In this article, we compare the support for SIMD instructions for Julia and Fortran. The comparison is carried out according to the methodology described in work of T. Kalibera, R. …
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations, computer algebra systems are employed. In our research, we have been using …
To construct realistic mathematical models from the first principles, the authors suggest using the stochastization method. In a number of works different approaches to …
This paper discusses the application of stochastic Runge-Kutta-like numerical methods with weak and strong convergences for systems of stochastic differential equations in Itô …
When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we …
The retrial queuing system with general renovation is under investigation. The mechanism of general renovation with retrials means that the packet at the end of its service in …
Self-oscillating modes in control systems of computer networks quite negatively affect the characteristics of these networks. The problem of finding the areas of self-oscillations …
The article is devoted to the application of Markov modu- lated arrival processes (Markov modulated Poisson process — MMPP, Markov modulated Bernoulli process — MMBP and Markov …
Spinors are more special objects than tensor. Therefore possess more properties than the more generic objects such as tensors. Thus, the group of Lorentz two-spinors is the …
For the study and verification of our mathematical model of telecommunication systems a discrete simulation model and a continuous analytical model were developed. However, for …
Representing a probability density function (PDF) and other quantities describing a solution of stochastic differential equations by a functional integral is considered in this …
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number …
This paper studies program implementation problem of pseudo-random number generators in OpenModelica. We give an overview of generators of pseudo-random uniform distributed …
The mathematical model of light propagation in a planar gradient optical waveguide consists of the Maxwell's equations supplemented by the matter equations and boundary conditions. …
Background. By the means of the method of stochastization of one-step processes we get the simplified mathematical model of the original stochastic system. We can explore these …
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. …
This paper describes Lorentz two-spinors and proposes using them in calculations with Dirac four-spinors and quaternions.
In this article we present two examples solved in a new problem-oriented computer algebra system Cadabra. Solution of the same examples in widespread universal computer algebra …