Displaying similar documents to “A characterization of symplectic groups related to Fermat primes”

Special Lagrangian linear subspaces in product symplectic space

Małgorzata Mikosz (2004)

Banach Center Publications

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The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism f : ( 2 n , σ = i = 1 n d x i d y i ) ( 2 n , σ ) to be a special Lagrangian linear subspace in ( 2 n × 2 n , ω = π * σ - π * σ ) . This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian S Λ 2 n S U ( 2 n ) / S O ( 2 n ) is defined.

Generalized Conley-Zehnder index

Jean Gutt (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit 1 as an eigenvalue. Robbin and Salamon define a generalization of the Conley-Zehnder index for any continuous path of symplectic matrices; this generalization is half integer valued. It is based on a Maslov-type index that they define for a continuous path of Lagrangians in a symplectic vector space ( W , Ω ¯ ) , having chosen a given...

Characterization of diffeomorphisms that are symplectomorphisms

Stanisław Janeczko, Zbigniew Jelonek (2009)

Fundamenta Mathematicae

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Let ( X , ω X ) and ( Y , ω Y ) be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that Φ * ω Y = c ω X .

𝒞 0 -rigidity of characteristics in symplectic geometry

Emmanuel Opshtein (2009)

Annales scientifiques de l'École Normale Supérieure

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The paper concerns a 𝒞 0 -rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.

Rational symplectic field theory over 2 for exact Lagrangian cobordisms

Tobias Ekholm (2008)

Journal of the European Mathematical Society

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We construct a version of rational Symplectic Field Theory for pairs ( X , L ) , where X is an exact symplectic manifold, where L X is an exact Lagrangian submanifold with components subdivided into k subsets, and where both X and L have cylindrical ends. The theory associates to ( X , L ) a -graded chain complex of vector spaces over 2 , filtered with k filtration levels. The corresponding k -level spectral sequence is invariant under deformations of ( X , L ) and has the following property: if ( X , L ) is obtained by...

Rabinowitz Floer homology and symplectic homology

Kai Cieliebak, Urs Frauenfelder, Alexandru Oancea (2010)

Annales scientifiques de l'École Normale Supérieure

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The first two authors have recently defined Rabinowitz Floer homology groups R F H * ( M , W ) associated to a separating exact embedding of a contact manifold ( M , ξ ) into a symplectic manifold ( W , ω ) . These depend only on the bounded component V of W M . We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V , which in turn maps to Rabinowitz Floer homology R F H * ( M , W ) , which then maps to symplectic cohomology of V . We compute R F H * ( S T * L , T * L ) , where S T * L is the unit cosphere bundle of a closed...

Symplectic critical surfaces in Kähler surfaces

Xiaoli Han, Jiayu Li (2010)

Journal of the European Mathematical Society

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Let M be a Kähler surface and Σ be a closed symplectic surface which is smoothly immersed in M . Let α be the Kähler angle of Σ in M . We first deduce the Euler-Lagrange equation of the functional L = Σ 1 cos α d μ in the class of symplectic surfaces. It is cos 3 α H = ( J ( J cos α ) ) , where H is the mean curvature vector of Σ in M , J is the complex structure compatible with the Kähler form ω in M , which is an elliptic equation. We call such a surface a symplectic critical surface. We show that, if M is a Kähler-Einstein surface...

On a divisibility problem

Shichun Yang, Florian Luca, Alain Togbé (2019)

Mathematica Bohemica

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Let p 1 , p 2 , be the sequence of all primes in ascending order. Using explicit estimates from the prime number theory, we show that if k 5 , then ( p k + 1 - 1 ) ! ( 1 2 ( p k + 1 - 1 ) ) ! p k ! , which improves a previous result of the second author.

Bigraphic pairs with a realization containing a split bipartite-graph

Jian Hua Yin, Jia-Yun Li, Jin-Zhi Du, Hai-Yan Li (2019)

Czechoslovak Mathematical Journal

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Let K s , t be the complete bipartite graph with partite sets { x 1 , ... , x s } and { y 1 , ... , y t } . A split bipartite-graph on ( s + s ' ) + ( t + t ' ) vertices, denoted by SB s + s ' , t + t ' , is the graph obtained from K s , t by adding s ' + t ' new vertices x s + 1 , ... , x s + s ' , y t + 1 , ... , y t + t ' such that each of x s + 1 , ... , x s + s ' is adjacent to each of y 1 , ... , y t and each of y t + 1 , ... , y t + t ' is adjacent to each of x 1 , ... , x s . Let A and B be nonincreasing lists of nonnegative integers, having lengths m and n , respectively. The pair ( A ; B ) is potentially SB s + s ' , t + t ' -bigraphic if there is a simple bipartite graph containing SB s + s ' , t + t ' (with s + s ' vertices x 1 , ... , x s + s ' in the part of size m ...

E 1 -degeneration and d ' d ' ' -lemma

Tai-Wei Chen, Chung-I Ho, Jyh-Haur Teh (2016)

Commentationes Mathematicae Universitatis Carolinae

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For a double complex ( A , d ' , d ' ' ) , we show that if it satisfies the d ' d ' ' -lemma and the spectral sequence { E r p , q } induced by A does not degenerate at E 0 , then it degenerates at E 1 . We apply this result to prove the degeneration at E 1 of a Hodge-de Rham spectral sequence on compact bi-generalized Hermitian manifolds that satisfy a version of d ' d ' ' -lemma.

