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Ahmedabad: Nov 15, 2012
Virender Sehwag blasted his first half century in nearly 10 months and put on an unbeaten century stand with Gautam Gambhir as India made a blazing start on the opening morning of the first Test against England here today.
Sehwag was batting on 79 off only 66 balls, laced with 12 fours and a six while Gambhir remained unconquered on 37 in 103 balls as India went for lunch at 120 for no loss after skipper Mahendra Singh Dhoni opted to bat first at the Sardar Patel Stadium.
The Delhi duo, who had failed to fire in unison for some time, stitched their 11th century stand for the opening wicket and their first in nearly two years. The last century stand between them was the 137 at Centurion Park in second innings of the opening Test against South Africa in December, 2010.
Sehwag and Gambhir started a tad shakily with the latter inside-edging James Anderson close to his stumps for the first of his three boundaries and the former being almost bowled by Stuart Broad while attempting an expansive drive and missing the ball.
However, after Sehwag whipped a ball from Anderson off his hips for his first four in the fifth over, things settled down for the Delhi duo on a bone-dry wicket of a slow pace pitch where the ball hardly rose above shin level unless banged short.
Sehwag packed off Anderson from the attack by smacking him for three fours between third man and covers in the bowler's fourth over while Gambhir struck his second four by turning Broad off his legs. Anderson's opening spell was a costly 4-0-24-0.
The duo's aggressive batting helped India race to 50 in the 12th over and at the end of the first hour, the hosts were 61 without loss, prompting England to summon off-spinner Graeme Swann in place of Broad immediately after the first drinks break. Broad gave away 23 runs in his six-over spell.
Sehwag hit the accurate Tim Bresnan for a couple of boundaries in the off side when the bowler erred in line. The Najafgarh marauder pushed Swann for a single to the off to complete his 50 in 45 balls and 81 minutes.
It was the batsman's 33rd half ton in his 99th Test and the second after his second innings 62 against Australia in the fourth and final Test at Adelaide in January.
Growing in confidence, Sehwag blasted Bresnan for two four and a six over long on in successive balls to further stamp his authority on the proceedings.
Fifteen runs came off the 19th over of the innings as the home team's as well as the partnership's hundred came in the first ball of the next over in 89 minutes. It was the duo's first three-figure stand after 26 innings.
Bresnan, after his expensive sixth over, was replaced by Broad at the far end of the ground to bowl the 21st over. The pace bowler operated without a slip fielder against Sehwag just before lunch.
Brief Scores: India 120 for no loss (Virender Sehwag 79*, Gautam Gambhir 37*) vs England


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Chicken Scarpariello
To make her Sunday-supper scarpariello—chicken sautéed in a tangy lemon glaze with bell pepper—Fran Parisi always uses a whole chicken cut into pieces, then cooks it on the stove for hours. Grace Parisi opts for faster-cooking boneless thighs and skips the bell pepper in favor of jarred Peppadews, sweet-spicy pickled peppers from South Africa, sold in many US supermarkets.
- Total Time:
- Servings: 4
- 8 small skinless, boneless chicken thighs (2 pounds)
- Salt and freshly ground pepper
- All-purpose flour, for dusting
- 1/2 cup extra-virgin olive oil
- 8 garlic cloves, halved lengthwise and lightly smashed
- 4 large rosemary sprigs, broken into 2-inch pieces
- 2 cups chicken stock or low-sodium broth
- 2 tablespoons fresh lemon juice
- 2 tablespoons unsalted butter
- 1/2 cup Peppadew peppers or other pickled peppers, sliced
How to make this recipe
Season the chicken with salt and pepper and dust with flour. In a large skillet, heat the oil until shimmering. Add the chicken and cook over high heat, turning once, until browned and crusty on both sides, about 10 minutes. Add the garlic and rosemary and cook for 3 minutes, until the garlic is lightly browned. Transfer the chicken to a platter, leaving the rosemary and garlic in the skillet.
Add the stock to the skillet and cook over high heat, scraping up any browned bits, until reduced by half, about 5 minutes. Add the lemon juice and butter and swirl until emulsified. Return the chicken and any accumulated juices to the skillet. Add the peppers and cook, turning the chicken until coated in the sauce, about 3 minutes. Transfer the chicken and sauce to the platter and serve.
Serve With
Crusty bread.
Suggested Pairing
Bright, cherry-rich Chianti Classico.

subset: commoncrawl


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What's New
Please e-mail me updates and font release news!
Rifleman Font by Open Window
What a nice tranquil feeling you get from the wide forms of this font. The air of spontaneity was the most important thing about developing Rifleman. The forms were carefully and slowly constructed and then loosely traced with a paintbrush. Maybe the original drawings will become a font someday but i like to think that they won't for some reason. Surprisingly Rifleman is left to only the bare essential elements, anything that wasn't necessary was left out or removed.
The goal was to make it as lightweight as possible to make up for the intricate detail.
Rifleman is a surprisingly lightweight font offering lends itself to speedy typesetting!
Tags: Distressed, Font, Serif


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Rainbow Tube II is an upgraded American DJ LED color tube. While featuring the same cost as the original Rainbow Tube and the same LED technology, it has been improved with RGB color mixing and 0-100% dimming for more control and more mood-setting options. Suited for illumination of bars, lounges, club foyers, restaurants, architectural applications, and even retail displays, the high output tube is easy to use and more versatile than ever. It can be used two ways: either on its own with ...
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Hufft Projects is a diverse design collective with a passion for quality craftsmanship and a keen interest in the developing roll of the designer and fabricator in the modern world. Our studio is comprised of architects, artists, designers and craftsmen, whose varied mix of experience, backgrounds and areas of expertise help to define Hufft Projects' uniquely holistic approach to design. Our formula is simple- we listen to the needs of our clients and then apply extraordinary amounts of experience, craft and technical innovation to create beautiful and thought provoking design. We view every project and program is a new challenge, so while our basic formula stays the same, our design process is fluid and ever-changing.
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text: Trent Richardson Doesn't Know How Much He Can Bench, Because Trainers Won't Let Him Try More Than 475Sports Radio Interviews11/03/11 4:35pmFiled to: trent richardsonAlabama Crimson TideCollege FootballweightliftingRepublishedSports radio interviewsNewstweetTop241EditPromoteShare to KinjaToggle Conversation toolsGo to permalinkEvery morning, the fine folks at Sports Radio Interviews sift through the a.m. drive-time chatter to bring you the best interviews with coaches, players, and personalities across the sports landscape. Today: Trent Smash!AdvertisementRichardson joined The Dan Patrick Show to talk about not being allowed to bench press more than 475, how good he thinks this year's Alabama team is, how frequently his head coach Nick Saban yells at him, what LSU defender stands out most when watching film in preparation for the Tigers' defense, what he thinks his Heisman chances are, when will he decided if he's going to return to Alabama for his senior season, and why he's leaning at the present moment towards returning for his senior season. How much do you bench press? "I really can't tell you the truth because I really don't know the truth. But I did 475 easy, and they won't let me go above 475."AdvertisementWait, you bench 475? "Yeah I did 475 easily and they won't let me go up."How good is this 'Bama team? "Alabama man, we're good. We're a working team, and that's just something we pride ourselves in and try to get better every day at. And every game we try to show something new and let everybody know and just try to showcase our skills man."How often does Nick Saban yell at you? "He don't yell at me too often, but when he does, it hits me right there in the gut. Because what I'm doing wrong, I need to make sure I don't get that yelling too many times."SponsoredWhich LSU defender stands out the most when watching film of the Tigers' defense? "I mean, they've got a real good safety. He's real good. He comes down hill and makes a lot of their tackles, and he makes them in the box too. So it's almost like…when they're in the nickel, it's like he's playing linebacker, for real. So they've got a real good safety. And Morris Claiborne, he is what he is. He's probably one of the best cornerbacks I've seen in a long time. He's a real good playmaker, he makes a lot of plays out there, and we can't wait to go head-to-head with each other and bump heads; that's going to be a real good collision. I really can't just wait to get out there and have fun with everybody."When do you decide if you're coming back? "Well I haven't made no decisions yet, but I only have like 38 hours left in school and I'm taking 15 now; and I'm going to change my degree. So it's a big chance of me staying here, but that's something you look down the road, because right now I don't have no reason to go nowhere now."AdvertisementSo you're leaning towards staying at Alabama if you had to say today? "Yeah, yeah. I'm not worried about getting to the league. The league's not going nowhere, and right now I just want to play football in college. College football is where it's at right now - it's fun, I'm having fun with it, and college football has been good to me."This post, written by Michael Bean, appears courtesy of Sports Radio Interviews. For the complete highlights of the interview, as well as audio, click here.More from Sports Radio Interviews • Les Miles is letting his team get excited. • Jake Locker likes to watch. • Chauncey Billups doesn't think most players can miss a year of paychecks.Reply24 repliesLeave a reply


