Authors:L. V. Dorodnitsyn Abstract: We consider central-difference schemes for the transport equation that can be integrated over time by explicit multistage Runge–Kutta methods. Such algorithms are the basis for modeling in modern aeroacoustics problems. Their stability is determined by the hyperbolic Courant number. The effect of discrete boundary conditions on the stability of the schemes is investigated. A procedure is proposed for approximate analysis of high-frequency modes that are responsible for the value of the maximum time increment. A three-point central-difference scheme with various boundary conditions is studied in detail and quantitative results are obtained for the analytical method error. We conclude that the boundary conditions have but a marginal effect on the maximum Courant number. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9400-y

Authors:A. G. Perevozchikov; V. Yu. Reshetov; I. E. Yanochkin Abstract: The article generalizes Germeier’s attack-defense model to allow for integer-valued and nonhomogeneous opponent resources and echeloned defense. It performs target allocation by solving the classical transportation problem on each level, which leads to discrete minimax problems for the best guaranteed defense outcome. These minimax problems can be solved by a coordinatewise-descent method based on a discrete analogue of Germeier’s equalization principle. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9396-3

Authors:A. A. Belolipetskii; M. A. Lepskaya Abstract: We consider the probability of ruin of a pension fund on a finite time interval. The basis is provided by the standard Cramer–Lundberg model, which is modified by specifying enrolment and contribution parameters in the form of random variables. A number of factors may be treated as random variables in the model: the date of member’s death, members’ wages, the number of fund members, financial indicators (discounting and return rates, inflation, wage growth rates). Each of these factors specified as a random variable affects the nondeterministic behavior of the fund’s receipts and payouts. In this article, the random factors include the number of members joining the pension fund in the relevant year and random mortality. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9404-7

Authors:E. S. Kurkina Abstract: The article investigates the dynamics of various interactions between two partners described by a system of two nonlinear ordinary differential equations. The partners may be various social subjects, ranging from individuals and social groups to states and nations. The models are an extension of the Murray–Gottman model originally proposed to describe relationships between married people. New functions are introduced describing the own behavior of the actors in the absence of interactions as well as functions modeling the mutual influence of the partners. Phase portraits are constructed for systems with excitable, self-sufficient, and some other types of actors that do not strive to attain a neutral state, as in the Murray–Gottman model. New types of dynamic behavior are discovered. In particular, two nonlinear conservative models are proposed that demonstrate an oscillatory dynamic about the center. The models examined in this article demonstrate a rich set of phase portraits and may be applied to model various social interactions between two partners. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9399-0

Authors:A. A. Vasin; I. A. Lesik; O. M. Grigor’eva Abstract: We consider the design of a transport network in a multinode market assuming time-dependent nonstationary demand. A gradient algorithm is proposed for capacity optimization of transport lines in the network. Numerical results are reported. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9402-9

Authors:G. V. Milovanović Abstract: Numerical integration of one class of quasi-singular integrals appearing in the convenient formulas of electromagnetic field components and potential functions of linear source distributions is considered. Some comments to a recent paper by S.R. Jena, D. Nayak, and M.M. Acharya [Comput. Math. Modeling, 28, 267–276 (2017)] on this subject are given, as well as some illustrative numerical examples. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9401-x

Authors:V. S. Laponin; S. A. Skladchikov; N. P. Savenkova; V. V. Novoderezhkin Abstract: The article describes the reasons for elevated intraocular pressure due to obstruction of fluid outflow, which may lead to the development of glaucoma, cataract, and other pathologies. Mathematical modeling is carried out of the dynamics of fluid flow in the eye anterior chamber near and inside Schlemm’s canal. The effect of the position of Schlemm’s canal on the quality of fluid outflow from the eye is investigated in detail. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9397-2

