A bracket algebra is an algebraic system that connects the notion of a supersymmetry algebra with a symbolic representation of projective invariant s. Given that L is a proper signed alphabet and Super L is the supersymmetric algebra, the bracket algebra Bracket L of dimension n over the field K is the quotient of the algebra Brace L obtained by imposing the congruence relations below, where w , w , ..., w are any monomials in Super L w 0 if length w &ne n w w nowiki nowiki ... w 0 whenever any positive letter a of L occurs more than n times in the monomial w w ... w . Let w w ... w be a monomial in Brace L in which some positive letter a occurs more than n times, and let b , c , d , e , ..., f , g be any letters in L . References Citation last1 Anick first1 David last2 Rota first2 Gian Carlo author2 link Gian Carlo Rota year 1991 title Higher Order Syzygies for the Bracket Algebra and for the Ring of Coordinates of the Grassmanian periodical Proceedings of the National Academy of Sciences volume 88 issue 18 date September 15, 1991 pages 8087 8090 doi 10.1073 pnas.88.18.8087 issn 0027 8424 jstor 2357546 . Citation last1 Huang first1 Rosa Q. last2 Rota first2 Gian Carlo last3 Stein first3 Joel A. year 1990 title Supersymmetric Bracket Algebra and Invariant Theory periodical Acta Applicandae Mathematicae volume 21 pages 193 246 publisher Kluwer Academic Publishers url http www.springerlink.com content q821633w3291351g doi 10.1007 BF00053298 . Category Invariant theory Category Algebras ... more details
Mergeto ESPN Sports Saturday date April 2010 Infobox television show name Winners Bracket format Sports radio Sports Talk runtime 60 minutes starring Michelle Beadle br Marcellus Wiley country United States num episodes network American Broadcasting Company ABC first aired start date 2010 4 03 last aired end date 2012 4 28 location Bristol, Connecticut Winners Bracket was a sport s related television program that airs on American Broadcasting Company ABC . Hosted by Michelle Beadle and Marcellus Wiley , it premiered at 5 p.m. Eastern Time ET April 3, 2010 on the American Broadcasting Company . ref http www.espnmediazone3.com us 2010 03 winners bracket to debut saturday on abc as part of new espn sports saturday block ref The show is the second hour of the two hour block ESPN Sports Saturday . The show consists of a recap and debate of the week in sports by pitting 16 of the biggest stories of the week against each other in a seeded bracket. Along with Beadle and Wiley, other ESPN experts such as Mike Greenberg , Digger Phelps , Jalen Rose , and Colin Cowherd offer their perspective during each round of debate. Each competition is generally themed most shocking, best defense, etc. , with online voters determining the winner of each competition. The show is broadcast from the same studio used for SportsNation TV series SportsNation which is also co hosted by Beadle , and borrows several elements from that show. Other segments of the show include a collection of sound bytes from athletes and coaches, a taste of that week in sports history, a countdown of the 20 lowlights from the week, sports themed web videos, and some of the highlights that just missed being in the bracket. References reflist ESPN ABC Sports Category American Broadcasting Company network shows Category ABC Sports Category 2010 American television series debuts Category 2010s American television series Category ESPN network shows Category American sports television series ... more details
Infobox musical artist See Wikipedia WikiProject Musicians name Bracket image caption From left to right ... Castro past members Larry Tinney notable instruments Bracket is an American punk rock band from Forestville ... Angelo Celli replacing founding member Larry Tinney in 1999. Bracket has issued albums through ... s name was changed to Bracket prior to releasing the self financed Giant Midget Extended Play EP in 1993. The following year Bracket released their debut album 924 Forestville St. , which also marked ... down by Caroline Records, Bracket began issuing the format on Fat Wreck Chords during the interim ... Stones Sticky Fingers and Pearl Jam s Vs. Pearl Jam album Vs. respectively. In 1995 Bracket released ..., Bracket was dropped from Caroline Records and the album never saw official release. ref label ... , a Split album split with Humble Beginnings on Too Hep Records. On November 19, 1996, Bracket ... album, Bracket toured the United States with the likes of NOFX , Snuff , Smoking Popes , MxPx ... 1997 s Novelty Forever , produced by Bracket with Ryan Greene and Fat Mike . Having toured throughout ... as co writing the track. On February 26, 2002, Bracket released Live in a Dive Bracket album ... . Requiem and recent activity 2005 present In 2005, Bracket released Requiem Bracket album Requiem ... s 4 Wheel Vibe to not be released through Fat Wreck Chords. Instead, the album marked Bracket s debut ... Crisis in 2007 to act as an outlet for different types of music between Bracket albums, with Gregori ... performing locally, with sets that consisted of original material, Bracket tracks, and occasional cover ... Wreck Chords Live in a Dive Bracket album Live in a Dive 2002 Fat Wreck Chords Requiem Bracket album ... Chords Trailer Park Bracket Isn t It? 1995 Hi Rise Recordings For Those About to Mock 1995 Fat Wreck ... 09 bracket like you know unreleased lp.html Wilfully Obscure Like You Know note label allmusic 3 none Allmusic class artist id bracket p165303 biography pure url yes Allmusic Bracket biography External ... more details
