Let L be a lattice with the least element 0. An element x ∈ L is a zero divisor if x∧ y = 0 for some y ∈ L∗ = L \ {0}. The set of all zero divisors is denoted by Z(L). We associate a simple graph Γ(L) to L with vertex set Z(L)∗ = Z(L) \ {0}, the set of non-zero zero divisors of L and distinct x, y ∈ Z(L)∗ are adjacent if and only if x ∧ y = 0. In this paper, we obtain certain properties and dia...

One of the most natural approaches to the study of regular semigroups is to impose restrictions on the partial ordering of their idempotents (erg/^e/—jfe==e). The principal object of this note is to describe the structure of the classes of regular semigroups whose idempotents form a tree or a unitary tree, respectively (see Definition 1). We determine, among other things, a complete set of inva...

We introduce a new redistancing method for level set functions. This method applies in a finite element setting and uses a gradient recovery technique. Based on the recovered gradient a quasi-normal field on the zero level of the finite element level set function is defined and from this an approximate signed distance function is determined. For this redistancing method rigorous error bounds ar...

Example. Every non-zero element of ⋀ V is trivially totally decomposable. Example. If dimV = 3, then every non-zero element of ⋀ V is totally decomposable. Proof. Given a sum v1 ∧v2 +v3 ∧v4 of two non-zero elements of ⋀ V , the two-dimensional subspaces Span(v1, v2) and Span(v3, v4) must intersect. If w1 is in the intersection, then we can rewrite v1∧v2 = w1 ∧w2 for some w1 ∈ Span(v1, v2). Simi...

a single column cation exchanger resin was used to eliminate cations from renet cheese whey, with particular reference to the improvement of taste and flavor. ten panelists were convened to assess the contribution of the mineral components to the salty taste of whey, judging on the basis of taste, flavor and color. the organoleptic characteristics of untreated whey were arbitrarily assigned...

A least-squares spectral finite element method was used to develop an accurate computer code for prediction of solidification from a melt under the influence of an externally applied magnetic field. The computational results indicate significantly different flow-field patterns and thermal fields in the melt and the accrued solid in the cases of full gravity, reduced gravity, and an applied unif...