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"FLAG"
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Flag-Transitive 2-v,5,λ Designs Admitting a Two-Dimensional Projective Group
2024
The focus of this study is to classify flag-transitive 2-designs. We have come to the conclusion that if D is a nontrivial 2-design having block size 5 and G is a two-dimensional projective special linear group which acts flag-transitively on D with q≢1 (mod 4), then D is a 2-(11, 5, 2) design, a 2-(11, 5, 12) design, a 2-q+1,5,2q−1 design with q≡3 (mod 4) or a 2-q+1,5,q−1/3 design with q=2f (where f>2 is an even).
Journal Article
Affine flag varieties and quantum symmetric pairs
by
Wang, Weiqiang
,
Lai, Chun-Ju
,
Fan, Zhaobing
in
Affine algebraic groups
,
Algebra, Homological
,
Flag manifolds
2020
The quantum groups of finite and affine type A admit geometric realizations in terms of partial flag varieties of finite and affine type A. Recently, the quantum group associated to partial flag varieties of finite type B/C is shown to be a coideal subalgebra of the quantum group of finite type A. In this paper the authors study the structures of Schur algebras and Lusztig algebras associated to (four variants of) partial flag varieties of affine type C. The authors show that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine \\mathfrak{sl} and \\mathfrak{gl} types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types. The authors construct monomial and canonical bases of all these quantum (Schur, Lusztig, and coideal) algebras. For the idempotented coideal algebras of affine \\mathfrak{sl} type, the authors establish the positivity properties of the canonical basis with respect to multiplication, comultiplication and a bilinear pairing. In particular, the authors obtain a new and geometric construction of the idempotented quantum affine \\mathfrak{gl} and its canonical basis.
Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting
by
Han, Yongsheng
,
Wick, Brett D.
,
Lee, Ming-Yi
in
Hardy spaces
,
Littlewood-Paley theory
,
Maximal functions
2022
In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag
setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood–Paley square function
and area integral, Riesz transforms and the atomic decomposition in the multi-parameter flag setting. The novel ingredients in this
paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the
Plancherel–Pólya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels
and flag version of harmonic functions; (3) developing an atomic decomposition via the finite speed propagation and area function in
terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the
multi-parameter Hardy space with the flag structure.
931 EP061 – Injuries can be prevented in contact flag football
2024
PurposeThis original prospective cohort study was conducted in an attempt to significantly reduce the incidence and the severity of injuries in an intervention cohort as compared to a two-season historical cohort, and to provide recommendations to the International Federation of Football (IFAF) pertaining to prevention measures to make the game safer.Methods1260 amateur male (mean age: 20.4 ± 3.9yrs) and 244 female (mean age: 18.5 ± 1.7 yrs) players participated in the study. Four prevention measures were implemented: The no-pocket rule, self-fitting mouth guards, ankle braces (for those players with recurrent ankle sprains) and an injury treatment information brochure.All time-loss injuries sustained in game sessions were recorded by the off-the-field medical personnel and followed up by a more detailed phone injury surveillance questionnaire.Results There was an 54% reduction in the total number of injuries, and a significant reduction in the incidence rate and incidence proportion between the intervention cohort as compared to the historical cohort (P<0.001). There was no statistically significant reduction in the number of injuries in any of the body parts, except for in hand/wrist injuries related to the use of pockets (p<0.001), as well as the severity of mild-moderate injuries (p<0.05).ConclusionsThis study provided evidence that hand/wrist injuries can be significantly reduced in flag football. Recommendations to the IFAF include strict enforcement of the no-pocket rule, the use of soft headgear, comfortable-fitting ankle braces and mouth guards and additionally, to change game rules concerning blocking.
Journal Article
Trump calls London protests against his trip 'fake news'
in
Flags
2019
While large crowds were protesting his visit to London, President Trump dismissed the demonstrations as \"fake news\" at a June 4 press conference with the British prime minister.
Streaming Video
Tom Brady to play flag football in Saudi Arabia
in
Brady, Tom
,
Flag football
2025
Ava Wallace and Ben Strauss break down why some current and former NFL players are going to play flag football in Saudi Arabia, and how Fanatics is involved.
Streaming Video