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The cowballs just don't get it...very good players don't make a very good team...Romo can't make the big play in a crucial game...there is a reason he went undrafted....
He relies too much on Witten and doesn't go through his progressions. IMO if you want to be a winning QB you need to go to your WR first then TE. Only the Pats can get away with this but they haven't won anything in almost a decade either.
Been in Mexico for the last week but still was able to catch the game (although in Spanish).
I would have hoped he was past this, but then again it was only hope. I've been down on Romo the entire year so I suppose his brain fart wasn't a surprise.
Last edited by Ntegrase96; 01-04-2013 at 12:17 PM.
We have a good group of of young core players Bryant, Murray, Smith, Harris, Claiborne, Carr, Carter, Lee... but the 'talented' staples of the team are getting older and much less effective, and have been overrated for a while now... the young guys? Underrated.
Coaching isn't great, but I'd be okay with sticking with Garrett provided he shows some improvement (I felt he and Ryan did an excellent job with what they had to work with for most of the season).
Can't do anything about Jerry, so I think the best move the Cowboys could make is start grooming another QB to take over for Romo in 2014 when many of the core players I mentioned above will be in their prime.
Poor Dallas. They're hopes are so high every year to win a Super Bowl, let alone make playoffs, and in steps Tony Romo. Sad, sad story. Haha.
nah betch
Maybe his arm got tired in that last game.
Yes... So high. Seems like every year we have the most talent in the league but somehow we don't win it all. Woe is me. Everyone else is lucky and so on and so forth.
End /red
Seriously though, anyone who doesn't think their team has a chance-- what's the point of even watching? And any fan that expects a championship is delusional.


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by Paul Hernandez
"If I can make it there, I'll make it anywhere" — I can practically hear Frank Sinatra singing those words as my imagination conjures them. Why is that song stuck in my head? You might be surprised at first, but I have been hearing this song in my head when I've met some of the New Yorkers served by the Food Bank For New York City.
Sinatra himself clearly had made it in New York. But, I would argue, there are many more people to whom this statement should apply as well: the recipients and beneficiaries of the Food Bank's programs and services.
Many of the people I've met who rely on the Food Bank have lived in New York City for many years, if not their whole lives. We've come to know them and their families through our citywide network of food assistance programs — including our Community Kitchen in Harlem — as well as our tax assistance, food stamp outreach and nutrition and health education programs. And we can certainly attest to the fact that they have "made it" here.
New York City's working poor often find themselves holding down more jobs, for more hours, than is imaginable to many of us — on top of supporting children, attending school and caring for sick or elderly family members. Many of them are bilingual and multi-cultural — both accepting and knowledgeable about peoples and cultures from around the world. They are street smart and personable, reasonable and kind, quick to help and quick to tell someone when they aren't helping. In other words, they're New Yorkers, making it here every day, resting assured that they could make it anywhere, if they so choose.
Paul Hernandez, a recent graduate of Princeton University, works in the Food Bank's Business Partnerships department.
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April 1st, 2012, 08:41 PM | #1 |
90% Restored 1988 K5 Blazer - Lifted 6''
1988 Chevrolet K5 Blazer
Truck is almost fully restored - was done a few years back so it isnt perfect but it is pretty nice. Black with red interior and red pinstriping. Tailgate is wavy but the rest is nice. I have a line on a really nice solid tailgate for $200 6'' Rough country lift kit. All of the fuel injection and wiring has been removed. Swapped in a carburated 355 / th350. Tranny is built, high dollar parts, redline clutches b&m 1900-2300 torque converter. 1/2 ton axels with 4.10 gears Interior is really nice. Factory seats that look like new, guages work. has sunpro 3 pack guage set under dash that works. Has CD mp3 ipod ready deck with pioneer speakers. Indoor / outdoor grey carpet that somehow fits really well. I have 3 sets of tires to work with on the selling price. 35'' mickey thompson atzs with probably 50% tread 33'' bfg mud terrain km1s with 75-80% tread - light weather checking and a mix matched set of 31s on fake beadlocks. all are 75-80% tread - i used them as rollers to get it in and out of the garage. I have a 2nd top for it in good shape - i was going to sand it smooth and paint it to match the blazer - ill sell this seperately or put it with the selling price for $150 I also have a core support, 2 grilles, headlights, and trim to swap the front to a 89-91 style. again will sell this seperately or with the blazer for $100 Have a black brush guard / push bar that will bolt onto it - $75 on the selling price or sell seperately I hate to get rid of this, but I could use the cash in other areas. $4300 obo i am negotiable on the price all depends on what tires i throw in with it and what spare parts do / dont go with it. Pictures will be posted tomorrow (4/2/12) |
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When LeVar Burton reached out to members of the online community to help bring back his PBS children's program Reading Rainbow, it would seem unlike that he would expect the project to have been as successful as it was. Having already reached its one million goal in just a mater of hours.
With this success, the Kickstarter has only expanded, now having passed the $3 million mark, as Burton and his crew have decided to re-adjust their plans with their new-found success.
Hoping to bring long-running, award-winning literacy program to a new, digital generation, Burton has noted on the project's Kickstarter that they are introducing "stretch goals" which will allow the funds earned to expanded their reach to 7,500 classrooms, as well as introduce Reading Rainbow to the web, but also to mobile, Android, consoles and OTT boxes.
More information and details are provided on the Kickstarter page, as well as on their website.
Considering that the project has already earned three times its goal with 31 days still left to go, it is not hard to imagine that Burton will be successful in making these "stretched goals" a reality from "viewers like you."
More details on this should become available in the days to come.
Will Ashton is a staff writer for TheCelebrityCafe.com, as well as contributor for CutPrintFilm. When he's not covering the latest news and reviews, you can hopefully find him with friends as he enjoys the finer things in life.


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#246 Classic Deer Weathervane
24×32 $260.00 Shown without set-up |
24×32 $260.00 shown with set-up (included) |
24×32 $260.00 Shown without set-up |
Measurements are of the weathervane ornament only.
Length by Height
Add 9″ to 12″ for total weathervane height.
Each Classic Weather Vane comes complete with a steel pole, brass ring, brass directionals and two copper balls and is available in either polished or antique finish unless noted.
Please note: Different lighting and camera settings produce varying colors in the polished copper, in the antiqued green patina copper, and in the background. All polished copper pictures on this page are of the same weathervane. All pictures of green patina copper weathervanes are of a different weathervane. I am obviously NOT a professional photographer!
Back to Classic Design Weathervanes
Contact and Ordering Information


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Davis campus. Shelved in the wine cellar at Davis are samples of the U.C. vintages dating back to the 1930s. A number of the quality wines now important in California industry were created in the Department of Viticulture and Enology.
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HERCULES Series Natural Wood Finished Vertical Slat Back Wooden Restaurant Barstool - Burgundy Vinyl Seat
(0)- Wood Barstool
- Vertical Slat Back Design
- Burgundy Vinyl Upholstered Seat
- 2.5'' Thick Foam Padded Seat
- Solid European Beech Hardwood Construction
- Mortise and Tenon Style Construction with metal wood screw reinforcements
- Two Curved Support Bars
- Footrest
- Natural Wood Frame Finish
- Plastic Floor Glides
- CA117 Fire Retardant Foam
- Designed for Commercial Use; Suitable for Home Use
The wood barstool will offer a classic, elegant look when furnishing your establishment. This stool will make an attractive addition to your restaurant, pool hall, lounge, bar or other high traffic venue. This stool is easy to clean, which is an important aspect when it comes to a business. This stool was designed to withstand the daily rigors in the hospitality industry, but will also provide a warm and inviting quality to your home. The thick, foam padded seat will keep users comfortable. The durable Beechwood frame is stabilized using two support bars, which includes a footrest. The floor glides help protect your floors and ensure smooth gliding. This elegantly styled stool will highlight your home or business without disappointment.
Assembled product length | 19 |
Assembled Product Width | 17.5 |
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Seat-Height | 31"H |
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Color | Burgundy, Natural |
Finish | Natural Wood |
Upholstery | Burgundy Vinyl |
Material | Foam, Vinyl, Wood |
Warranty Comments | 2 Years Parts Only |
Assembly Required | Yes |


