Possible applications of spline mathematics is discussed for situations typical for
geophysical observations when only numerical values of time series of data are known, to build
a physical dynamic model is either impossible or too complicated, unreasonable mainly because
of complexity of geological “scene” on which the events occur. Dipmeter survey, systematic
measurements of varying level and temperature of ground water, radon concentration in wells
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The spectral problem on a string cross with the terms of the boundary conditions
of q-periodicity, the contact conditions , balance condition of tension in the overall site is considered.
The calculation results gave out the complex-valued eigenfunctions. For two-demensional and three-
demensional cross string we have two-demensional and one-demensional eigenspaces. Their structure
depend on parameter q.
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In March 2015, the famous domestic mathematician, doctor of physical and mathematical sciences, professor, laureate of the State award of Ukraine, Honored Worker of Science and Technology of Ukraine, Honored Worker of Education of the Crimea, head of the Department of Mathematical Analysis of the Crimean Federal University named after V.I. Vernadsky, the organizer and the permanent leader of the Crimean Autumn Mathematical School-Symposium (KROMSH) for 26 years, our dear teacher Nikolai Dmitrievich Kopachevsky turned 75 years old.
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Plane-parallel flows of an incompressible fluid in a bounded domain with minimum mean square vorticity are considered. The flow function is biharmonic function. Such flows include, for example, the stationary solution of 2D Stocks problem with a potential righthand side. If the velocity on the boundary is specified, then definition of the flow is reduced to the solution of the boundary value problem of the biharmonic equation. The projection algorithm for solving boundary value problems for the biharmonic equation in complicated domains is presented.
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On a segment $[a, b]$, we consider integral equations
\[y_k(t) = y_k(a) + \int \limits_{[a,t)} (d{\bf p}_k)y_k(s) + \int \limits_{[a,t)} (d{\bf m}_k)f_k(s)ds, ~~~k = 0, 1, 2, ... ,\]
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In mathematical game theory, recent years are characterized by active studying of the concept of Berge equilibrium as antipode to widely used Nash equilibrium. Difference is in the fact that the concept of Nash equilibrium has “egoistic character” — every player tries to increase his payoff only. On the contrary, Berge equilibrium has altruistic character: its goal is to increase payoffs of all other players. The Golden rule of morality forms the basis of it: Do as you would be done by.
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In single-criteria problem under strategical uncertainty from the point of view of DM tasks of decision making are examined. DM tries to increase the guaranteed outcome with possible smaller guaranteed risk. We are based on the principle of minimax regret (SavageNichans) with the help of mathematical apparatus of the method of dynamic programming for discrete problems.
First, we examine single-criteria problem of two forms which differs by pairs: contrstrategy — pure uncertainty and pure strategy — strategical uncertainty.
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The problem of piecewise-linear constraints reconstruction arising in optimization problems with incomplete data is considered in the paper. To reconstruct unknown constraints a perceptron is used. The lexicographical method is proposed to optimize obtained solution. A square matrix is built on the base of initial data and perceptron outputs, which is optimized due to the extraction of comparable row vector pairs and crossing out matrix rows and columns, corresponding to the lower vectors. The corresponding perceptron outputs are deleted too.
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The program implementation description of the multicriterion pseudo-Boolean optimization with incomplete initial information about criteria are given in the article. Basic theoretical results, the problem solving algorithms descriptions for the case of complete and partial information about criteria are taken from [8]. Algorithms of complete search, linear convolution of criteria and local search are implemented in the Visual C++ 6 environment.
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At creation of systems of speech recognition the important role is played a choice of features, for references of phoneme generation. For the decision of this task in the article the technique of formation of the references of phoneme is developed. It is based on wavelet transformation. For increase of probability of recognition for each pair phoneme classes from an proposed set of features the optimal feature select, on which the division of this classes is made.
Математическая модель для исследования влияния флуктуации на трансформацию пространства безопасности
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The mathematical model is proposed for investigation of various fluctuations impact c-i transformation of fields of technogenic, social, economic and environmental risks with the help of catastrophes theory, theory of chaos and bifurcation. It permits to investigate the catastrophes; nonlinear dynamics and to estimate the levels of technogenic and environmental vulnerability efficacy of politics in the field of social and economic security.
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In this paper we propose principle, which alow us to make an automatical choice of most informative elements of multi-component decreet signals of different lengths. Besides we show an example of applying this approach to on-line signature verification problem.
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For mining a natural language interface of the automatic control system (ACS) in the article the methodology of creation semiology-algebraic (SEMAL) of model of a technical language is offered, on which one the interplay between the person and ACS implements. Within the framework of this methodology the assay techniques and synthesis of the forms of words is set up.