Bracket buster, as a generic phrase, refers to an United States American college basketball team, usually from a so called mid major school, which upsets a highly ranked team in the NCAA Men s Division I Basketball Tournament . The tournament schedule is set up as a single elimination bracket format. When the tournament s selection committee announces the teams that are invited to play and the schedule of the games, fans will try to guess the outcome of as many games as possible by filling out the bracket form for each round. This is often accompanied by gambling on the outcome of these predictions this often takes the form of an informal pool where participants stake a certain amount of money, and the most successful predictor wins the pooled stakes. When a lightly regarded mid major team upsets a traditional powerhouse team, the result often knocks out subsequent predictions of many players in these informal pools, who are said to have had their brackets busted hence, the term bracket buster. There are numerous examples of a bracket buster teams over the years of the NCAA Tournament, even dating back before the tournament came to be the widespread cultural event that it is today. One early example is the March 18, 1971 Mideast Regional game in which Western Kentucky Hilltoppers basketball Western Kentucky defeated its better known in state big brother, Kentucky Wildcats men s basketball ... six round bracket and 68 teams including 4 play in games , bracket busters became more of a phenomenon ... bracket busters. In the second round, a ten seed St. Mary s defeated a two seed Villanova University ... seed, Kansas . In ESPN s bracket challenge, over 42 ref http games.espn.go.com tcmen en whopickedwhom ... where possible bracket buster teams would play each other outside of regular conference play. The idea ... on the ESPN family of networks. ref cite news first Bobbi last Roquemore title Bracket Buster loses ... External links http www.espnbracketbusters.com Official site DEFAULTSORT Bracket Buster Category ... more details
A bracket is a tree diagram that represents the series of games played during a tournament , named as such because it appears to be a large number of interconnected punctuational bracket s. There are several kinds of brackets, adapted to different types of tournaments. The most common are Single elimination tournament Single elimination brackets Double elimination tournament Double elimination brackets Triple elimination tournament Triple elimination brackets The art of filling in brackets, especially in NCAA Men s Division I Basketball Championship NCAA basketball , is referred to as bracketology . Usage in North America Brackets are commonly found in major North American professional sports leagues . Often, at the end of the regular Season sports season , the league holds a post season tournament most commonly called a playoff to determine which team is the best out of all of the other teams in the league. This is done because often in professional sports there are at least two different Conference sports conferences , and teams mostly play other teams in their own conference. Examples of this are the American Football Conference and the National Football Conference in the NFL , the American League and the National League in Major League Baseball , and the Eastern Conference NBA Eastern Conference and the Western Conference NBA Western Conference in the NBA or NHL . When there are only two different conferences, there are two sides of the bracket. One conference is on one side, while the other is on the opposite side. Teams that qualify for the post season tournament only compete against teams in their own conference, until only one team from each conference remains. These two teams, called the conference champions, play each other to determine the best in the league. Other ... player, single elimination tournament bracket. The quarterfinals have been completed, and the semifinal ... people who win in the semifinals. Image NSB doubleelim draw 2004.png A double elimination bracket ... more details
