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 Computational Mathematics and ModelingJournal Prestige (SJR): 0.241 Number of Followers: 8      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-837X - ISSN (Online) 1046-283X Published by Springer-Verlag  [2469 journals]
• The Length of Single Fault Detection Tests with Respect to Substitution of
Gates with Inverters

Abstract: We show that for an arbitrary Boolean function realized by a combinational circuit over an arbitrary com-plete basis, there exists an irredundant circuit that admits a single fault detection test with at most 12 tuples with respect to substitutions of gates with inverters.
PubDate: 2022-05-06

• The Inverse Problem for a Mathematical Model of Deionization Aqueous
Solutions

Abstract: We consider a mathematical model of the deionization of aqueous solutions described by a mixed initial–boundary-value problem for a partial-differential system. Uniqueness of the solution if proved. The inverse problem is posed for the ion absorption kinetics given the integral ion concentration observed at the output. Unique solvability of the inverse problem is proved. A numerical method is proposed for the inverse problem. Results of computational experiments demonstrate the efficiency of the proposed numerical method.
PubDate: 2022-05-05

• Maximin Problem of Communication Network Synthesis

Abstract: The article generalizes the classical Ford–Fulkerson maximum-flow problem in a directed network by allowing for its possible defense-driven augmentation that increases the transmission capacity of the network edges. The generalization is based on Hohzaki and Tanaka [2], but unlike the previous authors we increase the transmission capacity of each arc rather than decreasing the flow. This leads in general to a maximin problem that can be solved by subgradient ascent. The same method is applied in the integer-valued setting to obtain branch-and-bound upper bounds. Numerical examples are presented.
PubDate: 2022-05-05

• Artificial Neural Networks and Logic Circuit Synthesis

Abstract: We consider the application of artificial neural networks to logic circuit synthesis. The potential promise of this method is shown. Circuit optimization in a majority logic basis is demonstrated. A method is proposed for the application of recursive neural networks for the construction of an algorithm for logiccircuit synthesis and size optimization.
PubDate: 2022-05-05

• Wave Propagation Characteristics of Thermoelastic Graphene Platelet
Reinforced Polygonal Ring with Phase Lags

Abstract: This article studies a new analytical method for clamped free generalized thermoelastic waves in a doubly connected polygonal ring reinforced with graphene platelets under the exact heat conduction equation with delay. The plain strain model of generalized thermoelastic polygonal ring of homogeneous isotropic is considered. Four different distribution patterns are considered via Eshelby–Mori–Tanaka homogenizing idea. The complex characteristic equations are obtained through the nonlinear surface of the grapheme platelets reinforced composite (GPLRC) ring by using Fourier expansion collocation method. The triangular, square, pentagonal and hexagonal GPLRC ring is evaluated via numerical values. The results of the physical variants like stress, strain, and mechanical displacement, weight fraction of grapheme platelets (GPL), dimensionless frequency and temperature rise are explored in tabular and graphical form. Some validations are presented between the frequency of square cross section plates and peer-reviewed literature to show the accuracy and the convergence of this method. These results can be beneficial to design thermal polygonal composite GPL ring structures in diverse environments.
PubDate: 2022-05-05

• A Numerical Approach to Deriving Statistical Estimates of the Residual
Mass, the Impact Point, and Other Meteorite Parameters from the Bright
Section of the Trajectory

Abstract: Meteorite flight in the Earth’s atmosphere can be uniquely described by a system of ordinary differential equations (ODE), which requires two initial conditions and the values of five coefficients. The proposed approach chooses these unknowns from the range of physically substantiated values and then solves numerically millions of similar ODE systems. A sample of 100 simulated virtual meteorites is selected; these meteorites provide the best fit to tabular data for altitude and velocity, which in turn are reconstructed from real photographs. The selected virtual meteorites produce statistical estimates for all the unknown parameters, as well as flight distance and residual mass. The proposed approach is demonstrated in application to the Innisfree meteorite.
PubDate: 2022-05-05

• Lower Bound of the Length of a Single Fault Diagnostic Test with Respect
to Insertions of a Mod-2 Adder

Abstract: We prove that almost all Boolean functions of n variables implements by arbitrary logic circuits in any functionally complete basis admit a minimal single-fault test of length not less than with respect to the insertion of mod-2 adders. With two bases, a similar result is established for implementation of functions by nonredundant circuits.
PubDate: 2022-05-05

