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

PubDate: 2021-07-01

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• A Comparison of Block Based Kalman Filter and H-Infinity Algorithms for
Blind Image Separation

Abstract: Blind image separation is a method of recovering the original images from a set of image mixtures, with no information about the source images or about the mixing process. Blind source separation problem has been used to extract sources from one-dimensional mixture signals such as speech, whereas, application of source separation for images (two-dimensional signals) has been examined to a limited extent. The independent component analysis (ICA) method assumes statistical independence of the source signals and at least one of the source could be non-gaussian. These assumptions do not hold for image mixing conditions. An alternative approach is to use Kalman filter that operates on the noisy input data recursively to produce statistically optimal estimate of the underlying sources. In this paper, a robust filter on H-infinity norm is proposed and compared with for image separation of Kalman filter. The extension of the algorithms to a simple and block based approach wherein the image mixture is converted to a sparse representation is proposed. The image mixture is subdivided into blocks of known sizes and the sparseness of each block is measured using l_0 norm and the block with maximum sparseness is used for extraction of original sources. This reduces the computational complexity that exists with the large dimensions of images. The algorithms are validated for natural image data sets and also for window reflection images taken under different lighting conditions. The analysis results suggest that the proposed methods provide significantly good quality of separation as measured by the performance metrics.
PubDate: 2021-07-01

• Diffraction of the Fundamental Waveguide Wave on an Inductive Cylinder in
a Rectangular Waveguide

Abstract: We apply the integral equation method to the diffraction of a waveguide wave on an impedance inductive cylinder in a rectangular waveguide. The Green’s function determining the kernel of the relevant integral equation is constructed for a plane waveguide using the reflection method and the Poisson transform.
PubDate: 2021-04-01

• Positional Flight Control of a Hybrid Propulsion Spacecraft

Abstract: We consider the transfer to a Kepler orbit of a controlled spacecraft whose dynamics is described by a mathematical model of motion under gravity and light pressure. The spacecraft has a hybrid propulsion system consisting of a jet engine with a fuel tank and a solar sail. A class of positional controls of the propulsion system by radial and transverse thrust is described, solving the problem of controllability of transfer to a specified orbit. The positional controls are derived in analytical form. Numerical calculations are reported for the positional control and controlled flight trajectories with test parameters.
PubDate: 2021-04-01

• Testing Read-Once Functions in a Median-Augmented Element Basis

Abstract: We construct a checking test for a read-once alternative in a median-augmented element basis. We prove that the augmentation of the element basis with a median conserves the linearity of the Shannon function for the test length with respect to a read-once alternative.
PubDate: 2021-04-01

• Regularization Methods in the Analysis of a Series of Scintillation
Fluorescence Microscopy Images

Abstract: We consider the construction of high-resolution images from a time series of fluorescence microscopy images obtained using a scintillator. A regularization method is applied and the results are compared for various stabilizers, including the RED (regularization-by-denoising) approach. Tests conducted for two series of microtubule structures have proved the applicability of the proposed methods.
PubDate: 2021-04-01

• Solitons and Other Solutions for the Nonlinear
Convection–Diffusion–Reaction Equation with Power-Law Nonlinearity by
the Extended Simplest Equation Method

Abstract: Based on the extended simplest equation method, we construct solitons and other solutions for the nonlinear convection-diffusion-reaction equation with power-law nonlinearity. This equation is the generalization of some nonlinear partial differential equations (NLPDEs), e.g., the Fisher equation or the logistic equation, the Zeldovich equation, the Newell–Whitehead or amplitude equation and the Nagumo or bistable equation. Dark solitons, singular solitons, combo bright-singular solitons, combo singular solitons, the combination of combo singular solitons and bright solitons and the combination of combo dark-bright solitons and singular solitons have been found. The new solutions in this article confirm that the used method is an efficient technique for analytic treatments of a wide variety of other NLPDEs in mathematical physics.
PubDate: 2021-04-01

• Numerical Simulation of Influence of Surface Features on the
Elastohydrodynamic Lubrication of Sliding Line Contact Using Krylov
Subspace Method

Abstract: The article presents an efficient novel numerical method to investigate overrolling (with slip) of transient EHL line contact problem with surface asperities. Jacobian free Newton–Krylov subspace (JFNK) method is used for the solution of discretized transient Reynolds and film thickness equations. The dense nonsymmetric large system of linear equations is solved using an iterative strategy based on wavelet based preconditioned generalized minimal residual (GMRES) algorithm incorporating a line search scheme to archive global convergence. The focus is on highly loaded (with Hertz pressure 2GPa) line contact EHL problem to obtain pressure and film profiles as functions of the slide to roll ratio. The nonsynchronization of pressure and film profiles (especially at dent locations) is found explicitly which is more pronounced as the dent approaches the contact central region and moves towards the exit. Leading/trailing of film profile is observed as the dent (attached with an upper surface) moves slower/faster compared with average speed (of surfaces). Also, there is an increase (in height as well as a spread) of Petrusevich pressure spike as dent moves through the contact region towards the exit. For the waviness attached with the upper surface, the pressure and film profiles are obtained again as functions of a slide to roll ratio. Pressure profiles are invariant with respect to this parameter whereas film profiles are entirely different in all these cases. The proposed method, with projection features, captures salient aspects of the model problem with much lesser degrees of freedom compared with conventional schemes.
PubDate: 2021-04-01

• Guaranteed Deterministic Approach to Superhedging: Structural Stability
and Approximation

Abstract: The discrete-time superreplication problem is considered in the guaranteed deterministic setting: the problem requires a guaranteed coverage of contingent claims on an option for all possible scenarios. These scenarios are described by a priori specified compacta dependent on price history: the price increases at each instant are contained in the corresponding compacta. Trade constraints and zero transaction costs are assumed. The problem is formulated in a game-theoretical setting, which leads to the Bellman–Isaacs equations in both pure and mixed “market” strategies. Assuming structural stability of the model (robust condition of no guaranteed unlimited-profit arbitrage), we obtain bounds on the approximation accuracy of price dynamics for two classes of models: models with unbounded conical trade constraints and models with bounded trade constraints.
PubDate: 2021-04-01

• The Effect of Diffusion on Propagation and Reflection of Waves in a
Thermo-Microstretch Solid Half-Space

Abstract: Lord–Shulman theory of generalized thermoelasticity is employed to derive the governing equations of generalized thermo-microstretch elasticity with diffusion. The governing equations are specialized in x-y plane and solved for plane wave solutions. It is found that there exist six plane waves propagating with distinct speeds in a thermo-microstretch medium with diffusion. Reflection phenomenon of these plane waves is studied from a stress-free thermally insulated/isothermal surface of a half-space. With the use of relevant boundary conditions, the expressions of amplitude and energy ratios for reflected waves are obtained. The speeds and energy ratios of all reflected waves are computed for relevant physical parameters of the model. The numerical results are illustrated graphically to observe the effect of diffusion parameters on the speeds and energy ratios of reflected waves.
PubDate: 2021-04-01

• Generalized Target-Allocation Functions and their Evaluation by the
Branch-And-Bound Method

Abstract: In this article, we generalize Krasnoschekov’s scheme [6] to improve the solution of the max-min targetallocation problem by excluding some types of targets that are not entirely suited for the allocation of the available defense tools. The problem is not submodular, it is therefore solved by the general branchand- bound method using objective-function upper bounds. We show how to construct such bounds using Germeier’s generalized equalization principle. This development endows the branch-and-bound method with new practical significance.
PubDate: 2021-04-01

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