In mathematics, the Toda bracket is an operation on homotopy classes of maps, in particular on homotopy groups of spheres , named after Hiroshi Toda who defined them and used them to compute homotopy groups of spheres in harv Toda 1962 . Definition See harv Kochman 1990 or harv Toda 1962 for more information. Suppose that math W stackrel f to X stackrel g to Y stackrel h to Z math is a sequence of maps between space, such that gf and hg are both nullhomotopic. Given a space A , let CA denote the cone of A . Then we get a non unique map from CW to Y from a homotopy from gf to a trivial map, which when composed with h gives a map from CW to Z . Similarly we get a non unique map from CX to Z from a homotopy from hg to a trivial map, which when composed with Cf , the cone of the map f , gives another map from CW to Z . By joining together these two cones on W and the maps from them to Z , we get a map f ,&thinsp g ,&thinsp h in the group SW , Z of homotopy classes of maps from the suspension SW to Z , called the Toda bracket of f , g , and h . It is not uniquely defined up to homotopy, because there was some choice in choosing the maps from the cones. Changing these maps changes the Toda bracket by adding elements of h SW , Y and SX , Z f . There are also higher Toda brackets of several elements, defined when suitable lower Toda brackets vanish. This parallels the theory of Massey product s in cohomology . The Toda bracket for stable homotopy groups of spheres The Direct sum of groups direct sum math pi ast S bigoplus k ge 0 pi k S math of the stable homotopy groups of spheres is a supercommutative ring supercommutative graded ring mathematics ring , where multiplication called composition product is given by composition of representing maps, and any element of non zero degree is nilpotent harv Nishida 1973 . If f and g and h are elements of sub sub sup S sup with f g 0 and g h 0, there is a Toda bracket f ,&thinsp g ,&thinsp h of these elements. The Toda bracket ... more details
The Dirac bracket is a generalization of the Poisson bracket developed by Paul Dirac to correctly treat ... s. More abstractly the two form implied from the Dirac bracket is the restriction of the Symplectic ... of Dirac s modified Hamiltonian formalism are summarized to put the Dirac bracket in context. Inadequacy .... Consistency conditions The equations of motion become more compact when using the Poisson bracket ..., H PB approx f, H PB sum k u k f, phi k PB , math if one assumes that the Poisson bracket with the math ... becomes important. The Dirac bracket Above is everything needed to find the equations ... first class if its Poisson bracket with all of the constraints weakly vanishes, that is, math f, phi ... combination of the constraints. One can demonstrate that the Poisson bracket of two first ... formalism. For the purposes of introducing the Dirac bracket, of more immediate interest are the second ... bracket with at least one other constraint. For instance, consider constraints math phi 1 math and math phi 2 math whose Poisson bracket is simply a constant, math c math , math phi 1, phi 2 PB c. math ... operators whose commutators become math i hbar math times their classical Poisson bracket. Assuming ... bracket that respects the system s constraints, and leads to a consistent quantization procedure. The new bracket should be bilinear, antisymmetric, satisfy the Jacobi identity as does the Poisson bracket, reduce to the Poisson bracket for unconstrained systems, and additionally the bracket ... phi b PB . math In which case, the Dirac bracket of two functions on phase space, math f math and math ... of the Dirac bracket satisfies all of the desired properties. When using canonical quantization ... times their classical Dirac bracket . Since the Dirac bracket respects the constraints, one does ... bracket. Note that while the Poisson bracket of a bosonic Grassmann even variables with itself must vanish, the Poisson bracket of a fermion represented as a Grassmann number Grassmann variables ... more details
In mathematics, the bracket ring is the subring of the ring of polynomials k x sub 11 sub ,..., x sub dn sub generated by the determinants of d by d minors of the matrix x sub ij sub . References Citation last1 Dieudonn first1 Jean A. last2 Carrell first2 James B. title Invariant theory, old and new doi 10.1016 0001 8708 70 90015 0 id MR 0255525 year 1970 journal Advances in Mathematics issn 0001 8708 volume 4 pages 1 80 Citation last1 Dieudonn first1 Jean A. last2 Carrell first2 James B. title Invariant theory, old and new publisher Academic Press location Boston, MA isbn 978 0 12 215540 6 doi 10.1016 0001 8708 70 90015 0 id MR 0279102 year 1971 Citation last1 Sturmfels first1 Bernd author1 link Bernd Sturmfels last2 White first2 Neil title Stanley decompositions of the bracket ring id MR 1096453 year 1990 journal Mathematica Scandinavica issn 0025 5521 volume 67 issue 2 pages 183 189 Category Invariant theory mathematics stub ... more details
Lagrange brackets are certain expressions closely related to Poisson bracket s that were introduced by Joseph Louis Lagrange in 1808 1810 for the purposes of mathematical formulation of classical mechanics , but unlike the Poisson brackets, have fallen out of use. Definition Suppose that q sub 1 sub , &hellip , q sub n sub , p sub 1 sub , &hellip , p sub n sub is a system of canonical coordinates on a phase space . If each of them is expressed as a function of two variables, u and v , then the Lagrange bracket of u and v is defined by the formula math u, v p,q sum i 1 n left frac partial q i partial u frac partial p i partial v frac partial p i partial u frac partial q i partial v right . math Properties Lagrange brackets do not depend on the system of canonical coordinates q , p . If Q , P Q sub 1 sub , &hellip , Q sub n sub , P sub 1 sub , &hellip , P sub n sub is another system of canonical coordinates, so