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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: 2021-07-19 DOI: 10.1007/s10598-021-09521-2

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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: 2021-07-19 DOI: 10.1007/s10598-021-09524-z

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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: 2021-07-19 DOI: 10.1007/s10598-021-09529-8

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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: 2021-07-19 DOI: 10.1007/s10598-021-09520-3

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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: 2021-07-19 DOI: 10.1007/s10598-021-09528-9

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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: 2021-07-19 DOI: 10.1007/s10598-021-09526-x

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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: 2021-07-19 DOI: 10.1007/s10598-021-09522-1

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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: 2021-07-19 DOI: 10.1007/s10598-021-09527-w

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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: 2021-07-19 DOI: 10.1007/s10598-021-09525-y

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Abstract: We develop a mathematical model of the coronavirus propagation in different countries (Brazil, India, US, Japan, Israel, Spain, Sweden), in the city of Moscow, and across the world. The pandemic spreads by a highly complex dynamics because it occurs in open nonhomogeneous systems where new infection foci erupt from time to time, triggering new transmission chains from infected to susceptible people. In general, statistical data collected as cumulative and epidemic curves are a superposition of many distinct local pandemic waves. In our modeling, we use the system of Feigenbaum’s discrete logistic equations (a logistic map) that describes the variation of the total number of infected over time. We show that this is the optimal model for the description of pandemic propagation in open nonhomogeneous systems with large errors in statistical data. We develop a procedure for isolating local waves, determining their model parameters, and predicting further evolution of each wave. We show that this model provides a good description of the statistical data and makes realistic forecasts. The forecast horizon depends on the degree of system closure and homogeneity. We calculate the start and end times of each wave, the peak, and the total number of infected in the current wave. PubDate: 2021-07-19 DOI: 10.1007/s10598-021-09523-0

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Abstract: The article focuses on a numerical analysis of the projected use of the T-15MD tokamak machine after its physical launch for generating a configuration with negative triangularity of the plasma filament cross section (an inverted D shape) on the installed magnetic field coils. The study is of interest in connection with recent experiments on several tokamaks that have demonstrated a distinct improvement achieved with such operating regimes compared with standard plasma containment configurations. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09512-3

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Abstract: We consider a guaranteed deterministic approach to discrete-time super-replication for guaranteed coverage of contingent claims on options for all possible asset-price scenarios. Price increases during a period are assumed to be contained in a priori specified compacta dependent on price history. A game problem is stated and reduced to the solution of the corresponding Bellman–Isaacs equation. Numerical solution algorithms on a discrete lattice are considered for the Bellman–Isaacs equation. Results of a numerical experiment are reported for various model specifications. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09514-1

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Abstract: The present research paper deals with the effectiveness of the solvability of two dimensional (2D) models. This study explores the new fractional derivatives and extended transforms for a class of bidimensional models. A 2D Sumudu and 2D Laplace transforms are used to establish the solution of the continuous Fornasini-Marchesini models by the use of the conformable derivatives. A new definition and properties of Sumudu in two dimensional case are given. Finally, an illustrative example is given to show the accuracy and applicability of the developed methods. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09519-w

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Abstract: In this paper, the Discrete Sources Method has been extended to describe the influence of the geometry asymmetry of a core-shell particle accounting for the effect of spatial dispersion inside the plasmonic metal shell. We found that varying the plasmonic shell thickness has more influence on the near field intensity distribution then on the average enhancement factor. Besides, we demonstrates that the effect of spatial dispersion can decrease the near field intensity up to 60% of its value and it provides a small blue shift. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09517-y

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Abstract: We investigate a stochastic model of the galactic dynamo in the planar approximation, assuming that turbulent diffusivity is a renewal process. For linear and nonlinear modifications of this model, numerical methods are applied to construct statistical moments and correlation tensors of the magnetic field. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09515-0

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Abstract: The barycentric method is applied to numerical solution of electromagnetic wave diffraction on screens of arbitrary shape. The main assumption involves the piecewise-linear specification of the screen boundary. A distinctive feature of the barycentric method is the order in which the global basis-function system is generated for the representation of the screen in barycentric coordinates. Existence and uniqueness are established for the solution of the integral electric-field equation on an arbitrarily shaped screen by the barycentric method and rate of convergence bounds are obtained. The main algorithmic procedures are refined by improving the evaluation of the singular integral. The performance of the barycentric method is compared with the Rao–Wilton–Glisson (RWG) on test cases. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09513-2

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Abstract: Nanometer to micrometer scale colloidal particles are regularly found in applications in which surface forces dominate behavior. Consequently, a wide range of surface force measurement tools have been developed to probe interactions as a function of physiochemical properties. One tool, Total Internal Reflection Microscopy (TIRM), is an exceptionally sensitive probe of both conservative and non-conservative surface forces. A recent variant of TIRM called Scattering Morphology Resolved (SMR) TIRM utilizes the morphology of scattered light in concert with the integrated intensity to measure the position and orientation of a colloidal particle. Although the target of SMR-TIRM is the field of non-spherical “anisotropic” particles, spherical particles have been found to scatter evanescent waves with surprising morphology. Herein, we present experiments and simulations of the scattering morphology of a spherical particle. The morphology was probed as a function of particle size, incident beam polarization, and particle separation distance. We found that spherical particles scattered light with a noncircular morphology. Moreover, we found the morphology depended upon both the scaled particle size with respect to the incident beam wavelength and the incident beam polarization. Although the scattering morphology from the sphere was surprisingly complex, we did not find that these effects would alter the interpretation of scattering as a function of particle separation distance. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09518-x

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Abstract: Leprosy (Hansen’s disease) is an infectious, neglected tropical disease caused by the bacterium or scientifically Mycobacterium Leprae (M. Leprae). Every year approximately 214,000 new cases of leprosy are reported globally. Leprosy affects the skin or more precisely epidermal layer but M. Leprae specifically targets the Schwann cells of myelinated axons. In this article, we have proposed a three dimensional mathematical model involving the concentrations of healthy Schwann cells, infected Schwann cells and Bacteria (M. Leprae) to predict the dynamical changes of the cells during this disease progression. We have also studied the control mathematical model by introducing two bounded control parameters into our model. For detail analysis of this control system, by considering a minimization problem for the concentration of infected Schwann cells and Bacteria, we have applied the Pontryagin maximum principle. As a result of this analysis, the properties of the optimal controls and their possible types have been established. All analytical outcomes have been verified by numerical simulations. PubDate: 2021-06-23 DOI: 10.1007/s10598-021-09516-z

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Abstract: We consider a one-sector model with time-dependent economic indicators and the cor-responding optimal control problem in the presence of delays in the commissioning of new assets. The problem is constructed by the method of additional phase variables. An analytical solution of the control problem is presented. The parameters of a suboptimal solution are obtained numerically. PubDate: 2021-01-28 DOI: 10.1007/s10598-021-09505-2