Journal of Applied and Industrial Mathematics最新文献

As a model of shear rupture in the Earth’s crust at the depths of seismic activity, whichgrows with a velocity exceeding the velocity of longitudinal waves, we consider a Volterra edgedislocation moving in an infinite isotropic elastic medium under the action of preliminarytangential stresses. In the plane strain approximation, the equations of stationary motion of themedium around the dislocation are reduced to a hyperbolic system of equations for velocities andstresses, which is integrated by the method of characteristics. Using the invariant( J )–integral, an estimate of the energy released during the motion of dislocationis obtained, depending on the velocity, the value of tangential stress at infinity, the length of thefan adjacent to the vertex of dislocation, and on the nature of the distribution of the Burgersvector in the fan.

In today’s inventory management, there is a need to optimize new models in order toselect the best solution to ensure order fulfillment. These models must take into account variousuncertainties, as well as the concept of time value of money. At the same time, it is important tonote that in practice, appropriate solutions are often multicriteria due to the complex nature ofsupply chains.

To address this, the authors have developed a method for optimizing such tasksbased on a combination of multicriteria optimization procedures and decision making underuncertainty. However, this approach is shown to require further refinement in practice. Theproposed refinement aims to assist managers in avoiding undesirable outcomes related toalternative selection. These are situations related to phenomena that lead to the selection ofalternatives that may not be optimal for the preferences of the decision maker.

The corresponding adjustment would result in introduction of a specific feature inthe form of optimization procedures. In such an adjustment, it is proposed to present initialindicators of given specific criteria on the basis of so-called aggregated data, which eliminates thefactor of dimensionality. A numerical example is provided using the development of a stockmanagement strategy as an example, considering the need to select a logistics intermediary and inconditions of uncertainty regarding demand and potential delays in delivery. In this scenario,a weighted average of estimates of specific criteria is used as the selection criterion and theHurwitz criterion is employed to account for uncertainty.

The paper presents the homogenization of the nonstationary model of the linear theory ofelasticity by the method of conditional moments, as a result of which the effective coefficients ofthe linear theory of elasticity and the effective density are obtained. As a result of performingoperations, the obtained effective coefficients depend on the scales of phase correlation in time andspace and are interdependent. The occurrence of correlation scales is a consequence of calculatingthe integrals containing the Green’s function (the solution for the operator of the nonstationarymodel of the linear theory of elasticity) and the correlation function of the structure in time andspace. The effective density is investigated.

We analyze the complexity of one extremal problem of choosing a subset of( p ) points in a given finite set in a metric space. The chosen subset of points isrequired to describe given clusters in the best way from the point of view of some geometriccriterion. This problem is a formalization of one applied problem from data mining that consistsin finding a subset of typical representatives of a dataset based on the rival similarity function. Weprove that the problem under consideration is NP-hard by polynomially reducing the well-knownNP-hard 3D-Matching problem to this one.

An eternal dominating set of a graph isa dominating set( D ) on which mobile guards are initially located (at most one guard is allowed onany vertex). For any infinite sequence of attacks occurring sequentially at vertices, the set( D ) can be modified by moving the guard from an adjacent vertex to the attackedvertex, provided the attacked vertex has no guard on it at the time it is attacked. Theconfiguration of guards after each attack must induce a dominating set. The eternal domination number of a graph is the cardinality of itsminimum eternal dominating set. We prove that the eternal domination number of any planargraph of diameter 2 is equal to its clique covering number.

The paper is devoted to the regularization of the population “predator-prey” dynamicswith the preys’ intraspecific competition. The model has the form of the hybrid system consistingof the two two-dimensional systems switching between each other. The switching of the systemsallows us to reproduce the special Refuge-regime when the prey number is very small and thepredators have complications to find preys. The regularization of the system by using twoswitching lines to avoid chattering is provided. The limit sets for the regularized model areestablished. The model sensitivity to the switchings is investgated. The condition under which thehybridization does not change the global stability of an equilibrium is derived. In the other casethe limit sets are cycles.

A computational algorithm has been developed for solving the inverse problem of electricalimpedance tomography in a complete electrode model, which is an inverse coefficient problem fora difference scheme built on unstructured grids for an elliptic equation with integro-differentialboundary conditions. The iteration algorithm is based on the iterative regularized Gauss–Newtonmethod in which the inverse matrix of the main matrix of the system of linear equations iscalculated; the derivatives of the main matrix whose coefficients depend linearly on conductivityare found analytically. The implementation of the computational algorithm is performed for thetwo-dimensional case of a 16-electrode disk model with one insert. The influence of the choice ofthe initial approximation and the error in the input data on the convergence of the iterationprocess has been studied.

An application of constructive nonsmooth analysis methods to the problem of minimizinga convex piecewise affine function defined as the sum of absolute values of affine functions isdemonstrated. Hypodifferential calculus was used in the general (multidimensional) case, whilesubdifferential calculus was employed in the scalar case. Analyzing the optimality criterion, onecan reveal that the point delivering the global minimum can be found by solving thecorresponding linear programming problem. In the scalar case, the solution can also be found inclosed form as the weighted median of the nodes of a broken line.

The paper is concerned with a junction problem for Timoshenko elastic inclusions placedin an elastic body with a crack. It is assumed that the crack crosses the thin inclusion at somepoint. This point is a mutual contact point. Inequality-type boundary conditions are imposed atthe point of contact and on the crack edges to prevent mutual penetration between inclusion partsand crack edges, respectively. Existence and uniqueness theorems are established. Differentialformulation in the form of a boundary value problem that contains junction boundary conditionsis presented.

In this paper, we study the first boundary value problem for the( p(x) )-Laplacian with one spatial variable in the presence of gradient terms that donot satisfy the Bernstein–Nagumo condition. A class of gradient nonlinearities is defined for whichthe existence of a viscosity solution that is Lipschitz continuous in( x ) and Hölder continuous in( t ) is proven.