that math Q Q q,p , P P q,p math is a canonical transformation , then the Lagrange bracket is an invariant of the transformation, in the sense that math u, v q,p u , v Q,P math Therefore, the subscripts indicating the canonical coordinates are often omitted. If &Omega is the symplectic form on the 2n dimensional phase space W and u sub 1 sub ,&hellip , u sub 2n sub form a system of coordinates on W , then canonical coordinates q , p may be expressed as functions of the coordinates u and the matrix mathematics matrix of the Lagrange brackets math u i, u j p,q , quad 1 leq i,j leq 2n math represents the components of &Omega , viewed as a tensor , in the coordinates u . This matrix is the inverse matrix inverse of the matrix formed by the Poisson brackets math u i, u j , quad 1 leq i,j leq 2n math of the coordinates u . As a corollary of the preceding properties, coordinates Q sub 1 sub , &hellip , Q sub n sub , P sub 1 sub , &hellip , P sub n sub on a phase ... 277. MathSciNet id 1659212 External links SpringerEOM author A.P. Soldatov title Lagrange bracket urlname ... more details
Dr. Evadne Hinge and Dame Hilda Bracket were the stage personae of the musical performance and female ... it clear that he did not miss the Hinge persona. Feeling that the appeal of Hinge and Bracket ... comedian. Since Patrick is no longer with us, Hinge and Bracket can never happen again. When you ve ... After Fyffe s death in 2002, and with very little of Hinge and Bracket s work available ... campaigning by http www.hingeandbracket official.co.uk BBC Blog Of Hinge And Bracket Releases.html ... of The Random Jottings of Hinge and Bracket . ref Hinge George Logan Dame Hilda Nemone Bracket Patrick Fyffe . Dame Hilda Bracket is portrayed as a lively, fun loving, flamboyant doyenne of opera. She ..., vocal support for Dame Hilda Bracket s singing performances. Cutting a modest, almost apologetic figure ... other recordings of Gilbert and Sullivan songs by Hinge and Bracket are the following Hinge and Bracket ... with Hinge and Bracket , EMI records One Up, OU 2181, 1977 includes Blameless Dances from Ruddigore and Regular Royal Queen from the Act I finale of The Gondoliers and Hinge and Bracket at Abbey Road ... Handbags Hinge and Bracket were never seen on stage without their handbags, and with each successive .... Gay references These were present throughout the stage shows, some examples in the Hinge and Bracket ..., Hinge and Bracket were inveterate teasers of their audience. In the course of their shows ... and Bracket s fictional home life, referred to constantly in their shows, is further developed in the radio ... town of Stackton Tressel in Suffolk , which, in the words of Bracket, lies 17 miles from Bury St ... poison the visiting team. Appeal of the Act Reinventing Drag To label Hinge and Bracket a drag .... Dropping an Octave Though Hinge and Bracket were not a drag act in the traditional sense, the drag ... effective because, in all other aspects of performance, Hinge and Bracket were impeccable in the image ... The appeal of Hinge and Bracket worked on several levels gay, highbrow cultural, mainstream ... more details
In mathematics , the Iverson bracket , named after Kenneth E. Iverson mentioned here so it s clear that it s an upper case i not an l . , is a notation that denotes a number that is 1 if the condition in square brackets is satisfied, and 0 otherwise. More exactly, math P begin cases 1 & text if P text is true 0 & text otherwise. end cases math where math P is a statement logic statement that can be true or false. This notation was introduced by Kenneth E. Iverson in his programming language APL programming language APL , ref Ronald Graham , Donald Knuth , and Oren Patashnik . Concrete Mathematics , Section 2.2 Sums and Recurrences. ref while the specific restriction to square brackets was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions. ref Knuth 1992. ref Uses The notation is useful in expressing sums or integrals without boundary conditions. For example math sum 1 le i le 10 i 2 sum i i 2 1 le i le 10 . math In the first sum, the index math i math is limited to be in the range 1 to 10. The second sum is allowed to range over all integers, but where i is strictly less than 1 or strictly greater than 10, the summand is 0, contributing nothing to the sum. Such use of the Iverson bracket can permit easier manipulation of these expressions. add an example of such a manipulation Another use of the Iverson bracket is to simplify equations with special cases. For example, the formula math sum 1 le k le n atop gcd k,n 1 k frac 1 2 n varphi n math a number theory number theoretic identity involving the Euler phi function which is valid only for math n 1 math may be written math sum 1 le k le n atop k,n 1 k frac 1 2 n varphi n n 1 math which is valid for all positive integers n . Special cases The Kronecker delta notation is a specific case of Iverson notation when the condition is equality. That is, math delta ij i j . , math The indicator function , another specific case, has set membership as its condition math mathbf I A x x in A . math The sign ... more details
