Let L be a restricted Lie algebra with the restricted enveloping algebra u(L) over a perfect field of positive characteristic p. The restricted isomorphism problem asks what invariants of L are determined by u(L). This problem is the analogue of the modular isomorphism problem for finite p-groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacycl...

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic p ≥ 5.

A restricted-orientation convex set, also called an O-convex set, is a set of points whose intersection with lines from some xed set is empty or connected. The notion of O-convexity generalizes standard convexity and orthogonal convexity. We explore some of the basic properties of O-convex sets in two and higher dimensions. We also study O-connected sets, which are restricted O-convex sets with...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

The simple restricted modules for the restricted simple Cartan-type Lie algebras fall into two classes. There is a large class consisting of modules induced from simple modules for the subalgebra of nonnegative components. Then there is the small class of exceptional simple modules. Explicit constructions of these exceptional modules and formulas for their dimensions were obtained by Shen [9] f...

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on c...

As is well known, the Shapovalov bilinear form and its determinant is an important tool in the representation theory of semisimple Lie algebras over char. 0. To our knowledge, the corresponding study of the Shapovalov bilinear form and its determinant is not available in the literature in char. p or the quantum case at roots of unity. The aim of this paper is to fully determine the Shapovalov d...

There is no need to show the importance of the ltering tech niques to solve constraint satisfaction problems i e to nd values for problem variables subject to constraints that specify which combinations of values are consistent They can be used during a preprocessing step to remove once and for all some local inconsistencies or during the search to e ciently prune the search tree Recently in a ...

It is shown that, with a few exceptions, the simple restricted modules for a restricted contact Lie algebra are induced from those for the homogeneous component of degree zero. In [3], Shen constructed the simple restricted modules for the restricted Witt, special and hamiltonian Lie algebras which comprise three of the four classes of restricted Lie algebras of Cartan type. His methods, howeve...

in this study, the effects of late gestational undernutrition (lgu) on plasma concentration of insulin-like growth factor 1 (igf-i), leptin, insulin and glucose in subsequent sucking lambs was investigated. ten twin-bearing ewes were fed either restrictedly (restricted) or adequately (control) during the last six weeks of gestation and were fed ad libitum after parturition. blood samples were t...