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Colorado prosecutors have asked a judge to charge accused Aurora movie theater shooter James Holmes with 10 more counts, bringing the total number of charges against him to 152, the Denver Post reported on Wednesday.
Specifics about the new charges and how the others would be changed were not immediately available in the case's court register.
In the motion, prosecutors also asked to amend 17 charges, including 16 attempted murder charges. Judge William Sylvester of the 18th Judicial District must approve the changes, according to the Post.
As it stands, Holmes, 24, faces 142 charges – 24 counts of first-degree murder and 116 counts of attempted murder. He is accused of shooting up a packed movie theater in Aurora, Colo., on July 20. Twelve people were killed and 58 were injured.
Holmes, a former graduate student in neuroscience, allegedly arrived at the midnight showing of the latest Batman movie armed with weapons and explosives.
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Cape Canaveral & on the Seas
Trip Start
Nov 08, 2008
Trip End
Nov 24, 2008
We finally met up with everyone who was going on the cruise and we knew so many folks. The parent of the bride hosted a meet and greet party at the Radisson. We had so much fun meeting everyone. Everybody was in such a great mood and all were visiting like mad. So many pictures were taken, but our camera went for a walk - darn it! Jamie kindly gave us copies of all his pictures though and we were doing most of the same things.
Well the morning came around pretty quickly. Good thing we packed the evening before. We were some of the first to arrive at the port so were able to just kick back for a bit. No rushing - just the way we like it. We were given priority boarding due to the wedding taking place - that was the cat's ass and highly recommend it!
Once we were all onboard up to the 11th deck for brunch as the rooms weren't quite ready (not until 1:00). The wedding was at 1:00, so watched the beautiful bride and groom and their wonderful kids and parents. It was so beautiful. Even had a little tear build up. Didn't feel bad though cause I looked around the room and sure enough others experiencing the same thing. It was short and simple and just perfect!
Ended up heading to our room and having a rest, then unpacking everything. It was good to get settled knowing we weren't going anywhere for a week. A home away from home, only this one has rocking motion!
Met up with Dana & Jamie for a walk about of the ship. This thing is huge-ola. Grabbed a soda insulated cup that gave you pop each day for $48/week. This was the greatest idea cause we used it throughout the trip.
Met everyone in the dining lounge for dinner then went to the casino afterwards. We had such a great group at our dinner table - lots of fun. Sherry & I decided to play some blackjack in the casino with Jamie. Dana just wanted to hang out and watch, then go and explore around. We were having so much fun and winning money to boot! Ended up pocketing US$600 that night. We had mostly non-smokers at our table which was totally refreshing for all of us. Called it a night before midnight cause we were tired from all the traveling, visiting and excitement.
Next day we were at sea so enjoyed hanging out at the poolside watching all the festivities. Explored more of the ship and visited with everyone. Man oh man can Gary's brothers (and daughters) ever partay! I'm so not worthy...heheh.
Dinner was awesome again. This time we decided to join everyone afterwards for some fun times. This was such a fun group to hang with. Folks we haven't hung with before and just had the best of times. Bernie and Gary sure picked a great group for this cruise. Was nice to get to know her family a bit more as well. Decided to hit the pub for a bit, then went to the Dragon's Liar dance club after that. Man oh man was it good to get out on the dance floor. Sherry & I even decided to sandwich this black fella on the dance floor - was he ever smilin! So were we, just fun, fun, fun.
Our group closed down the place and both Sherry & I were exhausted and hungry. I don't know what it is about ships, but eating is a frequent occurence. Room service!!! Gotta love being able to order it 24/7!!


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I hope you get to play as the face hugger in multiplayer. That was fun stuff in AVP 2. Unless the players where cheap and waited for you to burst out of there chest .. Wonder if you can still regain health by eating your victims like in the last game. Anyway, looks like this is coming along nicely. This is a must have title for me.
Written by: T0SH
- Cofounder of PS3Blog.net


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Bern or Berne (bĕrn) [key], canton (1990 pop. 937,365), 2,658 sq mi (6,883 sq km), W central Switzerland. The second most populous and second largest canton of the country, Bern comprises three sections—the Bernese Alps, or Oberland [Ger., = highlands], with many resorts and peaks, notably the Finsteraarhorn and Jungfrau, and with meadows and pastures in the valleys; the Mittelland [midlands], in the fertile northern foothills of the Alps, and including the Emmental; and the lake region around Biel. The Jura canton to the north was until 1979 a part of Bern canton. Tourism, cattle raising, dairying, and hydroelectric power generation are the chief means of livelihood in the Oberland. The Mittelland is the most industrialized region of the canton and a fertile agricultural region. The lake region has a thriving vine culture. The population of the canton is predominantly Protestant and German-speaking.
Bern or
Bern was founded, according to tradition, in 1191 by Berchtold V of Zähringen as a military post. It was made (1218) a free imperial city by Emperor Frederick II when Berchtold died without an heir. Bern grew in power and population and in 1353 joined the Swiss Confederation, of which it became the leading member. Its conquests included Aargau (1415) and Vaud (1536), besides numerous smaller territories. The area was governed until 1798 by an autocratic urban aristocracy. Bern accepted the Reformation in 1528. When Switzerland was invaded (1798) by the French during the French Revolutionary Wars, Bern was occupied, its treasury pillaged, and its territories dismembered. At the Congress of Vienna (1815), Bern failed to recover Vaud and Aargau, but received the Bernese Jura (the former Bishopric of Basel). A liberal constitution was adopted in 1831, and in 1848 Bern became the capital of the Swiss Confederation.
The city is largely medieval in its architecture. It has a splendid 15th-century town hall, a noted minster (begun 15th cent.), and numerous other historic structures. There are many picturesque patrician houses and old guild halls. An elaborate medieval clock tower and a pit in which bears (Bern's heraldic animal for seven centuries) are kept are well known to tourists. More modern buildings include the 19th-century federal parliament building, many fine museums (including one devoted to Paul Klee), and the university (1834).
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.


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The Black Diamond Index Ascender features a trigger release for fast, effortless operation on hard-to-clean pitches and uses an ergonomic, dual-density grip to increase comfort for...Continue Reading
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Written and directed by Joel and Ethan Coen Starring Oscar Isaac, Carey Mulligan, John Goodman, Garret Hudlund, Justin Timberlake and F. Murray Abraham
Nominated for two Academy Awards! Grand Prize of the Jury, 2013 Cannes Film Festival
New York, 1962. The downtown folk scene. Solo singers, duos and trios are playing the Gaslight and cutting and releasing records. And the talented, abrasive Llewyn Davis (Oscar Isaac) is getting beaten to a pulp in the back alley... again. The picaresque and panoramic film, named after the protagonist's no-sell recording debut, ponders the question: how can someone be an angel when he's singing and playing and a miserable lout the instant the music stops? Like all of the greatest films of Joel and Ethan Coen, this one is many things at once: visually and verbally virtuosic, tonally complex, beautifully constructed, peopled with larger-than-life characters and ultimately magical. With Carey Mulligan, Justin Timberlake, Garrett Hedlund, F. Murray Abraham and –unforgettably– John Goodman as a foul-mouthed, bombastic jazz musician. The glorious score of folk standards was loving curated and executive produced by T. Bone Burnett. (Courtesy of New York Film Festival)
DIR/SCR/PROD Joel Coen, Ethan Coen; PROD Olivier Courson, Robert Graf, Ron Halpern, Scott Rudin. US, 2013, color, 105 min. RATED R
Official Website


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Hey all, I am a new glock owner... just picked up my G20. Here are some 'unboxing' photos (I did the actual unboxing before accepting the FFL). The second to last photo is a comparison with my Walther PPQ and the lats photo (from left to right) is 9 mm, .40 S&W, and 10 mm. I'm really excited about it and can't wait to shoot it, and to be an owner of a Glock! Still not sure about popping on a #22 spring and new guide rod; I know this is a heavily debated issue here and on other gun sites. Might be worth 25 bucks just to see!
I've got a G20 too and a few thousand rounds through it. For ordinary weak target ammo the 17 pound spring they come with will work fine. When you step up to somewhat hotter stuff go with a 20, and for really hot stuff like Buffalo Bore or Underwood, use a 22 pounder. 10MM ammo comes in such a wide variety of power levels that there's really no one spring weight that could be considered the one choice for all occasions. Whether you use a metal guide rod or the stock plastic type never changed the way mine performs as far as I can tell. A non-captured metal rod sure makes it easy to change springs quickly if you're only going to have the one rod, but the easiest way to change springs (by far) is just to buy a selection of stock plastic captured rods and just leave the different springs permanently installed on the rods. The extra weight of a metal rod on a G20 really doesn't change the muzzle flip enough to be noticeable. Really hot 10MM ammo DOES need the heavier springs. That's for sure. Weak springs will allow the breech to open to soon and your chrono will show less consistent velocities - meaning many of your shots will have less velocity than they would with the 22 pound spring.
Thanks everybody! I got a chance to finally bring it out to the range today, and it was a blast to shoot! I ran it completely stock (I was only shooting 180 gr plinking ammo). I also picked up a 22 lbs spring. I know there is a lot of controversy here and on other forums about running these springs, but I do plan on shooting 200 gr rounds and such, so I figured it was at least worth a few bucks to play around with.
Welcome to GT and welcome to the G20 club! I have always run a 22# spring when shooting my heavy loads and after 100's of them, I see no reason not too. Light range or comp loads do not require the extra spring weight, so I have a couple of stock spring assemblies around for that. I have close to 10,000 rounds through mine and all I have ever changed is springs. Every other parts seems to work fine even after years of abuse.
Will a 22 lbs recoil spring cycle 180 gr ammo (I use Gerogia Arms for plinking, for example)? I've heard some people say they've shot 9 mm ammo in an aftermarket barrel with a big spring, and other say it wont cycle any of the lighter 10 mm loads. I guess I will just test it myself, but I'm curious about others experiances.
Yes, the 22# spring will still allow your G20 to cycle with lighter loads. The only time I ran into an issue was when I had produced a load so light that it was below .40SW territory. Then the stock assembly worked fine.
Thanks klmmicro... thats sort of what I figured.... but its nice to hear it from somebody who actually runs one. Anyway, I'm very satisfied with this G20, it was definatly 550 dollars well spent!


