Asymptotic behavior of solutions to Emden–Fowler type differential equation with a negative power of nonlinearity was investigated. The existance and nonexistance of solutions vanishing at some point is established. The asymptotic formula to these solutions was derived. The uniquness of these solitions was proved 

The generalization of branches and bounds method, called plaits and bounds method, for solving the quadratic assignment problem (QAP) is proposed. Plaits technique is developed. Experiments showed the possibility of solving some hard QAP instances 

We have proposed a constructive formula for enlisting elements of the set of constraints on a distribution of probabilistic assignments in a conjunction chains ideal. The set of constraints is generated to meet the requirements of probabilistic theory axioms. To notate the formula, we use some properties of the binary nonnegative integer representation in computers. The resulting notation of the set of constraints is compact and observable. In contrast to the earlier and less formal descriptions, the new formula notation clearly specifies the generating algorithm for the set of constraints on the distribution 

The probabilistic stability of the perturbed motion of a nonlinear system with parameters under the action of a general Markov process is studied. The phase vector is assumed to experience random jumps when the structure the system suffers random jumps 

This article describes and compares two wavelet transforms: Butterworth wavelet transform and Daubechies 9/7 wavelet transform 

The approach of solving of the conditional pseudo-Boolean optimization problems with algorithmically given functions has been researched. Constraints accounting in this approach is realized by generalized function with penalty. Properties of feasible decisions set of the problem and properties of the generalized penalty functions have been discovered. Comparative analysis of efficiency of local search algorithms has been carried out 

We propose and investigate a risk process model that extends the classical risk model. In this model a total claim amount process is considered to be the same as in the classical model while a premium income is a stochastic process unlike the classical case. A formula for a ruin probability of an insurance company with this risk process is derived and the comparison of the two models in terms of ruin probabilities is given 

При разработке численного метода решения некоторой задачи нужно иметь в виду, что метод будет реализован в форме алгоритма, а затем программы. Конечным звеном этой цепочки является программа, и именно программа характеризует качество цепочки в целом. Обычно существует несколько способов решения поставленной задачи. Каждый способ реализуется своей программой. Как конечный продукт, программа может быть примитивной или изящной, красивой. К сожалению, понятие «красивая программа» не формализуется. К необходимым условиям для составления такой программы следует отнести стремление к минимизации количества операций и используемой памяти. Этого можно достичь с помощью математических приемов. В определенном смысле, хорошая программа основана на хорошей математике ...  

We consider the system ${P_n^{alpha,eta}(t)}_{n=0}^{N-1}$ of the classical Jacobi polynomials of degree at most $N$ which generate an orthogonal system on the discrete set $Omega_Nsubset [-1,1]$ of the zeros of the Jacobi polynomial $P_N^{alpha,eta}(t)$. Given an arbitrary continuous function $f(t)$ on the interval $[-1,1]$, we construct the discrete Fourier–Jacobi sums $S_{n,N}^{alpha,eta}(f,t)$ over the orthonormal system introduced above. We prove that the order of Lebesgue function $L_{n,N}^{alpha,eta}(t)$ of the discrete Fourier–Jacobi sums for $-1/2

The problem of minimizing a nonsmooth composition of minimum functions is considered. The main properties of such problems are their nonsmoothness and essential multi-extremality. It is caused by nonconvexity of the functionals under considerations. However, this class of functionals possesses one important property: the problem of minimizing these functionals can be reduced to solving a finite number of “simpler” problems (for instance, minimax ones). A necessary condition for a point to be a global minimizer is deduced, a sufficient condition for a point to be a local minimizer is obtained. Two numerical methods (an exchange algorithm and an ε -exchange algorithm) are described