Image DragRacerPurgingNitrousOxide.jpg thumb alt Bracket racing is a form of drag racing that allows for a handicap between predicted elapsed time of the two cars over a standard distance, usually 1 4 mile 402.336 m or 1 8 mile 201.168 m . Goal The effect of the bracket racing rules is to place a premium on consistency of performance of the driver and car rather than on raw speed, which in turn makes victory much less dependent on large infusions of money, and more dependent on mechanical and driving skill, such as reaction time s, shifting abilities, and ability to control the car. Therefore, bracket racing using the aforementioned handicapping system is popular with casual weekend racers. Many of these recreational racers will drive their vehicles to the track, race them, and then simply drive them home. Fact date May 2008 This format allows for a wide variety of cars racing against each other. While traditional drag racing separates cars into a wide variety of classes based on power and weight, bracket racing classes can be simpler, and can accommodate any vehicle with basic technical safety inspection. Race events organized in this way are sometimes called run what ya brung . Fact date May 2008 Format Dial in Each car chooses a dial in time before the race, predicting the elapsed time the driver estimates it will take his or her car to cross the finish line. This is usually displayed on one or more windows so the starter can adjust the christmas tree starting lights accordingly. The slower car in the race is given the green light before the faster car by a margin of the difference between their two dial in time s. In principle, if both drivers have equal reaction times and their cars run exactly their posted dial ins, both cars should cross the finish line at precisely the same time. In reality, this is an extremely rare occurrence. Measuring devices ... Racing Explained DEFAULTSORT Bracket Racing Category Drag racing sv Bracket ... more details
The Battle of the Bulge was a major World War II German offensive. Battle of the Bulge may also refer to Battle of the Bulge film Battle of the Bulge film , a 1965 film Battle of the Bulge 1991 game Battle of the Bulge 1991 game , a board wargame by Avalon Hill Axis & Allies Battle of the Bulge , by Avalon Hill The Battle of the Bulge... The Brave Rifles , a 1965 documentary film Battle of the Bulge Hitler s Alternate Scenarios , an alternate history anthology no info on these on Wikipedia, nothing to disambiguate Battle of the Bulge 1965 game Battle of the Bulge 1965 game , published by Avalon Hill Battle of the Bulge 1981 game Battle of the Bulge 1981 game , by Avalon Hill an update of the 1965 version Battle of the Bulge 1985 game Battle of the Bulge 1985 game , by Epoch disambig nl Battle of the Bulge ... more details
Infobox film name The Battle of the Bulge... The Brave Rifles image caption director producer Laurence E. Mascott writer narrator Arthur Kennedy actor Arthur Kennedy starring music cinematography editing distributor released film date 1965 runtime 52 minutes country Film US language English budget The Battle of the Bulge... The Brave Rifles is a 1965 documentary film produced by Laurence E. Mascott . It was nominated for an Academy Award for Academy Award for Documentary Feature Best Documentary Feature . ref name NY Times cite web url http movies.nytimes.com movie 283489 Battle of the Bulge The Brave Rifles overview title NY Times The Battle of the Bulge... The Brave Rifles accessdate 2008 11 09 work NY Times ref References reflist External links imdb title id 0058948 title The Battle of the Bulge... The Brave Rifles DEFAULTSORT Battle Of The Bulge The Brave Rifles Category 1965 films Category American films Category English language films Category American documentary films Category Black and white documentary films Category 1960s documentary films Category Documentary films about World War II Category Battle of the Bulge war documentary film stub ... more details
Infobox VG title Battleground Bulge Ardennes image Image Battleground Bulge Ardennes Coverart.png caption developer TalonSoft publisher TalonSoft distributor designer license series engine version released 1995 in video gaming 1995 genre Turn based strategy br Real time tactics modes Single player , Head to Head Modem play ratings Entertainment Software Rating Board ESRB Kids to Adults platforms Microsoft Windows Windows media requirements input Computer keyboard Keyboard , Mouse computing mouse Battleground Bulge Ardennes is the first game to be released in the Battleground series. It was developed and published by TalonSoft and released in 1995. br References moby game id battleground ardennes name Battleground Bulge Ardennes Battleground video games Category 1995 video games Category Real time tactics video games Category Turn based strategy video games Category Windows games es Battleground Bulge Ardennes TakeTwo studio stub strategy videogame stub ... more details