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Ben Green, Tamar Ziegler, and I have just uploaded to the arXiv our paper "An inverse theorem for the Gowers U^{s+1}[N] norm", which was previously announced on this blog. We are still planning one final round of reviewing the preprint before submitting the paper, but it has gotten to the stage where we are comfortable with having the paper available on the arXiv.
The main result of the paper is to establish the inverse conjecture for the Gowers norm over the integers, which has a number of applications, in particular to counting solutions to various linear equations in primes. In spirit, the proof of the paper follows the 21-page announcement that was uploaded previously. However, for various rather annoying technical reasons, the 117-page paper has to devote a large amount of space to setting up various bits of auxiliary machinery (as well as a dozen or so pages worth of examples and discussion). For instance, the announcement motivates many of the steps of the argument by heuristically identifying nilsequences with bracket polynomial phases such as . However, a rather significant amount of theory (which was already worked out to a large extent by Leibman) is needed to formalise the "bracket algebra" needed to manipulate such bracket polynomials and to connect them with nilsequences. Furthermore, the "piecewise smooth" nature of bracket polynomials causes some technical issues with the equidistribution theory for these sequences. Our original version of the paper (which was even longer than the current version) set out this theory. But we eventually decided that it was best to eschew almost all use of bracket polynomials (except as motivation and examples), and run the argument almost entirely within the language of nilsequences, to keep the argument a bit more notationally focused (and to make the equidistribution theory easier to establish). But this was not without a tradeoff; some statements that are almost trivially true for bracket polynomials, required some "nilpotent algebra" to convert to the language of nilsequences. Here are some examples of this:
- It is intuitively clear that a bracket polynomial phase e(P(n)) of degree k in one variable n can be "multilinearised" to a polynomial of multi-degree in k variables , such that and agree modulo lower order terms. For instance, if (so k=3), then one could take . The analogue of this statement for nilsequences is true, but required a moderately complicated nilpotent algebra construction using the Baker-Campbell-Hausdorff formula.
- Suppose one has a bracket polynomial phase e(P_h(n)) of degree k in one variable n that depends on an additional parameter h, in such a way that exactly one of the coefficients in each monomial depends on h. Furthermore, suppose this dependence is bracket linear in h. Then it is intuitively clear that this phase can be rewritten (modulo lower order terms) as e( Q(h,n) ) where Q is a bracket polynomial of multidegree (1,k) in (h,n). For instance, if and , then we can take . The nilpotent algebra analogue of this claim is true, but requires another moderately complicated nilpotent algebra construction based on semi-direct products.
- A bracket polynomial has a fairly visible concept of a "degree" (analogous to the corresponding notion for true polynomials), as well as a "rank" (which, roughly speaking measures the number of parentheses in the bracket monomials, plus one). Thus, for instance, the bracket monomial has degree 7 and rank 3. Defining degree and rank for nilsequences requires one to generalise the notion of a (filtered) nilmanifold to one in which the lower central series is replaced by a filtration indexed by both the degree and the rank.
There are various other tradeoffs of this type in this paper. For instance, nonstandard analysis tools were introduced to eliminate what would otherwise be quite a large number of epsilons and regularity lemmas to manage, at the cost of some notational overhead; and the piecewise discontinuities mentioned earlier were eliminated by the use of vector-valued nilsequences, though this again caused some further notational overhead. These difficulties may be a sign that we do not yet have the "right" proof of this conjecture, but one will probably have to wait a few years before we get a proper amount of perspective and understanding on this circle of ideas and results.
Ben Green, Tamar Ziegler, and I have just uploaded to the arXiv the note "An inverse theorem for the Gowers norm (announcement)", not intended for publication. This is an announcement of our forthcoming solution of the inverse conjecture for the Gowers norm, which roughly speaking asserts that norm of a bounded function is large if and only if that function correlates with an -step nilsequence of bounded complexity.
The full argument is quite lengthy (our most recent draft is about 90 pages long), but this is in large part due to the presence of various technical details which are necessary in order to make the argument fully rigorous. In this 20-page announcement, we instead sketch a heuristic proof of the conjecture, relying in a number of "cheats" to avoid the above-mentioned technical details. In particular:
- In the announcement, we rely on somewhat vaguely defined terms such as "bounded complexity" or "linearly independent with respect to bounded linear combinations" or "equivalent modulo lower step errors" without specifying them rigorously. In the full paper we will use the machinery of nonstandard analysis to rigorously and precisely define these concepts.
- In the announcement, we deal with the traditional linear nilsequences rather than the polynomial nilsequences that turn out to be better suited for finitary equidistribution theory, but require more notation and machinery in order to use.
- In a similar vein, we restrict attention to scalar-valued nilsequences in the announcement, though due to topological obstructions arising from the twisted nature of the torus bundles used to build nilmanifolds, we will have to deal instead with vector-valued nilsequences in the main paper.
- In the announcement, we pretend that nilsequences can be described by bracket polynomial phases, at least for the sake of making examples, although strictly speaking bracket polynomial phases only give examples of piecewise Lipschitz nilsequences rather than genuinely Lipschitz nilsequences.
With these cheats, it becomes possible to shorten the length of the argument substantially. Also, it becomes clearer that the main task is a cohomological one; in order to inductively deduce the inverse conjecture for a given step from the conjecture for the preceding step , the basic problem is to show that a certain (quasi-)cocycle is necessarily a (quasi-)coboundary. This in turn requires a detailed analysis of the top order and second-to-top order terms in the cocycle, which requires a certain amount of nilsequence equidistribution theory and additive combinatorics, as well as a "sunflower decomposition" to arrange the various nilsequences one encounters into a usable "normal form".
It is often the case in modern mathematics that the informal heuristic way to explain an argument looks quite different (and is significantly shorter) than the way one would formally present the argument with all the details. This seems to be particularly true in this case; at a superficial level, the full paper has a very different set of notation than the announcement, and a lot of space is invested in setting up additional machinery that one can quickly gloss over in the announcement. We hope though that the announcement can provide a "road map" to help navigate the much longer paper to come.
Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our paper "Approximate subgroups of linear groups", submitted to GAFA. This paper contains (the first part) of the results announced previously by us; the second part of these results, concerning expander groups, will appear subsequently. The release of this paper has been coordinated with the release of a parallel paper by Pyber and Szabo (previously announced within an hour(!) of our own announcement).
Our main result describes (with polynomial accuracy) the "sufficiently Zariski dense" approximate subgroups of simple algebraic groups , or more precisely absolutely almost simple algebraic groups over , such as . More precisely, define a -approximate subgroup of a genuine group to be a finite symmetric neighbourhood of the identity (thus and ) such that the product set can be covered by left-translates (and equivalently, right-translates) of .
Let be a field, and let be its algebraic closure. For us, an absolutely almost simple algebraic group over is a linear algebraic group defined over (i.e. an algebraic subvariety of for some with group operations given by regular maps) which is connected (i.e. irreducible), and such that the completion has no proper normal subgroups of positive dimension (i.e. the only normal subgroups are either finite, or are all of . To avoid degeneracies we also require to be non-abelian (i.e. not one-dimensional). These groups can be classified in terms of their associated finite-dimensional simple complex Lie algebra, which of course is determined by its Dynkin diagram, together with a choice of weight lattice (and there are only finitely many such choices once the Lie algebra is fixed). However, the exact classification of these groups is not directly used in our work.
Our first main theorem classifies the approximate subgroups of such a group in the model case when generates the entire group , and is finite; they are either very small or very large.
Theorem 1 (Approximate groups that generate) Let be an absolutely almost simple algebraic group over . If is finite and is a -approximate subgroup of that generates , then either or , where the implied constants depend only on .
The hypothesis that generates cannot be removed completely, since if was a proper subgroup of of size intermediate between that of the trivial group and of , then the conclusion would fail (with ). However, one can relax the hypothesis of generation to that of being sufficiently Zariski-dense in . More precisely, we have
Theorem 2 (Zariski-dense approximate groups) Let be an absolutely almost simple algebraic group over . If is a -approximate group) is not contained in any proper algebraic subgroup of of complexity at most (where is sufficiently large depending on ), then either or , where the implied constants depend only on and is the group generated by .
Here, we say that an algebraic variety has complexity at most if it can be cut out of an ambient affine or projective space of dimension at most by using at most polynomials, each of degree at most . (Note that this is not an intrinsic notion of complexity, but will depend on how one embeds the algebraic variety into an ambient space; but we are assuming that our algebraic group is a linear group and thus comes with such an embedding.)
In the case when , the second option of this theorem cannot occur since is infinite, leading to a satisfactory classification of the Zariski-dense approximate subgroups of almost simple connected algebraic groups over . On the other hand, every approximate subgroup of is Zariski-dense in some algebraic subgroup, which can be then split as an extension of a semisimple algebraic quotient group by a solvable algebraic group (the radical of the Zariski closure). Pursuing this idea (and glossing over some annoying technical issues relating to connectedness), together with the Freiman theory for solvable groups over due to Breuillard and Green, we obtain our third theorem:
