I am trying to understand a beautiful work of Pierre Schapira [5]. Notations and Conventions • For any set S we denote by IS the identity map S → S. For any subset A ⊂ S we denote by 1A the characteristic function of A. • In the sequel all manifolds will be assumed real analytic. A morphism of manifolds will be a real analytic map between two manifolds. Introduction Suppose we are given a simpl...

The purpose of this note is to announce a number of results concerning the various approaches to fractional integration on the real line E as due to H. Weyl [9], M. Riesz [7], W. Feller [4] and G. O. Okikiolu [ô]. Our principal contributions are on extensions of theorems of J. L. B. Cooper [3], on the interchange of the operations of fractional integration (differentiation) and the Hilbert tran...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...

This paper is a contribution to harmonic analysis of compact solvmanifolds. We consider the four-dimensional oscillator group ${\rm Osc}_1$, which semi-direct product three-dimensional Heisenberg and real line. classify lattices Osc}_1$ up inner automorphisms Osc}_1$. For every lattice $L$ in we compute decomposition right regular representation on $L^2(L\backslash{\rm Osc}_1)$ into irreducible...

This talk is based on work with N. Khuri and H. Ren.[1,2] The main new tools we use are theorems by Voronin on the universality properties of the Riemann Zeta function, ζ(s), in the critical strip, 1 2 < Re s < 1. Given any real continuous function, φ(x), 0 ≤ x ≤ L, we can choose a mapping, s(x), which maps the line, 0 ≤ x ≤ L, onto a line s(x) that lies in the strip 1 2 < Re s < 1, then given ...

conclusions shedding of l. monocytogenes in different animal species, and different samples are different. due to antibiotic resistance, especially in l. monocytogenes, veterinarians should pay more attention to prescribe antibiotics. we recommend using the real-time pcr for safe, sensitive, and rapid detection of l. monocytogenes in clinical samples, and using the disk diffusion methods to pre...