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

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We consider elementary operators x j = 1 n a j x b j , acting on a unital Banach algebra, where a j and b j are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families a j and b j , i.e. a j = a j ' + i a j ' ' ( b j = b j ' + i b j ' ' ), where all a j ' and a j ' ' ( b j ' and b j ' ' ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class...

A compactness result in thin-film micromagnetics and the optimality of the Néel wall

Radu Ignat, Felix Otto (2008)

Journal of the European Mathematical Society

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In this paper, we study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem for S 1 -valued maps m ' (the magnetization) of two variables x ' : E ε ( m ' ) = ε | ' · m ' | 2 d x ' + 1 2 | ' | - 1 / 2 ' · m ' 2 d x ' . We are interested in the behavior of minimizers as ε 0 . They are expected to be S 1 -valued maps m ' of vanishing distributional divergence ' · m ' = 0 , so that appropriate boundary conditions enforce line discontinuities. For finite ε > 0 , these line discontinuities are approximated by smooth transition layers, the so-called Néel...

Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. Adams, Mathew Omonigho Omeike, Idowu A. Osinuga, Biodun S. Badmus (2023)

Mathematica Bohemica

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We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results....

Duality of matrix-weighted Besov spaces

Svetlana Roudenko (2004)

Studia Mathematica

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We determine the duals of the homogeneous matrix-weighted Besov spaces p α q ( W ) and p α q ( W ) which were previously defined in [5]. If W is a matrix A p weight, then the dual of p α q ( W ) can be identified with p ' - α q ' ( W - p ' / p ) and, similarly, [ p α q ( W ) ] * p ' - α q ' ( W - p ' / p ) . Moreover, for certain W which may not be in the A p class, the duals of p α q ( W ) and p α q ( W ) are determined and expressed in terms of the Besov spaces p ' - α q ' ( A Q - 1 ) and p ' - α q ' ( A Q - 1 ) , which we define in terms of reducing operators A Q Q associated with W. We also develop the basic theory of these reducing operator Besov spaces....

On hyperbolic partial differential equations in Banach spaces

Bogdan Rzepecki (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica z x y ′′ = f ( x , y , z , Z x , z y ) sul planiquarto x 0 , y 0 . Qui, f è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza α .

Convolution theorems for starlike and convex functions in the unit disc

M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)

Annales Polonici Mathematici

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Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let P β = f A : R e f ' ( z ) > β , z Δ . For λ > 0, suppose that denotes any one of the following classes of functions: M 1 , λ ( 1 ) = f : R e z ( z f ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 2 ) = f : R e z ( z ² f ' ' ( z ) ) ' ' > - λ , z Δ , M 1 , λ ( 3 ) = f : R e 1 / 2 ( z ( z ² f ' ( z ) ) ' ' ) ' - 1 > - λ , z Δ . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in γ or γ , γ ∈ [0,1/2]. Here γ and γ respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...

Existence of solutions for a coupled system with φ -Laplacian operators and nonlinear coupled boundary conditions

Konan Charles Etienne Goli, Assohoun Adjé (2017)

Communications in Mathematics

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We study the existence of solutions of the system ( φ 1 ( u 1 ' ( t ) ) ) ' = f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , ( φ 2 ( u 2 ' ( t ) ) ) ' = f 2 ( t , u 1 ( t ) , u 2 ( t ) , u 1 ' ( t ) , u 2 ' ( t ) ) , a.e. t [ 0 , T ] , submitted to nonlinear coupled boundary conditions on [ 0 , T ] where φ 1 , φ 2 : ( - a , a ) , with 0 < a < + , are two increasing homeomorphisms such that φ 1 ( 0 ) = φ 2 ( 0 ) = 0 , and f i : [ 0 , T ] × 4 , i { 1 , 2 } are two L 1 -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

On Fourier asymptotics of a generalized Cantor measure

Bérenger Akon Kpata, Ibrahim Fofana, Konin Koua (2010)

Colloquium Mathematicae

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Let d be a positive integer and μ a generalized Cantor measure satisfying μ = j = 1 m a j μ S j - 1 , where 0 < a j < 1 , j = 1 m a j = 1 , S j = ρ R + b j with 0 < ρ < 1 and R an orthogonal transformation of d . Then ⎧1 < p ≤ 2 ⇒ ⎨ s u p r > 0 r d ( 1 / α ' - 1 / p ' ) ( J x r | μ ̂ ( y ) | p ' d y ) 1 / p ' D ρ - d / α ' , x d , ⎩ p = 2 ⇒ infr≥1 rd(1/α’-1/2) (∫J₀r|μ̂(y)|² dy)1/2 ≥ D₂ρd/α’ , where J x r = i = 1 d ( x i - r / 2 , x i + r / 2 ) , α’ is defined by ρ d / α ' = ( j = 1 m a j p ) 1 / p and the constants D₁ and D₂ depend only on d and p.