Previous studies have shown that the kagome lattice has a remarkably high fracture toughness. This architecture is one of eight semi-regular tessellations, and this work aims to quantify toughness three other unexplored lattices: snub-trihexagonal, snub-square elongated-triangular lattices. Their mode I was obtained with finite element simulations, using boundary layer technique. These simulati...

Let us say that an $n$-sided polygon is semi-regular if it circumscriptible, and its angles are all equal but possibly one which then larger than the rest. Regular polygons, in particular, semi-regular. The main result of paper that, class convex polygons uniquely determined by just three geometric quantities: area, perimeter, a third quantity depending only on interior appears heat trace asymp...

The purpose of this paper is to introduce new separation axioms semi*-regular, semi*-normal, s*regular, s**-normal using semi*-open sets and investigate their properties. We also study the relationships among themselves and with known axioms regular, normal, semi-regular and semi-normal. Mathematics Subject Classification 2010: 54D10, 54D15

We consider strongly regular graphs r = (V, E) on an even number, say 2n, of vertices which admit an automorphism group G of order n which has two orbits on V. Such graphs will be called strongly regular semi-Cayley graphs. For instance, the Petersen graph, the Hoffman-Singleton graph, and the triangular graphs T(q) with q = 5 mod 8 provide examples which cannot be obtained as Cayley graphs. We...

The article deals with regular, semi-regular and irregular plane partitions, among the latter are partitions into equal polygons arbitrary simple knots. It continues author's supplementary lectures to university textbook «Crystallography» by G. M. Popov I. Shafranovsky, which was recommended students of geology St. Petersburg Mining University. new topic is interesting because first problem sol...

We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a Cayley graph, is based on methods akin to those of Lovász and Babai ([L], [B]). It turns out that the algebraic degree of the eigenvalues is at most 5, achieved at two 3-dimensional solids.

The paper studies the evaluation of regular path queries on semi-structured data, i.e. path queries of the form nd all objects reachable by path whose labels form a word in p where p is a regular expression. We use local information expressed in the form of path inclusions in the optimization of path queries. These constraints are of the form L v where L is a regular language and v is a word; L...

We investigate the question whether semi-completeness, i.e., weak termination plus connuence, of term rewriting systems is preserved under the normalization of right-hand sides. We give a simple counterexample showing that in general this transformation neither preserves weak termination nor (local) connuence. Moreover we present two conditions which are suucient for the preservation of semi-co...