finite von Neumann Algebras
Makarov, Konstantin A.; Skripka, Anna
In the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements $H_0$ and $H$ in the algebra and relate it to the concept of the de la Harpe--Skandalis homotopy invariant determinant associated with piecewise $C^1$-paths of operators joining $H_0$ and $H$. We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman--Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier--Fuglede--Kadison differentiation formula.
| Special Values of Class Group $L$-Functions for CM Fields
Masri, Riad
Let $H$ be the Hilbert class field of a CM number field $K$ with maximal totally real subfield $F$ of degree $n$ over $\mathbb{Q}$. We evaluate the second term in the Taylor expansion at $s=0$ of the Galois-equivariant $L$-function $\Theta_{S_{\infty}}(s)$ associated to the unramified abelian characters of $\operatorname{Gal}(H/K)$. This is an identity in the group ring $\mathbb{C}[\operatorname{Gal}(H/K)]$ expressing $\Theta^{(n)}_{S_{\infty}}(0)$ as essentially a linear combination of logarithms of special values $\{\Psi(z_{\sigma})\}$, where $\Psi\colon \mathbb{H}^{n} \rightarrow \mathbb{R}$ is a Hilbert modular function for a congruence subgroup of $SL_{2}(\mathcal{O}_{F})$ and $\{z_{\sigma}: \sigma \in \operatorname{Gal}(H/K)\}$ are CM points on a universal Hilbert modular variety. We apply this result to express the relative class number $h_{H}/h_{K}$ as a rational multiple of the determinant of an $(h_{K}-1) \times (h_{K}-1)$ matrix of logarithms of ratios of special values $\Psi(z_{\sigma})$, thus giving rise to candidates for higher analogs of elliptic units. Finally, we obtain a product formula for $\Psi(z_{\sigma})$ in terms of exponentials of special values of $L$-functions.
| Mutually Aposyndetic Decomposition of Homogeneous Continua
Prajs, Janusz R.
A new decomposition, the mutually aposyndetic decomposition of homogeneous continua into closed, homogeneous sets is introduced. This decomposition is respected by homeomorphisms and topologically unique. Its quotient is a mutually aposyndetic homogeneous continuum, and in all known examples, as well as in some general cases, the members of the decomposition are semi-indecomposable continua. As applications, we show that hereditarily decomposable homogeneous continua and path connected homogeneous continua are mutually aposyndetic. A class of new examples of homogeneous continua is defined. The mutually aposyndetic decomposition of each of these continua is non-trivial and different from Jones' aposyndetic decomposition.
| Interior $h^1$ Estimates for Parabolic Equations with $\operatorname{LMO}$ Coefficients
Tang, Lin
In this paper we establish a priori $h^1$-estimates in a bounded domain for parabolic equations with vanishing $\operatorname{LMO}$ coefficients.
| The General Definition of the Complex Monge--Ampère Operator on Compact Kähler Manifolds
Xing, Yang
We introduce a wide subclass ${\mathcal F}(X,\omega)$ of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well defined and the convergence theorem is valid. We also prove that ${\mathcal F}(X,\omega)$ is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.
| A Second Order Smooth Variational Principle on Riemannian Manifolds
Azagra, Daniel; Fry, Robb
We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.
| Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials
Chiang, Yik-Man; Ismail, Mourad E. H.
No abstract.
| On the Spectrum of the Equivariant Cohomology Ring
Goresky, Mark; MacPherson, Robert
If an algebraic torus $T$ acts on a complex projective algebraic variety $X$, then the affine scheme $\operatorname{Spec} H^*_T(X;\mathbb C)$ associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector space $H_2^T(X;\mathbb C).$ In many situations the ordinary cohomology ring of $X$ can be described in terms of this arrangement.
| Self-Maps of Low Rank Lie Groups at Odd Primes
Grbić, Jelena; Theriault, Stephen
Let G be a simple, compact, simply-connected Lie group localized at an odd prime~p. We study the group of homotopy classes of self-maps $[G,G]$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H[G,G]$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.
| Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators
Hua, He; Yunbai, Dong; Xianzhou, Guo
Let $\mathcal H$ be a complex separable Hilbert space and ${\mathcal L}({\mathcal H})$ denote the collection of bounded linear operators on ${\mathcal H}$. In this paper, we show that for any operator $A\in{\mathcal L}({\mathcal H})$, there exists a stably finitely (SI) decomposable operator $A_\epsilon$, such that $\|A-A_{\epsilon}\|<\epsilon$ and ${\mathcal{\mathcal A}'(A_{\epsilon})}/\operatorname{rad} {{\mathcal A}'(A_{\epsilon})}$ is commutative, where $\operatorname{rad}{{\mathcal A}'(A_{\epsilon})}$ is the Jacobson radical of ${{\mathcal A}'(A_{\epsilon})}$. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang.
| Some Rigidity Results Related to Monge—Ampère Functions
Jerrard, Robert L.
The space of Monge-Ampère functions, introduced by J. H. G. Fu, is a space of rather rough functions in which the map $u\mapsto \operatorname{Det} D^2 u$ is well defined and weakly continuous with respect to a natural notion of weak convergence. We prove a rigidity theorem for Lagrangian integral currents that allows us to extend the original definition of Monge-Ampère functions. We also prove that if a Monge-Ampère function $u$ on a bounded set $\Omega\subset\mathcal{R}^2$ satisfies the equation $\operatorname{Det} D^2 u=0$ in a particular weak sense, then the graph of $u$ is a developable surface, and moreover $u$ enjoys somewhat better regularity properties than an arbitrary Monge-Ampère function of $2$ variables.
| Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs
Král', Daniel; Máčajová, Edita; Pór, Attila; Sereni, Jean-Sébastien
It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration $C_{14}$. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations. Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective non-affine point-transitive Steiner triple system S.
| Verma Modules over Quantum Torus Lie Algebras
Lü, Rencai; Zhao, Kaiming
Representations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras $\mathfrak{L}_q$. The center of $\mathfrak{L}_q$ now is generally infinite dimensional.
