Vol 68, No 1 (2022): Science — Technology — Education — Mathematics — Medicine

In this paper, the considered problem consists in estimation of conditional survival function by right random censoring model in the presence of a covariate. We propose a new estimator of conditional survival function which is extension of relative-risk power estimator of independent censoring and study its large sample properties. We present result of asymptotic normality with the same limiting Gaussian process as for copula-graphic estimator.

In the paper, we investigate the question of obtaining the algebraic condition for the exponential stability of the numerical solution of the upwind difference scheme for the mixed problem posed for onedimensional symmetric t-hyperbolic systems with constant coefficients and with dissipative boundary conditions. An a priori estimate for the numerical solution of the boundary-value difference problem is obtained. This estimate allows us to state the exponential stability of the numerical solution. A theorem on the exponential stability of the numerical solution of the boundary-value difference problem is proved. Easily verifiable algebraic conditions for the exponential stability of the numerical solution are given. The convergence of the numerical solution is proved.

In the present paper, we study local and 2-local derivations of the classical locally simple Lie algebras. Firstly, we prove that every local and 2-local derivations on classical locally simple Lie algebra is a derivation. Further, we show that every local derivation of Borel subalgebras of locally simple Lie algebras is a derivation.

Based on the methods of the theory of bifurcations, the problem of perturbation of linear equations by small analytic terms is considered. In contrast to the work of Trenogin [7], the case of an incomplete generalized Jordan set of a linear Fredholm operator acting from one Banach space to another Banach space is studied. A technique is proposed that uses the regularization of the Fredholm operator by a specially constructed finite-dimensional operator.

Historically, the idea of reaching consensus through repeated averaging was introduced by De Groot for a structured time-invariant and synchronous environment. Since that time, the consensus, which is the most ubiquitous phenomenon of multi-agent systems, becomes popular in the various scientific fields such as biology, physics, control engineering and social science. In this paper, we give an overview of the recent development of applications of quadratic stochastic operators to nonlinear consensus problems. We also present some refinement and improvement of the previous results.

We give a review of recent results in multivariate complex analysis related to matrix Siegel domains.

Optimization of computational methods in functional spaces is one of the main problems of computational mathematics. In this paper, algebraic and functional assertions for the problem of difference formulas are discussed. For optimization of difference formulas, i.e., for construction of optimal difference formulas in functional spaces, an important role is played by the extremal function of the given difference formula. In this work, we explicitly find in Sobolev spaces the extremal function of the difference formula and compute the norm of the error functional of the difference formula. Furthermore, we prove existence and uniqueness of the optimal difference formula.