On the restriction of processes by the Clausius-Duhem inequality

Zusammenfassung Die thermodynamische Theorie von Coleman und Noll wird durch die Annahme erweitert, dass die Ungleichung von Clausius-Duhem sowohl Prozesse wie auch Stoffgleichungen einschränkt. Diese verallgemeinerte Interpretation der Clausius-Duhem-Ungleichung wird durch zwei Beispiele illustriert. Das erste bildet den Rahmen für eine Plastizitätstheorie, in der die Einschränkung der Prozesse sich als ebenso wesentlich herausstellt wie diejenige der Stoffgleichung.Das zweite Beispiel betrifft das klassische Ergebnis von Duhem, dass in linearen zähen Flüssigkeiten keine Beschleunigungswellen auftreten können.     

Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff-Young inequality

We establish the existence of Salem sets in the ring of integers of any local field and study the Fourier restriction phenomenon on such sets. Optimal extension of the Hausdorff-Young inequality, initially attained for the torus by G. Mockenhaupt and W. Ricker, is also established in the local field setting.     

Generalization of an elementary inequality in Fourier analysis

The inequality plays an important role in Fourier analysis and approximation theory. It has recently been generalized by Telyakovskii and Leindler. This paper further generalizes and improves their results by introducing a new class of sequences called γ-piecewise bounded variation sequence (γ-PBVS).     

On an adjoint initial-boundary value problem

We study an adjoint initial-boundary value problem for linear parabolic equations; which arises when modeling the unidirectional motion of two viscous fluids with a common interface under the action of a pressure gradient. Under some conditions on the pressure gradient, we obtain a priori estimates and show that the solution enters a stationary mode. For semibounded layers, we find the solution in closed form and indicate the case of a self-similar solution. We determine the volume flow rates in the layers.     

On the harnack inequality for the equation formally adjoint to a linear elliptic differential equation

Baku. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 100–106, September–October, 1992.     

On an adjoint functor to the Thom functor

We construct a right adjoint functor to the Thom functor, i.e., to the functor which assigns the Thom space to a vector bundle .

     

On an integral inequality

In this paper we deduce an integral inequality which is an analog of a known two-parameter inequality of Hardy and Littlewood ([1], Theorem 382). A need for inequalities of a similar type arises, for example, in studying the imbedding of the functional spaces B _p ^l in the space L_q if this study leads to a basis of the method of integral representations of functions.Translated from Matematicheskie Zametki, Vol. 6, No. 2, pp. 139–148, August, 1969.     

On an operator inequality

Jensen's operator inequality characterizes operator convex functions of two variables (F. Hansen, Proc. Amer. Math. Soc. 125 (1997) 2093–2102). We give a simplified proof of this theorem formulated for matrices.     

On an inequality of Edgar

LetE′ be the separable dual of a Banach spaceE. LetK be the class of all non-empty convex, weak^*-compact subsets ofE′. In this paper we prove that Edgar’s inequality, given in [2], extends to adapted sequences ofK-valued random variables.     

On the means of Fourier integrals and Bernstein inequality in the two-weighted setting

The norm estimation problem for Cesaro and Abel–Poisson operators acting from L_w^p(\mathbbR){L_{w}^{p}(\mathbb{R})} to L_v^q (\mathbbR){L_{v}^{q} (\mathbb{R})} where 1 < p ≤ q < ∞ was investigated. These results were generalized to the multidimensional case and applied to obtain generalizations of the Bernstein inequality for integral functions of finite degree of one and several variables.     

On an inequality in probability

Inequalities are obtained forΣⁿ_im1P(A₁) when P(A₁A₁) 1? i < j ? n are known. The result improves an elementary inequality due to Erdös, Neveu, Renyi and Zybrzyck.