Abstract: We consider the choice of image denoising parameters in an algorithm based on singular decomposition and minimization of the weighted nuclear norm. An automated parameter-choosing method is proposed that analyzes the structures on a difference image between the original noisy image and the denoised result and performs a quantitative assessment of the structures — computes the mutual information coefficient. We also analyze the choice of optimal parameters for different noise levels using a database of photographic images with normally distributed simulated noise. The denoising results are compared for the optimal choice of parameters and the choice of parameters by the mutual information coefficient, and also with denoising by a Peron–Malik diffusion algorithm. PubDate: 2020-10-17

Abstract: We consider a new formulation of the Fourier-filtering problem that uses matrix Fourier-filters as the controls in nonlinear optical models described by quasi-linear functional-differential diffusion equations. Solvability of the control problem is proved for various classes of matrix Fourier-filters with a time-integral objective functional. Differentiability of the functional with respect to the matrix Fourier-filter and convergence of a variant of the gradient projection method are proved. Examples of numerical simulation of controlled structure formation are presented, and the advantages of matrix Fourier-filters compared with traditional multiplier filters are demonstrated. PubDate: 2020-10-17

Abstract: An algorithm is proposed for a fast discrete finite Hankel transform of a function in a thin annulus. The transform arises in a natural way in the Neumann boundary-value problem for the Poisson equation in an annulus when spectral methods are applied for its numerical solution. The proposed algorithm uses the limiting properties of eigenvalues and eigenfunctions of the Laplace operator as the annulus thickness goes to zero. PubDate: 2020-10-15

Abstract: We consider the construction of a universal function for classes of modulo 2 sums of three arguments. The definition domain of the universal functions is of cardinality Θ(log n). PubDate: 2020-10-15

Abstract: We propose a two-dimensional mathematical model based on Galerkin’s spatial method combined with a theta time scheme applied to the heat equations. This model has been applied to a hypothetical example in which the obtained results are compared with the real experimental data. This comparison allow us to predict the soil temperature at different depths as well as at different time periods according to certain conditions imposed on the weather. PubDate: 2020-10-15

Abstract: We introduce the notion of reflexive-recursive circuits and consider classes of many-output and scalar reflexive-recursive circuits of bounded depth in an arbitrary basis. Methods are proposed for deriving lower and upper bounds on the Shannon function for the complexity of circuits from these classes and asymptotic expressions are established. We also derive upper bounds for the realization complexity in these classes of circuits for some functions and systems of functions occurring in applications. PubDate: 2020-10-15

Abstract: A new version of the synthetic turbulent velocity generator is proposed for simulation of turbulent flows. The method is fully stochastic and generates a statistically anisotropic and nonhomogeneous random field, which provides the initial and boundary conditions for the deterministic eddy-resolving model of turbulence. The simulation method has been tested on a three-dimensional problem of developed turbulent channel flow. PubDate: 2020-10-15

Abstract: We analyze the parallelism particularities of finite volume based computational algorithms. We use a problem set from electrodynamics and parallelize its solution. It serves as an example and illustration of our findings. The tests are carried out on the Zhores supercomputer. The hardware used to run parallel algorithms includes Nvidia Tesla V100 GPUs and Intel Xeon CPUs. We find that finite volume method discretizations work well with parallelization on GPUs. The speedup can be increased by proper CUDA optimizations. However, it is very resource consuming to perform all computations on supercomputer GPUs if the problem size is exceptionally big. Hence, it is necessary to harness every processing power that a supercomputer can offer including CPUs. We offer ways to parallelize the posed problem in a hybrid fashion. PubDate: 2020-10-15

Abstract: We consider a guaranteed deterministic formulation for the super-replication problem in discrete time: find a guaranteed coverage of a contingent claim on an option under all possible scenarios. These scenarios are specified by a priori compacta that depend on historical prices: the price increments at each instant should be in the corresponding compacta. We assume the presence of trading constraints and the absence of transaction costs. The problem is posed in a game-theoretical setting and leads to Bellman–Isaacs equations in both pure and mixed “market” strategies. In the present article, we investigate the sensitivity of the solutions to small perturbations of the compacta that describe price uncertainties over time. Numerical methods are proposed allowing for the problem’s specific features. PubDate: 2020-10-15

Abstract: A model of an energy harvester is considered a system intended for the conversion of residual thermal energy into electric energy. Periodic motions are a key factor in the operation of the harvester. We search for model parameters that produce self-oscillations in the systems. The problem is solved by numerical simulation and evolutionary computation. PubDate: 2020-10-15

Abstract: The Fractional derivative is a widely accepted theory to describe physical phenomena and the processes with memory effects which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a thermoelastic rod in the context of the Lord–Shulman (LS) theory of generalized thermo-visco-elasticity. Both ends of the rod are fixed and are thermally insulated. Employing the Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained on applying the numerical inversion of the Laplace transform, which has been carried out employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod is carried out and have been demonstrated graphically. The results also demonstrate how the speed of the moving heat source influences the thermophysical quantities. It is observed that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. Also, significant differences in the thermophysical quantities are revealed due to the influence of the magnetic field and memory effect PubDate: 2020-06-10

