Displaying similar documents to “The infinitesimal counterpart of tangent presymplectic groupoids of higher order”

Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

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Given a groupoid G , , and k 3 , we say that G is antiassociative if an only if for all x 1 , x 2 , x 3 G , ( x 1 x 2 ) x 3 and x 1 ( x 2 x 3 ) are never equal. Generalizing this, G , is k -antiassociative if and only if for all x 1 , x 2 , ... , x k G , any two distinct expressions made by putting parentheses in x 1 x 2 x 3 x k are never equal. We prove that for every k 3 , there exist finite groupoids that are k -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

On the topology of polynomials with bounded integer coefficients

De-Jun Feng (2016)

Journal of the European Mathematical Society

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For a real number q > 1 and a positive integer m , let Y m ( q ) : = i = 0 n ϵ i q i : ϵ i 0 , ± 1 , ... , ± m , n = 0 , 1 , ... . In this paper, we show that Y m ( q ) is dense in if and only if q < m + 1 and q is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

L p inequalities for the growth of polynomials with restricted zeros

Nisar A. Rather, Suhail Gulzar, Aijaz A. Bhat (2022)

Archivum Mathematicum

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Let P ( z ) = ν = 0 n a ν z ν be a polynomial of degree at most n which does not vanish in the disk | z | < 1 , then for 1 p < and R > 1 , Boas and Rahman proved P ( R z ) p ( R n + z p / 1 + z p ) P p . In this paper, we improve the above inequality for 0 p < by involving some of the coefficients of the polynomial P ( z ) . Analogous result for the class of polynomials P ( z ) having no zero in | z | > 1 is also given.

Global analytic and Gevrey surjectivity of the Mizohata operator D 2 + i x 2 2 k D 1

Lamberto Cattabriga, Luisa Zanghirati (1990)

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

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The surjectivity of the operator D 2 + i x 2 2 k D 1 from the Gevrey space E s R 2 , s 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

Geometric rigidity of × m invariant measures

Michael Hochman (2012)

Journal of the European Mathematical Society

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Let μ be a probability measure on [ 0 , 1 ] which is invariant and ergodic for T a ( x ) = a x 𝚖𝚘𝚍 1 , and 0 < 𝚍𝚒𝚖 μ < 1 . Let f be a local diffeomorphism on some open set. We show that if E and ( f μ ) E μ E , then f ' ( x ) ± a r : r at μ -a.e. point x f - 1 E . In particular, if g is a piecewise-analytic map preserving μ then there is an open g -invariant set U containing supp μ such that g U is piecewise-linear with slopes which are rational powers of a . In a similar vein, for μ as above, if b is another integer and a , b are not powers of a common integer, and if ν is...

A Hardy type inequality for W 0 m , 1 ( Ω ) functions

Hernán Castro, Juan Dávila, Hui Wang (2013)

Journal of the European Mathematical Society

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We consider functions u W 0 m , 1 ( Ω ) , where Ω N is a smooth bounded domain, and m 2 is an integer. For all j 0 , 1 k m - 1 , such that 1 j + k m , we prove that i u ( x ) d ( x ) m - j - k W 0 k , 1 ( Ω ) with k ( i u ( x ) d ( x ) m - j - k ) L 1 ( Ω ) C u W m , 1 ( Ω ) , where d is a smooth positive function which coincides with dist ( x , Ω ) near Ω , and l denotes any partial differential operator of order l .

On square functions associated to sectorial operators

Christian Le Merdy (2004)

Bulletin de la Société Mathématique de France

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We give new results on square functions x F = 0 F ( t A ) x 2 d t t 1 / 2 p associated to a sectorial operator A on L p for 1 &lt; p &lt; . Under the assumption that A is actually R -sectorial, we prove equivalences of the form K - 1 x G x F K x G for suitable functions F , G . We also show that A has a bounded H functional calculus with respect to . F . Then we apply our results to the study of conditions under which we have an estimate ( 0 | C e - t A ( x ) | 2 d t ) 1 / 2 q M x p , when - A generates a bounded semigroup e - t A on L p and C : D ( A ) L q is a linear mapping.

A propagation theorem for a class of microfunctions

Andrea D&amp;#039;Agnolo, Giuseppe Zampieri (1990)

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

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Let A be a closed set of M R n , whose conormai cones x + y x * A , x A , have locally empty intersection. We first show in §1 that dist x , A , x M A is a C 1 function. We then represent the n microfunctions of C A | X , X C n , using cohomology groups of O X of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of C A | X π ˙ - 1 x 0 , x 0 A , satisfy the principle of the analytic continuation in the complex integral manifolds of H ϕ i C i = 1 , , m , ϕ i being a base for the linear hull of γ x 0 * A in T x 0 * M ; in particular we get Γ A × M T * M X C A | X A × M T ˙ * M X = 0 . When A is a half space with...

Embeddings between weighted Copson and Cesàro function spaces

Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver (2017)

Czechoslovak Mathematical Journal

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In this paper, characterizations of the embeddings between weighted Copson function spaces Cop p 1 , q 1 ( u 1 , v 1 ) and weighted Cesàro function spaces Ces p 2 , q 2 ( u 2 , v 2 ) are given. In particular, two-sided estimates of the optimal constant c in the inequality d ( 0 0 t f ( τ ) p 2 v 2 ( τ ) d τ q 2 / p 2 u 2 ( t ) d t ) 1 / q 2 c 0 t f ( τ ) p 1 v 1 ( τ ) d τ q 1 / p 1 u 1 ( t ) d t 1 / q 1 , d where p 1 , p 2 , q 1 , q 2 ( 0 , ) , p 2 q 2 and u 1 , u 2 , v 1 , v 2 are weights on ( 0 , ) , are obtained. The most innovative part consists of the fact that possibly different parameters p 1 and p 2 and possibly different inner weights v 1 and v 2 are allowed. The proof is based on the combination of duality techniques...

Calculus of variations with differential forms

Saugata Bandyopadhyay, Bernard Dacorogna, Swarnendu Sil (2015)

Journal of the European Mathematical Society

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We study integrals of the form Ω f d ω , where 1 k n , f : Λ k is continuous and ω is a k - 1 -form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.

Invariants for the modular cyclic group of prime order via classical invariant theory

David L. Wehlau (2013)

Journal of the European Mathematical Society

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Let 𝔽 be any field of characteristic p . It is well-known that there are exactly p inequivalent indecomposable representations V 1 , V 2 , ... , V p of C p defined over 𝔽 . Thus if V is any finite dimensional C p -representation there are non-negative integers 0 n 1 , n 2 , ... , n k p - 1 such that V i = 1 k V n i + 1 . It is also well-known there is a unique (up to equivalence) d + 1 dimensional irreducible complex representation of S L 2 ( ) given by its action on the space R d of d forms. Here we prove a conjecture, made by R. J. Shank, which reduces the computation...

Existence and multiplicity of solutions for a fractional p -Laplacian problem of Kirchhoff type via Krasnoselskii’s genus

Ghania Benhamida, Toufik Moussaoui (2018)

Mathematica Bohemica

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We use the genus theory to prove the existence and multiplicity of solutions for the fractional p -Kirchhoff problem - M Q | u ( x ) - u ( y ) | p | x - y | N + p s d x d y p - 1 ( - Δ ) p s u = λ h ( x , u ) in Ω , u = 0 on N Ω , where Ω is an open bounded smooth domain of N , p > 1 , N > p s with s ( 0 , 1 ) fixed, Q = 2 N ( C Ω × C Ω ) , λ > 0 is a numerical parameter, M and h are continuous functions.