49,170 research outputs found
ON WEIGHTED COMPLEX RANDERS METRICS
No full textNSF [DMS 0713348]; NCETFJ; NSFC [10971170, 10601040]In this paper we introduce the weighted complex Randers metric F = h + Sigma(m)(i=1)vertical bar B(i)vertical bar(1/i) on a complex manifold M, here h is a Hermitian metric on M and B(i), i = 1 , ... ,m are holomorphic symmetric forms of weights i on M, respectively. These metrics are special case of jet metric studied in Chandler Wong [6]. Our main theorem is that the holomorphic sectional curvature hbsc(F) of F is always less or equal to hbsc(h). Using this result we obtain a rigidity result, that is, a compact complex manifold M of complex dimension n with a weighted complex Randers metric F of positive constant holomorphic sectional curvature is isomorphic to P(n)
Einstein metrics of Randers type
No full textThis thesis presents a study of Einstein Randers metrics. Initially introduced
within the context of relativity, Randers metrics have a strong
presence in both the theory and applications of Finsler geometry. The starting
point is a new characterization of Einstein metrics of Randers type by
three conditions. The conditions form a coupled, highly non-linear (due to
the presence of a Riemannian Ricci tensor), second order system of partial
differential equations. The equations are polynomial in the unknowns; a
Riemannian metric ã and differential 1-form b.
Recently Z. Shen has generalized Zermelo's problem of navigation on the
plane to arbitrary Riemannian manifolds. (The goal is to identify the paths
of shortest time on a Riemannian manifold (M, ă) under the influence of an
external force W = Wi∂xi.) In this context, Randers metrics may be viewed
as solutions to Zermelo's problem. The navigation structure yields the main
result of the thesis, a succinct geometric description of Einstein metrics
of Randers type. Explicitly, the Randers metric arising as the solution to
Zermelo's problem on (ă, W) is Einstein if and only if the Riemannian metric
ă is Einstein itself, and W is an infinitesimal homothety of ă.
The navigation description quickly yields a Schur lemma for the Ricci
curvature of Randers metrics. It is a testament to the navigation description
that this result, the first Schur lemma for Ricci curvature in (non-
Riemannian) Finsler geometry, is obtained with relative ease. An extension
of Matsumoto's Identity for Randers metrics of constant flag curvature to
the Einstein setting then follows.
Having established these general results, I then explore three scenarios:
Einstein metrics on surfaces of revolution, constant flag curvature metrics,
and Einstein metrics on closed manifolds. The thesis closes with a collection
of open questions.Science, Faculty ofMathematics, Department ofGraduat
On the Projective Algebra of Randers Metrics of Constant Flag Curvature
Full text linkThe collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2
On generalized Douglas-Weyl Randers metrics
Full text linksummary:We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is not Einsteinian. By using -homothetic deformation of a Kenmotsu or Sasakian manifold, we construct a family of generalized Douglas-Weyl Randers metrics and show that the Lie group of projective transformations does not act transitively on the set of generalized Douglas-Weyl Randers metrics
Fællesskab og integration – De bosniske krigsflygtninge i Randers 1993-2010
Full text linkKulturhistorisk Museum Randers har i de senere år sat øget fokus på byens indvandrerhistorie. I 2003 dokumenterede museet de tyrkiske gæstearbejderes historie, og i 2005 blev der set nærmere på tyrkernes børn. Tyrkerne var den første store gruppe af indvandrere i Randers, men er i antal siden blevet overhalet af bosnierne, hvoraf de første kom til byen som krigsflygtninge i 1993. Denne artikel er baseret på en undersøgelse af de bosniske krigsflygtninge, som museet foretog henover sommeren 2010. Udover at klarlægge det historiske forløb for bosniernes tilværelse i Randers, giver undersøgelsen gennem tolv interviews et indblik i, hvordan bosnierne er faldet til i byen. Det beskrives desuden, hvorledes det er at være bosnier i Randers i dag. Interviewgruppen udgjordes af otte kvinder og fire mænd. Blandt kvinderne var der fire, der aldersmæssigt befandt sig i tyverne, mens de resterende befandt sig i henholdsvis trediverne, fyrrerne og halvtredserne. For mændenes vedkommende var den ene halvdel i fyrrerne og den anden i halvtredserne. Undersøgelsen viser blandt andet, at de mål for integration, som Randers Kommune satte sig, da det fra 1995 stod klart, at de bosniske flygtninge ville blive i byen, på de fleste områder stemte overens med ønskerne fra størstedelen af bosnierne. For kommunen blev det i løbet af kort tid det væsentligste, at de mange nye borgere blev i stand til at klare sig selv gennem sprog, beskæftigelse og bolig, mens det for bosniernes vedkommende handlede om hurtigst muligt at komme i gang med det liv, som krig og uvished havde afbrudt. At de bosniske flygtninge skulle integreres socialt i det danske fællesskab og gennem danske netværk var af begge parter prioriteret lavere. Selvom kontakten til danskerne i Randers stadig mest er begrænset til arbejde og uddannelse, opfattes bosnierne i Randers i dag, både af dem selv og den danske majoritetsbefolkning, alligevel som den mest velintegrerede større indvandrergruppe i byen
