Journal of Applied and Industrial Mathematics最新文献

The problem of identifying Volterra kernels is an important stage in the construction ofintegral models of nonlinear dynamical systems based on the tool of Volterra series. The paperconsiders a new class of two-dimensional integral equations that arise when recoveringnonsymmetric kernels in a Volterra polynomial of the second degree, where( x(t) ) is the input vector function of time. The strategy for choosing test signalsused to solve this problem is based on applying piecewise linear functions (with a rising edge). Anexplicit inversion formula is constructed for the selected type of Volterra equations of the first kindwith variable integration limits. The questions of existence and uniqueness of solutions of thecorresponding equations in the class( C_{[0,T]} ) are studied.

The paper considers a mathematical model of the filtration of two immiscibleincompressible fluids in deformable porous media. This model is a generalization of theMusket–Leverett model, in which porosity is a function of the space coordinates. The model understudy is based on the equations of conservation of mass of liquids and porous skeleton, Darcy’s lawfor liquids, accounting for the motion of the porous skeleton, Laplace’s formula for capillarypressure, and a Maxwell-type rheological equation for porosity and the equilibrium condition ofthe “system as a whole.” In the thin layer approximation, the original problem is reduced to thesuccessive determination of the porosity of the solid skeleton and its speed, and then theelliptic-parabolic system for the “reduced” pressure and saturation of the fluid phase is derived. Inview of the degeneracy of equations on the solution, the solution is understood in a weak sense.The proofs of the results are carried out in four stages: regularization of the problem, proof of themaximum principle, construction of Galerkin approximations, and passage to the limit in terms ofthe regularization parameters based on the compensated compactness principle.

The paper examines the problem of the distribution of public space. We use the methodsof cooperative game theory to solve this problem. Players are districts, while the value of thecharacteristic function is the total number of people interested in a particular type of public spacein the areas under consideration. The axioms that are characteristic of the problem of division arecompiled. A special value of the cooperative game is derived that depends on the weights of theplayers. It is shown how to choose the weights by optimization methods.

A general method for the enumeration of various classes of chord diagrams with even andodd numbers of chord intersections is considered. The method is based on the calculation of thePfaffian and Hafnian of the constraint matrix characterizing a class of diagrams.

The aim of this paper is to study the solvability of inverse problems of determining,together with the solution of the heat equation, its right-hand side or an unknown externalinfluence. The specific feature of the problems studied is that the unknown external influence isdetermined by two functions of which one depends only on the spatial variable and the other, onlyon the time variable.

This paper is devoted to the construction of a time-optimal method for measuring themaximum permissible (critical) value of the supply voltage (as well as other parameters) of thedevice on which the cryptographic algorithm is performed. Knowledge of these values is necessaryfor successful conduct of error injection, as part of a fault attack. The method is based ondynamic programming.

Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in theclass of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewiseparabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe andHarten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers,the numerical solution is free from artifacts. In the case of equations of special relativisticmagnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quitecomplex and does not have an analytical solution. The present paper proposes the development ofRusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in theequations of special relativistic magnetohydrodynamics. The developed scheme was verified usingeight classical problems on the decay of an arbitrary discontinuity that describe the main featuresof relativistic magnetized flows.

A convex continuation of an arbitrary Boolean function to the set( [0,1]^n ) is constructed. Moreover, it is proved that for any Boolean function( f(x_1,x_2,dots ,x_n) ) that has no neighboring points on the set( mathrm{supp} f ), the constructed function( f_C(x_1,x_2, dots ,x_n) ) is the only totally maximally convex continuation to( [0,1]^n ). Based on this, in particular, it is constructively stated that the problem ofsolving an arbitrary system of Boolean equations can be reduced to the problem of minimizing afunction any local minimum of which in the desired region is a global minimum, and thus for thisproblem the problem of local minima is completely resolved.

In this paper, we study a nonlinear dynamical system of autonomous ordinary differentialequations with a small parameter( mu ) such that two variables( x ) and( y ) are fast and another one( z ) is slow. If we take the limit as( mu to 0 ), then this becomes a “degeneratesystem” included in the one-parameter family of two-dimensional subsystems offast motions with the parameter( z ) in some interval. It is assumed that in each subsystem there existsa structurally stable limit cycle( l_z ). In addition, in the completedynamical system there is some structurally stable periodic orbit( L ) that tends to a limit cycle( l_{z_0} ) for some( z=z_0 ) as( mu ) tends to zero. We can define the first return map, or the Poincarémap, on a local cross section in the hyperplane( (y,z) ) orthogonal to( L ) at some point. We prove that the Poincaré map has an invariantmanifold for the fixed point corresponding to the periodic orbit( L ) on a guaranteed interval over the variable( y ), and the interval length is separated from zero as( mu ) tends to zero. The proved theorem allows one to formulate some sufficientconditions for the existence and/or absence of multipeak oscillations in the complete dynamicalsystem. As an example of application of the obtained results, we consider some kinetic model ofthe catalytic reaction of hydrogen oxidation on nickel.

We propose a method for calculating the kinetics of ultrasonic coagulation of PM2.5during fine gas cleaning that provides an order of magnitude higher calculation performance.Increased productivity is achieved through the proposed and justified method of reducing theoriginal three-dimensional problem to a two-dimensional one. The proposed reduction method isbased on the fact that the time of complete rotation of vortex acoustic flows turns out to be muchshorter than the characteristic coagulation time during fine gas cleaning. This makes it possible topresent the fractional composition of aerosol particles as a function of two stream functionsinstead of three coordinates. Calculations carried out using the proposed method make it possibleto identify the possibility of increasing the efficiency of coagulation in three-dimensional flows dueto the following mechanisms: a local increase in concentration caused by the inertial transfer ofparticles to the periphery of three-dimensional vortices in the gas phase, increasing the frequencyof particle collisions due to three-dimensional turbulent disturbances in ultrasonic fields with ahigh amplitude of oscillatory velocity (more than 10 m/s), and increasing productivity andensuring the possibility of continuous implementation of the process in flow mode due to thetransfer of particles between the streamlines of the main vortices initiated by ultrasonic vibrationsas well as due to external flows perpendicular to the plane of the vortices in three-dimensionalspace. The developed set of programs for implementing calculations can be used in the design ofgas cleaning equipment.