A.a. 2011/12

a.a. 2011/12

Let be a square region and an integer. A point in the interior of is called n-ray partitional if there are rays emanating from that divide into triangles of equal area. How many points are -ray partitional but not -ray partitional?

There must be four rays emanating from that intersect the four corners of the square region. Depending on the location ofthe number of rays distributed among these four triangular sectors will vary. We start by finding the corner-most point that is -ray partitional let this point be the bottom-left-most point. We first draw the four rays that intersect the vertices.

At this point, the triangular sectors with bases as the sides of the square that the point is closest to both do not have rays dividing their areas. Therefore, their heights are equivalent since their areas are equal.

The remaining rays are divided among the other two triangular sectors, each sector with rays, thus dividing these two sectors into triangles of equal areas. Let the distance from this corner point to the closest side be and the side of the square be. From this, we get the equation. Solve for to get. Therefore, point is of the side length away from the two sides it is closest to.

By moving to the right, we also move one ray from the right sector to the left sector, which determines another -ray partitional point. We can continue moving right and up to derive the set of points that are -ray partitional. In the end, we get a square grid of points each apart from one another. Since this grid ranges from a distance of from one side to from the same side, we have a grid, a total of -ray partitional points. To find the overlap from the -ray partitional, we must find the distance from the corner-most -ray partitional point to the sides closest to it.

Since the -ray partitional points form a grid, each point apart from each other, we can deduce that the -ray partitional points form a grid, each point apart from each other. To find the overlap points, we must find the common divisors of and which are and. Therefore, the overlapping points will form grids with points,and away from each other respectively. Since the grid with points away from each other includes the other points, we can disregard the other grids.

The total overlapping set of points is a grid, which has points. Subtract from to get. Position the square region so that the bottom-left corner of the square is at the origin. Then define to be the sidelength of and to be the pointwhere. There must be four rays emanating from that intersect the four corners of.

The areas of the four triangles formed by these rays are then,and. If a point is -ray partitional, then there exist positive integers such that and. Substituting in our formulas for,and and canceling equal terms, we get. Taking and solving forwe getand taking and solving forwe get. Finally, fromwe have. So for a point to be -ray partitional,so. Since is in the interior ofand can be any positive integer from to with and just equaling andrespectively.It might have come a year later than expected, but LeBron James lifts his first trophy for the Heat.

The one thing that eluded him, an NBA championship, would finally be in his grasp by the end of the season. A lockout of the players by the NBA's owners, which began on June 30,led to the cancellation of the entire preseason as well as hundreds of regular-season games.

A resolution was finally reached on Nov. James and the Heat made a statement on Christmas Day, handily beating the defending champion Mavericks in Dallas, before rolling to a second consecutive Southeast Division crown and the No. Led by Tony Parker, coach Gregg Popovich and a team-first mentality, the Spurs tied the Bulls with a league-best mark.

While the Heat, Spurs, Thunder and Bulls comprised the elite of the NBA in the season, other once-rebuilding teams made their presence felt in the standings.

Indiana, which hadn't posted a season better than. The shortened offseason made for a flurry of player movement. Behind the All-Star point guard's floor leadership -- as well as the play from reigning Rookie of the Year Blake Griffin -- the Clips wentchallenged the Lakers for the Pacific crown and reached the playoffs for the first time since In the postseason, two upsets stood out in the first round.

Chicago's hopes of making the step from conference finalist in to the NBA Finals in were dashed in Game 1 of its series against Philadelphia.

Serie A 2011-12

He missed the rest of the playoffs and the Bulls were ousted in Game 6. Paul and the Clippers also scored a minor upset when they stunned the fourth-seeded Grizzlies in Game 7 in Memphis. Eventually, the Heat, Celtics, Thunder and Spurs would reach the respective conference finals, where Miami would outlast Boston in Game 7 while Oklahoma City would rally from a series hole to top San Antonio, The Heat might not have made the Finals were it not for the play of James in the East semifinals and finals.

With All-Star forward Chris Bosh hobbled by injury, James took over several games throughout both series most notably Games 6 and 7 of the East finals to drive Miami back to the title round. After his Heat fell behindhe was simply dominant as Miami claimed its second-ever championship in Game 5. In the clincher, James became the fifth player in NBA history to record a triple-double in a championship-clinching game. Men's National Team won its second consecutive gold medal at the Olympics, beating Spain in the title game.

