Software Tools for Some Natural Language Texts Computer Processing

Software tools are developed for computer realization of syntactic, semantic, and morphological models of natural language texts, using rule based programming. The tools are efficient for a language, which has free order of words and developed morphological structure like Georgian. For instance, a Georgian verb has several thousand verb-forms. It is very difficult to express rules of morphological analysis by finite automaton and it will be inefficient as well. Resolution of some problems of full morphological analysis of Georgian words is impossible by finite automaton. Splitting of some Georgian verb-forms into morphemes requires non-deterministic search algorithm, which needs many backtrackings. To minimize backtrackings, it is necessary to put constraints, which exist among morphemes and verify them as soon as possible to avoid false directions of search. Software tool for syntactic analysis has means to reduce rules, which have the same members in different order. The authors used the tool for semantic analysis as well. Thus, proposed software tools have many means to construct efficient parser, test and correct it. The authors realized morphological and syntactic analysis of Georgian texts by these tools. In the presented paper, the authors describe the software tools and its application for Georgian language.

Generation of Zonal Flow and Magnetic Field by Planetary Waves in the Earth’s Ionosphere

Possibility of generation of large-scale sheared zonal flow and magnetic field by coupled under the typical ionospheric conditions short-scale planetary low-frequency waves is shown. Propagation of coupled internal-gravity-Alfven, Rossby-Khantadze, Rossby-Alfven-Khantadze and collision-less electron skin depth order drift-Alfven waves is revealed and investigated in detail. To describe the nonlinear interaction of such coupled waves with sheared zonal flow the corresponding nonlinear equations are deduced. The instability mechanism is based on the nonlinear parametric triple interaction of the finite amplitude short-scale planetary waves leading to the inverse energy cascade toward the longer wavelengths. It is shown that under such interaction intense sheared magnetic fields can be generated. Appropriate growth rates are discussed in detail.

On Some Bending Problems of Prismatic Shell with the Thickness Vanishing at Infinity

The present work is devoted to the bending problems of prismatic shell with the thickness vanishing at infinity as an exponential function. The bending equation in the zero approximation of Vekua＇s hierarchical models is considered. The problem is reduced to the Dirichlet boundary value problem for elliptic type partial differential equations on half-plane. The solution of the problem under consideration is constructed in the integral form.

Computation of the Multivariate Normal Integral over a Complex Subspace

The computation of the multivariate normal integral over a Complex Subspace is a challenge, especially when the inte-gration region is of a complex nature. Such integrals are met with, for example, in the generalized Neyman-Pearson criterion, conditional Bayesian problems of testing many hypotheses and so on. The Monte-Carlo methods could be used for their computation, but at increasing dimensionality of the integral the computation time increases unjustifiedly. Therefore a method of computation of such integrals by series after reduction of dimensionality to one without information loss is offered below. The calculation results are given.

The Use of Imitation Models at Developing and Introducing Information-Control Systems

Imitation models for computing the environmental water pollution level depending on the intensity of pollution sources created by the author over the years are presented. For this purpose, an additive model of a non-stationary random process is considered. For the modeling of its components, models that consider only dilution and self-purification processes are proposed for waste water and three-dimensional turbulent diffusion equations for river waters, and multidimensional Gaussian Markov series are proposed for modeling the random component. The purpose, the capabilities and the peculiarities of such imitation models are discussed taking into account the peculiarities of the water objects. The modular principle of creating imitation models is proposed to facilitate their development and use.

ECONOMICAL DIFFERENCE SCHEME FOR ONE MULTI-DIMENSIONAL NONLINEAR SYSTEM

The multi-dimensional system of nonlinear partial differential equations is considered. In two-dimensional case, this system describes process of vein formation in higher plants. Variable directions finite difference scheme is constructed. The stability and convergence of that scheme are studied. Numerical experiments are carried out. The appropriate graphical illustrations and tables are given.

Constrained Bayesian Method for Testing the Directional Hypotheses

The paper discusses the generalization of constrained Bayesian method （CBM） for arbitrary loss functions and its application for testing the directional hypotheses. The problem is stated in terms of false and true discovery rates. One more criterion of estimation of directional hypotheses tests quality, the Type III errors rate, is considered. The ratio among discovery rates and the Type III errors rate in CBM is considered. The advantage of CBM in comparison with Bayes and frequentist methods is theoretically proved and demonstrated by an example.

Stability and convergence of the variable directions difference scheme for one nonlinear two-dimensional model

The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.

On Ordinary and Standard Products of Infinite Family of σ-finite Measures and Some of Their Applications

We introduce notions of ordinary and standard products of a-finite measures and prove their existence. This approach allows us to construct invariant extensions of ordinary and standard products of Haar measures. In particular, we construct translation-invariant extensions of ordinary and standard Lebesgue measures on R∞ and Rogers-Fremlin measures on l∞, respectively, such that topological weights of quasi-metric spaces associated with these measures are maximal （i.e., 2c）. We also solve some Fremlin problems concerned with an existence of uniform measures in Banach spaces.

On a Linear Partial Differential Equation of the Higher Order in Two Variables with Initial Condition Whose Coefficients are Real-valued Simple Step Functions

By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.