Fællesskab og integration – De bosniske krigsflygtninge i Randers 1993-2010
Full text linkKulturhistorisk Museum Randers har i de senere år sat øget fokus på byens indvandrerhistorie. I 2003 dokumenterede museet de tyrkiske gæstearbejderes historie, og i 2005 blev der set nærmere på tyrkernes børn. Tyrkerne var den første store gruppe af indvandrere i Randers, men er i antal siden blevet overhalet af bosnierne, hvoraf de første kom til byen som krigsflygtninge i 1993. Denne artikel er baseret på en undersøgelse af de bosniske krigsflygtninge, som museet foretog henover sommeren 2010. Udover at klarlægge det historiske forløb for bosniernes tilværelse i Randers, giver undersøgelsen gennem tolv interviews et indblik i, hvordan bosnierne er faldet til i byen. Det beskrives desuden, hvorledes det er at være bosnier i Randers i dag. Interviewgruppen udgjordes af otte kvinder og fire mænd. Blandt kvinderne var der fire, der aldersmæssigt befandt sig i tyverne, mens de resterende befandt sig i henholdsvis trediverne, fyrrerne og halvtredserne. For mændenes vedkommende var den ene halvdel i fyrrerne og den anden i halvtredserne. Undersøgelsen viser blandt andet, at de mål for integration, som Randers Kommune satte sig, da det fra 1995 stod klart, at de bosniske flygtninge ville blive i byen, på de fleste områder stemte overens med ønskerne fra størstedelen af bosnierne. For kommunen blev det i løbet af kort tid det væsentligste, at de mange nye borgere blev i stand til at klare sig selv gennem sprog, beskæftigelse og bolig, mens det for bosniernes vedkommende handlede om hurtigst muligt at komme i gang med det liv, som krig og uvished havde afbrudt. At de bosniske flygtninge skulle integreres socialt i det danske fællesskab og gennem danske netværk var af begge parter prioriteret lavere. Selvom kontakten til danskerne i Randers stadig mest er begrænset til arbejde og uddannelse, opfattes bosnierne i Randers i dag, både af dem selv og den danske majoritetsbefolkning, alligevel som den mest velintegrerede større indvandrergruppe i byen.</p
Heart Rate and Perceived Experience Differ Markedly for Children in Same- versus Mixed-Gender Soccer Played as Small- and Large-Sided Games
Full text linkThis study examines heart rate (HR) and perceived experience during same- versus mixed-gender soccer played as small- (SSG) and large-sided (LSG) games. HR, rating of perceived exertion (RPE), and fun scores were determined in 134 pupils (50 girls, 84 boys) randomly assigned to same- and mixed-genders formats playing 2x15-min of SSG (2v2, 4v4) and LSG (12v12) in a random order (50 m2/player). HR was lower (p≤0.03) for girls when playing together with boys than when playing alone (71±10 versus 77±7%HRmax), while being similar for boys playing mixed- or same-gender games (74±7 versus 77±4%HRmax). Boys perceived less fun when playing together with girls than when playing alone (4.4±2.3 versus 6.3±2.3, p<0.001). Irrespective of gender, higher (p<0.001) HRmean, %time>80%HRmax, and RPE were observed during 2v2 (78±9%HRmax, 43±33%, 5.5±2.5) and 4v4 (76±9%HRmax, 39±32%, 5.5±2.7) than during 12v12 (70±10%HRmax, 23±27%, 3.8±2.9). Cardiovascular strain was lower for girls when playing together with boys than when playing alone in LSG. SSG were more intense than LSG when girls played mixed-gender games and when boys played mixed- and same-gender games. When boys played mixed-gender games, SSG were considered more fun than LSG. Physical education teachers and coaches should consider gender and game format differences when using soccer.</p
Measurement of the ratio of branching fractions B(B0→K∗0γ )/B(B0s→φγ ) and the directCP asymmetry inB 0→K∗0γ
Full text linkThe ratio of branching fractions of the radiative B decays B0→K⁎0γ and B0s→ϕγ has been measured using an integrated luminosity of 1.0 fb−1 of pp collision data collected by the LHCb experiment at a centre-of-mass energy of s√=7TeV. The value obtained is
B(B0→K⁎0γ)B(B0s→ϕγ)=1.23±0.06(stat.)±0.04(syst.)±0.10(fs/fd),
where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is associated with the ratio of fragmentation fractions fs/fd. Using the world average value for B(B0→K⁎0γ), the branching fraction B(B0s→ϕγ) is measured to be (3.5±0.4)×10−5.
The direct CP asymmetry in B0→K⁎0γ decays has also been measured with the same data and found to be
ACP(B0→K⁎0γ)=(0.8±1.7(stat.)±0.9(syst.))%.
