The paper deals with the problems on statics, stability, eigenoscillations and small movements of an ideal incompressible fluid in a vessel with bottom holes.
A rectangular channel (plane problem) and cylindrical container (axisymmetric problem) are considered. It is assumed that hydrosystem is under low gravity conditions, and therefore the action of surface tension forces and weak gravitational forces are considered.
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Taurida University was officially opened in the Crimea on October 14, 1918. It was established in the crucial period and fully experienced all the difficulties and trials on the way of its development. On the eve of the centennial of the University awareness comes of a historic role it had played in the establishment of scientific and cultural traditions and of the entire system of education in Crimea.
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Let $B$ linear bounded operator and let spectral radius is $R\left ( B \right )=1$. Well-known that the resolvent operator can be represented by power series $\left ( B-\lambda I \right )^{-1}=-\sum_{n=0}^{\infty }\lambda ^{-n}B^{n-1}$ and the norm of the resolvent holds
$\left \| \left ( B-\lambda I \right )^{-1} \right \|\leq \varphi _{B}(\frac{1}{\left | \lambda \right |})$ $(\left | \lambda \right |> 1)$,
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Let $V$ be a domain in $R^{n}$, $n>2$. A set A is a regular simplex, whose edge is $\sqrt{2}$, in four-dimensional space. Some problems about functions is locally integrable on a set $V$ with vanishing integrals over all images $\lambda A\subset V$ , $\lambda \in M(n)$ of a fixed compact set $A\subset R^{n}$ are studied in the present paper. If the only function is locally integrable on a set $V$ and satisfying this condition is $f=0$ then the set $A$ is called a Pompeiu set in $V$.
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The paper is devoted to investigation of the problem on small movements and eigenoscillations of a system that consists of an ideal incompressible fluid and barotropic gas, and is situated in bounded vessel.
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Zero sets of solutions of the hyperbolic Darboux equation Volchkov V. V. and Volchkov Vit. V.
A hyperbolic analog of the generalized Darboux equation is considered. We investigate the structure of zero sets of its solutions for the case where the solution is a radial function of second variable. We show that every solution vanishing on some annulus must be zero in some other annulus containing the first one.
Keywords: Darboux equation, hyperbolic plane, zero sets, uniqueness theorems, transmutation maps.
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In the paper, we consider a problem on small motions of a system of viscoelastic fluid and gas in a stationary container. One of models of such viscoelastic fluid is Oldroid’s model. It is described, for example, in the book Eirich, F. R. Rheology. Theory and Applications. New York: Academic Press, 1956. It should be noted that the present paper is based on the previous N. D. Kopachevsky works together with Azizov, T. Ya., Orlova L. D., Krein, S. G.
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The optimization problem with precedent (training sample) initial information is considered. Some approaches for reconstruction of the target function of such optimization problem are proposed. The open problems that must be solved to obtain better quality solutions of this problem are highlighted.
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A search of all potentional keys of the relation is the most important in the problem of database normalizing. The new method of all keys determination is presented. It is based on the matrix representation of boolean functions.
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In this article we consider the information flows as the process of addition of incomplete mi ll information. The operations on the information flows and information flows properties are csidered in it. Actuality of this approach is determined by availability of information flows for t decision general schemes construction of the problems with incomplete initial information. It proposed to use this schemes for building the decision making interactive subsystems of the igence information systems.