Forecasting of static processes and estimation of random fields of a different nature is becoming more widespread among scientists of different specialties, and a new branch of science appears with its specific methodology. That problems of estimation of the unknown values of random fields are generalization of problems of extrapolation, interpolation and filtering of stochastic processes. The study of the dependence of the obtained formulas on the geometry and the number of embeds are the topic...

Mathematical Analysis  Applied Statistical Mathematics  Algebra 

Doi:10.18523/2617-7080i2018p49-53

Nearrings arise naturally in the study of systems of nonlinear mappings, and they have been studied for many decades. Basic definitions and many results concerning nearrings can be, for instance, found in [G. Pilz. Near-rings. The theory and its applications. North Holland, Amsterdam, 1977]. Nearrings are generalized rings in the sense that the addition need not be commutative and only one distributive law is assumed. Clearly, every associative ring is a nearring, and each group is an additive ...

Algebra 

Doi:10.18523/2617-7080i2018p38-48

The Sylow 2-subgroups of symmetric groups was described by Leo Kaluzhnin. He presented the elements of these groups as a tables, i.e. the ordered sets of polynomials of a certain form. The Sylow 2-subgroups of symmetric groups was studied by V. Sushchanskii, Yu. Dmytruk, A. Slupik and other mathematicians. In this paper the Sylow 2-subgroups of alternating groups are characterized. The system of computer algebra GAP was used for this characterization. System of computer algebra GAP is the most ...

Algebra 

Doi:10.18523/2617-7080i2018p30-33

Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems. The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civil...

Applied Statistical Mathematics  Dynamical System  Algebra 

Doi:10.18523/2617-7080i2018p21-24

Hidden Markov models are a well-known probabilistic graphical model for time series of discrete, partially observable stochastic processes. We consider the method to extend the application of hidden Markov models to non-Gaussian continuous distributions by embedding a priori probability distribution of the state space into reproducing kernel Hilbert space. Corresponding regularization techniques are proposed to reduce the tendency to overfitting and computational complexity of the algorithm, i.e...

Applied Statistical Mathematics  Algebra 

Doi:10.18523/2617-7080i2018p15-20

Spectral graph theory uses the eigenvalues of matrices associated with a graph to determine the structural properties of the graph. The spectrum of the generalized adjacency matrix is considered in the paper. Graphs with the same spectrum are called cospectral. Is every graph uniquely determined by its spectrum (DS for short)? This question goes back for about half a century, and originates from chemistry. In 1956 Gunthard and Primas raised the question in a paper that related the theory of gra...

Algebra 

Doi:10.18523/2617-7080i2018p11-14

Biotope spaces were introduced by Marchevsky-Steinhaus in for the needs of mathematical biology, namely the study of ecosystems. Biotope distance is defined on the set of all subsets of some finite set X. The distance between any subsets A1 and A2 of X is calculated by the rule: d(A1, A2) = (0, if A1 = A2 = ？; |A1⊕A2| |A1∪A2| , if A1, A2 ∈ B(X)).We introduce a new generalization of a biotope metric to the infinite case using supernatural or Steinitz numbers. A supernatural number (or Steinitz nu...

Applied Statistical Mathematics  Algebraic Geometry  Geometry  Combinatorial Mathematics  Algebra 

Doi:10.18523/2617-7080i2018p6-10