Abstract: We investigate the allocation of resources in a two-sector economic model with a Cobb–Douglas production function for different depreciation rates with an integral functional on a finite time horizon. The problem is reduced to some canonical form by the scaling of phase variables and time. The extremal solution constructed by Pontryagin’s maximum principle is shown to be optimal. For a sufficiently large planning horizon, the optimal control has two or three switch points, contains one singular section, and vanishes on the final section. A transition “calibration” regime is observed between the singular section, where the system moves along a singular ray, and the final section. The maximum-principle boundary-value problem is solved in explicit form and the solution is illustrated with graphs based on numerical calculations. PubDate: 2020-06-05

Abstract: We consider a controlled model of a firm that produces to inventory while simultaneously repaying its debt. Maximization of a terminal functional for this model is considered. The corresponding optimal solutions are analyzed by Pontryagin’s maximum principle. All optimal controls are found depending on the parameters of the original model and the functional weighting coefficient. An appropriate economic interpretation is proposed for the results. Numerical calculations reported in the article establish validity of the theoretical results. PubDate: 2020-06-05

Abstract: The problem of free convective steady boundary layer flows over a solid horizontal flat plate nested in a porous medium filled with a nanofluid containing gyrotactic microorganisms is considered. The exponent of the temperature, the nanoparticle volume fraction and the density of motile microorganisms are introduced to make the quantities dimensionless. The impacts of the considered exponent and bioconvection parameters on the dimensionless temperature, velocity, nanoparticle concentration and density of motile microorganisms along with Nusselt, Sherwood and motile microorganism numbers are tabulated and shown graphically. For a regular fluid and also for the isothermal case, the results are compared with the existing data and excellent compatibility is found. PubDate: 2020-06-05

Abstract: We seek a control that satisfies the boundary conditions for a linear controlled system whose trajectory passes outside some neighborhood of a given phase-space point. Existence conditions are derived. Numerical calculations of the control and the trajectory are presented for an inertial system of second order. PubDate: 2020-06-04

Abstract: We consider a terminal control problem for an underactuated nonlinear control system with phase constraints. The control is sought by the linearization method in which the control is determined by solving the Cauchy problem for a nonlinear parametric system of auxiliary differential equations. An auxiliary extremum problem with boundary conditions of general type is proposed for the numerical calculation of the control parameters. Examples of control are computed for a process with test parameters. PubDate: 2020-06-04

Abstract: Controlled quarrying models have been considered in [1, 2] and elsewhere. These models are the product of a collaboration between the Department of Optimal Control at the Lomonosov State University’s Faculty of Computation Mathematics and Cybernetics and the international mining company BHPB Billiton. The present article is a continuation of [1, 2]. Our quarrying model is highly simplified. Yet it reflects some important theoretical aspects that arise in mining. PubDate: 2020-06-04

Abstract: In this paper, we discuss the parameter-uniform overlapping numerical method for a coupled first-order system with prescribed initial conditions. An overlapping interval is used to form a numerical method for this problem. The problem is discretized using the mid-point difference scheme on the boundary and non-layer regions. The convergence analysis is given, and the method is proved to be second order uniformly convergent in maximum norm with respect to the singular perturbation parameter ' Numerical experiments are conducted to demonstrate the theoretical results. PubDate: 2020-06-04

Abstract: We investigate a controlled version of the well-known business cycle model proposed by Nicholas Kaldor. The control is introduced by a parameter that characterizes demand stimulation by the state. The cost of the stimulating policy is a quadratic function; the instantaneous utility function is defined as the national income less demand-stimulation costs. We show that with nearly-maximal demand, an asymptotically stable stationary state always exists in the model. Under fairly general assumptions, we prove existence and uniqueness of the optimal stationary state. The problem of the shortest-time transition of the system to a given stationary state is considered. Numerical simulation results are reported. Keywords: dynamic models in economics, Kaldor business-cycle model, stability, optimality, stationary state, minimum-time problem. PubDate: 2020-06-04

Abstract: We consider a mathematical model that describes biological treatment of wastewater. The model is a controlled nonlinear three-dimensional system of differential equations. A minimum-time optimal control problem is posed that achieves the required contaminant concentration in the shortest possible time. The problem is investigated by Pontryagin’s maximum principle. The optimal control in this problem is represented by a switching function and its properties are analyzed. The results of this analysis make it possible to reduce the solution of the problem to a successive application of finite-dimensional constrained minimization and the parameter continuation method. The application of these approaches is discussed in detail, and the relevant numerical results are reported. PubDate: 2020-06-04