The concept of Steiner tree minimal with respect to inclusion is under consideration. The algorithm of constructing all Steiner trees minimal with respect to inclusion and its substantiation are given. The Steiner tree minimal with respect to inclusion which has minimal weight is considered as the solution of the Steiner tree problem.
Все статьи журнала
Журнал:
The problem of the ecological safety of production on regional level is considered in the article. The model of functioning of a region is built taking into account the technogenic loading on an environment and the rational use of natural resources
Журнал:
In the paper, approach is expounded to the analysis of the linear optimization models built on precedent initial learning information. In supposition, that all numerical parameters are rational and limited by the bit net of computer, estimations of Kolmogorov’s complexity and nonrandomness of extraction of model as empirical regularity are got from the sample.
Журнал:
The formulation of the optimization problem with precedent initial information is proposed. The main problems and tasks of the constructing reliable schemes for solving such optimization problems are highlighted. The approach for solving such problems based on the loss function is described. The example based on the metric classifiers is considered. The new class of the collective learning by precedent is introduced.
Журнал:
We consider the travelling wave solutions of a nonlinear parabolic equation of the
second order, namely the equation of the Kolmogorov — Petrovsky — Piskunov type with the heat
release function on the right–hand side being analytical. We found a new analytic representation
for such a solution or, more accurately, for its inverse function which is represented as a sum
of an explicitly calculated summand and an auxiliary function defined on the unit interval. An
Журнал:
Let $G_1$ and $G_2$ be two joined bodies with masses $m_1$ and $m_2$. Each of them has
a cavity partially filled with homogeneous incompressible ideal fluids situated in domains ${\Omega}_1$
и ${\Omega}_2$ with free boundaries ${\Gamma}_1(t)$, ${\Gamma}_2(t)$ and rigid parts $S_1$, $S_2$. Let ${\rho}_1$, ${\rho}_2$ be densities of fluids.
We suppose that the system oscillates (with friction) near the points $O_1$, $O_2$ which are spherical
hinges.
We use the vectors of small angular displacement
Журнал:
The paper deals with the essentially infinite-dimensional elliptic operator $(Lu)(x) = j(u''(x))$ (of the Laplace-L´evy type), proposed by Yu.V. Bogdansky in 1977, for
Журнал:
In this paper the problem of deposit allocation between the assets is considered. The sum of the individual deposit between the three assets (unrisky and two risky) increased within a year one can offer in the form
$$f(x, y) = r(1 − x_1 − x_2) + x_1y_1 + x_2y_2,$$
where r – profitability of unrisky assets; $y_i$ – profitability of risky assets i; action $x = (x_1, x_2)$ and $x_i (i = 1, 2)$ – part of investing funds in assets i.
Журнал:
In this paper, the problem of minimal matrix correction of a system of linear algebraic inequalities was consider with the use of minimax criteria. The initial problem (a system of linear inequalities without a given property)
$$Ax ≤ b, A ∈ \mathbb{R}^{m×n}, b ∈ \mathbb{R}^m$$
there is assigned the class of corrected problems describing the independent variation of initial data
$$(A + H)x ≤ b + h.$$
Журнал:
The paper considers one of the well-known mathematical models in economics, called "Aggregate Demand - Aggregate Supply model"(AD-AS). Originally this model takes the form of the following ordinary differential equation
\begin{equation*}
\dot{p} = D(p) − S(p),
\end{equation*}
where $p = p(t)$ – price, $D(p)$ – demand, $S(p)$ – supply. This functions are considered with the natural assumptions for macroeconomics.
Журнал:
The notion of «Berge equilibrium» (BE) appeared in Russia in 1994-1995 in the thesis written by Vaisman (post-graduate student of Zhukovskiy V.I. at that time; he died at the
Журнал:
The competition of two firms on the market of one product with regard to import is considered. The particular volume of product supplied to the market by the importer is unknown to both producers. They know only restrictions about volume of import defined by the market. Non-cooperative game of two persons under uncertainty will serve as a mathematical model where "the role"of uncertainty "plays"the quantity of export goods, "the role"of players strategy - the quantity of goods supplied by them on the sale, payoff function - the income of the player.
Журнал:
In the present work, we consider the integral equation
$$y(t) = x_0 - iJ\int_{[a, t)} d\textbf{p}(s)y(s) - iJ\int_{[a, t)}d\textbf{m}(s)f(s)$$
where $t \in [a, b], b > a; y$ is a unknown function; $\textbf{p}, \textbf{m}$ are operator-valued measures defined on Borel sets $\Delta \subset [a, b]$ and taking values in the set of linear bounded operators acting in a separable Hilbert space $H$; $J$ is a linear operator in
Журнал:
In recent years, there is an active formation of the mathematical theory of Berge equilibrium, proposed in 1994, by Russian mathematician, K.S. Vaisman (who died in 1998, did not live up to 36 years). However, the use of this balance is not beyond the scope of matrix games of two persons. This article, apparently for the first time, breaks this tradition.