Theorem 3 (Freiman's theorem in ) Let be a -approximate subgroup of . Then there exists a nilpotent -approximate subgroup of size at most , such that is covered by translates of .
This can be compared with Gromov's celebrated theorem that any finitely generated group of polynomial growth is virtually nilpotent. Indeed, the above theorem easily implies Gromov's theorem in the case of finitely generated subgroups of .
By fairly standard arguments, the above classification theorems for approximate groups can be used to give bounds on the expansion and diameter of Cayley graphs, for instance one can establish a conjecture of Babai and Seress that connected Cayley graphs on absolutely almost simple groups over a finite field have polylogarithmic diameter at most. Applications to expanders include the result on Suzuki groups mentioned in a previous post; further applications will appear in a forthcoming paper.
Apart from the general structural theory of algebraic groups, and some quantitative analogues of the basic theory of algebraic geometry (which we chose to obtain via ultrafilters, as discussed in this post), we rely on two basic tools. Firstly, we use a version of the pivot argument developed first by Konyagin and Bourgain-Glibichuk-Konyagin in the setting of sum-product estimates, and generalised to more non-commutative settings by Helfgott; this is discussed in this previous post. Secondly, we adapt an argument of Larsen and Pink (which we learned from a paper of Hrushovski) to obtain a sharp bound on the extent to which a sufficiently Zariski-dense approximate groups can concentrate in a (bounded complexity) subvariety; this is discussed at the end of this blog post.
Ben Green, and I have just uploaded to the arXiv a short (six-page) paper "Yet another proof of Szemeredi's theorem", submitted to the 70th birthday conference proceedings for Endre Szemerédi. In this paper we put in print a folklore observation, namely that the inverse conjecture for the Gowers norm, together with the density increment argument, easily implies Szemerédi's famous theorem on arithmetic progressions. This is unsurprising, given that Gowers' proof of Szemerédi's theorem proceeds through a weaker version of the inverse conjecture and a density increment argument, and also given that it is possible to derive Szemerédi's theorem from knowledge of the characteristic factor for multiple recurrence (the ergodic theory analogue of the inverse conjecture, first established by Host and Kra), as was done by Bergelson, Leibman, and Lesigne (and also implicitly in the earlier paper of Bergelson, Host, and Kra); but to our knowledge the exact derivation of Szemerédi's theorem from the inverse conjecture was not in the literature. Ordinarily this type of folklore might be considered too trifling (and too well known among experts in the field) to publish; but we felt that the venue of the Szemerédi birthday conference provided a natural venue for this particular observation.
The key point is that one can show (by an elementary argument relying primarily an induction on dimension argument and the Weyl recurrence theorem, i.e. that given any real and any integer , that the expression gets arbitrarily close to an integer) that given a (polynomial) nilsequence , one can subdivide any long arithmetic progression (such as ) into a number of medium-sized progressions, where the nilsequence is nearly constant on each progression. As a consequence of this and the inverse conjecture for the Gowers norm, if a set has no arithmetic progressions, then it must have an elevated density on a subprogression; iterating this observation as per the usual density-increment argument as introduced long ago by Roth, one obtains the claim. (This is very close to the scheme of Gowers' proof.)
Technically, one might call this the shortest proof of Szemerédi's theorem in the literature (and would be something like the sixteenth such genuinely distinct proof, by our count), but that would be cheating quite a bit, primarily due to the fact that it assumes the inverse conjecture for the Gowers norm, our current proof of which is checking in at about 100 pages…
Ben Green, and I have just uploaded to the arXiv our paper "An arithmetic regularity lemma, an associated counting lemma, and applications", submitted (a little behind schedule) to the 70th birthday conference proceedings for Endre Szemerédi. In this paper we describe the general-degree version of the arithmetic regularity lemma, which can be viewed as the counterpart of the Szemerédi regularity lemma, in which the object being regularised is a function on a discrete interval rather than a graph, and the type of patterns one wishes to count are additive patterns (such as arithmetic progressions ) rather than subgraphs. Very roughly speaking, this regularity lemma asserts that all such functions can be decomposed as a degree nilsequence (or more precisely, a variant of a nilsequence that we call an virtual irrational nilsequence), plus a small error, plus a third error which is extremely tiny in the Gowers uniformity norm . In principle, at least, the latter two errors can be readily discarded in applications, so that the regularity lemma reduces many questions in additive combinatorics to questions concerning (virtual irrational) nilsequences. To work with these nilsequences, we also establish a arithmetic counting lemma that gives an integral formula for counting additive patterns weighted by such nilsequences.
The regularity lemma is a manifestation of the "dichotomy between structure and randomness", as discussed for instance in my ICM article or FOCS article. In the degree case , this result is essentially due to Green. It is powered by the inverse conjecture for the Gowers norms, which we and Tamar Ziegler have recently established (paper to be forthcoming shortly; the case of our argument is discussed here). The counting lemma is established through the quantitative equidistribution theory of nilmanifolds, which Ben and I set out in this paper.
The regularity and counting lemmas are designed to be used together, and in the paper we give three applications of this combination. Firstly, we give a new proof of Szemerédi's theorem, which proceeds via an energy increment argument rather than a density increment one. Secondly, we establish a conjecture of Bergelson, Host, and Kra, namely that if has density , and , then there exist shifts for which contains at least arithmetic progressions of length of spacing . (The case of this conjecture was established earlier by Green; the case is false, as was shown by Ruzsa in an appendix to the Bergelson-Host-Kra paper.) Thirdly, we establish a variant of a recent result of Gowers-Wolf, showing that the true complexity of a system of linear forms over indeed matches the conjectured value predicted in their first paper.
In all three applications, the scheme of proof can be described as follows:
- Apply the arithmetic regularity lemma, and decompose a relevant function into three pieces, .
- The uniform part is so tiny in the Gowers uniformity norm that its contribution can be easily dealt with by an appropriate "generalised von Neumann theorem".
- The contribution of the (virtual, irrational) nilsequence can be controlled using the arithmetic counting lemma.
- Finally, one needs to check that the contribution of the small error does not overwhelm the main term . This is the trickiest bit; one often needs to use the counting lemma again to show that one can find a set of arithmetic patterns for that is so sufficiently "equidistributed" that it is not impacted by the small error.
To illustrate the last point, let us give the following example. Suppose we have a set of some positive density (say ) and we have managed to prove that contains a reasonable number of arithmetic progressions of length (say), e.g. it contains at least such progressions. Now we perturb by deleting a small number, say , elements from to create a new set . Can we still conclude that the new set contains any arithmetic progressions of length ?
Unfortunately, the answer could be no; conceivably, all of the arithmetic progressions in could be wiped out by the elements removed from , since each such element of could be associated with up to (or even ) arithmetic progressions in .
But suppose we knew that the arithmetic progressions in were equidistributed, in the sense that each element in belonged to the same number of such arithmetic progressions, namely . Then each element deleted from only removes at most progressions, and so one can safely remove elements from and still retain some arithmetic progressions. The same argument works if the arithmetic progressions are only approximately equidistributed, in the sense that the number of progressions that a given element belongs to concentrates sharply around its mean (for instance, by having a small variance), provided that the equidistribution is sufficiently strong. Fortunately, the arithmetic regularity and counting lemmas are designed to give precisely such a strong equidistribution result.
A succinct (but slightly inaccurate) summation of the regularity+counting lemma strategy would be that in order to solve a problem in additive combinatorics, it "suffices to check it for nilsequences". But this should come with a caveat, due to the issue of the small error above; in addition to checking it for nilsequences, the answer in the nilsequence case must be sufficiently "dispersed" in a suitable sense, so that it can survive the addition of a small (but not completely negligible) perturbation.
One last "production note". Like our previous paper with Emmanuel Breuillard, we used Subversion to write this paper, which turned out to be a significant efficiency boost as we could work on different parts of the paper simultaneously (this was particularly important this time round as the paper was somewhat lengthy and complicated, and there was a submission deadline). When doing so, we found it convenient to split the paper into a dozen or so pieces (one for each section of the paper, basically) in order to avoid conflicts, and to help coordinate the writing process. I'm also looking into git (a more advanced version control system), and am planning to use it for another of my joint projects; I hope to be able to comment on the relative strengths of these systems (and with plain old email) in the future.
Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our announcement "Linear approximate groups", submitted to Electronic Research Announcements.
The main result is a step towards the classification of -approximate groups, in the specific setting of simple and semisimple Lie groups (with some partial results for more general Lie groups). For , define a -approximate group to be a finite subset of a group which is a symmetric neighbourhood of the origin (thus and is equal to ), and such that the product set is covered by left-translates (or equivalently, right-translates) of . For , this is the same concept as a finite subgroup of , but for larger values of , one also gets some interesting objects which are close to, but not exactly groups, such as geometric progressions for some and .
The expectation is that -approximate groups are -controlled by "structured" objects, such as actual groups and progressions, though the precise formulation of this has not yet been finalised. (We say that one finite set -controls another if is at most times larger than in cardinality, and can be covered by at most left translates or right translates of .) The task of stating and proving this statement is the noncommutative Freiman theorem problem, discussed in these earlier blog posts.
