# On solutions of a composite equation related to subsemigroups determination

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A subgroup H of a finite group G is called an -subgroup of G if the following condition is satisfied: NG(H) âˆ© Hg â‰¤ H,mbox for all g âˆˆ G. The set of all -subgroups of a group G will be denoted by (G). In this paper, some new results for a finite group to be supersolvable or...

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A finite group G is said to be recognizable by spectrum if every finite group with the same set of element orders as G is isomorphic to G. We prove that all finite simple symplectic and orthogonal groups over fields of characteristic 2, except S( q), S(2), O (2), and S( q), are recognizable by...

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The resource-constrained elementary shortest path problem (RCESPP) aims to determine the shortest elementary path from the origin to the sink that satisfies the resource constraints. The resource-constrained kth elementary shortest path problem (RCKESPP) is a generalization of the RCESPP that...

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In this paper, we introduced the basic knowledge of set pair analysis at the first place. Then we defined the general form of basic operations and the properties of connection number, in the end we give the corresponding application examples. The concepts and methods of the operations are the...

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We present necessary conditions for the diagonal bi-act $$_S(S\times S)_S$$ over an epigroup $$S$$ to be finitely generated. They imply that this bi-act is not finitely generated whenever $$S$$ is infinite and locally finite. This solves a problem posed by Gallagher.

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All critical groups with identity Frattini subgroup are described for a formation with the generalized Wielandt property for residuals. We also constructed a new series of these formations.

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Let G be a group. The intersection of normal subgroups N of G in which G/N is soluble is called soluble residual of G. Soluble residuals are important tools since they are perfect and contains all perfect subgroups. We will give soluble residuals of some maximal subgroups of Sp(6,r).

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- On the existence and smoothness of a generalized solution of a nonlinear differential equation with degeneration. Iskhokov, S. // Differential Equations;Feb2008, Vol. 44 Issue 2, p241
Let Î© be an arbitrary open set in R n , and let Ïƒ( x) and g i ( x), i = 1, 2, ..., n, be positive functions in Î©. We prove a embedding theorem of different metrics for the spaces W (Î©, Ïƒ, $$ \vec g $$ ), where r âˆˆ N, p â‰¥ 1, and $$ \vec g $$ ( x) = ( g 1( x), g 2( x),...