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Algorithms for object surface model reconstruction of tree-dimensioned medical images are investigated. The first one is based on using simplex-meshes, and the second uses 2.5D active contours. Experiments on generation of solid models from surface models were carried out using computer-aided design software. The simulation of solid model characteristics under loads was performed.
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Authors describe (on a material of Russian) the technique of use of the information of the theory of the Semantic Class (of the sort) of reality's object designated by a word, for elimination of ambiguities at construction of a tree of Natural Language's phrase's deep syntax. The special attention is given to formalized description of theories for Words's Lexical Meanings and relations set by them. The approach to ordering the mentioned theories is offered. It is based on ideas and methods of the Formal Concept Analysis.
Оценка неслучайности интервальных импликативных зависимостей, содержащихся в булевых таблицах данных
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An interval implicative dependency concept and a statistical estimation of its nonrandom appearance in Boolean empirical data tables are considered in the paper.
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The analysis of the сonsequent aсhievements and publiсations devoted to the issue of synthesis of high-performanсe and exaсt algorithms of сlassification reveals that the issue of the problem-solving procedure when a «simple» deсision rule is required still remains open. The method of attaсk, based on the synthesis of the «virtual» preсedents for сlassification, of which high-accuracy but not inadmissibly «complicated» algorithms are used, is offered in this article. The main concepts of the approach are demonstrated with the mode! examples.
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A clear outliers detection algorithm (training sample filtering algorithm) based on the empirical decision forest with branches' rank r is proposed in the paper. The generalization performance increase of decision tree constructed after filtering in comparison with the decision tree, constructed before filtering, is grounded empirically.
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New upper bounds of the independent set number in graphs with great minimal degree are obtained.
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In this paper we consider general SAT problem as a problem of global optimization for associated functional. Without loss of generality it can be considered for 3-SAT problem too. Our aim was not local search but applying Newton's methods and Newton-like procedures for direct solution. We show so for the naive Newton method has a nontrivial kernel and there are no any kind of convergence. But, we have success on the way of modification for simple iteration method with 'inertia'.
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Two сombinatorial problems, Three-elements affine separating committee (3-ASC) and Minimal affine separating committee (MASC), which are closely connected with a training problem in the special case of perceptrons, are considered. It is proven that the former problem is NP - complete and the later is NP -hard and does not belong to Apx. Also some approximation algorithm for the MASC problem is discussed.
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Evolution of the Edgeworth-Pareto prinсiple, whiсh is well-known in deсision making, from its naive version of the nineteen сenture to the most general axiomatiс one in terms of сhoiсe funсtion is presented.
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In this article we investigate an easy enough algorithm for solving of a very important problem of recognition of unknown objects, which appear when we find the dependence rate between random samples of observations for the case of Gaussian random variables.
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The language $L$ is used for specifying finite automata, and is a fragment of a first order language with monadiс prediсates. Cheсking speсification for satisfiability plays an important role in the development of reactive algorithms. Restricted syntax of this language and interpreting it over the integers make it possible to substantially improve resolution-based methods for satisfiability checking. In this paper, we present an improvement to the method based on the restriction of the type of atoms upon which the resolution is allowed.
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It is proved that the point $\varsigma=0$ in difference of other points of continious spectrum is point of branchement of logarithmic type of the resolvent of transport operator.
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The properties of characteristic vector families for intervals of the feature space are under investigation. The search algorithms for the closed characteristic vectors and vectors generating the maximum intervals of the specified feature space region are considered in the paper.
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In this paper we study the identification problem of determining the complex-valued coefficient for non-stationary equation quasi optics. In this case we prove existence and uniqueness of the solution of identification problem. In addition, the necessary condition for solution of identification problem of the variational inequality type is established.
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The mathematical model of the optimum planning of the use of monies facilities acting from investors is represented in the article, with the purpose of implementation of some great number of projects providing the receipt of income. By the decision of tasks proper to this model, there is the optimum sequence of start of the chosen projects in time, providing a maximum of income.
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The properties of the stationary structures in a nonlinear optical resonator with lateral inversions transformer in feedback are investigated. The mathematical description of optical structures is based on the scalar parabolic equation with inversion spatial arguments and Neumann's condition on the segment. We determine the forms of stationary structures and investigate its stability as the diffusion coefficient decrease, parabolic equation, bifurcation, stationary structure, stability, center manifold.
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We prove that the problem of classifation (up to a similarity transformation) the pair of nilpotent operators $(A, B), A^3 = B^3 = 0$ with condition of $q$-commutation $BA$ = $qAB$, where $q\in\mathbf{C}, q \ne 0,$ is "wild".