Axis & Allies Battle of the Bulge is a board game which depicts the Battle of the Bulge , the German s last ditch offensive of World War II . It is similar to Axis & Allies D Day in that the game is played on a tactical rather than strategic level, although the gameplay is radically different from D Day or any other previous Axis and Allies game. It is designed by Larry Harris game designer Larry Harris , and published by Avalon Hill . Objective A&A Battle of the Bulge is played between two players one commanding the Germans and the other the Allied forces. Unlike previous Axis & Allies games, where American and British forces are controlled by different players, the Allied player controls both American and British forces, due to the small numbers of British forces represented. American and British forces are identical in this game, and the different colors are used solely for historical accuracy. Battle of the Bulge is played on a hexagonal grid, with the eastern parts of the board representing Germany and the large majority representing Belgium , although Antwerp , the Germans eventual objective, is not represented on the map. The objective of Battle of the Bulge is for the Germans to acquire 24 Victory Points, or, in the Allies case, to prevent Germany from acquiring 24 points at the end of eight turns of play. This objective was set at 24 points to reflect the Germans actual progression in World War II, which would have been worth the equivalent of 23 points. Thus, Germany ... Citation last Bender first Kevin title Axis & Allies Battle of the Bulge review newspaper Knucklebones ... have also been added to Battle of the Bulge , facilitating the transport of infantry, artillery, and supplies ... that are on the German side of the front line at the end of the turn. See also Battle of the Bulge game Battle of the Bulge 1991 game References references External links bgg 22457 Axis & Allies Battle of the Bulge http www.axisandallies.org battleofthebulge Axis & Allies Battle of the Bulge ... more details
off 50 feet 15.25 m of her bulge. Later designs of bulges incorporated various combinations of air ... combinations of narrow and internal bulges appeared throughout the 1920s and into the 1930s. The bulge ... more details
Infobox Game subject name Battle of the Bulge image link Image BotB 91 cover.jpg none Box art for Battle of the Bulge image caption Cover art for Battle of the Bulge players 2 ages 10 and up setup time 10 minutes playing time 2 hours complexity Medium strategy Medium random chance Medium skills Planning, Terrain control, Delay tactics footnotes For other games with this title, see Battle of the Bulge game Battle of the Bulge is a board wargame published by Avalon Hill as part of the Smithsonian American History Series . The game simulates the World War II battle Battle of the Bulge of the same name and is designed for two players. It is based upon the general Avalon Hill system of combat and movement factors with a focus upon ease of play. The basic rules cover a single sheet of approximately Paper size Current U.S. loose paper sizes legal sized paper . Aggressive gameplay is required by the Germany German player, who must exceed the historical success of his forces. The United States American player must be able to transition from delaying tactics in the early game to assaults once force superiority is gained. The rules provide for a short game covering the initial five days of the battle beginning 1944 December 12 16 , a mid length game covering the Allied counterattack, including the encirclement of the 101st Airborne Division , and a long game covering 16 days. Advanced game rules include aerial warfare air power , supply line supply , and fuel usage. Components Board The gameboard covers portions of Germany, Luxembourg , and Belgium known as the Ardennes forest with a hex map hexagonal grid . Geographic features include hills, forests, and rivers. Additional features ... but generally possess some flexibility regarding entry position. Movement Movement in Battle of the Bulge ..., strategy, and expansion Avalon Hill s magazine The General made Battle of the Bulge the featured ... must be hand made. See also Axis & Allies Battle of the Bulge Battle of the Bulge game Category ... more details
Unreferenced date November 2009 Infobox film name Battle of the Bulge image Bulge sheet A.jpg caption Original movie poster producer Sidney Harmon br Milton Sperling br Philip Yordan director Ken Annakin writer Bernard Gordon writer Bernard Gordon br John Melson br Milton Sperling br Philip Yordan starring Henry Fonda br Robert Shaw actor Robert Shaw br Robert Ryan music Benjamin Frankel cinematography Jack Hildyard editing Derek Parsons narrator William Conrad distributor Warner Brothers released Film date 1965 12 16 runtime 167 minutes language English Battle of the Bulge is a widescreen war film produced in Spain that was released in 1965. It was directed by Ken Annakin . It starred Henry Fonda , Robert Shaw actor Robert Shaw , Telly Savalas , Robert Ryan , Dana Andrews and Charles Bronson . The feature was filmed in Ultra Panavision 70 and exhibited in 70 mm Cinerama . Battle of the Bulge had its world premiere on December 16, 1965, the 21st anniversary of the battle, at the Pacific Cinerama Dome Theatre in Hollywood, California . The original VHS release of the film for home video use was heavily edited and used a full screen pan and scan technique often employed in