| On p-Adic Properties of Central L-Values of Quadratic Twists of an Elliptic Curve
Prasanna, Kartik
We study $p$-indivisibility of the central values $L(1,E_d)$ of quadratic twists $E_d$ of a semi-stable elliptic curve $E$ of conductor $N$. A consideration of the conjecture of Birch and Swinnerton-Dyer shows that the set of quadratic discriminants $d$ splits naturally into several families $\mathcal{F}_S$, indexed by subsets $S$ of the primes dividing $N$. Let $\delta_S= \gcd_{d\in \mathcal{F}_S} L(1,E_d)^{\operatorname{alg}}$, where $L(1,E_d)^{\operatorname{alg}}$ denotes the algebraic part of the central $L$-value, $L(1,E_d)$. Our main theorem relates the $p$-adic valuations of $\delta_S$ as $S$ varies. As a consequence we present an application to a refined version of a question of Kolyvagin. Finally we explain an intriguing (albeit speculative) relation between Waldspurger packets on $\widetilde{\operatorname{SL}_2}$ and congruences of modular forms of integral and half-integral weight. In this context, we formulate a conjecture on congruences of half-integral weight forms and explain its relevance to the problem of $p$-indivisibility of $L$-values of quadratic twists.
| Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk
Sun, Shunhua; Zheng, Dechao; Zhong, Changyong
In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.
| On Hankel Forms of Higher Weights: The Case of Hardy Spaces
Sundhäll, Marcus; Tchoundja, Edgar
In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundhäll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
| The Chowla—Selberg Formula and The Colmez Conjecture
Yang, Tonghai
In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
| Goresky—MacPherson Calculus for the Affine Flag Varieties
Yun, Zhiwei
We use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety $\mathcal{F}\ell_G$ generated by degree 2. We use this result to show that the vertices of the moment map image of $\mathcal{F}\ell_G$ lie on a paraboloid.
| Elements of Algebraic Geometry and the Positive Theory of Partially Commutative Groups
Casals-Ruiz, Montserrat; Kazachkov, Ilya V.
The first main result of the paper is a criterion for a partially commutative group $\mathbb G$ to be a domain. It allows us to reduce the study of algebraic sets over $\mathbb G$ to the study of irreducible algebraic sets, and reduce the elementary theory of $\mathbb G$ (of a coordinate group over $\mathbb G$) to the elementary theories of the direct factors of $\mathbb G$ (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group $\mathbb H$. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of $\mathbb H$ has quantifier elimination and that arbitrary first-order formulas lift from $\mathbb H$ to $\mathbb H\ast F$, where $F$ is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.
| Computing Noncommutative Deformations of Presheaves and Sheaves of Modules
Eriksen, Eivind
We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures and the noncommutative deformation theory of modules over algebras due to Laudal.
| More Variations on the Sierpiński Sieve
Hare, Kevin G.
This paper answers a question of Broomhead, Montaldi and Sidorov about the existence of gaskets of a particular type related to the Sierpiński sieve. These gaskets are given by iterated function systems that do not satisfy the open set condition. We use the methods of Ngai and Wang to compute the dimension of these gaskets.
| Whittaker Functions on Real Semisimple Lie Groups of Rank Two
Ishii, Taku
We give explicit formulas for Whittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we compute certain archimedean zeta integrals.
| On the Distribution of Pseudopowers
Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
An x-pseudopower to base g is a positive integer that is not a power of g, yet is so modulo p for all primes $ple x$. We improve an upper bound for the least such number, due to E.~Bach, R.~Lukes, J.~Shallit, and H.~C.~Williams. The method is based on a combination of some bounds of exponential sums with new results about the average behaviour of the multiplicative order of g modulo prime numbers.
| On Locally Uniformly Rotund Renormings in C(K) Spaces
Martínez, J. F.; Moltó, A.; Orihuela, J.; Troyanski, S.
A characterization of the Banach spaces of type $C(K)$ that admit an equivalent locally uniformly rotund norm is obtained, and a method to apply it to concrete spaces is developed. As an application the existence of such renorming is deduced when $K$ is a Namioka--Phelps compact or for some particular class of Rosenthal compacta, results which were originally proved with ad hoc methods.
| Translation Groupoids and Orbifold Cohomology
Pronk, Dorette; Scull, Laura
We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: K-theory and Bredon cohomology for certain coefficient diagrams.
| Reducibility in AR(K), CR(K), and A(K)
Rupp, R.; Sasane, A.
Let $K$ denote a compact real symmetric subset of $\mathbb{C}$ and let $A_{\mathbb R}(K)$ denote the real Banach algebra of all real symmetric continuous functions on $K$ that are analytic in the interior $K^\circ$ of $K$, endowed with the supremum norm. We characterize all unimodular pairs $(f,g)$ in $A_{\mathbb R}(K)^2$ which are reducible. In addition, for an arbitrary compact $K$ in $\mathbb C$, we give a new proof (not relying on Banach algebra theory or elementary stable rank techniques) of the fact that the Bass stable rank of $A(K)$ is $1$. Finally, we also characterize all compact real symmetric sets $K$ such that $A_{\mathbb R}(K)$, respectively $C_{\mathbb R}(K)$, has Bass stable rank $1$.
| The Supersingular Locus of the Shimura Variety for GU(1,s)
Vollaard, Inken
In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for $GU(1,s)$ in the case of an inert prime $p$. Using Dieudonné theory we define a stratification of the corresponding moduli space of $p$-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat--Tits building of a unitary group. In the case of $GU(1,2)$, we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.
| Formal Fibers of Unique Factorization Domains
Boocher, Adam; Daub, Michael; Johnson, Ryan K.; Lindo, H.; Loepp, S.; Woodard, Paul A.
Let $(T,M)$ be a complete local (Noetherian) ring such that $\dim T\geq 2$ and $|T|=|T/M|$ and let $\{p_i\} _{i \in \mathcal I}$ be a collection of elements of T indexed by a set $\mathcal I$ so that $|\mathcal I | < |T|$. For each $i \in \mathcal{I}$, let $C_i$:={$Q_{i1}$,$\dots$,$Q_{in_i}$} be a set of nonmaximal prime ideals containing $p_i$ such that the $Q_{ij}$ are incomparable and $p_i\in Q_{jk}$ if and only if $i=j$. We provide necessary and sufficient conditions so that T is the ${\bf m}$-adic completion of a local unique factorization domain $(A, {\bf m})$, and for each $i \in \mathcal I$, there exists a unit $t_i$ of T so that $p_{i}t_i \in A$ and $C_i$ is the set of prime ideals $Q$ of $T$ that are maximal with respect to the condition that $Q \cap A = p_{i}t_{i}A$.
| Approximation by Dilated Averages and K-Functionals
Ditzian, Z.; Prymak, A.
