The problem of maximizing a convex function on a so-called simple set is considered. Based on the optimality conditions [19], an algorithm for solving the problem is proposed. This numerical algorithm is shown to be c...
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The problem of maximizing a convex function on a so-called simple set is considered. Based on the optimality conditions [19], an algorithm for solving the problem is proposed. This numerical algorithm is shown to be convergent. The proposed algorithm has been implemented and tested on a variety of test problems.
We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex function...
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We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity;then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.
Vibration problems of pipelines made of composite materials conveying pulsating flow of gas and fluid are investigated in the paper. A dynamic model of motion of pipelines conveying pulsating fluid flow supported by a...
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Vibration problems of pipelines made of composite materials conveying pulsating flow of gas and fluid are investigated in the paper. A dynamic model of motion of pipelines conveying pulsating fluid flow supported by a Hetenyi's base is developed taking into account the viscosity properties of the structure material, axial forces, internal pressure and Winkler's viscoelastic base. To describe the processes of viscoelastic material strain, the Boltzmann-Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov-Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations (IDE). A computational algorithm is developed based on the elimination of the features of IDE with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, flow rate and base parameters on the vibration of a viscoelastic pipeline conveying pulsating fluid is analyzed. The convergence analysis of the approximate solution of the Bubnov-Galerkin method is carried out. It was revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in the critical flow rate. It was stated that an increase in excitation coefficient of pulsating flow and the parameter of internal pressure leads to a decrease in the critical flow rate. It is shown that an increase in the singularity parameter, the Winkler base parameter, the rigidity parameter of the continuous base layer and the Reynolds number increases the critical flow rate.
In the framework of a discrete radiative transfer model, a method is proposed for finding the reflection and transmission operators in the conservative case.
In the framework of a discrete radiative transfer model, a method is proposed for finding the reflection and transmission operators in the conservative case.
The problem of the variational data assimilation of the sea-surface temperature for the model of the Black Sea dynamics has been formulated and numerically studied to reproduce surface heat fluxes. An analysis of sens...
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The problem of the variational data assimilation of the sea-surface temperature for the model of the Black Sea dynamics has been formulated and numerically studied to reproduce surface heat fluxes. An analysis of sensitivity of the optimal solution to errors in observation data has been conducted. The results of numerical experiments have been presented.
We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinat...
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We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash
The evolution of an initial perturbation in an axisymmetric subsonic normal inviscid gas flow through a pipe is directly simulated. The basic (unperturbed) flow has a zero radial velocity component, while its axial ve...
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The evolution of an initial perturbation in an axisymmetric subsonic normal inviscid gas flow through a pipe is directly simulated. The basic (unperturbed) flow has a zero radial velocity component, while its axial velocity component (along the axis of symmetry) increases or decreases linearly with the radius. The perturbation is specified as a swirl (rotation about the axis) with a positive or negative velocity vanishing on the central axis and the lateral surface. Irrespective of its direction, the swirl gives rise to a steady-state vortex carried by the flow. It shape is spherical (contiguous to the rotation axis) or circular (sliding along the impermeable lateral surface).
This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. numerical examples are carried out to illustrate the performance of our approach.
This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. numerical examples are carried out to illustrate the performance of our approach.
A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a ...
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A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.
This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions...
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This paper describes the results from a numerical estimation of the force exerted by long surface waves on a fixed and partially immersed rectangular structure. The topic is connected with the need of making decisions on the design, placement and operation of hydrotechnical structures of this kind. The wave-structure interaction is simulated in the framework of a nonlinear potential flow model. The results obtained allow to determine the dependence of the hydrodynamic force on the length and amplitude of a single wave, the length and submergence of the structure. We compare the results obtained for different initial wave shapes, and consider the differences between the forces acting on a vertical wall and a partially immersed structure. In particular, it is shown that at relatively small submergence of the structure, longer waves affect it less, while at large submergence and in the case of wave-wall interaction, the opposite behaviour is observed.
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