While this problem remains unsolved for general groups, significant progress has been made in special groups, notably abelian, nilpotent, and solvable groups. Furthermore, the work of Chang (over ) and Helfgott (over ) has established the important special cases of the special linear groups and :
Theorem 1 (Helfgott's theorem) Let and let be either or for some prime . Let be a -approximate subgroup of .
- If generates the entire group (which is only possible in the finite case ), then is either controlled by the trivial group or the whole group.
- If , then is -controlled by a solvable -approximate subgroup of , or by itself. If , the latter possibility cannot occur, and must be abelian.
Our main result is an extension of Helfgott's theorem to for general . In fact, we obtain an analogous result for any simple (or almost simple) Chevalley group over an arbitrary finite field (not necessarily of prime order), or over . (Standard embedding arguments then allow us to in fact handle arbitrary fields.) The results from simple groups can also be extended to (almost) semisimple Lie groups by an approximate version of Goursat's lemma. Given that general Lie groups are known to split as extensions of (almost) semisimple Lie groups by solvable Lie groups, and Freiman-type theorems are known for solvable groups also, this in principle gives a Freiman-type theorem for arbitrary Lie groups; we have already established this in the characteristic zero case , but there are some technical issues in the finite characteristic case that we are currently in the process of resolving.
We remark that a qualitative version of this result (with the polynomial bounds replaced by an ineffective bound ) was also recently obtained by Hrushovski.
Our arguments are based in part on Helfgott's arguments, in particular maximal tori play a major role in our arguments for much the same reason they do in Helfgott's arguments. Our main new ingredient is a surprisingly simple argument, which we call the pivot argument, which is an analogue of a corresponding argument of Konyagin and Bourgain-Glibichuk-Konyagin that was used to prove a sum-product estimate. Indeed, it seems that Helfgott-type results in these groups can be viewed as a manifestation of a product-conjugation phenomenon analogous to the sum-product phenomenon. Namely, the sum-product phenomenon asserts that it is difficult for a subset of a field to be simultaneously approximately closed under sums and products, without being close to an actual field; similarly, the product-conjugation phenomenon asserts that it is difficult for a union of (subsets of) tori to be simultaneously approximately closed under products and conjugations, unless it is coming from a genuine group. In both cases, the key is to exploit a sizeable gap between the behaviour of two types of "pivots" (which are scaling parameters in the sum-product case, and tori in the product-conjugation case): ones which interact strongly with the underlying set , and ones which do not interact at all. The point is that there is no middle ground of pivots which only interact weakly with the set. This separation between interacting (or "involved") and non-interacting (or "non-involved") pivots can then be exploited to bootstrap approximate algebraic structure into exact algebraic structure. (Curiously, a similar argument is used all the time in PDE, where it goes under the name of the "bootstrap argument".)
Below the fold we give more details of this crucial pivot argument.
One piece of trivia about the writing of this paper: this was the first time any of us had used modern version control software to collaboratively write a paper; specifically, we used Subversion, with the repository being hosted online by xp-dev. (See this post at the Secret Blogging Seminar for how to get started with this software.) There were a certain number of technical glitches in getting everything to install and run smoothly, but once it was set up, it was significantly easier to use than our traditional system of emailing draft versions of the paper back and forth, as one could simply download and upload the most recent versions whenever one wished, with all changes merged successfully. I had a positive impression of this software and am likely to try it again in future collaborations, particularly those involving at least three people. (It would also work well for polymath projects, modulo the technical barrier of every participant having to install some software.)
This is an adaptation of a talk I gave recently for a program at IPAM. In this talk, I gave a (very informal and non-rigorous) overview of Hrushovski's use of model-theoretic techniques to establish new Freiman-type theorems in non-commutative groups, and some recent work in progress of Ben Green, Tom Sanders and myself to establish combinatorial proofs of some of Hrushovski's results.
Ben Green, Tamar Ziegler and I have just uploaded to the arXiv our paper "An inverse theorem for the Gowers norm". This paper establishes the next case of the inverse conjecture for the Gowers norm for the integers (after the case, which was done by Ben and myself a few years ago). This conjecture has a number of combinatorial and number-theoretic consequences, for instance by combining this new inverse theorem with previous results, one can now get the correct asymptotic for the number of arithmetic progressions of primes of length five in any large interval .
To state the inverse conjecture properly requires a certain amount of notation. Given a function and a shift , define the multiplicative derivative
and then define the Gowers norm of a function to (essentially) be the quantity
where we extend f by zero outside of . (Actually, we use a slightly different normalisation to ensure that the function 1 has a norm of 1, but never mind this for now.)
Informally, the Gowers norm measures the amount of bias present in the multiplicative derivatives of . In particular, if for some polynomial , then the derivative of is identically 1, and so is the Gowers norm.
However, polynomial phases are not the only functions with large Gowers norm. For instance, consider the function , which is what we call a quadratic bracket polynomial phase. This function isn't quite quadratic, but it is close enough to being quadratic (because one has the approximate linearity relationship holding a good fraction of the time) that it turns out that third derivative is trivial fairly often, and the Gowers norm is comparable to 1. This bracket polynomial phase can be modeled as a nilsequence , where is a polynomial orbit on a nilmanifold , which in this case has step 2. (The function F is only piecewise smooth, due to the discontinuity in the floor function , so strictly speaking we would classify this as an almost nilsequence rather than a nilsequence, but let us ignore this technical issue here.) In fact, there is a very close relationship between nilsequences and bracket polynomial phases, but I will detail this in a later post.
The inverse conjecture for the Gowers norm, GI(s), asserts that such nilsequences are the only obstruction to the Gowers norm being small. Roughly speaking, it goes like this:
Inverse conjecture, GI(s). (Informal statement) Suppose that is bounded but has large norm. Then there is an s-step nilsequence of "bounded complexity" that correlates with f.
This conjecture is trivial for s=0, is a short consequence of Fourier analysis when s=1, and was proven for s=2 by Ben and myself. In this paper we establish the s=3 case. An equivalent formulation in this case is that any bounded function of large norm must correlate with a "bracket cubic phase", which is the product of a bounded number of phases from the following list
for various real numbers .
It appears that our methods also work in higher step, though for technical reasons it is convenient to make a number of adjustments to our arguments to do so, most notably a switch from standard analysis to non-standard analysis, about which I hope to say more later. But there are a number of simplifications available on the s=3 case which make the argument significantly shorter, and so we will be writing the higher s argument in a separate paper.
The arguments largely follow those for the s=2 case (which in turn are based on this paper of Gowers). Two major new ingredients are a deployment of a normal form and equidistribution theory for bracket quadratic phases, and a combinatorial decomposition of frequency space which we call the sunflower decomposition. I will sketch these ideas below the fold.
For a number of reasons, including the start of the summer break for me and my coauthors, a number of papers that we have been working on are being released this week. For instance, Ben Green and I have just uploaded to the arXiv our paper "An equivalence between inverse sumset theorems and inverse conjectures for the norm", submitted to Math. Proc. Camb. Phil. Soc.. The main result of this short paper (which was briefly announced in this earlier post) is a connection between two types of inverse theorems in additive combinatorics, namely the inverse sumset theorems of Freiman type, and inverse theorems for the Gowers uniformity norm, and more specifically, for the norm
on finite additive group G, where is a complex-valued function.
As usual, the connection is easiest to state in a finite field model such as . In this case, we have the following inverse sumset theorem of Ruzsa:
Theorem 1. If is such that , then A can be covered by a translate of a subspace of of cardinality at most .
The constant has been improved for large in a sequence of papers, from by Ruzsa, by Green-Ruzsa, by Sanders, by Green and myself, and finally by Konyagin (private communication) which is sharp except for the precise value of the O() implied constant (as can be seen by considering the example when A consists of about 2K independent elements). However, it is conjectured that the polynomial loss can be removed entirely if one modifies the conclusion slightly:
Conjecture 1. (Polynomial Freiman-Ruzsa conjecture for .) If is such that , then A can be covered by translates of subspaces of of cardinality at most |A|.
This conjecture was verified for downsets by Green and myself, but is open in general. This conjecture has a number of equivalent formulations; see this paper of Green for more discussion. In this previous post we show that a stronger version of this conjecture fails.
Meanwhile, for the Gowers norm, we have the following inverse theorem, due to Samorodnitsky:
Theorem 2. Let be a function whose norm is at least 1/K. Then there exists a quadratic polynomial such that .
Note that the quadratic phases are the only functions taking values in [-1,1] whose norm attains its maximal value of 1.
It is conjectured that the exponentially weak correlation here can be strengthened to a polynomial one:
Conjecture 2. (Polynomial inverse conjecture for the norm). Let be a function whose norm is at least 1/K. Then there exists a quadratic polynomial such that .
The first main result of this paper is
Theorem 3. Conjecture 1 and Conjecture 2 are equivalent.
This result was also independently observed by Shachar Lovett (private communication). We also establish an analogous result for the cyclic group , in which the notion of polynomial is replaced by that of a subexponential , and in which the notion of a quadratic polynomial is replaced by a 2-step nilsequence; the precise statement is a bit technical and will not be given here. We also observe a partial partial analogue of the correpsondence between inverse sumset theorems and Gowers norms in the higher order case, in particular observing that inverse theorems imply a certain rigidity result for "Freiman-quadratic polynomials" (a quadratic version of Conjecture 3 below).
Below the fold, we sketch the proof of Theorem 3.