For a positive finite measure $d\mu(\mathbf{u})$ on $\mathbb{R}^d$ normalized to satisfy $\int_{\mathbb{R}^d}d\mu(\mathbf{u})=1$, the dilated average of $f( \mathbf{x})$ is given by \[ A_tf(\mathbf{x})=\int_{\mathbb{R}^d}f(\mathbf{x}-t\mathbf{u})d\mu(\mathbf{u}). \] It will be shown that under some mild assumptions on $d\mu(\mathbf{u})$ one has the equivalence \[ \|A_tf-f\|_B\approx \inf \{ (\|f-g\|_B+t^2 \|P(D)g\|_B): P(D)g\in B\}\quad\text{for }t>0, \] where $\varphi(t)\approx \psi(t)$ means $c^{-1}\le\varphi(t)/\psi(t)\le c$, $B$ is a Banach space of functions for which translations are continuous isometries and $P(D)$ is an elliptic differential operator induced by $\mu$. Many applications are given, notable among which is the averaging operator with $d\mu(\mathbf{u})= \frac{1}{m(S)}\chi_S(\mathbf{u})d\mathbf{u}$, where $S$ is a bounded convex set in $\mathbb{R}^d$ with an interior point, $m(S)$ is the Lebesgue measure of $S$, and $\chi_S(\mathbf{u})$ is the characteristic function of $S$. The rate of approximation by averages on the boundary of a convex set under more restrictive conditions is also shown to be equivalent to an appropriate $K$-functional.
| General Preservers of Quasi-Commutativity
Dolinar, Gregor; Kuzma, Bojan
Let ${ M}_n$ be the algebra of all $n \times n$ matrices over $\mathbb{C}$. We say that $A, B \in { M}_n$ quasi-commute if there exists a nonzero $\xi \in \mathbb{C}$ such that $AB = \xi BA$. In the paper we classify bijective not necessarily linear maps $\Phi \colon M_n \to M_n$ which preserve quasi-commutativity in both directions.
| An Explicit Treatment of Cubic Function Fields with Applications
Landquist, E.; Rozenhart, P.; Scheidler, R.; Webster, J.; Wu, Q.
We give an explicit treatment of cubic function fields of characteristic at least five. This includes an efficient technique for converting such a field into standard form, formulae for the field discriminant and the genus, simple necessary and sufficient criteria for non-singularity of the defining curve, and a characterization of all triangular integral bases. Our main result is a description of the signature of any rational place in a cubic extension that involves only the defining curve and the order of the base field. All these quantities only require simple polynomial arithmetic as well as a few square-free polynomial factorizations and, in some cases, square and cube root extraction modulo an irreducible polynomial. We also illustrate why and how signature computation plays an important role in computing the class number of the function field. This in turn has applications to the study of zeros of zeta functions of function fields.
| Extrema of Low Eigenvalues of the Dirichlet-Neumann Laplacian on a Disk
Legendre, Eveline
We study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet--Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact $1$-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.
| BMO Functions and Carleson Measures with Values in Uniformly Convex Spaces
Ouyang, Caiheng; Xu, Quanhua
This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbf{T}$, respectively. For $1< q<\infty$ and a Banach space $B$, we prove that there exists a positive constant $c$ such that $$\sup_{z_0\in D}\int_{D}(1-|z|)^{q-1}\|\nabla f(z)\|^q P_{z_0}(z) dA(z) \le c^q\sup_{z_0\in D}\int_{\mathbf{T}}\|f(z)-f(z_0)\|^qP_{z_0}(z) dm(z)$$ holds for all trigonometric polynomials $f$ with coefficients in $B$ if and only if $B$ admits an equivalent norm which is $q$-uniformly convex, where $$P_{z_0}(z)=\frac{1-|z_0|^2}{|1-\bar{z_0}z|^2} .$$ The validity of the converse inequality is equivalent to the existence of an equivalent $q$-uniformly smooth norm.
| Biflatness and Pseudo-Amenability of Segal Algebras
Samei, Ebrahim; Spronk, Nico; Stokke, Ross
We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, $L^1(G)$, and the Fourier algebra, $A(G)$, of a locally compact group~$G$.
| The Brascamp-Lieb Polyhedron
Valdimarsson, Stefán Ingi
A set of necessary and sufficient conditions for the Brascamp--Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank $1$. This complements the result of Barthe concerning the case where the linear maps all have rank $1$. Pushing our analysis further, we describe the case where the maps have either rank $1$ or rank $2$. A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp--Lieb inequality to hold. We present an algorithm which generates such a list.
| Singular Integral Operators and Essential Commutativity on the Sphere
Xia, Jingbo
Let ${\mathcal T}$ be the $C^\ast $-algebra generated by the Toeplitz operators $\{T_\varphi : \varphi \in L^\infty (S,d\sigma )\}$ on the Hardy space $H^2(S)$ of the unit sphere in $\mathbf{C}^n$. It is well known that ${\mathcal T}$ is contained in the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$. We show that the essential commutant of $\{T_\varphi : \varphi \in \operatorname{VMO}\cap L^\infty (S,d\sigma )\}$ is strictly larger than ${\mathcal T}$.
| Reducibility of the Principal Series for Sp~2(F) over a p-adic Field
Zorn, Christian
Let $G_n=\mathrm{Sp}_n(F)$ be the rank $n$ symplectic group with entries in a nondyadic $p$-adic field $F$. We further let $\widetilde{G}_n$ be the metaplectic extension of $G_n$ by $\mathbb{C}^{1}=\{z\in\mathbb{C}^{\times} \mid |z|=1\}$ defined using the Leray cocycle. In this paper, we aim to demonstrate the complete list of reducibility points of the genuine principal series of ${\widetilde{G}_2}$. In most cases, we will use some techniques developed by Tadić that analyze the Jacquet modules with respect to all of the parabolics containing a fixed Borel. The exceptional cases involve representations induced from unitary characters $\chi$ with $\chi^2=1$. Because such representations $\pi$ are unitary, to show the irreducibility of $\pi$, it suffices to show that $\dim_{\mathbb{C}}\mathrm{Hom}_{{\widetilde{G}}}(\pi,\pi)=1$. We will accomplish this by examining the poles of certain intertwining operators associated to simple roots. Then some results of Shahidi and Ban decompose arbitrary intertwining operators into a composition of operators corresponding to the simple roots of ${\widetilde{G}_2}$. We will then be able to show that all such operators have poles at principal series representations induced from quadratic characters and therefore such operators do not extend to operators in $\mathrm{Hom}_{{\widetilde{G}_2}}(\pi,\pi)$ for the $\pi$ in question.