Western Conference first round L. Clippers defeated Memphis L. Western Conference semifinals Oklahoma City defeated L. Lakers San Antonio defeated L. Clippers All rights reserved.The —12 Serie A known as the Serie A TIM after its headline sponsors was the th season of top-tier Italian footballthe 80th in a round-robin tournamentand the second since its organization under a league committee separate from Serie B.

세리에 A 2011-12

It began on 3 September and ended on 13 May The league title was won by Juventuswinning its 28th official Serie A title or Scudettoand first since the —03 season. The team completed the season undefeated, becoming the first team to do so in a game league season in Italy. Perugia were undefeated in the game —79 seasonthough they finished second in the table. Milan were unbeaten and won the title in the game —92 season. Since Italy dropped from third to fourth place in the UEFA association coefficient rankings at the end of the —11 season, [7] the league lost a group stage berth for the UEFA Champions League from the —13 season.

Clubs could now sign two non-EU players. This was a reverse of the decision made the previous summer in the wake of Italy 's failure at the World Cup that limited clubs to the signing of just one such player. In Italy, football managers are only permitted to manage one club per season. From Wikipedia, the free encyclopedia. Source: Lega Serie A Rules for classification: 1 points; 2 head-to-head points; 3 head-to-head goal difference; 4 head-to-head goals scored; 5 goal difference; 6 number of goals scored C Champion; D Disqualified; R Relegated.

As they finished fifth, the sixth-placed team of the league also qualified for the Europa League. Source: La Gazzetta dello Sport kicker. Main article: List of Serie A hat-tricks. Retrieved 19 May Retrieved 25 September Bert Kassies. Retrieved 14 April US Lecce in Italian. Archived from the original on 20 March Retrieved 28 May AC Cesena in Italian. Archived from the original on 12 July Retrieved 4 June Bologna FC in Italian.

Archived from the original on 19 July AC ChievoVerona in Italian. Archived from the original on 21 March AC ChievoVerona. Archived from the original on 22 June Retrieved 9 June With the new deal in place, the regular season was shortened from the normal 82 games per team to 66, because of nearly two months of inactivity. The season began on December 25,and ended on April 26, The playoffs started on April 28 and ended on June 21 when the Miami Heat defeated the Oklahoma City Thunder in Game 5 of their series, —, winning the Finals4—1 and to capture the franchise's second NBA title.

Free agency started on December 9, The lockout was the fourth work stoppage in the history of the NBA. The main issues dividing the owners and the players were revenue sharing and the structure of the salary cap. During the lockout, teams could not trade, sign or contact players and players couldn't access NBA team facilities, trainers, or staff members.

All preseason games scheduled to begin October 9 and the first six weeks of the regular season scheduled to begin November 1, through December 15 were canceled. On November 26,after 15 hours of talks, a tentative deal was reached; once officially ratified, the NBA started a revised —12 season. On December 8,the lockout ended when the owners and players ratified a new CBA agreement. Training camp began on December 9. A revised two-game preseason schedule took place.

A revised game regular season began on December 25,with five Christmas Day gamestwo more than the original schedule. The number of games between conferences was affected as was the case in the lockoutwhen each team played only five or six interconference games in a game schedule.

Normally, each team plays teams in the other conference twice each. The exception was the then champion Dallas Mavericks, who never had a set of 3 consecutive back to backs. The Heat were not immune, losing Chris Bosh for most of the playoffs en route to their championship. Commissioner David Stern initially said there was no connection between the injuries and the game schedule compressed into days; however, he backed off those comments a week later, saying more research was needed.

The following players won the Community Assist Award. From Wikipedia, the free encyclopedia. Sports season. Main article: List of —12 NBA season transactions. Main article: NBA lockout.

Eastern Conference Atlantic Division v t e. Eastern Conference v t e. Main article: NBA Playoffs. This bracket: view talk edit. This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources.The Oakland Athletics ' season was the 44th for the franchise in the Bay Areaas well as the th in club history.