Журнал:
Source of the Golden Rule: «Do with respect to someone in such way as you would like him to do with respect to you» one can find in New Testament.
Such approach in economics results to altruistic rules of behavior «help others, forgetting about yourself». The concept of Berge equilibrium strictly formalized in Russia in 1994 in thesis and first articles of Vaisman K.S. fully meets such approach. Then this method of conflict balancing began to be used in works of western colleagues.
Журнал:
In this paper new solution for portfolio selection problem under uncertainty is formalized. It is based on three concepts: guaranteed result, regret function, Pareto optimal solution.
Журнал:
The study of completely positive linear maps is motivated by applications of the theory of completely positive linear maps to quantum information theory, where operator valued completely positive linear maps on $C^\ast$-algebras are used as a mathematical model for quantum operations and quantum probability.
Журнал:
In this paper we analyze the stability of the two-parametric secant type method to errors calculations for solving nonlinear equations and estimate the total error.
Журнал:
Parameter estimation for Levy processes has generated much research effort lately with a strong injection of interest coming from finance. Within this context the problem can be framed as estimation using increments from an infinitely divisible distribution, for which empirical characteristic functions (ecf) are convenient tools. However convergence of ecf’s to Gaussian processes has not been exploited as fully as it might have been.
Журнал:
Estimates for the convergence speed models isotropic random fields on the sphere in the norms of Orlich space. The resulting estimates are used to construct models of random fields on the sphere. Models approximate the random field with given accuracy and reliability.
Журнал:
This paper contains the substantiation of the scheme of partial averaging for one class of hybrid systems where one equation is a differential equation with Hukuhara derivative and the other one is an ordinary differential equation.
Журнал:
The creation and justification of the methods for guaranteed estimation of linear functionals from solutions to the boundary value problems for linearized stationary Navier-Stokes equations in bounded open Lipschitzian domains are considered.
Журнал:
In this paper, we discuss a method of auxiliary controlled models and the application of this method to solving some problems of robust control for differential equations. As objects for the approbation of the method, a system of nonlinear differential equations describing some ecological and economic processes is used. A solving algorithm, which is stable with respect to informational noises and computational errors, is presented.
Журнал:
The concept of languages similarity of Petri nets is introduced. It is determined, that mapping of languages similarity of Petri nets is a surjective homomorphism. The similarity of languages of component Petri net and original detailed Petri model of the investigated parallel distributed system is considered. The work reveals that the language of the original detailed Petri net model can always be restored using the language of its component model.
Журнал:
In the article the theoretical and practical results of researches are generalized on the problem of intellectualization of decision-making in the conditions of global informatively-communication environment. Results are got within the framework of implementation of the proper scientific programs and realization of the different (including international) applied projects.
Журнал:
In this paper consider the optimal control problem on infinite time interval with quadratic cost functional. State of this problem is defined by the evolutionary inclusion of reaction-diffusion type. We prove the solvability of such a problem. In the case of rapidly oscillating coefficients in coefficients of differential operator and multivalued interaction function we prove the convergence of $\varepsilon $-dependent optimal process to optimal process of the corresponding averaged problem.
Журнал:
A model of oscillations of Earth’s poles is constructed on the basis of the analysis of the gravitational torques from Sun and Moon. The model reflects physical processes and does not imply using curve fitting techniques, based, for example, on the polynomial approximation. Within the framework of this model, the Chandler frequency is interpreted as the fundamental frequency of oscillations of the mechanical system and the annual frequency as the frequency of the excitation force.
Журнал:
The first part of the paper designs a deterministic model to describe cancer prevalence and mortality in a population. Next the asymptotic properties of the model are investigated. In the second part, the model is applied to real-world data. For selected model data, a numerical solution is found to the differential equations describing the model, a long-term prediction is made with its results compared with those of predictions made by regression analysis, which are often used to model the prevalence and mortality in the present literature.
Журнал:
The algorithm of reduction of the number of carrier elements of a discrete fuzzy number with the realization of an opportunity to save the information about values is proposed in the article. It is proposed that the information is given by the fuzzy number.
Журнал:
Problem of grouping information: recovering function, represented by its observations, and the of classification (problem) clusterization problem, is of great importance for applied research. Choice of math object which represent the object under investigations largely determines the effectiveness: scalars, vectors or objects of other kinds. Such choice is determined by the richness of mathematical structures within which “representatives” are investigated. Euclidean spaces $R^{n}$ are common in this choosing.