TAAC'2011, Section Two: Systems analysis

In this paper solution of hyperbolic heat conduction equation is given for sphere. Hyperbolic heat equation describes heat processes in intensive steel quenching — with extremely fast cooling rates. Numerical results are obtained for 1D case with linear and non linear boundary conditions.

We consider the task of classifying sincere weakly positive forms over integers. We examine the means by which such forms can be obtained computationally and suggest an algorithm that uses these means. By implementing the algorithm within a Python computer program the number of sincere weakly positive forms for $n \leq 8$ is obtained. We then review the results and consider the further course of research.

A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown. To address that, we propose a novel method called Pareto Lipshitzian Optimization (PLO) that provides solutions within fixed error limits for functions with unknown Lipschitz constants.In the proposed approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO).

Financial time series data reveal the presence of jumps. These jumps can be big, small, finite or infinite depending on many economic factors. This paper demonstrates the exceptional quality of L\'{e}vy processes in capturing jumps. It further illustrates that financial models based on Brownian motion and or Poisson distributions are just special cases of general L\'{e}vy process models.

A new proximity measure between samples with repetitions based on confidence bounds for the bulk of a general population is considered. The measure proposed ia an extension of the p-statistics. It relaxes requirements for samples and allows to apply it to samples with repetitions too. To do this we proved an extension of the Hill assumption for truncated sample values

Анализ распределения плотности в колпачке электродетонатора

The deciding factor in choosing the directions of development of various technological devices and structures are the results of the pre-simulation facility. Reflux of polymer films, realized through the spinnerets, accompanied not only by the deviation niyami process parameters, and disturbances of various kinds. Evaluation of the possibility of obtaining polymer films with desired physical, mechanical and technical characteristics is based on studies of the effectiveness of control channels process of reflux of the films. These channels can be realized only when the rational is chosen design dies and the optimum technological conditions.

Maximum likelihood estimators for autoregressive time series observed under interval censoring are constructed, comparison of the maximum likelihood estimators and the least square estimators is made.

The model of financial data as integral of diffusion process is proposed in this paper.. The correlation function and one-dimensional distributions of the model have been examined, estimates for the model parameters have been built, and prediction problem for the special case has been solved. Two examples of financial data prove the adequacy of the proposed model.

The solvability of nonlinear problem with unknown discontinuity line of initial data of the hyperbolic system of first-order quasi-linear equations with two independent variables in curvilinear sector is considered. Same problems model some questions to solve of hydro- and gasdynamics etc. The proposed method of proof permits to find the solution by calculate method applying characteristic nets.

New estimation of recognition error using a probabilistic neural network with N inputs obtaining element of a random sample is proposed. A modified differential representation of Wilcoxon statistics is described, a formula for modification of network coefficients is derived and an optimal learning method is formulated.

The paper deals with a group of algorithms and programs to provide computer implementation method of separating the kernels in the solution of integral equations of Volterra type I. To this end, we proposed and studied the method for approximating the kernels of arbitrary form (as a function of two variables) by the sum of products of pairs of functions of one independent variable. This allows the development of Matlab effective software tools that combine the preliminary procedure of approximation the nucleus and the subsequent recursive computation for the solutions of these equations based on the use of quadrature formulas of various kinds. The technique takes into account the intrinsic equations of Volterra type I incorrectness by choosing the step of discreteness. Proposed and implemented algorithms can be applied to solve both linear and nonlinear equations of this class.

The problem of statistical simulation of homogeneous and isotropic random fields on the plane has been considered. It has been constructed the model and algorithm for the statistical simulation of this fields realizations on the base of its spectral decomposition.

We study eigenvibrations for inhomogeneous media consisting of two parts with strongly contrasting stiffness and mass density. We ivestigated the asymptotic behaviour of eigenvalues and eigenfunction.

There is offered some methods for calculation of equivalent samples boundaries and auxiliary coefficient too, which have influence on kernel width in point-distribution method for several density function laws? those it are necessary on first stage of calculation of small size sample parameters ( \(n \div 3-15\) elements) of higher effectiveness.

In the paper we consider the first basic boundary problem for a two-dimensional fractional diffusion equation. Methods of integral transformations and integral equations are used. The results of the numerical solution of boundary problems for elliptic and circular areas with different input parameters are presented.

In this paper structure of eigenspace for the spectral problem on a string cross with the terms of the boundary conditions of p-periodicity, the contact conditions, balance condition of tension in the overall site is considered. The calculation results gave out the complexly-place eigenfunctions.

In this paper properties of maximal by inclusion set of weak inner practical stability of differential inclusion with impulse impact are analyzed. Also we state the conditions which hold, when a point belongs to the border of maximal set. Further, Minkowski functional, support functional and criteria of belonging point to the border of maximal by inclusion set in linear case are obtained.

In this paper we consider problem to minimize time for project completion in a multi-processor system with various processor speeds. The work suggests an approximation algorythm of solving this problem . Proved is that the suggested algorythm has an asymptotic coefficient of effectiveness equal to 2.

In the paper we offer a functional-discrete method (FD-method) for solving the second ordre hyperbolic partial differential equation. The case of quasi-linear equation with bounded nonlinearity has been considered. The sufficient conditions that provide the superexponential convergence rate of FD-method have been found. Property parallel computing algorithm of the FD-method allows us to use it in calculations with the use of multiprocessor systems.

Method of empirical estimation for one-dimentional model with discrete time is considered. Strong consistency of one estimation is proved.

Applying the method of contractive mappings the conditions global solvability of mixed problem for hyperbolic system of first order semilinear equations with horizontal characteristics are established.

In this work a new mathematical structure, arc cutting of graph, which can be presented as a set of Q matrices and vectors of a certain gradation and which in turn can serve as some invariant of graph, is entered. It is known that in the process of its solution the task of recognition of graph isomorphism is broken up on two component stages. The first stage is checking of graph for isomorphism. In case of positive results on the first stage there is a search of correspondence on the second stage. On the first stage the determination of isomorphism is produced by comparison of two sets of matrices and vectors. The results of the given research are applicable for the decision of many applied tasks: in the tasks of recognition of patterns, in chemistry, planning of PC etc.

In the work the were given a model, which optimizes the value of the project in case of the availability of risk. It depends on the number of works, the number and type of resources required to perform certain work, the time required to perform work in case of the absence of risk and from minimized project delay function. The last on is calculated in days and is found with the help of Markov Decision Processes. There were made an assumption that risks aren’t correlated with each other.

The method of modeling the adsorption of molecular hydrogen in the long carbon nanotubes by event-driven algorithm was described. This method reduces the computation time on a computer. Numerical calculations of hydrogen adsorption were carried out at T = 80 K and pressures of 4 and 6 MPa. The quantitative distribution of hydrogen molecules inside the nanotube along its axis was obtained. It was found that the density distribution along the length of CNT is substantially inhomogeneously.

An approach to numerical solution of nonlinear systems of equations arising in implementation of implicit methods for stiff systems is proposed. It is based on the so-called steadying principle. The derived iterative processes don’t involve matrix factorizations and are capable of solving systems with complex eigenvalues of the Jacobi matrix. They can be used either independently or as a smoothers for multigrid methods.

The article presents developed by the author algorithm of problem-solving method for economic modeling problem based on Box’s method, which is originally a modification of deformed polyhedron method and aimed at solving of nonlinear programming problem with inequality constraints. The adapted Box’s method allows solving optimization problems with linear and nonlinear functional. The method uses one constraint matrix for determination of optimal values for linear (maximum profit) and nonlinear (maximum profitability and labor efficiency) function. All specified values are located inside of feasibility region thus increasing tolerance of the solution.