Vol 31, No 3 (2023)


Asymptotic diffusion analysis of the retrial queuing system with feedback and batch Poisson arrival

Nazarov A.A., Rozhkova S.V., Titarenko E.Y.


The mathematical model of the retrial queuing system \(M^{[n]}/M/1\) with feedback and batch Poisson arrival is constructed. Customers arrive in groups. If the server is free, one of the arriving customers starts his service, the rest join the orbit. The retrial and service times are exponentially distributed. The customer whose service is completed leaves the system, or reservice, or goes to the orbit. The method of asymptotic diffusion analysis is proposed for finding the probability distribution of the number of customers in orbit. The asymptotic condition is growing average waiting time in orbit. The accuracy of the diffusion approximation is obtained.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):205-217
pages 205-217 views

Numerical integration of the Cauchy problem with non-singular special points

Belov A.A., Gorbov I.V.


Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero into a simple one. The calculation of the latter is not difficult. This makes it possible to dramatically improve the accuracy and reliability of the calculation. Illustrative examples have been carried out, which confirm the advantages of the proposed method.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):218-227
pages 218-227 views

On a stable calculation of the normal to a surface given approximately

Laneev E.B., Baaj O.


The paper proposes a stable method for constructing a normal to a surface given approximately. The normal is calculated as the gradient of the function in the surface equation. As is known, the problem of calculating the derivative is ill-posed. In the paper, an approach is adopted to solving this problem as to the problem of calculating the values of an unbounded operator. To construct its stable solution, the principle of minimum of the smoothing functional in Morozov’s formulation is used. The normal is obtained in the form of a Fourier series in the expansion in terms of eigenfunctions of the Laplace operator in a rectangle with boundary conditions of the second kind. The functional stabilizer uses the Laplacian, which makes it possible to obtain a normal in the form of a Fourier series that converges uniformly to the exact normal vector as the error in the surface definition tends to zero. The resulting approximate normal vector can be used to solve various problems of mathematical physics using surface integrals, normal derivatives, simple and double layer potentials.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):228-241
pages 228-241 views

Hodge-de Rham Laplacian and geometric criteria for gravitational waves

Babourova O.V., Frolov B.N.


The curvature tensor \(\hat{R}\) of a manifold is called harmonic, if it obeys the condition \(\Delta^{\text{(HR)}}\hat{R}=0\), where \(\Delta^{\text{(HR)}}=DD^{\ast} + D^{\ast}D\) is the Hodge–de Rham Laplacian. It is proved that all solutions of the Einstein equations in vacuum, as well as all solutions of the Einstein–Cartan theory in vacuum have a harmonic curvature. The statement that only solutions of Einstein’s equations of type \(N\) (describing gravitational radiation) are harmonic is refuted.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):242-246
pages 242-246 views

Hamiltonian simulation in the Pauli basis of multi-qubit clusters for condensed matter physics

André E.L., Tsirulev A.N.


We propose an efficient method for Hamiltonian simulation of multi-qubit quantum systems with special types of interaction. In our approach, the Hamiltonian of a \(n\)-qubit system should be represented as a linear combination of the standard Pauli basis operators, and then decomposed into a sum of partial Hamiltonians, which are, in general, not Pauli operators and satisfy some anticommutation relations. For three types of Hamiltonians, which are invariant with respect to permutations of qubits, the effectiveness of the main algorithm in the three-qubit cluster model is shown by calculating the operator exponentials for these Hamiltonians in an explicit analytical form. We also calculate the density operator, partition function, entropy, and free energy of the cluster weakly coupled to a thermal environment. In our model, the cluster is in the Gibbs state in the temperature interval \(0.1\!-\!2\:\!\text{K}\), which corresponds to the operating range of modern quantum processors. It follows from our analysis that the thermodynamic properties of such systems strongly depend on the type of internal interaction of qubits in the cluster.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):247-259
pages 247-259 views

Identification of COVID-19 spread factors in Europe based on causal analysis of medical interventions and socio-economic data

Brou K.A.


Since the appearance of COVID-19, a huge amount of data has been obtained to help understand how the virus evolved and spread. The analysis of such data can provide new insights which are needed to control the progress of the epidemic and provide decision-makers with the tools to take effective measures to contain the epidemic and minimize the social consequences. Analysing the impact of medical treatments and socioeconomic factors on coronavirus transmission has been given considerable attention. In this work, we apply panel autoregressive distributed lag modelling (ARDL) to European Union data to identify COVID-19 transmission factors in Europe. Our analysis showed that non-medicinal measures were successful in reducing mortality, while strict isolation virus testing policies and protection mechanisms for the elderly have had a positive effect in containing the epidemic. Results of Dumitrescu-Hurlin paired-cause tests show that a bidirectional causal relationship exists for all EU countries causal relationship between new deaths and pharmacological interventions factors and that, on the other hand, some socioeconomic factors cause new deaths when the reverse is not true.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):260-272
pages 260-272 views

Brain-computer interaction modeling based on the stable diffusion model

Shchetinin E.Y.


This paper investigates neurotechnologies for developing brain-computer interaction (BCI) based on the generative deep learning Stable Diffusion model. An algorithm for modeling BCI is proposed and its training and testing on artificial data is described. The results are encouraging researchers and can be used in various areas of BCI, such as distance learning, remote medicine and the creation of robotic humanoids, etc.

Discrete and Continuous Models and Applied Computational Science. 2023;31(3):273-281
pages 273-281 views

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