network telecasts of widescreen motion pictures. The DVD released in 2005 , however, is uncut and uses a letterbox ... World War II epics, Battle of the Bulge contains virtually no portrayals of actual senior Allied ... s decision to split the Bulge front into two, ceding temporary command of two American armies to Bernard Law Montgomery Field Marshal Montgomery in the northern half of the Bulge implying a totally ... in Italy at the time of the Battle of the Bulge. Although Patton was in charge of Third United States ... September 2010 DEFAULTSORT Battle Of The Bulge Category 1965 films Category American films Category ... giganti nl Battle of the Bulge 1965 ja no Ardennerslaget film pl Bitwa o Ardeny film pt Battle of the Bulge sl Bitka za gorivo film fi Taistelu Ardenneilla tr Battle of the Bulge film zh ... more details
good article Infobox military conflict conflict Second Battle of Naktong Bulge partof the Battle of Pusan Perimeter image File 9th Infantry Regiment tank desant.jpg 300px alt Men sit on a tank which is holding position among a line of troops caption Troops of the US 9th Infantry await North Korean attacks across the Naktong River , September 3. date September 1 12, 1950 place Naktong River , South ... of Naktong Bulge was an engagement between United Nations UN and North Korean NK forces early in the Korean ... Bulge , the US Army s US 2nd Infantry Division 2nd Infantry Division was moved to defend the Naktong ... forces were able to force the North Koreans out of the Naktong Bulge region. The North Koreans were ... First Battle of Naktong Bulge From the outbreak of the Korean War and the invasion of South Korea ... 4th Division and the US 24th Infantry Division sparred in the Naktong Bulge area. In the First Battle of Naktong Bulge , the North Korean division was unable to hold its bridgehead across the river ... 10th Division break through the US 2nd Infantry Division at the Naktong Bulge to Miryang and Yongsan ... Infantry Regiment held a sector more than convert 20,000 yd long, including the bulge area of the Naktong where the First Battle of Naktong Bulge had taken place earlier in August. ref name Fehr141 ... attack was to outflank and destroy the US troops at Naktong Bulge by capturing the Miryang ... This ferry was located at the middle of the Naktong Bulge where the Yongsan road came down to the Naktong ... terrain where so much heavy fighting had taken place in the first battle of the Naktong Bulge. ref ... Bulge, September 4. At 09 00 Walker requested the US Air Force to make a maximum effort along ... was most critical in the Naktong Bulge area of the US 2nd Division sector. ref name ... for the Naktong Bulge at 13 30. ref name Apple453 North Korean advance The situation on the front ..., 1950. North of the US 9th Infantry and the battles in the Naktong Bulge and around Yongsan, the US ... more details
Infobox military conflict conflict First Battle of Naktong Bulge partof the Battle of Pusan Perimeter image File Marines at Naktong River.jpg 250px alt Two men in military uniforms standing on a ledge overlooking a river caption US Marines resting on a newly captured position overlooking the Naktong River, August 19, 1950. date August 5 19, 1950 place Yeongsan, Changnyeong , South Korea result United Nations victory combatant1 Flag United States 1912 combatant2 Flag North Korea commander1 Flagicon United States 1912 John H. Church commander2 Flagicon North Korea Lee Kwon Mu strength1 20,000 strength2 7,000 casualties1 600 killed br 1,200 wounded or captured casualties2 1,200 killed br 2,300 wounded, captured, and desertion deserted campaignbox Campaignbox Korean War Campaignbox Pusan Perimeter The First Battle of Naktong Bulge was an engagement between United States and North Korean forces early in the Korean War from August 5 19, 1950 in the vicinity of Yongsan Yeongsan, Changnyeong county and the Naktong River in South Korea . It was a part of the Battle of Pusan Perimeter , and was one of several large engagements fought simultaneously. The battle ended in a victory for the United States after large numbers of US reinforcements destroyed an attacking North Korean division. On August 5, 4th Division North Korea 4th Infantry Division , Korean People s Army North Korean People s Army KPA , crossed the Naktong River in the vicinity of Yongsan, attempting to cut US supply lines ... 2001 25 harvnb Catchpole 2001 p 25 ref ref harvnb Appleman 1998 p 247 ref Naktong Bulge About ... the Cloverleaf Hill and Oblong ni Ridge, critical terrain astride the main road in the bulge area ..., re entrants and pockets salient at the bulge. 9th Infantry was fresh and well equipped. ref name ... a third them killed. ref name Ecker26 In memory of the battle at Naktong Bulge, as well as other ... missing South Korea conflict yes DEFAULTSORT Naktong Bulge, Battle Of Category Conflicts in 1950 Category ... more details
