Let L be a link in S that is in thin position but not in bridge position and let P be a thin level sphere. We generalize a result of Wu by giving a bound on the number of disjoint irreducible compressing disks P can have, including identifying thin spheres with unique compressing disks. We also give conditions under which P must be incompressible on a particular side or be weakly incompressible...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

It is well known to generalize the meagre ideal replacing ℵ 0 by a (regular) cardinal λ > ℵ 0 and requiring the ideal to be λ +-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing ℵ 0 by λ, so requiring it to be (< λ)-complete. Of course, we would welcome additional properties generalizing the one...

Let g be a nonabelian Lie algebra over an algebraically closed field K of characteristic 0. One is interested in the (algebraically) irreducible representations of g acting on a vector space which is allowed to be infinite dimensional. The subject of enveloping algebras is largely concerned with these, but even in the simplest nonabelian case, with g = I) the 3-dimensional (nilpotent) Heisenber...

Let R be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly J-ideals as new generalization J-ideals. We call proper ideal I J-ideal if whenever a,b ? 0 ab and J(R), then b I. Many basic properties characterizations are studied. investigate under various contexts constructions such direct products, localizations, homomorphic images. Moreover, number exam...

the aim of the present study was to investigate the relationship between the polar surface area and other molecular properties of the model drugs and their transdermal permeability across the rat skin. few model drugs which are weakly acidic (ibuprofen, aceclofenac and glipizide) and weakly basic (olanzapine, telmisartan and sildenafil citrate) were selected for the study based on polar surface...

As an effective solution to protect the privacy of the data, homomorphic encryption has become a hot research topic. Existing homomorphic schemes are not truly practical due to their huge key size. In this paper, we present a simple weakly homomorphic encryption scheme using only elementary modular arithmetic over the integers rather than working with ideal lattices. Compared with DGHV’s constr...

Abstract We compute the generator rank of a subhomogeneous $C^*\!$ -algebra in terms covering dimension pieces its primitive ideal space corresponding to irreducible representations fixed dimension. deduce that every $\mathcal {Z}$ -stable approximately algebra has one, which means generic element such an is generator. This leads strong solution problem for classifiable, simple, nuclear -algebr...

An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples. Introduction. The question of the irreducibility of an ordinary linear differential operator is of interest in the Picard-Vessiot theory (see Kolchin [1, §22]). Indeed, the operator is irreducible if and o...