You are looking at 251 - 260 of 11,089 items for :

  • Mathematics and Statistics x
  • Refine by Access: All Content x
Clear All

We prove:

  1. (A) Let
    \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\Delta _c (x) = \log \frac{{\Gamma (x + 1)}}{{\sqrt {2\pi } (x/e)^x }} - \frac{1}{2}\psi (x + c) (x > 0; c \geqq 0).$$ \end{document}
    1. (i) −Δc is completely monotonic on (0, ∞) if and only if c ≧ 2/3.
    2. (ii) Δc is completely monotonic on (0, ∞) if and only if c = 0.
  2. (B) The inequalities
    \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{1}{2}\psi (x + a_0 ) < \log \frac{{\Gamma (x + 1)}}{{\sqrt {2\pi } (x/e)^x }} < \frac{1}{2}\psi (x + b_0 )$$ \end{document}
    hold for all x > 0 with the best possible constants a 0 = 0.52660… and b 0 = 2/3.

Restricted access

We prove the theorem mentioned in the title for ℝn where n ≧ 3. The case of the simplex was known previously. Also the case n = 2 was settled, but there the infimum was some well-defined function of the side lengths. We also consider the cases of spherical and hyperbolic n-spaces. There we give some necessary conditions for the existence of a convex polytope with given facet areas and some partial results about sufficient conditions for the existence of (convex) tetrahedra.

Restricted access
On étudie la positivité complète du noyau de convolution multiplicatif T associé au produit de deux variables aléatoires indépendantes B(a, b) et Γ(c). Ce noyau T est complétement positif d’ordre infini si b ∈ ℕ* ou si d = a + bc ∈ ℕ. Dans les autres cas la régularité du signe de T a toujours un ordre fini, qui est ici calculé. Plus précisément, pour tout n ≧ 1 on montre que T est complètement positif d’ordre n + 1 si et seulement si (d, b) est situé au dessus d’un certain escalier
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{E}_n$$ \end{document}
dessiné dans le demi-plan supérieur. Cet escalier caractérise aussi la constance du signe de plusieurs déterminants associés á la fonction hypergéométrique confluente de seconde espèce.
Restricted access

We analyse the oscillation and non-oscillation of second-order half-linear differential equations with periodic and asymptotically almost periodic coefficients, where the equations have the so-called Riemann-Weber form. For these equations, we find an explicit oscillation constant. Corollaries and examples are mentioned as well.

Restricted access
In this study, we define the spaces
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde M_u ,\,\tilde C_p ,\,\tilde C_{0p} ,\,\tilde C_{bp} ,\,\tilde C_r \,{\text{and}}\,\tilde L_q$$ \end{document}
of double sequences whose Cesàro transforms are bounded, convergent in the Pringsheim’s sense, null in the Pringsheim’s sense, both convergent in the Pringsheim’s sense and bounded, regularly convergent and absolutely q-summable, respectively, and also examine some properties of those sequence spaces. Furthermore, we show that these sequence spaces are Banach spaces. We determine the alpha-dual of the space
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde M_u$$ \end{document}
and the β(bp)-dual of the space
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde C_r$$ \end{document}
, and β(ϑ)-dual of the space
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde C_\eta$$ \end{document}
of double sequences, where ϑ, η ∈ {p, bp, r}. Finally, we characterize the classes (
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde C_{bp}$$ \end{document}
: C ϑ) and (μ:
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tilde C_\vartheta$$ \end{document}
) for ϑ ∈ {p, bp, r} of four dimensional matrix transformations, where μ is any given space of double sequences.
Restricted access

In this paper we study left amenability of Lau algebras by introducing left approximate diagonal and virtual diagonal for Lau algebras. Some results related to Hahn-Banach theorem property on foundation topological semigroups are obtained. We introduce the left contractibility of Lau algebras. Some examples for clarifying that left contractibility of Lau algebras is stronger than left amenability of them are given.

Restricted access

The problem when a paratopolgical group (or semitopological group) is a topological group is interesting and important. In this paper, we continue to study this problem. It mainly shows that: (1) Let G be a paratopological group and put τ = ω H s(G); then G is a topological group if G is a P τ-space; (2) every co-locally countably compact paratopological group G with ω H s(G) ≦ ω is a topological group; (3) every co-locally compact paratopological group is a topological group; (4) each 2-pseudocompact paratopological group G with ω H s(G) ≦ ω is a topological group. These results improve some results in [11, 13].

Restricted access

Let (R, m) be a Noetherian local ring and M a finitely generated R-module. In this paper, we study some invariants of the idealization RM of R and M such as the polynomial type introduced by Cuong [2] and the polynomial type of fractions introduced by Cuong-Minh [3]. As consequences, we characterize the Cohen-Macaulay, generalized Cohen-Macaulay, pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay properties of the idealization RM.

Restricted access

We are studying the representations of Artin’s braid group B n.

Restricted access

In this note the proof of a slight generalization of the Maximal Ergodic Inequality is a bit simplified and it is shown that from this generalized inequality Birkhoff’s Pointwise Ergodic Theorem follows almost immediately.

Restricted access