Campaignbox Battle of the Bulge This is the order of battle of German and Allied forces during the Battle of the Bulge . u Caveat u This Battle lasted more than a month, with assignments in considerable flux. Any hierarchy of unit within Corps within Army within Army Group is inherently a snapshot of a single moment in that flux. The hierarchy given here is at a moment nearly at the end of the Battle. To fully understand the hierarchy at any given moment in the Battle, you must not rely on this page alone. u For example u , the hierarchy here places the U. S. 7th Armored Division in XVIII Corps in U. S. First Army in 12th Army Group. However, when the German attack began on 16 December 1944, the alignment of U. S. 7th Armored Division was XIII Corps, U. S. Ninth Army, 12th Army Group . Later that day, the alignment became VIII Corps, U. S. First Army, 12th Army Group . On 20 December, the alignment became XVIII Corps, U. S. First Army, 12th Army Group and on the same day XVIII Corps, U. S. First Army, 21st Army Group . On 18 January 1945, the final alignment became XVIII Corps, U. S. First Army, 12th Army Group the alignment in the hierarchy given here. Allied Forces Image SHAEF Schulterst ck.jpg 20px Supreme Headquarters Allied Expeditionary Forces General of the Army Dwight D. Eisenhower Image 12th Army Group.svg 20px 12th Army Group LTG Omar Bradley Omar N. Bradley Image 1st Army.svg 20px First United States Army U.S. First Army LTG Courtney Hodges Courtney H. Hodges 5th Free Belgian Forces Belgian Fusilier Battalion 143rd and 413th AA Gun Battalions 526th Armored Infantry Battalion 99th Infantry Battalion Norwegian Americans Image V Corps.svg 20px V Corps United States V Corps MG Leonard T. Gerow 102nd Cavalry Group, Mechanized 38th and 102nd Cavalry Recon Squadrons ... MacDonald, Charles B. A Time For Trumpets The Untold Story of the Battle of the Bulge. New York ... 5 DEFAULTSORT Battle Of The Bulge Order Of Battle Category World War II orders of battle ... more details
Infobox Single Name Up the Bracket Cover Libertines UpTheBracketSingle.jpg Artist The Libertines from Album Up The Bracket Released September 30, 2002 Format Compact Disc CD , Gramophone record 7 Genre Garage rock , post punk revival Length 2 38 Label Rough Trade Records Producer Mick Jones The Clash Mick Jones Last single What a Waster br 2002 This single Up the Bracket br 2002 Next single Time for Heroes br 2003 Up the Bracket is the second single from The Libertines and their first from debut album Up the Bracket . In May 2007, NME magazine placed Up the Bracket at number 47 in its list of the 50 Greatest Indie Anthems Ever. ref cite web url http www.nme.com news nme 28031 title The Greatest Indie Anthems Ever countdown continues accessdate 2007 05 02 date 2007 05 01 publisher NME ref Track listing CDS 1 Up the Bracket Boys in the Band Skag & Bone Man CDS 2 Up the Bracket The Delaney Plan A 7 Up the Bracket Boys in the Band Chart performance class wikitable align left Chart 2002 align left Peak br position ref cite web url http top40 charts.com song.php?sid 5191&sort chartid title Libertines Up The Bracket Top40 Charts.com accessdate 2007 10 26 publisher top40 charts.com ref align left UK Singles Chart align center 29 References references The Libertines Category 2002 singles Category The Libertines songs http www.songmeanings.net songs view 3530822107858502873 fr Up the Bracket chanson ja ... more details
In mathematics , the algebraic bracket or Nijenhuis Richardson bracket is a graded Lie algebra structure on the space of exterior product alternating multilinear forms of a vector space to itself, introduced by A. Nijenhuis and R. W. Richardson, Jr 1966, 1967 . It is related to but not the same as the Fr licher Nijenhuis bracket and the Schouten Nijenhuis bracket . Definition The primary motivation for introducing the bracket was to develop a uniform framework for discussing all possible Lie algebra structures on a vector space, and subsequently the deformation theory deformations of these structures. If V is a vector space and p &ge 1 is an integer, let math Alt p V wedge p 1 V otimes V math be the space of all skew symmetric p 1 multilinear mappings of V to itself. The direct sum Alt V is a graded vector space . A Lie algebra structure on V is determined by a skew symmetric bilinear map &mu V × V &rarr V . That is to say, &mu is an element of Alt sup 1 sup V . Furthermore, &mu must obey the Jacobi identity . The Nijenhuis Richardson bracket supplies a systematic manner for expressing this identity in the form &mu ,&mu 0. In detail, the bracket is a bilinear bracket operation defined on Alt V as follows. On homogeneous elements P &isin Alt sup p sup V and Q &isin Alt sup q sup V , the Nijenhuis Richardson bracket P , Q sup &and sup &isin Alt sup p q sup V is given by math ... elements, the bracket is extended by bilinearity. Derivations of the ring of forms The Nijenhuis Richardson bracket can be defined on the vector valued forms &Omega sup sup M , T M on a smooth ... bracket then corresponds to the commutator of two derivations. This identifies &Omega sup sup M ... for the structure of the full ring of all derivations see the article Fr licher Nijenhuis bracket . The Nijenhuis Richardson bracket and the Fr licher Nijenhuis bracket both make &Omega sup sup ... Fr licher Nijenhuis bracket P. W. Michor, H. Schicketanz, http arxiv.org math.DG 9201255 A cohomology ... more details
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