This paper presents some of our requirements for a Z type-checker: that the typechecker accept all well-typeable formulations, however contrived; that it gather information about uses of declarations as needed to support interactive browsing and formal reasoning; that it t the description given by draft standard Z; and that it be able to check some particular extensions to Z that are intended t...

The results of MNDO, AM1 and PM3 semi-empirical calculations and HF/6-31G*, MP/6-31G*, MP2/6-311+G**, and B3LYP/6-311G** and QCISD/6-31G* ab initio methods for angle strain and conjugation effects in twist-boat, boat, and half-chair geometries of (Z,Z,Z)-cycloocta-1,3,5-triene indicate that all methods, except PM3, predict wrong ordering of the conformations.

Let $R$ be a ring and $M$ a right $R$-module. We call $M$, coretractable relative to $overline{Z}(M)$ (for short, $overline{Z}(M)$-coretractable) provided that, for every proper submodule $N$ of $M$ containing $overline{Z}(M)$, there is a nonzero homomorphism $f:dfrac{M}{N}rightarrow M$. We investigate some conditions under which the two concepts coretractable and $overline{Z}(M)$-coretractable...

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

In this paper, we study self-dual codes over Z2× (Z2+uZ2), where u 2 = 0. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exists a code C ⊆ Z2×(Z2+uZ2) β are established. We also present several approaches to construct self-dual codes over Z2 × (Z2 + uZ2). Moreover, the structure of two-weight self-dual codes is completely obtained for α · β 6...