• The Complexity of the Standard Multiplexer Function in a Class of
Switching Circuits

Abstract: The article considers the synthesis of switching circuits that realize standard multiplexer Boolean functions of order n, i.e., Boolean multiplexer functions with n select lines and 2n data variables. A lower bound is derived on the complexity of realization of these Boolean functions in the class of so-called correct switching circuits, which is close to the known upper bound on their complexity in the class of arbitrary switching circuits.
PubDate: 2022-05-05

• Numerical Assessment of the Informational Influence of Election Campaigns
on the Electorate

Abstract: A numerical scheme is developed for the assessment of the informational influence of election campaigns on the electorate. It relies on the determination of the probability density function of stochastic dynamic system states that requires a numerical solution of the Fokker–Planck–Kolmogorov equation reduced to a system of ordinary differential equations in the projection form of the Galerkin method. The approximation of the probability density function in state variables is specified on a triangulation in the system of Gaussian basis functions assuming time-dependent expansion coefficients. Convergence of the proposed numerical scheme is examined in the context of the convergence of the mean-square approximation of a function on a simplex. Some features of the algorithmic implementation of the solution are considered and comparative modeling results are reported for test problems.
PubDate: 2022-05-05

• Benchmarks of Cuda-Based GMRES Solver for Toeplitz and Hankel Matrices and
Applications to Topology Optimization of Photonic Components

Abstract: Generalized Minimal Residual Method (GMRES) was benchmarked on many types of GPUs for solving linear systems based on dense and sparse matrices. However, there are still no GMRES implementation benchmarks on Tesla V100 compared to GTX 1080 Ti ones or even for Toeplitz-like matrices. The introduced software consists of a Python module and a C++ library which enable to manage streams for concurrent computations of separated linear systems on a GPU (and GPUs). The GMRES solver is parallelized for running on a NVIDIA GPGPU accelerator. The parallelization efficiency is explored when GMRES is applied to solve (Helmholtz equation) linear systems based on the use of Green’s Function Integral Equation Method (GFIEM) for computing electric field distribution in the design domain. The proposed implementation shew the maximal speedup of 55 ( $$\overline{t}=0.017\ \mathrm{s}$$ ) and of 125 ( $$\overline{t}=0.77\ \mathrm{s}$$ ) for 1024 × 1024 (on GTX 1080 Ti) and 8192 × 8192 (on Tesla V100) dense Toeplitz matrices generated from GFIEM. 1024 × 1024 resolution provides accuracy 6.1% that can be acceptable according to testing and demonstrating on gradient computations and topology optimization. We open up possibilities for robust topology optimization of passive photonic integrated components. That has the advantage, e. g., of faster and more accurate designing photonic components on a PC without a supercomputer.
PubDate: 2022-05-05

• Correction to: Quality of Control in the
Tavis–Cummings–Hubbard Model

PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09538-7

• A Special Grid for the Numerical Analysis of the Integral Equation Method
in the Magnetotelluric Sounding Problem

Abstract: The article carries out numerical analysis of the integral-equation method for the magnetotelluric sounding problem in a nonhomogeneous medium. The case of high-contrast conducting media is considered in detail, with a conducting nonhomogeneity embedded in a poorly conducting medium. Numerical analysis of the integral equation in this case shows that the solution has low accuracy if a traditional uniform rectangular grid is superposed on the nonhomogeneity and the electric field is evaluated at nodes traditionally placed at the centers of the grid cells. In this approach, nothing is done to resolve the field behavior at the nonhomogeneity boundary in the belied that the boundary conditions will be satisfied on their own automatically. Even the introduction of enhanced background conductivity does not improve the accuracy. A much better result is obtained when enhanced background conductivity is combined with a special nonuniform grid in which the cells in the top grid row have reduced height and the nodes are placed at the top boundary of these cells. This result is substantiated by allowing for the singularity of the integral equation.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09533-y

• The Length of Single-Fault Detection Tests with Respect to Substitution of
Inverters for Combinational Elements in Some Bases

Abstract: We show that for an arbitrary Boolean function realized by a combinational circuit with elements from a basis whose extension contains the function xy (x $$\overline{y}$$ ), there exists a circuit that allows a single-fault detection test with at most three (resp. four) tuples.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09540-z

• Uniqueness of the Two Functional Coefficients in the Population-Model
Boundary Conditions