| Multiplicative Isometries and Isometric Zero-Divisors
Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan
For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.
| Revisiting Tietze-Nakajima: Local and Global Convexity for Maps
Bjorndahl, Christina; Karshon, Yael
A theorem of Tietze and Nakajima, from 1928, asserts that if a subset $X$ of $\mathbb{R}^n$ is closed, connected, and locally convex, then it is convex. We give an analogous ``local to global convexity" theorem when the inclusion map of $X$ to $\mathbb{R}^n$ is replaced by a map from a topological space $X$ to $\mathbb{R}^n$ that satisfies certain local properties. Our motivation comes from the Condevaux--Dazord--Molino proof of the Atiyah--Guillemin--Sternberg convexity theorem in symplectic geometry.
| Curvature Bounds for Surfaces in Hyperbolic 3-Manifolds
Breslin, William
A triangulation of a hyperbolic $3$-manifold is L-thick if each tetrahedron having all vertices in the thick part of $M$ is $L$-bilipschitz diffeomorphic to the standard Euclidean tetrahedron. We show that there exists a fixed constant $L$ such that every complete hyperbolic $3$-manifold has an $L$-thick geodesic triangulation. We use this to prove the existence of universal bounds on the principal curvatures of $\pi_1$-injective surfaces and strongly irreducible Heegaard surfaces in hyperbolic $3$-manifolds.
| Functoriality of the Canonical Fractional Galois Ideal
Buckingham, Paul; Snaith, Victor
The fractional Galois ideal is a conjectural improvement on the higher Stickelberger ideals defined at negative integers, and is expected to provide non-trivial annihilators for higher $K$-groups of rings of integers of number fields. In this article, we extend the definition of the fractional Galois ideal to arbitrary (possibly infinite and non-abelian) Galois extensions of number fields under the assumption of Stark's conjectures and prove naturality properties under canonical changes of extension. We discuss applications of this to the construction of ideals in non-commutative Iwasawa algebras.
| Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R.
{Correspondence} between torsion-free connections with {nilpotent skew-symmetric curvature operator} and IP Riemann extensions is shown. Some consequences are derived in the study of four-dimensional IP metrics and locally homogeneous affine surfaces.
| On a Conjecture of S. Stahl
Chen, Yichao; Liu, Yanpei
S. Stahl conjectured that the zeros of genus polynomials are real. In this note, we disprove this conjecture.
| Heegner Points over Towers of Kummer Extensions
Darmon, Henri; Tian, Ye
Let $E$ be an elliptic curve, and let $L_n$ be the Kummer extension generated by a primitive $p^n$-th root of unity and a $p^n$-th root of $a$ for a fixed $a\in \mathbb{Q}^\times-\{\pm 1\}$. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of $E$ over $L_n$ in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.
| The Fundamental Group of $S^1$-manifolds
Godinho, Leonor; Sousa-Dias, M. E.
We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian $S^1$-action. Several examples are presented to illustrate our main results.
| Character Sums to Smooth Moduli are Small
Goldmakher, Leo
Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham--Ringrose and Iwaniec, we improve the Pólya--Vinogradov inequality for characters with smooth conductor.
| Degenerate p-Laplacian Operators and Hardy Type Inequalities on
H-Type Groups
Jin, Yongyang; Zhang, Genkai
Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \operatorname{div}_X (|\nabla_{X} u|^{p-2} \nabla_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$; for $\mathbb G$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.
| Moduli Spaces of Reflexive Sheaves of Rank 2
Kleppe, Jan O.
Let $\mathcal{F}$ be a coherent rank $2$ sheaf on a scheme $Y \subset \mathbb{P}^{n}$ of dimension at least two and let $X \subset Y$ be the zero set of a section $\sigma \in H^0(\mathcal{F})$. In this paper, we study the relationship between the functor that deforms the pair $(\mathcal{F},\sigma)$ and the two functors that deform $\mathcal{F}$ on $Y$, and $X$ in $Y$, respectively. By imposing some conditions on two forgetful maps between the functors, we prove that the scheme structure of e.g., the moduli scheme ${\rm M_Y}(P)$ of stable sheaves on a threefold $Y$ at $(\mathcal{F})$, and the scheme structure at $(X)$ of the Hilbert scheme of curves on $Y$ become closely related. Using this relationship, we get criteria for the dimension and smoothness of $ {\rm M_{Y}}(P)$ at $(\mathcal{F})$, without assuming $ {\textrm{Ext}^2}(\mathcal{F} ,\mathcal{F} ) = 0$. For reflexive sheaves on $Y=\mathbb{P}^{3}$ whose deficiency module $M = H_{*}^1(\mathcal{F})$ satisfies $ {_{0}\! \textrm{Ext}^2}(M ,M ) = 0 $ (e.g., of diameter at most 2), we get necessary and sufficient conditions of unobstructedness that coincide in the diameter one case. The conditions are further equivalent to the vanishing of certain graded Betti numbers of the free graded minimal resolution of $H_{*}^0(\mathcal{F})$. Moreover, we show that every irreducible component of ${\rm M}_{\mathbb{P}^{3}}(P)$ containing a reflexive sheaf of diameter one is reduced (generically smooth) and we compute its dimension. We also determine a good lower bound for the dimension of any component of ${\rm M}_{\mathbb{P}^{3}}(P)$ that contains a reflexive stable sheaf with ``small'' deficiency module $M$.
| Moments of the Critical Values of Families of Elliptic Curves, with Applications
Young, Matthew P.
We make conjectures on the moments of the central values of the family of all elliptic curves and on the moments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of $L$-functions. Notably, we predict that the critical values of all rank $1$ elliptic curves is logarithmically larger than the rank $1$ curves in the positive rank family.
| A Fractal Function Related to the John-Nirenberg Inequality for $Q_{\alpha}({\mathbb R^n})$
Yue, Hong
A borderline case function $f$ for $ Q_{\alpha}({\mathbb R^n})$ spaces is defined as a Haar wavelet decomposition, with the coefficients depending on a fixed parameter $\beta>0$. On its support $I_0=[0, 1]^n$, $f(x)$ can be expressed by the binary expansions of the coordinates of $x$. In particular, $f=f_{\beta}\in Q_{\alpha}({\mathbb R^n})$ if and only if $\alpha<\beta<\frac{n}{2}$, while for $\beta=\alpha$, it was shown by Yue and Dafni that $f$ satisfies a John--Nirenberg inequality for $ Q_{\alpha}({\mathbb R^n})$. When $\beta\neq 1$, $f$ is a self-affine function. It is continuous almost everywhere and discontinuous at all dyadic points inside $I_0$. In addition, it is not monotone along any coordinate direction in any small cube. When the parameter $\beta\in (0, 1)$, $f$ is onto from $I_0$ to $[-\frac{1}{1-2^{-\beta}}, \frac{1}{1-2^{-\beta}}]$, and the graph of $f$ has a non-integer fractal dimension $n+1-\beta$.
| Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces
Alzati, Alberto; Besana, Gian Mario
Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.
| Valuations for Matroid Polytope Subdivisions
Ardila, Federico; Fink, Alex; Rincón, Felipe
We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
| Quantum Cohomology of Minuscule Homogeneous Spaces III. Semi-Simplicity and Consequences
Chaput, P. E.; Manivel, L.; Perrin, N.