Authors:S. Manzetti Abstract: Quantum information processing is a critical part of the development of future computers, quantum computers, and quantum algorithms, where elementary particles such as photons and electrons can be applied in optomagnetic or optoelectronic devices. The computational physics behind these emerging approaches is also experiencing dramatic developments. In this paper I report on the most recent mathematical basics for quantum algorithms and quantum computing approaches. Some of these described approaches show intriguing methods for determining the states and wavefunction properties for anyons, bosons, and fermions in quantum wells that have been developed in the last years. The study also shows approaches based on N-quantum states and the reduced 1- and 2-fermion picture, which can be used for developing models for anyons and multi-fermionic states in quantum algorithms. Also, antisymmetry and generalized Pauli constraints have been given particular emphasis and include establishing a basis for pinning and quasipinning for exploring the symmetric states of many-fermionic subsets, as a foundation for quantum information processing, and are here briefly revisited. This study summarizes the developments in recent years of an advanced and important field for future computational techniques. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9405-6

Authors:V. I. Dmitriev Abstract: The article investigates the inverse sounding problem for a nonhomogeneous thin layer given the field on the surface of the half-space. A uniqueness theorem is proved for the solution of the inverse problem. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9395-4

Authors:S. I. Gurov Abstract: This article introduces a parity-check code based on the Rademacher function. The error-correction model of the code corresponds to a binary symmetrical channel: bits may be inverted randomly and independently, but no bit insertion/bit omission occurs. The code corrects a single error; its redundancy and coding/decoding features are virtually identical with those of the Hamming code, but it has clear advantages for application of redundant coding in fault-tolerant integrated-circuit design. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9403-8

Authors:P. Raja Sekhara Rao; K. Venkata Ratnam; P. Lalitha Abstract: In this article, we have considered a simple food-consumer dynamic model in which the supply of food and the death of consumer species play the major role. The parameters representing these factors are allowed to vary with respect to time. It is established that by proper selection of these parameter functions, the system may be made to approach a desired state. It is noticed that these parameters define a space of equilibria for the given system in the limiting case. In case of different consumer species surviving on the same food, when there is no interference in consumption of one by the other, the growth is as desired. Growth is not as desired when one of the species is interfering with the food consumption of the other and the growth of the larger consumer is dominating. By simple variations in the death/removal of dominating species, the situation may be reversed in favor of the other species. The growth is as desired when the parameters are fixed constants. Examples are provided to understand the results and to illustrate various situations. The approach is tried on a popular mathematical model of biology to draw some useful conclusions. The study opens interesting problems for further research. PubDate: 2018-02-24 DOI: 10.1007/s10598-018-9398-1

Authors:A. M. Denisov; S. I. Solov’eva Abstract: Numerical methods are proposed for determining the initial condition in Cauchy problems for a hyperbolic equation with a small parameter multiplying the highest-order derivative. Additional information for the inverse problem is provided by the solution of the Cauchy problem specified at x = 0 as a function of time. Results of numerical calculations illustrating the potential of the proposed method are reported. PubDate: 2018-01-12 DOI: 10.1007/s10598-018-9383-8

Authors:R. Buzhabadi Abstract: The DFOM method is an iterative method for computing the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ϵ ℂ n × n is a singular and in general non-Hermitian matrix that has an arbitrary index. This method is generally used with restarting. But the restarting often slows down the convergence and DFOM often stagnates. We show that adding some approximate error vectors or approximate eigenvectors (corresponding to a few of the smallest eigenvalues) to the Krylov subspace can improve the convergence just like the method proposed by R. Morgan in [8]. We derive the implementation of these methods and present some numerical examples to show the advantages of these methods. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9389-2

Authors:V. S. Laponin; S. A. Skladchikov; N. P. Savenkova Abstract: The article presents numerical modeling of the formation of a solitary wave in an annular channel under the action of a continuous wind generated by several sources distributed across the channel. The numerical results are compared with experimental data. Efficient application of parallel computational resources, produces a good result in acceptable time. The proposed model simulates the formation of solitary waves and the interaction of two nonlinear waves, and also produces the conditions of formation of 1, 2, 3, and 4 waves on a liquid surface. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9391-8

