Kuznetsov, D. F.
Published in
Journal of Mathematical Sciences

The problem of the Taylor–Stratonovich expansion of the Itô random processes in a neighborhood of a point is considered. The usual form of the Taylor–Stratonovich expansion is transformed to a new representation, which includes the minimal quantity of different types of multiple Stratonovich stochastic integrals. Therefore, these representations ar...

Kokhas, K. Latyshev, A.
Published in
Journal of Mathematical Sciences

Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. Each hat can have one of three colors. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess...

Duzhin, V. Vassiliev, N.
Published in
Journal of Mathematical Sciences

There exists a well-known hook-length formula for calculating the dimensions of two-dimensional Young diagrams. Unfortunately, an analogous formula for the three-dimensional case is unknown. We introduce an approach to calculating estimated dimensions of three-dimensional Young diagrams, also known as plane partitions. The most difficult part of th...

Yankovskii, А. P.
Published in
Journal of Mathematical Sciences

In the von Kármán approximation, we formulate the initial-boundary-value problem of dynamic deformation of flexible reinforced plates with nonlinear elastic behavior of the materials of the components of composition. We deduce the equations for the determination of the stress-strain states of these plates with different degrees of accuracy with reg...

Evtukhov, V. М. Kolun, N. P.
Published in
Journal of Mathematical Sciences

We establish the asymptotic properties of some types of solutions of the second-order differential equations whose right-hand sides contain a sum of terms with regularly and rapidly varying nonlinearities.

Bandura, A. I. Skaskiv, O. B.
Published in
Journal of Mathematical Sciences

We solve the problem of estimation of growth for the maximum modulus of an entire function of bounded L -index in a direction. Some generalizations of the earlier one-dimensional results are obtained.

Chernukha, О. Yu. Bilushchak, Yu. I.
Published in
Journal of Mathematical Sciences

We study the diffusion processes of an admixture in a two-phase stratified strip of randomly inhomogeneous structure with regard for the jumps of the concentration function and its derivative on the contact boundaries of the phases. A new representation of the operator of equation of mass transfer for the entire body is proposed. We formulate an eq...

Storozh, О. H.
Published in
Journal of Mathematical Sciences

In terms of abstract boundary conditions, we study a class of extensions of finite-dimensional restrictions of closed densely defined linear operators acting in Hilbert spaces. By the methods of the theory of linear relations, we find the resolvent sets and construct the resolvents of the analyzed extensions. The set of these extensions is paramete...

Кononov, Yu. М. Shevchenko, V. P. Dzhukha, Yu. O.
Published in
Journal of Mathematical Sciences

We deduce a frequency equation for the natural coupled axially symmetric vibrations of elastic bases (in the form of annular plates) and a heavy two-layer incompressible perfect liquid in a rigid annular cylindrical vessel. We consider different limiting cases: the case of degeneration of annular plates into membranes, the case of absolutely rigid ...

Tokovyy, Yu. V.
Published in
Journal of Mathematical Sciences

We developed a technique for the construction of solutions of axisymmetric problems of elasticity and thermoelasticity in stresses for a space and a half space whose elastic properties are arbitrary functions of the coordinate z. By using the direct integration method and the Hankel integral transformation, the problems are reduced to governing int...