In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

The vertex-degree function index Hf(Γ) is defined as Hf(Γ)=∑v∈V(Γ)f(d(v)) for a f(x) on non-negative real numbers. In this paper, we determine the extremal graphs with maximum (minimum) vertex degree in set of all n-vertex chemical trees, and connected graphs. We also present Nordhaus–Gaddum-type results Hf(Γ)+Hf(Γ¯) Hf(Γ)·Hf(Γ¯).

In this article we construct an irreducible simple subgroup G = 〈q, y, t, w〉 of GL8671(13) from an irreducible subgroup T of GL11(2) isomorphic to Mathieu’s simple group M24 by means of Algorithm 2.5 of [13]. We also use the first author’s similar construction of Fischer’s sporadic simple group G1 = Fi23 described in [11]. He starts from an irreducible subgroup T1 of GL11(2) contained in T whic...

In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n ≤ 2, while a proximity theorem can be established for any n, but o...

We establish that every bounded convex domain in C with an automorphism orbit accumulation at a boundary point at which the domain has a sphere contact from inside admits a non-compact 1-parameter subgroup of automorphisms. Notice that this in particular implies that no Teichmüller domain of a Riemann surface of genus g > 1 can be holomorphically imbedded as a convex domain in C .

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

insisting that the equality sign holds when k = n. Here, x[X] > • • • > x[n] are the xt arranged in decreasing order and, similarly, y[X] > • • • > y[n]. If (1) is only required for the increasing (decreasing) convex functions on R then one speaks of weak sub-majorization x >, respectively). The first is equivalent to (2). Let & be an open convex subset of R...