We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at $q=1$, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized at the quantum parameter. We check that this involution coincides with the strange duality defined in our previous article. We deduce Vafa--Intriligator type formulas for the Gromov--Witten invariants.
| Holomorphic variations of minimal disks with boundary on a Lagrangian surface
Chen, Jingyi; Fraser, Ailana
Let $L$ be an oriented Lagrangian submanifold in an $n$-dimensional Kähler manifold~$M$. Let $u \colon D \to M$ be a minimal immersion from a disk $D$ with $u(\partial D) \subset L$ such that $u(D)$ meets $L$ orthogonally along $u(\partial D)$. Then the real dimension of the space of admissible holomorphic variations is at least $n+\mu(E,F)$, where $\mu(E,F)$ is a boundary Maslov index; the minimal disk is holomorphic if there exist $n$ admissible holomorphic variations that are linearly independent over $\mathbb{R}$ at some point $p \in \partial D$; if $M = \mathbb{C}P^n$ and $u$ intersects $L$ positively, then $u$ is holomorphic if it is stable, and its Morse index is at least $n+\mu(E,F)$ if $u$ is unstable.
| A Generalized Poisson Transform of an $L^{p}$-Function over the Shilov Boundary of the $n$-Dimensional Lie Ball
El Wassouli, Fouzia
Let $\mathcal{D}$ be the $n$-dimensional Lie ball and let $\mathbf{B}(S)$ be the space of hyperfunctions on the Shilov boundary $S$ of $\mathcal{D}$. The aim of this paper is to give a necessary and sufficient condition on the generalized Poisson transform $P_{l,\lambda}f$ of an element $f$ in the space $\mathbf{B}(S)$ for $f$ to be in $ L^{p}(S)$, $1 > p > \infty.$ Namely, if $F$ is the Poisson transform of some $f\in \mathbf{B}(S)$ (i.e., $F=P_{l,\lambda}f$), then for any $l\in \mathbb{Z}$ and $\lambda\in \mathbb{C}$ such that $\mathcal{R}e[i\lambda] > \frac{n}{2}-1$, we show that $f\in L^{p}(S)$ if and only if $f$ satisfies the growth condition $$ \|F\|_{\lambda,p}=\sup_{0\leq r < 1}(1-r^{2})^{\mathcal{R}e[i\lambda]-\frac{n}{2}+l}\Big[\int_{S}|F(ru)|^{p}du \Big]^{\frac{1}{p}} < +\infty. $$
| Canonical Toric Fano Threefolds
Kasprzyk, Alexander M.
An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are $674,\!688$ such varieties.
| Iwahori--Hecke Algebras of $SL_2$ over $2$-Dimensional Local Fields
Lee, Kyu-Hwan
In this paper we construct an analogue of Iwahori--Hecke algebras of $\operatorname{SL}_2$ over $2$-dimensional local fields. After considering coset decompositions of double cosets of a Iwahori subgroup, we define a convolution product on the space of certain functions on $\operatorname{SL}_2$, and prove that the product is well-defined, obtaining a Hecke algebra. Then we investigate the structure of the Hecke algebra. We determine the center of the Hecke algebra and consider Iwahori--Matsumoto type relations.
| On Some Explicit Constructions of Finsler Metrics with Scalar Flag Curvature
Mo, Xiaohuan; Yu, Changtao
We give an explicit construction of polynomial (of arbitrary degree) $(\alpha,\beta)$-metrics with scalar flag curvature and determine their scalar flag curvature. These Finsler metrics contain all non-trivial projectively flat $(\alpha,\beta)$-metrics of constant flag curvature.
| Holomorphie des opérateurs d'entrelacement normalisés à l'aide des paramètres d'Arthur
Mœglin, C.
In this paper we prove holomorphy for certain intertwining operators arising from the theory of Eisenstein series. To do that we need to normalize using the Langlands--Shahidi's normalization arising from the twisted endoscopy and the associated representations of the general linear group.
| Homotopy Self-Equivalences of 4-manifolds with Free Fundamental Group
Pamuk, Mehmetcik
We calculate the group of homotopy classes of homotopy self-equivalences of $4$-manifolds with free fundamental group and obtain a classification of such $4$-manifolds up to $s$-cobordism.
| Characterizations of Extremals for some Functionals on Convex Bodies
Saroglou, Christos
We investigate equality cases in inequalities for Sylvester-type functionals. Namely, it was proven by Campi, Colesanti, and Gronchi that the quantity $$ \int_{x_0\in K}\cdots\int_{x_n\in K}[V(\textrm{conv}\{x_0,\dots,x_n\})]^pdx_0\cdots dx_n , n\geq d, p\geq 1 $$ is maximized by triangles among all planar convex bodies $K$ (parallelograms in the symmetric case). We show that these are the only maximizers, a fact proven by Giannopoulos for $p=1$. Moreover, if $h$: $\mathbb{R}_+\rightarrow \mathbb{R}_+$ is a strictly increasing function and $W_j$ is the $j$-th quermassintegral in $\mathbb{R}^d$, we prove that the functional $$ \int_{x_0\in K_0}\cdots\int_{x_n\in K_n}h(W_j(\textrm{conv}\{x_0,\dots,x_n\}))dx_0\cdots dx_n , n \geq d $$ is minimized among the $(n+1)$-tuples of convex bodies of fixed volumes if and only if $K_0,\dots,K_n$ are homothetic ellipsoids when $j=0$ (extending a result of Groemer) and Euclidean balls with the same center when $j>0$ (extending a result of Hartzoulaki and Paouris).
