Vol 29, No 3 (2023)

From August 28 to August 30, 2023, the All-Russian scientific conference “Mathematics and Mathematical Modeling” was held at Samara University, organized by the Samara division of the regional scientific and educational mathematical center of the Volga Federal District

In this article, we consider a problem with nonlocal integral conditions of the 1st kind for the one-dimensional wave equation. The kernels of the integral conditions depend on both spatial and time variables. In order to study this problem we reduce first the integral conditions of the 1st kind to the integral conditions of the 2nd kind. Under certain additional assumptions these nonlocal conditions are equivalent. Obtained restriction on input data enable to show uniqurness of generalized solution to the problem.

This article discusses the topological and geometric properties of the set of coupled systems and the properties of its subspaces that are homotopically dense. Theorems for a metrizable nondegenerate continuum are presented, conditions for a homotopically dense set of a compact set and conditions for determining a manifold for a finite-dimensional set depending on the fact that it does not contain a Hilbert cube are determined.

The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral representation of the functions under consideration. The article uses the definition and properties of gamma and beta functions, the hypergeometric Gauss function, as well as known identities for these functions. Hypergeometric functions are widely used in solving various types of differential equations. The presence of identities connecting the functions involved in the resulting formulas of solutions greatly simplifies both the final formulas and intermediate calculations in many problems related to solving hyperbolic, elliptic and mixed types of equations

One of the most common problems in various fields of real and complex analysis is the questions of the existence and construction for a given function of an envelope from below or from above of a function from a special class H. We consider a case when H is the convex cone of all subharmonic functions on the domain D of a finite-dimensional Euclidean space over the field of real numbers. For a pair of subharmonic functions u and M from this convex cone H, dual necessary and sufficient conditions are established under which there is a subharmonic function h ̸≡ −∞, “dampening the growth” of the function u in the sense that the values of the sum of u + h at each point of D is not greater than the value of the function M at the same point. These results are supposed to be applied in the future to questions of non-triviality of weight classes of holomorphic functions, to the description of zero sets and uniqueness sets for such classes, to approximation problems of the function theory, etc.

The article compares three types of estimates: exponential, multiplying and power structures for the survival function of three random censoring observations on the right. It was previously established that all these three estimates are equivalent with a growing sample size, i.e. three with the same centering and normalization converge to the same Gaussian process. For specific samples, it is shown that power estimates are defined on the entire line, in contrast to exponential and multiply estimates. Therefore, power estimates are better than the other two. Censored data is used in survival analyses, biomedical trials, and industrial experiments. There are several censoring schemes (right, left, both sides, combined with competing risks, and others). However, right-sided random censoring is common in the statistical literature because it is easy to describe from a methodological point of view. Here we also consider this type of censoring, to compare our results with others.

For modeling in time series, models with fractional differences are widely used. The best known model is the ARFIMA (autoregressive fractionally integrated moving average) model. It is known that for integer-order autoregressive models, autoregressive models with additive noise can outperform ARMA and autoregressive models in terms of accuracy. This article considers a class of autoregressive models with fractional order differences. The article presents a new method for estimating parameters autoregressive models with fractional differences in the presence of additive noise with an unknown variance of additive noise. The propose algorithm was realized in Matlab. The simulation results show the high efficiency of the propose algorithm.