text:
It's time for this months street style, sadly I didn't come across any stylish boys this week but I shall try harder next month ladies! The majority of these images are of Nottingham Trent Uni freshers as I was there most of the time, but there are a few others mixed in:
Love the splash of neon in this look! |
Beautifully Casual! |
This lovely lady looked amazing, I'd love to see more of her outfits! |
So I've numbered these photos simply to make it easier for you guys when discussing each girls style. I love numbers 3, 10, 13 and of course my big sis in 15! It'd be great to hear if you have a favourite, and if your going to try out any of these styles?
Chelsea Jade


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*This website DOES NOT constitute treatment and only provides information and advice in a Q&A format. For treatment (therapy and/or medications) you must go to a licensed professional in your area. Please note that anything said here is not private or confidential, as this is a public forum.
Hello and thank you for using JustAnswer. May I ask, what is your specific mental health question that you would like an answer to in regards ***** ***** situation?


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Boating in an urban area is tricky, even someplace with as fantastic lakes and waterfronts as Minneapolis. I've always, somehow, found an outlet. A cheap canoe off Craigslist; a shared set of kayaks with a friend; rentals and monthly trips to a lakefront cabin have always kept me on the water.
But I wanted to try my hand at sailing, and that's even trickier. A slip on an urban lake is no small expense, not to mention the price of a lake-worthy boat. The interminable Minnesota winters add the issue of storage and towing – not something my miniscule Honda is prepared for.
So when I heard about the Twin Cities Sailing Club, I was eager to sign up. The popularity meant I had to wait a while, and wake up far too early to mash the refresh button on my browser until the signup form was available. I managed to get in, and paid my dues (less than half the cost of a private slip).
I was enthusiastic to say the least; I even bought a pair of smart new boat shoes with all the money I saved.
The club has a really smart setup. You sail with experienced skippers until you've completed a long list of training requirements, then you have to abide by "the deal:" free access to the club boats as long as you help train new sailors a couple times a month.
When I showed up to my first meeting, I half expected a troop of Kennedy clones with big white teeth and dapper sweaters. Instead (for better or worse) I found a whole group of people just like me – sunscreen slathered urban professionals just excited to be on the water.
My first outing was a great experience, my very patient skipper let me refresh my skills with limited hand holding even though I could sense his distress when I heeled dangerously for my limited skills.
I made a good dent in my path toward being a skipper myself thanks to a little prior knowledge of sailing. But boy do I have to learn the terms – apparently "Duck!" is not sufficient warning when tacking.
I hope to write more about the club as I continue through the process, so stay tuned.


text:
COWBOYS & ALIENS Mondo Poster and Bonus Clips
Cowboys & Aliens Extended Edition arrives on Blu-ray Combo Pack on December 6th. To honor the release, MONDO, the Alamo Drafthouse's collectible art boutique has unveiled their fourth and final COWBOYS & ALIENS poster in their Jon Favreau-curated series.
The print was designed by Florian Bertmer and goes on sale Tuesday, December 6th at http://www.mondotees.com (follow @MondoNews for exact sale time). Check out the full-size image below:
Check out some cool clips from the Blu-ray below. First up is this cool stunts montage that takes you behind the scenes.
Here are some clips of the cast and crew talking about Daniel Craig and Harrison Ford:
Here is a clip that talks about the films classic western style:
No author bio. End of line.


text:
Submit News
LG Buys WebOS From HP for SmartTVs
Jason Mick
February 25, 2013 11:14 AM
Recipient E-mail
Sender E-mail
webOS is back from the dead
The strange saga of webOS has taken
another wild turn
with South Korean electronics giant LG Electronics Inc. (
) purchasing the operating system for an undisclosed price from Hewlett-Packard Comp. (
). LG says it does not plan to use the operating system in smartphones, but rather intends it to form the backbone of
its Smart TV offerings
I. A Troubled History
For a time many smartphone fans consider webOS a potential top contender, when Palm first
unveiled it in January 2009
. The successor to Palm OS, webOS tapped Palm's vast experience in the mobile industry it helped create, with unique features like swipe multi-tasking, Synergy (a service merging info from multiple email accounts, etc.), a complex notifications system and more.
But Palm's mobile efforts
under a sluggish hardware release pace and poor marketing. In April 2010 HP
scooped up Palm
for what seemed like a bargain, and many hoped that would be the start of a turnaround for the beloved, but troubled OS.
Instead, things got worse, with HP driving sales into the ground. Still, when HP
launched webOS printers
and the first webOS tablet --
the TouchPad
-- some hoped that the situation could improve. Instead HP decided to
pull the plug
on the troubled experiment,
firing most of the webOS staff
clearancing off the remaining hardware
HP decision to kill webOS sunk earnings. [Image Source: All About webOS]
New executive Meg Whitman would eventually
agree to open source
key parts of webOS in a move that pleased fans. But she always stated she
wanted to sell the platform
if the right buyer came along.
II. LG -- WebOS is for TVs Not Phones
That buyer appears to be LG. Skott Ahn, president and chief technology officer of LG Electronics states, "It creates a new path for LG to offer an intuitive user experience and Internet services across a range of consumer electronics devices."
LG's webOS team will constitute the webOS/Palm offices in San Jose, Calif. and Chicago, Ill. that HP had held onto. The core team, though, will be located at the new LG Silicon Valley Lab, with its Sunnyvale, Calif. and San Francisco, Calif. locations.
It is unclear how many veterans LG will be able to hang onto. Reportedly, a number of employees jumped ship when the decision to use webOS to move towards smart televisions was announced.
WebOS is back from the dead.
The team will continue to support HP and the former Palm's various webOS products, so the team will hang on to some of its traditional phone responsibilities. But LG made it clear that it is firmly committed to Android on the phone/tablet front, and will not be considering webOS for mobile devices.
Still the decision is a blow to Google Inc. (
) who was hoping to woo LG, one of the world's top TV makers, to use Android in its Smart TVs.
At first blush WebOS on a TV seems a questionable proposition. However, the OS did lend itself well to other embedded environments -- namely HP's smart printers. So perhaps with some TLC webOS may live again in a very different form.
"What would I do? I'd shut it down and give the money back to the shareholders." -- Michael Dell, after being asked what to do with Apple Computer in 1997
Related Articles
LG To Unveil New Refined Smart TV Lineup at CES 2013
December 31, 2012, 10:12 AM
HP Wanted $1.2B "Refund" Via WebOS Sale, Gets Smacked With Reality
December 29, 2011, 1:49 PM
Update: webOS is Going Open Source, Future HP Hardware Still Unlikely
December 9, 2011, 1:52 PM
HP Loses Another WebOS Supporter -- Its CTO
November 1, 2011, 5:53 PM
HP TouchPad Clearance Edition: First Impressions
August 30, 2011, 2:47 PM
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In this horror/suspense anthology picture, a group of co-ed college students meet at their demented psychology professor's house for some extracurricular pointers. The professor gets his kicks in class from scaring his students half to death. Each co-ed has to tell a story which is frightening or upsetting to her. Meanwhile, someone whom the professor really ticked off is out to get him. ~ Clarke Fountain, Rovi
All After Midnight cast + crew photos


