Все статьи журнала

The paper introduces the classification of informational situations for a zero-sum game with incomplete information based on uncertainty level. For each case the possible ways to deal with uncertainty are considered.
 

In the paper we develop solve-operator methods for high order modelling, simulation and optimization of risk controlled stochastic processes described by general graph-operator control systems with incomplete data.
 

The concept of a weakly guaranteed simultaneously under payoffs and risks solution of a one-criterion problem under uncertainty (OCPU) is proposed. Formalization is based on the concept of a vector saddle point from the theory of multicriteria problems with uncertainty.

Keywords: strategy, uncertainty, criterion, Slater optimum, vector saddle point.

Linear operators with partial integrals are studied. Using Banach’s closed graph
theorem, a general theorem on the continuity acting from a space $X$ to a space $Y$ of linear operator
$K$ with partial integrals is proved. Here $X$ and $Y$ are complete metric spaces of measurable
functions with a shift-invariant metric, and the space $X$ contains, together with each function,
its modulus. With the application of this theorem, the continuity acting of the operator $K$ in

Physical objects, describes the distribution of self-oscillating system is the
combustion front propagates in a homogeneous medium. Experimental studies conducted
Merzhanov, Borovinskaya showed that the stationary mode of propagation of the front becomes
unstable if the activation energy of the exothermic reaction exceeds a certain value. In the
instability of the stationary mode combustion front, staying flat, moving in an oscillatory mode. In

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

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.

On a segment $[a, b]$, we consider integral equations

\[y_k(t) = y_k(a) + \int \limits_{[a,t)} (d{\bf p}_k)y_k(s) + \int \limits_{[a,t)} (d{\bf m}_k)f_k(s)ds, ~~~k = 0, 1, 2, ... ,\]

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.

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.