‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

Some recent works have shown that the heat equation on whole Euclidean space is null-controllable in any positive time if and only control subset a thick set. This necessary sufficient condition for null-controllability linked to some

The paper describes new approach of potentiostat for very low sensor current measurements. Recent potentiostats were used as measurement devices which were standalone and sensors were connected by a screened wire. These concepts are inconvenient for the presented very low current measurements. The new approach is based on the potentiostat circuitry integrated on a chip that should be directly c...

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

Abstract In this paper we prove that the set $\{|x^1-x^2|,\dots,|x^k-x^{k+1}|\,{:}\,x^i\in E\}$ has non-empty interior in $\mathbb{R}^k$ when $E\subset \mathbb{R}^2$ is a Cartesian product of thick Cantor sets $K_1,K_2\subset\mathbb{R}$ . We also more general results where distance map $|x-y|$ replaced by function $\phi(x,y)$ satisfying mild assumptions on its partial derivatives. process, esta...

We present a determination of the thick disk iron abundance distribution obtained from an in situ sample of F/G stars. These stars are faint, 15 < ∼ V < ∼ 18, selected on the basis of color, being a subset of the larger survey of Gilmore and Wyse designed to determine the properties of the stellar populations several kiloparsecs from the Sun. The fields studied in the present paper probe the ir...

Cyclooxygenase-2 (COX-2) is constitutively expressed in a subset of thick ascending limb cells in the cortex and medulla and increases when the renin-angiotensin and kallikrein-kinin systems are activated. Although the contribution of angiotensin II to the regulation of COX-2 is known, the effects of bradykinin on COX-2 expression have not been determined in this nephron segment. We evaluated e...

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.

in this paper, a thermoelasticity solution for steady state response of thick cylinders which are subjected to pressure and external heat flux in inner surface is presented. displacement field obeys the kinematics of the first order shear deformation theory (fsdt). it is assumed that the temperature varies both along the length and the thickness. the variation of the temperature occurs linearly...