Abstract: We consider a model of biological population dynamics allowing for age structure. One of the boundary conditions in the model’s mixed initial–boundary-value problem is integral and nonlocal. The model is used for the inverse problem that simultaneously reconstructs the two coefficients in the model boundary conditions — the initial and the integral — given additional information on the solution of the forward problem in the form of two functions specifying the solution on the boundary. The uniqueness conditions for the inverse problem are proved. The integral relationships used to prove the uniqueness for the inverse problem lead to an iterative procedure to derive an approximate numerical solution of the inverse problem.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09531-0

• A Comparative Study on the Numerical Solution for Singularly Perturbed
Volterra Integro-Differential Equations

Abstract: This article essays the numerical solution of singularly perturbed Volterra integro-differential equations using some finite difference techniques. At first, the upwind scheme is applied for the derivative component and for the integral component, the trapezoidal rule in conjunction with the right side rectangular rule is used. This approach achieves first order uniform convergence. Furthermore, Richardson extrapolation is implemented to improve the accuracy by accelerating up the rate of convergence of the upwind scheme to obtain a second order accuracy. Finally, a hybrid scheme is applied, wherein central difference scheme is applied on the finer mesh region and midpoint difference operator on the coarser mesh region. The hybrid scheme also provides a second order uniform convergence. Numerical experiments are done with test problems and comparison is drawn with the existing methods to show the robustness of the proposed schemes.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09536-9

• A Dynamic Probabilistic Model of Two-Sided Combat

Abstract: A two-sided combat is modeled with each side characterized by the initial numbers, the probability of destruction of a unit of the enemy by a unit of own forces in a single period of fighting, and the critical level of losses when one side stops fighting and is declared the loser. Our problem is to find the win probability for each side. We separately consider the mean numbers dynamics (MND) when the losses of the sides in each period are equal to the expected values. In the MND framework, we consider the case when one of the sides detects only a certain part of the enemy units and study the influence of the detection efficiency on the combat outcome. We investigate the win probabilities of the two sides after a proportional increase of the initial numbers and establish their relationship with MND. An algorithm is proposed for calculating the win probabilities of the two sides. An approximate formula for the win probability is derived.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09534-x

• Automatic Quality Control in Lung X-Ray Imaging with Deep Learning

Abstract: The development of deep learning and its growing application in medical diagnosis have focused the attention on automatic control of image quality for neural-network medical image analysis algorithms. This article presents a method for automatic determination of the hardness (penetration) of lung X-ray images using standard criteria from chest X-ray diagnosis. The proposed method can be applied to automatically filter images by hardness (penetration) level and to detect low-quality images, thus facilitating the creation of high-quality data sets and increasing the efficiency of neural-network approaches to the analysis of lung X-ray images.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09539-6

• Image Key Point Matching by Phase Congruency

Abstract: A phase congruency measure calculated near image key points is proposed for key point matching. An algorithm for the construction and matching of key point descriptors is presented. The proposed method will match the key points of images of different sizes, with different rotation angles, and acquired under different illumination conditions. A modification of the proposed method can be used for the comparison of key points of iris images.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09532-z

• Virtual Element Method for Nonlinear Time-Dependent
Convection-Diffusion-Reaction Equation

Abstract: In this paper, we study the numerical solution of nonlinear time dependent convection-diffusion-reaction equation using virtual element method. We have used Virtual element discretization over polygonal meshes along with Streamline upwind Petrov–Galerkin stabilization (VEM-SUPG). The discrete terms are suitably modified to ensure the VEM computability with the help of projection operators $${\Pi}_p^0$$ and $${\Pi}_p^{\nabla }$$ respectively. For the time discretization, we used backward Euler finite difference method and the resulting nonlinear system is solved using Newton’s method. We have conducted several numerical experiments validating the performance of VEM-SUPG method along with rate of convergence and behavior of solutions over convex and non-convex polygonal meshes.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09537-8

• A Mathematical Model of Insurer Bankruptcy on a Finite Time Interval

Abstract: A discrete-time model is proposed for an insurance company with a Poisson stream of new insurance policies added to the portfolio and a mixed Poisson stream of insurance claims. Recursive formulas are derived for the first three moments of the risk surplus and a lower bound is obtained for the probability that the surplus remains positive on a given time interval.
PubDate: 2021-07-01
DOI: 10.1007/s10598-021-09530-1

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