Journal of Applied and Industrial Mathematics最新文献

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.

This paper is a survey of modern post-quantum cryptographic schemes based on codesand isogenies. Special attention is paid to cryptanalysis of these schemes. In particular, forcode-based cryptosystems we describe the information set decoding and the support splittingalgorithm as main attacks, and for cryptosystems based on isogenies we describe in detail theCastryck–Decru attack on SIDH/SIKE.

Seismic images of subsurface structures are the most valuable outcome of seismic dataprocessing. The image quality is strongly affected by the accuracy of background velocity model.In this paper, we develop a gradient-descent velocity update algorithm based on our originalhigh-frequency asymptotics of the Double Square Root equation, i.e., a special one-wayapproximation of the wave equation describing single-scattered wave field only. We propose a lossfunction consistent with widely adopted imaging condition and derive equations for its gradientcomputation. We test our method on noise-free synthetic datasets in 2D settings.

In 1961, L.M. Gluskin proved that a given set( X ) with an arbitrary nontrivial quasiorder( rho ) is determined up to isomorphism or anti-isomorphism by the semigroup( T_rho (X) ) of all isotone transformations of( (X,rho ) ), i.e., the transformations of( X ) preserving( rho ). Subsequently, L.M. Popova proved a similar statement for the semigroup( P_rho (X) ) of all partial isotone transformations of( (X,rho ) ); here the relation( rho ) does not have to be a quasiorder but can be an arbitrary nontrivial reflexiveor antireflexive binary relation on the set( X ). In the present paper, under the same constraints on the relation( rho ), we prove that the semigroup( B_rho (X) ) of all isotone binary relations (set-valued mappings) of( (X,rho ) ) determines( rho ) up to an isomorphism or anti-isomorphism as well. In addition, for each ofthe conditions( T_rho (X)=T(X) ),( P_rho (X)=P(X) ), and( B_rho (X)=B(X) ), we enumerate all( n )-ary relations( rho ) satisfying the given condition.

To study the flow in a far plane turbulent wake in a passively stratified medium, we use amathematical model that includes differential equations for the balance of turbulence energy, thetransfer of its dissipation rate, shear turbulent stress, a defect of the density of the liquid, and thevertical component of the mass flux vector. Algebraic truncation of the last equation leads to awell-known gradient relation for the vertical component of the mass flux vector. It is establishedthat under a certain constraint on the values of empirical constants in the mathematical modeland the law of time scale growth consistent with the mathematical model, this relation is adifferential constraint for the model. The equivalence of the local equilibrium approach for thevertical component of the mass flux vector and the zero Poisson bracket for the dimensionlessturbulent diffusion coefficient and the averaged density is shown. The results of numericalexperiments illustrating the theoretical results are presented.

A set( J_k ) of graph vertices is said to be( k )-dominating independent (( k geq 1 )) if its vertices are pairwise adjacent and every vertex not in( J_k ) is adjacent to at least( k ) vertices in( J_k ). In the present paper, we obtain new upper bounds for the number of( k )-dominating independent sets for( k geq 2 ) in some planar graph classes.

The paper considers the spectral problem associated with the study of local characteristicsof weakly coupled systems in reactor physics. The method of associated invariant subspaces basedon the matrix spectrum dichotomy method is described. With its help, distributions are foundthat reflect multiplicating properties of local areas in the system.

Arden and Lee proposed a class of chordal ring networks of degree three as communicationnetworks for multicomputer systems, derived a formula for the diameter, and produced analgorithm for finding the shortest paths for them. In this paper, it is shown that the formula forthe diameter and the routing algorithm presented by them are inaccurate. We have obtained alarge dataset containing parameters for describing optimal diameter chord rings for all thenumbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ringnetworks. A new method is proposed and the algorithms for automatic search for analyticaldescriptions of families of optimal chordal rings are realized based on an analysis of the database.Using the latter, analytical descriptions of over 500 new families of optimal chordal ring networksfor many values of the number of nodes are found (only six families have been known until now inthe literature).

In this paper, for the first time, we present a new model of current distribution in atungsten sample and of substance evaporation when the surface is heated by an electron beam.The model is based on solving electrodynamics equations in a cylindrical coordinate system usinga model temperature distribution in the sample and a thin layer of evaporated tungsten. Themodel is analyzed in a simplified formulation at constant values of electrical resistance andthermoelectric power in gas and metal. The dependence of the amplitude and isolines of thermalcurrents on the distribution of temperature at the sample surface is shown. The model parametersare taken from experiments at the Beam of Electrons for materials Test Applications (BETA)facility, created at the Budker Institute of Nuclear Physics of the Siberian Branch of the RussianAcademy of Sciences.