| BMO-Estimates for Maximal Operators via Approximations of the Identity with Non-Doubling Measures
Yang, Dachun; Yang, Dongyong
Let $\mu$ be a nonnegative Radon measure on $\mathbb{R}^d$ that satisfies the growth condition that there exist constants $C_0>0$ and $n\in(0,d]$ such that for all $x\in\mathbb{R}^d$ and $r>0$, ${\mu(B(x,\,r))\le C_0r^n}$, where $B(x,r)$ is the open ball centered at $x$ and having radius $r$. In this paper, the authors prove that if $f$ belongs to the $\textrm {BMO}$-type space $\textrm{RBMO}(\mu)$ of Tolsa, then the homogeneous maximal function $\dot{\mathcal{M}}_S(f)$ (when $\mathbb{R}^d$ is not an initial cube) and the inhomogeneous maximal function $\mathcal{M}_S(f)$ (when $\mathbb{R}^d$ is an initial cube) associated with a given approximation of the identity $S$ of Tolsa are either infinite everywhere or finite almost everywhere, and in the latter case, $\dot{\mathcal{M}}_S$ and $\mathcal{M}_S$ are bounded from $\textrm{RBMO}(\mu)$ to the $\textrm {BLO}$-type space $\textrm{RBLO}(\mu)$. The authors also prove that the inhomogeneous maximal operator $\mathcal{M}_S$ is bounded from the local $\textrm {BMO}$-type space $\textrm{rbmo}(\mu)$ to the local $\textrm {BLO}$-type space $\textrm{rblo}(\mu)$.


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21 U.S. Code § 206 - Revocation of license
The license of any person whose permanent allegiance is due to the United States to practice pharmacy in the consular districts of the United States in China may be revoked by the consul if such person be found to have obtained such license by fraud, or be addicted to the use of any narcotic or stimulant, or to be suffering from physical or mental disease, in such manner and to such extent as to render it expedient that in the interests of the public his license be canceled; or to be of an immoral character; or if such person be convicted in any court of competent jurisdiction of any offense involving moral turpitude. It shall be the duty of the consul to investigate any case in which it is discovered by him or made to appear to his satisfaction that any license issued under the provisions of this chapter is revocable and shall, after full hearing, if in his judgment the facts warrant it, revoke such license.
LII has no control over and does not endorse any external Internet site that contains links to or references LII.


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Philadelphia, PA -- Fr. Frank Pavone, national director of Priests for Life, issued the following statement today in response to new data from the Pennsylvania Department of Health about decreasing abortion rates in the state.
"The numbers of abortions continue to go down," stated Fr. Pavone. "We should avoid the temptation to oversimplify the explanations for this decrease, but we should all be happy about it and should recommit ourselves to creating alternatives to abortion and educating the public regarding what abortion is."
Explaining plans for the future, Fr. Pavone stated the following: "Starting in October, Priests for Life will launch an aggressive educational campaign about the most common abortion procedures, simply exposing the details through court testimony of practicing abortionists and medical textbooks and diagrams. That is enough for most people to reject the procedure altogether."
Priests for Life is the nation's largest Catholic pro-life organization dedicated to ending abortion and euthanasia. For more information, visit www.priestsforlife.org.


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You already know that the Florida-based Championship Fighting Alliance has the hottest roster of ring girls out of any regional MMA promotion. So why don't we get to know one of these ladies a little better today? Nicole Mejia is a model/actress based in Fort Lauderdale, who is also a full-time nursing student when she's not holding round cards for CFA and traveling around the world for modeling gigs. She's of Columbian and Italian descent, has been modeling for about two years, and enjoys working out and dancing.
Check out a glorious hand-picked selection of Nicole Mejia photos in our gallery above, and get to know her even better on her Facebook and Twitter pages.


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Yesterday Happened: Remembering H.M.
Yesterday Happened: Remembering H.M.
YESTERDAY HAPPENED: REMEMBERING H.M. at Central Square Theater
World Premiere Presented by Catalyst Collaborative@MIT
April 12 - May 13, 2012
Catalyst Collaborative@MIT, a science-theater collaboration between Underground Railway Theater and MIT, presents the World Premiere of YESTERDAY HAPPENED: REMEMBERING H.M., written and directed by Wesley Savick, running April 12 through May 13, 2012. The press performance for YESTERDAY HAPPENED: REMEMBERING H.M. is Sunday, April 15 at 2PM.
At the age of 27, Henry Molaison became frozen in time. After experimental brain surgery, H.M. (as he was known to the scientific community) was unable to form new memories. His personal tragedy became neuroscience's golden opportunity, contributing more to our understanding of the brain than had been learned in the previous 100 years. A scientific detective story, YESTERDAY HAPPENED: REMEMBERING H.M. explores the mysteries of his moving story, expanding on them and helping us understand ourselves.
After suffering from increasingly worse and more debilitating epilepsy from age 16, Henry Molaison underwent a bilateral medial temporal lobe resection by Dr. William Beecher Scoville. After the surgery, H.M. suffered from anterograde amnesia: the inability to form new declarative memories. A declarative memory (also known as an explicit memory) is any memory that is consciously recalled - knowledge that a person knows they recall - information, experiences or acquaintances. His amnesia was "pure," and his case initiated modern memory research. H.M. was studied by scientists from after the surgery in 1953 until his death in 2008 at age 82.
This World Premiere of YESTERDAY HAPPENED: REMEMBERING H.M. has been created in conversation between scientists who studied H.M. as well as inspired by transcripts from research studies. There are sections of the play that are word-for-word accounts of interactions between scientists and H.M., including tests that led to remarkable new discoveries about the nature of memory. Some events in the play are based on verbatim conversations with H.M., they and include phrases that he would often be heard to say, such as "I'm having a conversation with myself."
Like the scientists who studied him, playwright/director Wesley Savick also wanted to get inside H.M.'s head, but, as he explains, "I could only gain access indirectly, through documentation, remembrances, data and, ultimately, through imagination and empathy." In other words, he found invention necessary to explore H.M.'s personal experience. "We need to assume that scientific data alone can't account for the life of this man… Henry Molaison was a man with above-average intelligence. He had feelings and dreams. He could not remember whether or not the pants in his closet were his own, but I nevertheless had to assume that he had a complex and rich experience of his own life."