Both measurements are the most precise to date and are in agreement with the previous experimental results and theoretical expectations
Maximal Strength, Sprint, and Jump Performance in High-Level Female Football Players Are Maintained With a Customized Training Program During the COVID-19 Lockdown
Full text linkIntroduction: The COVID-19 outbreak with partial lockdown has inevitably led to an alteration in training routines for football players worldwide. Thus, coaches had to face with the novel challenge of minimizing the potential decline in fitness during this period of training disruption. Methods: In this observational pre- to posttest study involving Norwegian female football players (18.8 ± 1.9 years, height 1.68 ± 0.4 m, mass 61.3 ± 3.7 kg), we investigated the effects of a prescribed home-based and group-based intervention, implemented during the COVID-19 lockdown, on maximal muscular force production and high velocity variables. Specifically, maximal partial squat strength one repetition maximum (1RM), counter movement jump (CMJ) and 15 m sprint time were assessed 1 week prior to the lockdown and 12 weeks after the onset of lockdown. We also collected training content and volume from the prescribed training program and self-reported perceived training quality and motivation toward training. Results: We observed no change in 1RM [pretest: 104 ± 12 kg, posttest: 101 ± 11 kg (P = 0.28)], CMJ height [pretest: 28.1 ± 2.3 cm, posttest: 26.8 ± 1.9 (P = 0.09)], and 15 m sprint time [pretest: 2.60 ± 0.08 s, posttest: 2.61 ± 0.07 s (P = 0.52)]. Conclusion: Our findings suggest that a prescribed home-based and group-based intervention with increased training time devoted to strength, jump, and sprint ability, and regulated to obtain a sufficient infection control level is feasible and effective to preserve strength, jumping, and sprinting abilities of high-level female football players during a ∼ 3-month period of a pandemic-induced lockdown
The Kropina change of the projectively flat Randers metrics
Full text linkboyutlu bir manifoldu üzerinde bir Riemann metriği ve bir diferansiyel form olsun. aralığında sınıfından koşulunu sağlayan pozitif bir fonksiyon olmak üzere, fonksiyonunu göz önüne alalım. Herhangi bir için ise, fonksiyonu bir Finsler metriği oluşturur. Bu şekilde tanımlanan Finsler metriklerine metriği adı verilir. alınırsa metriklerinin özel bir sınıfını oluşturan Randers metriği elde edilir. ve , sırasıyla, ve metriklerine sahip iki Finsler uzayı olsun. ile tanımlanan metrik dönüşümüne bir Kropina dönüşümü denir (Singh, Prasad ve Kumari, 2003). Özel olarak, bir Riemann uzayının metriği olarak alınırsa, , bir Kropina uzayının metriğine indirgenmiş olur (Shen, 2001). Bu çalışmada, öncelikle aralarında bir Kropina dönüşümü tanımlı olan iki Finsler uzayının sprey katsayıları arasındaki ilişki elde edilmiştir. Daha sonra, bir Randers metriğinin projektif düz olması için gerek ve yeter olan koşulların, bu ilişkide kullanılması ile “projektif-düz bir Randers uzayını, projektif-düz bir Finsler uzayına dönüştüren Kropina dönüşümü” için gerek ve yeter koşul elde edilmiş ve bu koşul altında Finsler dönüşüm uzayının skaler flag eğriliği elde edilmiştir. Anahtar Kelimeler: Kropina dönüşümü, Randers metrikleri, -eğrilik, flag eğrilik, skaler flag eğrilik.Let M be a manifold. A function satisfying the following properties is called a Finsler metric: a) F is on b) for any , is a Minkowski norm on . The pair (M,F) is called a Finsler space. Let be a Riemannian metric and be a differential form on an dimensional manifold . Consider the function where is a positive function on and satisfying. Then, is a Finsler metric if for any (Shen Z., 2001). If then F becomes Randers metric. Every Finsler metric and the spray coefficients of induce a spray which determines the geodesics of M (Shen Z., 2001, Abate and Patrizio, 1994). And the spray coefficients of are . A geodesic on a Finsler space is given by the differential equation A Finsler metric on an open subset is projectively flat if and only if it satisfies the following system of equations (Rapcsák, 1961). In this case, the spray coefficients of are , where is given by. The scalar function is called the projective factor of . The Riemann curvature of a manifold with a Berwald connection is defined by For a tangent plane containing the flag curvature is defined by , where such that . If (a scalar function), is said to be of scalar flag curvature. If , is said to have a constant flag curvature (Bao and Robles, 2004, Shen Z., 2004). The transformation of the Finsler metric given by is called a Kropina change. If is a metric function of a Riemannian space, then reduces to the metric function of the Kropina space. In this work, a Kropina change of the metric function given by between projectively flat Randers space with metric and the Finsler space with metric is studied and it is proved that the Finsler space is projectively flat under a Kropina change if and only if the differential equation is satisfied. Next, it is shown that for a Kropina change between a projectively flat Randers space and a projectively flat Finsler space, the scalar flag curvature of is. Keywords: Kropina change, Randers metrics, -curvature, flag curvature, scalar flag curvature.
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