Young declined a 2-year contract offer and became Boston 's pitching coach. Steverson becomes hitting coach for Sacramento. The A's were known for sporting white jerseys at home and greys for away games. On top of that, the A's wore a black and a green alternate jersey. During the season, they added a new style. The A's started wearing a gold alternate home jersey to their apparel.

Manager Billy Beane referred to the look as "the Canary yellow" jerseys. A's relief pitcher Jerry Blevins said, "It might be hard not to notice us now". From Wikipedia, the free encyclopedia. Major League Baseball season. April 13— August 11— September 14— Retrieved March 21, Retrieved April 8, Retrieved April 7, Los Angeles Oakland Seattle Texas.

Oakland Athletics. Philadelphia Phillies San Francisco Giants. Owners: John J. Hidden categories: Use mdy dates from November Articles with short description Pages using infobox MLB yearly with unknown parameters Commons category link is on Wikidata. Namespaces Article Talk. Views Read Edit View history. Help Community portal Recent changes Upload file. Download as PDF Printable version.

Wikimedia Commons. American League since Western Division since Pitching coach for Sacramento. Los Angeles Angels of Anaheim. Seattle Mariners.

Blue Jays. Anderson 0—1. Baker 0—2. White Sox. Anderson 1—1. Anderson 2—1.About Me Adrienne View my complete profile. This is my first tutorial, and my first real attempt to blog and I'm new to the art of felt critters, so bear with me.

They do not label the felt, and I'm just learning to tell the wool blend from the acrylic, though I can usually tell the good pure wool. The felt here is probably wool blend and obviously wrinkly, but, because I wasn't completely sure, I didn't iron it. I also hate ironing. At this point, I lay out the colors and pretend that I actually keep my embroidery floss remotely neat. It really lives all bunched up in a pouch with a Snickers bar, but perhaps organizing it will be a resolution.

Cut out six pieces of the body shape templateand begin to sew it together. I am a fan of the blanket stitch. I've tried whip stitch and it's a good stitch, but I'm not good at it. I also sort of remember reading somebody else say that the blanket stitch was a bit "country" which works for me. I could have it completely backwards and she might have said whip stitch is "country", but I'm doing blanket.

Somewhere I envision camps of whip stitchers battling it out with blanket stitchers, but this is just fun to imagine while I'm stitching. Both work. More stitching At this point it looks a bit like a star fruit or something organic. I think. Now it is time to stuff it. Yes there is a bit of excess thread I didn't cut off, but the legs will be there and my laziness pays off.

I pull the extra thread through the body to create a bit more of a jellyfish shape. I tie off the thread at the top. Now the body is sewn. Here I've decorated the body with a bit of super simple stitching - one straight stitch on either side of a lazy daisy stitch toward the top center of each panel.

a.a. 2011/12

Time to add some legs! This is really a choice thing. The legs can be a single color of floss using all 6 strands about 8 inches long, and separating them at the end for fuller looking legs. I chose to make them 5 strands of different colors.

Season Review: 2011-12

Yes, 5 not 6. I also chose to use silver metallic floss, which is just a nightmare to work with.

a.a. 2011/12

I love the look, but it never cooperates. Tie off the legs with a simple slip knot. I try to make two rings of 6 legs each, which sort of gives it depth. The outer ring green circle I place at the seams for no other reason than I like it. The inner ring red circle I put towards the middle of each panel.The recall also includes the Ford Mustang and Lincoln Navigator. Ford dealers and Lincoln dealers will inspect the powertrain control module for diagnostic trouble codes tied to the problem.

If no related diagnostic trouble codes are present, dealers will update the powertrain control module software. As part of a customer satisfaction program, Ford will provide a one-time replacement of the lead frame at no charge within 10 years ormiles from the warranty start date. The recall is expected to begin on May Owners can contact Ford customer service at or Lincoln customer service at No information about the recall has been posted on the Web site of the National Highway Traffic Safety Administration, which oversees vehicle safety in the U.

Edmunds says: Owners of these vehicles should be prepared to make a service appointment in late May with their dealers. If you have an immediate concern, it's best to contact your dealer now.

Popular searches. My Account. April 28th, The defect has been traced to an output speed sensor on the vehicle's transmission lead frame. Affected vehicles are equipped with a 6R80 transmission. Other research topics. Most popular vehicles. See more.

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