Last month, excerpts from YESTERDAY HAPPENED: REMEMBERING H.M. were performed at the American Academy of Arts & Sciences, followed by a panel including Dr. Suzanne Corkin, Professor of Behavioral Neuroscience at MIT. Dr. Corkin worked with H.M. from 1964 until his death in 2008. She recognized playwright Wesley Savick and his creative team: "I want to give kudos to Wes Savick and his collaborators for dedicating so many months to getting to know Henry and slipping inside his brain so they could understand what he was feeling each time he said, 'You see, I don't remember things.'"
The story of H.M. is rife with paradox. He was the most studied man in the history of medical science, yet completely incapable of knowing how famous he was. He was incapable of personal change, yet he profoundly changed our understanding of memory. He could not retain names or new vocabulary, and yet he sustained a life-long addiction to crossword puzzles. His story is not only strange - it is also deeply moving. H.M. was a man on whom a terrible tragedy was perpetrated, yet he was above all concerned that, from his experience, "people would learn something."
The play is structured as a weave of encounters with H.M. as he deals with the perils of everyday life, relates his dreams and even sings. Other artists exploring H.M.'s experience join the ensemble of actors: a pianist improvising a soundtrack of his imaginings and a projectionist trying to visualize his mental images.
Wesley Savick (Playwright & Director) served as Artistic Director of the internationally acclaimed experimental company, Theatre X in Milwaukee, Interim Artistic Director of the Drama League of New York's Directors Project, Artistic Associate of Chicago's Organic Theatre and Resident Guest Director of the DARTS/Subaru Theatre in Tokyo, Japan. Mr. Savick has directed or acted in over 80 professional productions, almost all new works, including world premieres by Christopher Durang, Shel Silverstein, Derek Walcott, Howard Zinn and Robert Brustein. He has also written, co-written or adapted 20 produced plays, including Car Talk: The Musical!!! (with original music by Michael Wartofsky), opening this June at Central Square Theater. He is also the Founding Director of The National Theatre of Allston, a new company devoted to original, avant-garde, political work. Mr. Savick is a tenured Professor at Suffolk University.
About the Cast
Barlow Adamson (Henry Molaison) most recently appeared in Time Stands Still at the Lyric Stage Company of Boston. Other credits include: Arms and the Man, Private Lives and Noises Off (Lyric Stage Company); Almost Maine, Reckless, Fuddy Meers and Theater District (SpeakEasy Stage Company); The Maiden's Prayer and A Month in the Country (Huntington Theatre Company); On The Verge (The Nora Theatre Company); Dinner With Friends, Table Manners and Living Together (Gloucester Stage Company); The Real Inspector Hound (Publick Theatre Boston); and Tuesdays With Morrie (Worcester Foothills Theatre). He is an Artistic Associate of the Mill 6 Collaborative, serving as Director for Bunbury: A Serious Play for Trivial People, The Monster Tales and Shakespeare's R+J.
Steven Barkhimer (Ensemble) appeared in Underground Railway Theater's production of The Life of Galileo, directed by David Wheeler, as well as Alice's Adventures Underground and Einstein's Dreams. Most recently, he has been seen as Max in Superior Donuts (Lyric Stage Company of Boston) as well as Feste in Twelfth Night (Actors' Shakespeare Project), Norman in Alan Ayckbourn's Living Together (Gloucester Stage Company) and a homicidal border guard in Suzan Lori Parks' Book of Grace (Company One). He can be seen as the HBO producer in the motion picture The Fighter.
Anna Kohler (Ensemble) is a member of the Music and Theater Arts faculty at MIT. Ms. Kohler studied acting and directing at the Conservatory for Art and Drama and Mozarteum University of Salzburg. She received her degree in Acting and Aesthetic Studies at the Université IIIV Vincennes in Paris after studying mime with Etienne Decroux. Since joining the NYC experimental theater scene in1982, she has worked on stage with Stuart Sherman, John Jesurun, Richard Foreman, Fiona Templeton and Werner Herzog. She is an associate member of the Wooster Group. She has also worked with Steve Buscemi and Mark Boone Jr.. Her solo performance, D' Arc-ness, premiered at Amsterdam's Triple X Festival. More recently, she has toured Europe with Ode to the Man Who Kneels, written and directed by Richard Maxwell. She appeared in movies by Jonathan Demme, Peter Sellars and Hal Hartley. Her directing work has been shown in Salzburg; Kiel, Germany; Saõ Paulo and New York City.
Debra Wise (Ensemble, Artistic Director of Underground Railway Theater, Co-Director of Catalyst Collaborative@MIT) is a founding member of Underground Railway Theater and has served as Artistic Director since 1998. She has been involved in the collaborative creation of over 30 new works as performer, playwright, director and/or dramaturg. Ms. Wise is also Artistic Co-Director of Catalyst Collaborative@MIT, an initiative pairing theater artists and scientists to create new plays and to frame the production of classic plays with conversation about science and society. From 1997 - 2003, Ms. Wise co-directed the Women on Top Theater Festival of new works by New England women theater artists. She has performed with companies both in New York (The Public Theater and the Ark, with Julie Taymor and Elizabeth Swados) and in Boston. She is Theater Specialist for the Art Works for Schools Program, a collaboration with Harvard's Project Zero, teaching thinking in and through the arts and across the curriculum.
Tae Kim (Pianist), prize winner of Steinway Society Piano Competition and Arlington Young Artist Competition, received a BM from Boston Conservatory and an MM from New England Conservatory. He has gained widespread recognition as an up-and-coming pianist. Born in South Korea, Tae has studied piano since age 4. He has soloed with many ensembles, including Yurodivy Chamber Orchestra, Hemenway Strings and Boston Conservatory Orchestra. Headlined as a "Radiant Glimpse of Talent to Come," the Boston Globe praised his "sparkling performance" of Beethoven's 5th Piano Concerto. Tae also actively participates in chamber and contemporary ensembles, where he has worked with distinguished artists like Suren Bagratuni, Lynn Chang, Hsin-Yuan Huang, Alice Schoenfeld, Brinton Smith as well as Allison Eldredge and Irina Muresanu of The Boston Trio. His interest in contemporary improvisation has led him to collaborate with Tod Machover. Tae's teachers include Jonathan Bass, Bruce Brubaker, Janice Weber and Patricia Zander.
About the Creative Team
Wesley Savick, along with Debra Wise, has assembled a seasoned design team, many of whom have been collaborating and shaping the theatrical experience for the World Premiere of YESTERDAY HAPPENED: REMEMBERING H.M. for over a year. The team includes Justin Townsend (scenic and lighting), Jeff Adelberg (lighting), Tod Machover (composer/sound designer), Gail Astrid Buckley (costumes), Sam Sewell (properties coordinator) and Olivia Sebesky (projections). Dominique D. Burford is the production stage manager.