Authors:J. Mohapatra; M. K. Mahalik Abstract: In this paper, an initial value technique is presented to solve singularly perturbed two-point boundary value problems. Using the basic idea of the well known Wentzel – Kramers – Brillouin (WKB) method, an approximation due to asymptotic expansion of the solution of the problem is constructed. The original problem is reduced to a combination of an initial value problem and a terminal value problem. The terminal value problem is solved by the trapezoidal method and then the initial value problem is solved by the backward Euler method on an appropriate nonuniform mesh constructed adaptively by equidistributing a positive monitor function based on the solution. An error estimate is derived, and numerical experiments are conducted to illustrate the efficiency of the proposed method. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9387-4

Authors:M. S. Nikol’skii Abstract: We derive constructive sufficient conditions for linear controlled plants that guarantee a simple structure of the optimal controls in the time-optimal control problem. Strict convexity of the reachability set is proved for S-regular controlled plants. Uniqueness theorems for the optimal control are obtained. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9394-5

Authors:S. V. Aliukov Abstract: The problem of approximation of electrocardiograms has a great practical importance and it is constantly in the field of research. Solution of this problem allows us to automate and computerize the process of diagnosis and to detect timely deviations from normal characteristics of cardiograms of heartbeat in the early stages of appearance and development of a disease. There are different methods for approximation of cardiograms. All these methods have their drawbacks. The article deals with new methods of approximation of cardiograms, which do not have any disadvantages of the known methods. The developed mathematical models are based on new methods of approximation of step functions, and these methods can significantly reduce errors of the approximation of cardiograms. In this paper new methods of approximation of step functions with estimation of errors of the approximation are supposed. The proposed methods do not have any drawbacks of traditional expansions of step functions in Fourier series and can be used in problems of mathematical modeling of a wide class of processes and systems, in particular, for solution of medical and biological problems. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9388-3

Authors:A.V. Baev Abstract: We consider a nonlinear ordinary differential equation associated with a number of inverse scattering problems in acoustic and seismic sounding in which acoustic impedance and an impedance-dependent unknown damping coefficient are the unknown function. We prove that the Cauchy problem is uniquely solvable when the derivative is treated as a generalized function. It is established that the inverse scattering problem in a layered dissipative medium simultaneously determines the acoustic impedance and the damping coefficient. A regularized numerical algorithm is proposed and numerical results are reported. PubDate: 2018-01-06 DOI: 10.1007/s10598-018-9390-9

Authors:N. V. Ardelyan; K. V. Kosmachevskii; M. N. Sablin Abstract: Using grids (meshes) formed from polyhedra (polygons in the two-dimensional case), we consider differential and boundary grid operators that are consistent in the sense of satisfying the grid analog of the integral identity – a corollary of the formula for the divergence of the product or a scalar by a vector. These operators are constructed and applied in the Mimetic Finite Difference (MFD) method, in which grid scalars are defined inside the grid cells and grid vectors are defined by their local normal coordinates on the planar faces of the grid cells. We show that the basic grid summation identity is a limit of an integral identity written for piecewise-smooth approximations of the grid functions. We also show that the MFD formula for the reconstruction of a grid vector field is obtained by approximation analysis of the summation identity. Grid embedding theorems are proved, analogous to well-known finite-difference embedding theorems that are used in finite-difference scheme theory to derive prior bounds for convergence analysis of the solutions of finite-difference nonhomogeneous boundary-value problems. PubDate: 2018-01-05 DOI: 10.1007/s10598-018-9384-7

Authors:A. G. Belov Abstract: We consider a mathematical-statistics approach to least-squares parameter estimation in a linear multiple regression model. This approach has led to a detailed description of the basic premises for the emergence and application of the least-squares method, produced a number of general distributional and statistical formulas for the estimation of model parameters independently of a specific joint distribution of the random variables, provided a deeper understanding of the parameter estimation risks associated with model specification errors, and made it possible to identify the place and role of knowledge of the theoretical and empirical distributions of observation errors. PubDate: 2018-01-05 DOI: 10.1007/s10598-018-9385-6