text:
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Just saw from George Bremer that Sean Smith form the Dolphins is probably asking to much and will be let go. According to reports he wants 6 years at around 7 per which is what McCourty just signed with Tenn....
Good idea to reunite them?
I like Sean Smith. But he didn't have a great year this past year IIRC?
Are you serious with this comment? Let Bethea go to sign a lesser player lol? Yea that'll happen. Use your head man. Safety is safety, and Bethea could easily play SS and let Byrd play FS. Its a interchangeable position. I know its a different style but its still the same concept. Bethea is a good tackler and hitter and would be great in that spot.
Lucks on our side
Sean Smith at the right price would be a great addition! I know he had an off year but it seems as if Miami is somewhat a mess and maybe that had something to do with his and Long's play????
Bethea could move to SS easily as he is solid against the run....though I would rather have someone who hits like a freight train at SS.
If winning isn't everything, why do they keep score?
Sponsored Links |
Bethea hits pretty hard, just doesnt get credit for them like some others since hes in coverage more often than not.
Lucks on our side
Agreed! Luck has a gun and if they can create a hybrid that takes the best qualities of the WCO and the Vertical passing game....wow! A little more on the subject:
If winning isn't everything, why do they keep score?
Jake Long seeking 10M +
- He runs meetings like a coach. Basically, Im playing with a coordinator on the field. Hes a football God. He sees everything, and he sees the big picture of everything." - Frank Gore on Andrew Luck
- "He is as smart as Peyton, as accurate as Brady, tougher than Ben and as athletic as RG3." - Anonymous Head Coach on Andrew Luck
No really he isn't. He has ended the past two seasons on IR.
http://www.nfl.com/news/story/0ap100...r-10m-per-yearLong was considered the top tackle in the NFL at one point, but his play has slipped as he's been plagued with injuries. His run blocking is no longer near an elite level. Cleveland Browns tackle Joe Thomas his the highest paid tackle in the league with a eight-year, $92 million deal signed before the 2011 season.
He may get 10M a year from someone but at this point he is not worth it. Until he can prove he can stay healthy he isn't worth that kind of money.
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text:
Hello everyone,
I am a beginner working with Max/MSP/Jitter and I have a little problem. I would like to close two jit.window that I have created in my patch but I don't get how I can do that.
I saw that a jit.window can receive several messages and I think the one which is useful for me is the "bang" but I tried to sent them '0' or 'close' but it didn't work or maybe I didn't get what is a bang message.
Can someone know how I can do that?
What do you mean by "would like to close jit.window"? (Your tag mention is jit.pwindow) May you specify your question?
Hey Helmut,
yeah i saw that i made a mistake because I just want to close a jit.window and not a jit.pwindow which would be stupid as they are directly included IN my patch.
My question is for several jit.window which opens when I start my patch but they don't close at the end even if I send them bang messages as '0' or 'close' and I don't know if I can do that with a message as I saw the jit.window don't accept everything
Ok I just found out how i can do that. I was looking in the messages I could send to my jit.window but I totally forgot the attributes. I have to set the 'visible' attribute to 1 or 0.
Log in to reply
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text:
The Los Angeles Kings announced on Thursday that they will wear their alternate jerseys for every home game of the 2010 playoffs (knock on wood). There is no doubt the Kings 3rd sweater is popular, but it does make me wonder what the motivation behind this decision is.
I remember hearing the Kings were releasing a 3rd sweater 2 seasons ago and being excited. Then I remember hearing it would be black and being not-so-excited. A lot of teams released black alternate sweaters, but the Kings already had a black sweater! How different could it be? What logo would they use?
As it turned out, the alternate jersey was great. The body style was different than what the kings had worn for the past 10 years and the logo was a unique design. Several other teams have the old school "stamp style" logo, like Minnesota, but no other team has a flag style logo. It was an homage to the Black and Silver era jerseys, complete with the old-school "Kings" logo on the helmets. I was impressed.
I said before the beginning of this season that I thought the Kings would eventually make their 3rd jerseys their primary sweater and either retire the current home jersey or relegate it to the alternate. Is this the first step toward that happening? A return to the playoffs (knock on wood) marked with a sweater-rebirth?
Maybe. It also marks some smart marketing. Make the 3rd sweater standard for all home playoff (knock on wood) games and convince some fans to pick up the new item. Not a bad plan at all.
Check out the official release on the Kings website here also check out a history of Kings sweaters here, it's a good read. In classic "homer" fashion it refers to the Kings "Burger King" sweater as a "collectors item" and not atrocious.
In terms of the Kings playoff (knock on wood) hopes, the situation isn't as pretty as it could have been a handful of games ago. The logjam between 5th and 8th is a spread of 2 points between 4 teams. The downside? The Kings have been on a bit of a slide and their competitors have all made strides to make up ground. That's right, the Kings are sliding at the worst possible time.
The upside? The Kings own a game at hand on 8th place Detroit, 2 games at hand on 5th place Nashville, and are up 1 point on Colorado. Even if the Red Wings win their next contest and the Kings lose their next 2, the Kings would win the tie-break based on number of wins. Let's hope (knock on wood) it doesn't come to that.
The Kings face-off tonight in Los Angeles against the visiting Dallas Stars at 7:30 pm PT. Dallas will be hungry for a win tonight and avoid getting swept by the Kings for the season series. The Kings are 5-0 against the Stars this season.
Go Kings!
About the Author
Written by Eric Cooney
Eric Cooney was born in Pennsylvania, grew up in North Carolina, and lives in Los Angeles, CA. He shares his thoughts on the NHL as one man who is a northerner, southerner, east coaster, and west coaster. Follow him on Twitter @EricCooney


text:
Submitted by GoldCore
Perth Mint Demand Highest Since Lehman Brothers - Refines Coins, Bars At Weekend
Gold is slightly lower today after yesterday's consolidation on last week's gains.
Premiums continue to rise on physical product across the world to reflect a significant increase in demand and very tight supplies. Premiums on gold and silver coins and bars are increasing across the world - from London to Frankfurt to Zurich to Turkey to Dubai to Mumbai to Singapore to Hong Kong to Tokyo and across the U.S.
Physical gold stocks held at CME Group's Comex warehouses in New York have dropped to a near-five year low in a further sign that gold's recent weakness has unleashed a nascent mini gold rush of demand as people all over the world scramble to own bars and coins.
Premiums to secure supplies in India jumped to five times the level before the slump.
Physical bullion coins and bars for immediate delivery are not available in much of the world including in the Middle East and Singapore.
Consumers in Singapore and Hong Kong have seen premiums on bars rise sharply and Standard Merchant Bank (Asia) Ltd. said that "physical metal is still not available."
Gold in USD, 3 Day – (Bloomberg)
Australia's Perth Mint, the largest refinery in Australia and one of the largest in the world, said that demand has jumped to the highest level since the Lehman crisis in 2008.
Demand has been robust due to currency devaluation concerns and then the 15% price fall led to a massive surge in demand as store of wealth buyers leapt at the chance to acquire physical bullion at much cheaper prices.
This led to the Perth Mint which refines nearly all of the nation's bullion, having to stay open over the weekend to meet orders.
There's been strong interest, including from the U.S., with buyers confident that the metal will rebound from the decline, Ron Currie, sales and marketing director, told Bloomberg in a phone interview from Perth.
Gold in Euros, 3 Day – (Bloomberg)
"We haven't seen levels like this since the 2008 global financial crisis," Currie said yesterday. "Compared to March sales, April sales have doubled or tripled," he said.
"We worked all weekend to keep the factory running to make more stock and that was only to fill orders," Currie said from the facility founded in 1899. "We're being inundated with people buying products."
As the Perth Mint's Approved Dealer in the EU, GoldCore are seeing a similar increase in demand - particularly for Perth Mint gold bars and allocated bullion accounts.
Gold in British Pounds, 3 Day – (Bloomberg)
Bullion buyers who had been planning to buy coins and bars in the coming months have brought forward their purchases due to the much cheaper prices and concerns about rising premiums and difficulty in securing supply.
"We're seeing people are coming into the market because the price has come down, they think they can afford it now and expect that it will go up again," Currie said. "The U.S. has got the money to purchase metal and is doing so as a hedge," he said, referring to individual investors. "It's extremely busy for us in the U.S."
Coin sales by the U.S. Mint are set for the highest month since December 2009, while premiums to secure supplies in India rose to five times the level before the slump.
While prices have gained 11 percent from a two-year low on April 16, they are still heading for the biggest monthly loss since December 2011.
Increased physical purchases may help to offset declining holdings in ETPs, which are on course for a record contraction in tonnage terms this month, according to data compiled by Bloomberg. Holdings have contracted 168 tons in April as weak more speculative hands were shook out of the market on the price decline.
Billionaire John Paulson, the biggest investor in the largest exchange-traded product backed by bullion, reiterated his bullish view on prices.
The U.S. Mint said on April 23 it suspended sales of coins weighing a 10th of an ounce after demand more than doubled from a year earlier. The mint has sold 209,500 ounces of gold coins so far in April from 62,000 in March, according to data compiled by Bloomberg. The U.K. Mint said purchases tripled in April.
Gold is now testing resistance at the 50% retracement level and further price weakness is possible. However, the fundamentals remain as sound as ever and securing ownership of gold and silver bullion coins and bars at these prices and at these still relatively low premiums remains very prudent.


text:
Comic books
Shop category:
Artist Mikaël
Available series in store category "Comic books"Mikaël in the COMICLOPEDIA
" Mikaël is an allround comic book artist from Québec, who has built a poetic oeuvre aimed mainly at children. Active since the early 2000s, his first series was 'Junior l'Aventurier'. The comic, dealing with a 19th century English boy who travels the work..." [ Read more ]