Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

The fluorophore in green fluorescent protein (GFP) is localized in a highly constrained environment, protected from the bulk solvent by the barrel-shaped protein matrix. We have used the wavelength-selective fluorescence approach (red edge excitation shift, REES) to monitor solvent (environment) dynamics around the fluorophore in enhanced green fluorescent protein (EGFP) under various condition...

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid (or a polymatroid) and study their facets. Some application...

We consider the quotient of the Hermitian curve defined by the equation yq + y = xm over Fq2 where m > 2 is a divisor of q + 1. For 2 ≤ r ≤ q + 1, we determine the Weierstrass semigroup of any r-tuple of Fq2 rational points (P∞, P0b2 , . . . , P0br ) on this curve. Using these semigroups, we construct algebraic geometry codes with minimum distance exceeding the designed distance. In addition, w...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

With the exploitation of rare earth ore, more and more REEs came into groundwater. This was a waste of resources and could be harmful to the organisms. This study aimed to find an efficient adsorption material to mitigate the above issue. Through doping sodium alginate (SA) with poly-γ-glutamate (PGA), an immobilized gel particle material was produced. The composite exhibited excellent capacity...

In the present paper we give a partially negative answer to a conjecture of Ghahramani, Runde and Willis. We also discuss the derivation problem for both foundation semigroup algebras and Clifford semigroup algebras. In particular, we prove that if S is a topological Clifford semigroup for which Es is finite, then H1(M(S),M(S))={0}.

the main purpose of this paper is to establish a relation between universality of certain p-compactifications of a semitopological semigroup and their corresponding enveloping semigroups. in particular, we show that if we take p to be the property that the enveloping semigroup of a compactification of a semitopological semigroup s is left simple, a group, or the trivial singleton semigroup, the...