Scalar differential concomitants of first order of a symmetric connexion $Γ^i_{jk}$ in the two-dimensional space and their applications

Michał Lorens

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Annales Polonici Mathematici

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Symmetric products of the Euclidean spaces and the spheres

Naotsugu Chinen (2015)

Commentationes Mathematicae Universitatis Carolinae

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By $F_{n} (X)$ , $n \geq 1$ , we denote the $n$ -th symmetric product of a metric space $(X, d)$ as the space of the non-empty finite subsets of $X$ with at most $n$ elements endowed with the Hausdorff metric $d_{H}$ . In this paper we shall describe that every isometry from the $n$ -th symmetric product $F_{n} (X)$ into itself is induced by some isometry from $X$ into itself, where $X$ is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the $n$ -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence...

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (2010)

Journal of the European Mathematical Society

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Suppose that $μ$ is an absolutely continuous probability measure on $^{R}$ n, for large $n$ . Then $μ$ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if $n \geq {(C / ε)}^{C d}$ , then there exist $d$ -dimensional marginals of $μ$ that are $ε$ -far from being sphericallysymmetric, in an appropriate sense. Here $C > 0$ is a universal constant.

Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

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$𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠$ , that is to say, Lorentzian manifolds with vanishing second derivative $\nabla \nabla R \equiv 0$ of the curvature tensor $R$ , are characterized by several geometric properties, and explicitly presented. Locally, they are a product $M = M_{1} \times M_{2}$ where each factor is uniquely determined as follows: $M_{2}$ is a Riemannian symmetric space and $M_{1}$ is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., $\nabla R \neq 0$ at some point), the curvature...

Taylor towers of symmetric and exterior powers

Brenda Johnson, Randy McCarthy (2008)

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We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ , in terms of the first terms in the Taylor towers of $S p^{t}$ and $Λ^{t}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $S p^{t}$ and $Λ^{t}$ . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_{k} S p ⁿ$ and $D_{k} Λ ⁿ$ .

Some properties for $α$ -starlike functions with respect to $k$ -symmetric points of complex order

H. E. Darwish, A. Y. Lashin, S. M. Sowileh (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In the present work, we introduce the subclass $𝒯_{γ, α}^{k} (ϕ)$ , of starlike functions with respect to $k$ -symmetric points of complex order $γ$ ( $γ \neq 0$ ) in the open unit disc . Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

The real symmetric matrices of odd order with a P-set of maximum size

Zhibin Du, Carlos M. da Fonseca (2016)

Czechoslovak Mathematical Journal

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Suppose that $A$ is a real symmetric matrix of order $n$ . Denote by $m_{A} (0)$ the nullity of $A$ . For a nonempty subset $α$ of ${1, 2, ..., n}$ , let $A (α)$ be the principal submatrix of $A$ obtained from $A$ by deleting the rows and columns indexed by $α$ . When $m_{A (α)} (0) = m_{A} (0) + | α |$ , we call $α$ a P-set of $A$ . It is known that every P-set of $A$ contains at most $⌊ n / 2 ⌋$ elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As...

On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

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Annales Polonici Mathematici

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P. Srivastava, K. K. Azad (1981)

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$ℵ_{1}$ -incompactness of Z

Ralph McKenzie (1971)

Colloquium Mathematicae

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On a characterization of $L^{p}$ -norm

Janusz Matkowski (1989)

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Stephan Baier (2004)

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The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

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On the equation $ϕ (x + m) = ϕ (x) + m$

A. Makowski (1964)

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Stephan Baier (2005)

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M. K. Aouf (1988)

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An application of the method wherein the $p h i$ - and $c h i$ - methods are combined for the determination of the grating constant. [II.]

Swami Jnanananda (1936)

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Weakly hyperbolic equations of second order well-posed in some Gevrey classes

Enrico Jannelli (1983)

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

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L’equazione $u_{tt}=\sum_{ij=1}^{n}(a_{ij}(x,t)u_{x_{j}})_{x_{i}}$ in condizioni di debole iperbolicità $\big{(}\sum_{ij=1}^{n}a_{ij}(x,t)\xi_{i}\xi_{j}\geq 0\big{)}$ , è ben posta negli spazi di Gevrey $\gamma^{(s)}_{loc}$ con $1\leq s<1+\frac{\sigma}{2}$ , purché $a_{ij}$ sia di Gevrey in $x$ di ordine $s$ e risulti $\Big{[}\sum_{ij=1}^{n}a_{ij}(x,t)\xi_{i}\xi_{j}\Big{]}^{1/\sigma}\in BV\,([0,T% ]:\mathbf{L}_{loc}^{\infty})$

Sharp Ratio Inequalities for a Conditionally Symmetric Martingale

Adam Osękowski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let f be a conditionally symmetric martingale and let S(f) denote its square function. (i) For p,q > 0, we determine the best constants $C_{p, q}$ such that $s u p_{n} {(| f ₙ |}^{p} {) / (1 + S ₙ ² (f))}^{q} \leq C_{p, q}$ . Furthermore, the inequality extends to the case of Hilbert space valued f. (ii) For N = 1,2,... and q > 0, we determine the best constants $C_{N, q}^{'}$ such that $s u p_{n} (f ₙ^{2 N - 1}) {(1 + S ₙ ² (f))}^{q} \leq C_{N, q}^{'}$ . These bounds are extended to sums of conditionally symmetric variables which are not necessarily integrable. In addition, we show that neither of the inequalities above holds if...

Displaying similar documents to “Scalar differential concomitants of first order of a symmetric connexion Γ j k i in the two-dimensional space and their applications”

Displaying similar documents to “Scalar differential concomitants of first order of a symmetric connexion $Γ_{j k}^{i}$ in the two-dimensional space and their applications”