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We show that the Ceder plane M is a a-metrizable space, which does not have a development. For every quasicontinuous mapping f : X → M the continuity point set C(f) is residual. We investigate the continuity point set C(f) of a mapping f : X × Y → M, which is quasicontinuous with respect to the first variable and continuous with respect to the second one. [ABSTRACT FROM AUTHOR]

Our article considers the problem of optimization of incompletely specified functions, namely, functions which parameters are given within range of possible values. It is shown that solution of this problem also requires solving problem of determining stability of optimum of such functions to variation of values of their parameters. A method for obtaining such optimum of incompletely defined functions is presented. Method uses determination of problem. It allows to split original non-deterministic problem into two optimization problem of deterministic functions, which are solved separately. After that solutions are combined into one which is a solution of original problem. The article also provides a method for determining the stability of the optimum found of incompletely defined functions by methods of interval mathematics. We formulate 5 theorems determining the conditions for existence of optimum of incompletely defined function and its resistance to changing the function parameters. Algorithms for verifying the stability function are given [ABSTRACT FROM AUTHOR]

A new phenomenon was considered -- a cluster of chaotic oscillations, consisting of n homogeneous chaotic processes, at that inherent cluster mapping contains n² mapping functions, of which: n -- the number of mapping functions for homogeneous chaotic processes and n(n-1) -- the number of transfer mapping functions through which the transition from one homogeneous chaotic process to another within a cluster is made. During the course of a single uniform chaotic process, an integral component of the cluster is formed, defined as the sum of the integer time intervals of continuity of developable function, which leads to the formation of fractal sequence of integers, which is characteristic for each homogeneous chaotic process. The inception of each homogeneous chaotic process is situated in the limited and specific time zone of the interval of continuity of developable function. The concrete parameters of the equations for which the observed clusters of chaotic oscillations are given. [ABSTRACT FROM AUTHOR]

We obtain asymptotic equalities for upper bounds of the deviations of the right-angled Fourier sums taken over classes of periodical functions of two variables of high smoothness. These equalities in corresponding cases guarantee the solvability of the Kolmogorov-Hikol'skii problem for the right-angled Fourier sums on the specified classes of functions. [ABSTRACT FROM AUTHOR]

Let ζ = (ζn) be a complex sequence of genus zero, τ be its exponent of convergence, N(r) be its integrated counting function, π(z) = ∏ (1 - z/ζn) be the Weierstrass canonical product, and M(r) be the maximum modulus of this product. Then, as is known, the Wahlund-Valiron inequality ..., w(τ): = sin πτ/πτ, holds, and this inequality is sharp. It is proved that for the majority (in the probability sense) of sequences ζ the constant w(τ) can be replaced by the constant w (τ/2) in the Wahlund-Valiron inequality. [ABSTRACT FROM AUTHOR]

It is obtained a general solution of first-order linear partial differential equations in the class of separately differentiable functions. [ABSTRACT FROM AUTHOR]

The best possible estimates for Lebesgue integral means mq(r, F) (1 ≤ q < + ∞ ) for the pair of functions F = g + i ğ, here g -- Green's potential, ğ -- function conjugate to g, was obtained. It generalizes well-known results of Ya.V. Vasyl'kiv and A.A. Kondratyuk for logarithms log B of Blaschke products B in terms of counting function n(r, 0, B) (0 < r < 1) of their zeroes. [ABSTRACT FROM AUTHOR]

The problem of finding algebraic characteristics of representative classes of functions and predicates is closely connected with issues of the programming theory and practice. In this paper, we study a class of calculated functions and predicates for finite graphs. We choose graph structures because of their importance and popularity in the theoretical and applied programming. We also use the primitive program algebra as a research tool. Specifically, its carrier is a set of calculated functions and predicates for finite graphs and its signature comprises the parametric composition of superposition, branching and cycling. Emphasized here is finding a generating set of the primitive program algebra. In addition, we obtain useful necessary conditions for generating completeness of the generating set of the primitive program algebra calculated by functions and predicates for graphs. [ABSTRACT FROM AUTHOR]

The main subject of present article is to analyze some basic concepts in Kant's Critique of Pure Reason, here referred as metanotions, in purpose to designate their transcendental and reflexive functions. They all appear opposite couples, which indicate the nature of reason as situated in the tension of opposite attributes. These concepts are a priori - a posteriori, pure - empiric, synthetic - analytic, transcendent - immanent, transcendental - empirical, mathematical - dynamical, constitutive - regulative, intuitive - discursive and receptivity - spontaneity. [ABSTRACT FROM AUTHOR]

The paper considers the task on columns taking into account the properties of a great number of transpositions as domains of possible solutions of this task. We prove and algorithmize the localization method of the linear function value on a combinatorial set of transpositions. We also study the method of values organization of the efficiency function on a great number of transpositions that makes it possible to find the solutions of the task of linear function on transpositions with linear limitations. [ABSTRACT FROM AUTHOR]

The study under consideration provides the insights into the solution of the initial-value problem of the singularly perturbed systems of differential equations with degeneration in a point, using the method of boundary functions. [ABSTRACT FROM AUTHOR]

The potentialities of using the sensitivity theory apparatus, in particular the functions of relative sensitivity, for synthesis of algorithms of invariant transformation are considered. The method of searching the invariants of measuring transformation function is offered, the example of receiving the invariant of linear function is proposed. [ABSTRACT FROM AUTHOR]

The paper presents a new approach to DSS decision rule construction implying the elicitation of utility function which approximates a DM's preferences through learning from examples (the DMUFI approach). The authors also propose the structure of the approach that combines MCDA, data invetigation and active learning from examples to provide the utility function identification in a wide range of cases. GDMH algorithms are proposed for identification of the utility function of optimal complexity from minimum of ill-structured a-priori information. [ABSTRACT FROM AUTHOR]