The classical Hardy theorem on $\rr$ was generalized by Miyachi and Bonami, Demange, and Jaming. In this paper we show that Miyachi's theorem and Bonami-Demange-Jaming's one can be reformulated for the Jacobi transform in terms of the heat kernel.

The purpose of this paper is to study the stable extendibility of the tangent bundle $\tau_n(p)$ of the $(2n+1)$-\hspace dimensional standard lens space $\mL^n(p)$ for odd prime $p$. We investigate the value of integer $m$ for which $\tau_n(p)$ is stably extendible to $\mL^m(p)$ but not stably extendible to $\mL^{m+1}(p)$, and in particular we completely determine $m$ for $p=5$ or $7$. A stable splitting of $\tau_n(p)$ and the stable extendibility of a Whitney sum of $\tau_n(p)$ are also discussed.

In this paper, we give a formula for the quandle cocycle invariants associated with the Fox shadow $p$-coloring of all pretzel link.

In the present paper static and dynamical one-dimensional models for elastic rods are constructed. The existence and uniqueness of solutions to the corresponding boundary and initial boundary value problems are proved, the rate of approximation of the solutions to the original three-dimensional problems by vector-functions restored from the solutions of one-dimensional problems is estimated.

Bivariate and univariate gamma distributions are some of the most popular models for hydrological processes. In fact, the intensity and the duration of most hydrological variables are frequently modeled by gamma distributions. This raises the important question: what is the distribution of the total amount = intensity $\times$ duration? In this paper, the exact distribution of $P = X Y$ and the corresponding moment properties are derived when the random vector $(X, Y)$ has two of the most flexible bivariate gamma distributions. The expressions turn out to involve several special functions.

Let $r,k$ be integers with $r\ge 3, k\ge 2$. We prove that if $G$ is a $K_{1,r}$-free graph of order at least $(k-1)(2r-1)+1$ with $\delta(G)\ge 2$, then $G$ contains $k$ vertex-disjoint copies of $K_{1,2}$. This result is motivated by the problem of characterizing a forbidden subgraph $H$ which satisfies the statement "every $H$-free graph of sufficiently large order with minimum degree at least $t$ contains $k$ vertex-disjoint copies of a star $K_{1,t}$." In this paper, we also give the answer to this problem.

In this paper, we consider various categories of hyperbolic Riemann surfaces and show, in various cases, that the conformal or quasiconformal structure of the Riemann surface may be reconstructed, up to possible confusion between holomorphic and anti-holomorphic structures, in a natural way from such a category. The theory exposed in the present paper is motivated partly by a classical result concerning the categorical representation of sober topological spaces, partly by previous work of the author concerning the categorical representation of arithmetic log schemes, and partly by a certain analogy with $p$-adic anabelian geometry --- an analogy which the theory of the present paper serves to render more explicit.

We consider a time-dependent Schrödinger equation whose Hamiltonian is a $2\times 2$ real symmetric matrix. We study, using an exact WKB method, the adiabatic limit of the transition probability in the case where several complex eigenvalue crossing points accumulate to one real point.