MatSciNet

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

In the paper, the stability and convergence of difference schemes approximating semilinear parabolic equation with a nonlocal condition are considered. The proof is based on the properties of M-matrices, not requiring the symmetry or diagonal predominance of difference problem. The main presumption is that all the eigenvalues of the corresponding difference problem with nonlocal conditions are positive.

The paper extends the study of the modified Borwein method for the calculation of the Riemann zeta-function. It presents an alternative perspective on the proof of a local limit theorem for coefficients of the method. The new approach is based on the connection with the limit theorem applied to asymptotic enumeration.

In this paper, the numerical algorithms for solution of pore volume and surface diffusion model of adsorption systems are constructed and investigated. The approximation of PDEs is done by using the finite volume method for space derivatives and ODE15s solvers for numerical integration in time. The analysis of adaptive in time integration algorithms is presented. The main aim of this work is to analyze the sensitivity of the solution with respect to the main parameters of the mathematical model. Such a control analysis is done for a linearized and normalized mathematical model. The obtained results are compared with simulations done for a full nonlinear mathematical model.

In the paper, we obtain universality theorems and a lower estimate for the number of zeros for the composition F (ζ (s, α; a, b)), where F is an operator in the space of analytic functions satisfying the Lipschitz type condition, and ζ (s,α; a, b) is a collection consisting of periodic and periodic Hurwitz zeta-functions.

This manuscript starts with a detailed analysis of the current solution for the queueing system M/Er/1/∞. In the existing solution, Erlang’s service is caused by Poisson’s arrival process of groups, but not individual clients. The service of individual clients is still exponentially distributed, contrary to the declaration in Kendall’s notation. From the related theory of the Hidden Markov Model (HMM), for the advancement of queueing theory, the idea of “hidden Markov states” (HMS) was taken. In this paper, the basic principles of application of HMS have first been established. The abstract HMS states have a catalytic role in the standard procedure of solving the non-Markovian queueing systems. The proposed solution based on HMS exceeds the problem of accessing identical client groups in the current solution of the M/Er/r queueing system. A detailed procedure for the new solution of the queueing system M/Er/1/∞ is implemented. Additionally, a new solution to the queueing system M/N/1/∞ with a normal service time N(μ, σ) based on HMS is also implemented.

Numerical experiments as well as practical applications of zeta-functions require a great amount of computations. We introduce a modification of one of the efficient methods for calculating the Riemann zeta-function values—Borwein’s algorithm. We prove local and central limit theorems for the coefficients of a modified version of the method, as well as establish convergence rates to the limiting law. An asymptotic expression is derived for the coefficients of the modified version of the method. Calculation of the zeta-values with the resulting approximation is discussed.

In this paper, we propose a framework for extracting translation memory from a corpus of fiction and non-fiction books. In recent years, there have been several proposals to align bilingual corpus and extract translation memory from legal and technical documents. Yet, when it comes to an alignment of the corpus of translated fiction and non-fiction books, the existing alignment algorithms give low precision results. In order to solve this low precision problem, we propose a new method that incorporates existing alignment algorithms with proactive learning approach. We define several feature functions that are used to build two classifiers for text filtering and alignment. We report results on English-Lithuanian language pair and on bilingual corpus from 200 books. We demonstrate a significant improvement in alignment accuracy over currently available alignment systems.

A detailed analysis of absorbing boundary conditions for the linear Schrodinger equation is presented in this paper. It is focused on absorbing boundary conditions that are obtained by using rational functions to approximate the exact transparent boundary conditions. Different strategies are investigated for the optimal selection of the coefcients of these rational functions, including the Pade approximation, the L2 norm approximations of the Fourier symbol, L2 minimization of a reection coeficient, and two error minimization techniques for the chosen benchmark problems with known exact solutions. The results of computational experiments are given and a detailed comparison of the eficiency of these techniques is presented.