Volume 15, Issue 2

The well-posedness of the dirichlet and poincare problems in a cylindric domain for the multi-dimensional chapligin equation
Aldashev S. A.

This paper proves the unique solvability of the Dirichlet and Poincare problems in a cylindric domain for the multi-dimensional Chapligin equation.

CN-edge domination in graphs
Alwardi A., Soner N. D.

Let G=(V,E)   be a graph. A subset D   of V   is called common neighbourhood dominating set (CN-dominating set) if for every v∈V−D   there exists a vertex u∈D   such that uv∈E (G)   and |Γ(u, v)|≥1 , where |Γ(u, v)|   is the number of common neighbourhood between the vertices u   and v . The minimum cardinality of such CN-dominating set denoted by γ cn (G)   and is called common neighbourhood domination number (CN-edge domination) of G . In this paper we introduce the concept of common neighbourhood edge domination (CN-edge domination) and common neighbourhood edge domatic number (CN-edge domatic number) in a graph, exact values for some standard graphs, bounds and some interesting results are established.

Article (eng.) - [pdf] [zip-pdf]

Structure of some compact quantum semigroups
Aukhadiev M. A.

We show that the main results of multuplicative unitary theory do not hold for compact quantum semigroups and give examples. We suggest a new method to provide compact quantum semigroup structure by the use of pentagon equation, which gives a generalization of multiplicative unitary theory.

Article (rus.) - [pdf] [zip-pdf]

Inclusion properties for certain subclasses of p -valent functions associated
Eljamal E. A., Darus M.

In this paper we introduce several new classes of p -valent functions defined by new generalized derivative operator and investigate various inclusion properties of these classes. Some interesting applications involving classes of integral operators are also considered.

Article (eng.) - [pdf] [zip-pdf]

Infinitesimal MG-deformations of ovaloid
Zhukov D. A.

We consider infinitesimal deformations of a closed surface with positive Gaussian curvature, under which the variation of Gaussian curvature is given as a function on a surface and the Grassman image is kept invariant.

Article (rus.) - [pdf] [zip-pdf]

Regularization in inverse dynamic problems for the equation of SH-waves in a porous medium
Imomnazarov Kh. Kh., Imomnazarov Sh. Kh., Rakhmonov T. T.,
Yangiboyev Z. Sh.

Regularization algorithms for dynamic inverse problems for 1D equation of SH-waves in fluid saturated of porous media with energy dissipation at intercomponent friction have been constructed.

Article (rus.) - [pdf] [zip-pdf]

On automorphisms of strongly regular graphs with parameters (320,99,18,36)
Kagazezheva A. M., Makhnev A. A.

Pseudo-geometric graph for pG 2 (5,32)   has strongly regular subgraphs - local subgraph (pseudo-geometric graph for GQ(4,8) ) and second neighborhood of vertex (graph with parameters (320,99,18,36)). In this paper it is founded orders and fixed-point subgraphs of automorphisms of strongly regular graphs with parameters (320,99,18,36).

Article (rus.) - [pdf] [zip-pdf]

Strong insertion of an α -continuous function
Mirmiran M.

Necessary and sufficient conditions in terms of lower cut sets are given for the strong insertion of an α -continuous function between two comparable real-valued functions.

Article (eng.) - [pdf] [zip-pdf]

Extremal values of the integral of the mean curvature on the set of parallelepipeds with a given geodesic diameter
Rasskazova N. V.

In the paper, extremal values of the mean curvature integral on set of parallelepipeds with a given geodesic diameter are obtained. The maximal (minimal) value of the integral of mean curvature is attained for a degenerate parallelepiped with relation 0:1:1 (0:0:1, respectively) for its edge lengths.

Article (rus.) - [pdf] [zip-pdf]

Erratum to: "Infinitesimals in ordered vector spaces"
Emelyanov E. Yu.

In this note, Theorem 1 in the article which is cited in the title is corrected.

Article (eng.) - [pdf] [zip-pdf]