YESTERDAY HAPPENED: REMEMBERING H.M. plays at Central Square Theater, 450 Massachusetts Avenue in Cambridge, Massachusetts, Thursday, April 12 through Sunday, May 13. Performances are Wednesdays and Thursdays at 7:30PM, Fridays at 8PM, Saturdays at 3PM and 8 PM and Sundays at 2PM. Tickets may be purchased by calling 866.811.4111, at the Central Square Theater box office, or online at CentralSquareTheater.org. For box office hours, group discounts and more information please call 617.576.9278 x210.
Central Square Theater (CST) is a 4-year-old nonprofit organization, created through a groundbreaking partnership between The Nora Theatre Company (The Nora) and Underground Railway Theater (URT). This collaboration has been called a model for the arts community (The Boston Foundation, Culture is our Commonwealth and The National Collaboration Prize), as it has paired two like-minded performing arts organizations in a strategic alliance with the City of Cambridge and MIT, resulting in the development of a state-of-the-art performing arts center in the heart of Central Square. CST has a mission to support its two theaters-in-residence while maintaining a shared vision of artists and audiences creating theater vital to their communities. The Nora and URT have a combined 52-year track record of producing award-winning theater. Located in Central Square, Cambridge, Massachusetts, and steeped in its multiracial, intergenerational, ethnically and economically diverse neighborhoods, the CST theater experience exudes a democratic energy where classes, races and age groups come together to be inspired, entertained and energized.
The balance of Central Square Theater's 2011 - 2012 Season includes the professional premiere of Car Talk: The Musical!!! with book and lyrics by Wesley Savick and original music by Michael Wartofsky (June 14 - July 15, 2012) presented by Underground Railway Theater and Suffolk University.
All productions are performed at Central Square Theater, 450 Massachusetts Avenue, Central Square, Cambridge, Massachusetts. Central Square Theater is accessible to persons with special needs and to those requiring wheelchair seating.
For further information please call 617.576.9278 x210 or visit CentralSquareTheater.org.
by Wesley Savick
At the age of 27, Henry Molaison became frozen in time. After experimental brain surgery, H.M. (as he was known to the scientific community) was unable to form new memories. His personal tragedy became neuroscience's golden opportunity, contributing more to our understanding of the brain than had been learned in the previous 100 years. A scientific detective story, YESTERDAY HAPPENED: REMEMBERING H.M. explores the mysteries of his moving story, expanding on them and helping us understand ourselves. This World Premiere is being created in conversation between scientists who studied H.M. and artists: playwright Wesley Savick (Einstein's Dreams, Tru Grace), composer Tod Machover, and designer Justin Townsend.
Presented by: Catalyst Collaborative@MIT
Cast: Barlow Adamson, Steven Barkhimer, Anna Kohler, Debra Wise, Tae Kim (pianist)
Director: Wesley Savick
Production Stage Manager: Dominique D. Burford
Design Team: Justin Townsend (Scenic Design), Gail Astrid Buckley (Costume Design), Jeff Adelberg (Lighting Design), Tod Machover (Sound Design & Composer), Sam Sewell (Properties Coordinator), Olivia Sebesky (projections).
Performing at: Central Square Theater, 450 Massachusetts Avenue, Cambridge, MA 02139
Performance Dates: Thursday, April 12 through Sunday, May 13, 2012
Press Performance: Sunday, April 15, 2012 at 2PM
Performance Schedule: Weds. & Thurs. at 7:30PM, Fri. at 8PM, Sat. at 3PM & 8PM, Sun. at 2PM
Run Time: 90 minutes, no intermission
Ticket Prices:
Wednesday, Thursday: $40 adult $35 senior (62+), $15 back row/sides
Friday and Saturday (evenings & matinees), Sunday matinees: $45 adult $40 senior (62+), $15 back row
Students (with University ID): $25, Students (under 18): $15
Student Rush: $20 with valid college ID, day-of-show. Subject to availability
Box Office: (866) 811-4111, CentralSquareTheater.org
Media Information: Nicholas Peterson, (617) 576-9278 x205
Production photos will be available Thursday, April 12, 2012.


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15 U.S. Code § 3201 - Purposes; coverage
This chapter applies to each gas utility in any calendar year, and to each proceeding relating to each gas utility in such year, if the total sales of natural gas by such utility for purposes other than resale exceeded 10 billion cubic feet during any calendar year beginning after December 31, 1975, and before the immediately preceding calendar year.
The requirements of this chapter do not apply to the operations of a gas utility, or to proceedings respecting such operations, to the extent that such operations or proceedings relate to sales of natural gas for purposes of resale.
Before the beginning of each calendar year, the Secretary shall publish a list identifying each gas utility to which this chapter applies during such calendar year. Promptly after publication of such list, each State regulatory authority shall notify the Secretary of each gas utility on the list for which such State regulatory authority has ratemaking authority.
The definition of Secretary in section 2602 of Title 16, Conservation, applies to this section.
LII has no control over and does not endorse any external Internet site that contains links to or references LII.


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Final Fantasy 14: A Realm Reborn tours Gridania
Final Fantasy 14: A Realm Reborn has already offered us a preview of the Black Shroud, but Gridania is a very different place. Come take a wander through the peaceful city and surrounds.
Final Fantasy 14 Online is currently very much offline as it is rejigged as A Realm Reborn, a thorough overhaul of the much criticised MMORPG. It's currently in alpha testing, accessible only to a few community members. Beta and launch have not been dated.
Thanks, Massively.


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With Rockstar Games having already announced the eventual arrival of Grand Theft Auto: Vice City on iOS, they've now outlined the full details including official release date and pricing.
Rather than just releasing an unmodified version, Rockstar Games will be releasing a revised Grand Theft Auto: Vice City and dubbing it the 10th Anniversary Edition. Thanks to the celebratory nature of this release, they've gone ahead and gave it some special love and attention:
This 10th Anniversary Edition brings the full experience of Grand Theft Auto: Vice City to mobile devices, with native high-resolution graphics and several enhancements unique to the iOS and Android platforms including updated character models and lighting effects, new and more precise firing and targeting options, a fully customizable control layout and native support for Retina display devices.
If you've been waiting for this one, your wait will soon be over. Rockstar Games has announced pricing as well, which is set at $4.99 when it arrives in the App Store on December 6th, 2012.
Source: Rockstar Games