‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

a {em 2-rainbow dominating function} (2rdf) of a graph $g$ is a function $f$ from the vertex set $v(g)$ to the set of all subsets of the set ${1,2}$ such that for any vertex $vin v(g)$ with $f(v)=emptyset$ the condition $bigcup_{uin n(v)}f(u)={1,2}$ is fulfilled, where $n(v)$ is the open neighborhood of $v$. the {em weight} of a 2rdf $f$ is the value $omega(f)=sum_{vin v}|f (v)|$. the {em $2$-r...

Closure theorems in graph theory are of the following type: Let G be a graph, P a graph theoretic property, and let u and v be two non-adjacent vertices of G. If condition c(u, v) holds, then G has property P if and only if G+ uv has P. We discuss several such results of the above type where the condition c(u, v) refers to neighbourhood properties of u and v.

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

Closure theorems in hamiltonian graph theory are of the following type: Let G be a 2connected graph and let II, u be two distinct nonadjacent vertices of G. If condition c(u, u) holds, then G is hamiltonian if and only if G + MU is hamiltonian. We discuss several results of this type in which u and v are vertices of a subgraph H of G on four vertices and c(u, u) is a condition on the neighborho...

Let G = (V,E) be a graph and x, y, z ∈ V be three designated vertices. We give a necessary and sufficient condition for the existence of a rigid twodimensional framework (G, p), in which x, y, z are collinear. This result extends a classical result of Laman on the existence of a rigid framework on G. Our proof leads to an efficient algorithm which can test whether G satisfies the condition.

A general partition graph (gpg) is an intersection graph G on a set S so that for every maximal independent set M of vertices in G, the subsets assigned to the vertices in M partition S. These graphs have been characterized by the presence of special clique covers. The Triangle Condition T for a graph G is that for any maximal independent set M and any edge uv in G M, there is a vcrtex W E M so...

A rely/guarantee specification for a program P is a specification of the form R D G (R implies G), where R is a rely condition and G is a guarantee condition. A rely condition expresses the conditions that P relies on its environment to provide, and a guarantee condition expresses what P guarantees to provide in return. This paper presents a proof technique that permits us to infer that a progr...