Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...

we investigate the stability of generalizedderivations on banach algebras with a bounded central approximateidentity. we show that every approximate generalized derivation inthe sense of rassias, is an exact generalized derivation. also thestability problem of generalized derivations on the faithful banachalgebras is investigated.

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

The Tau Method, by construction, produces approximate polynomial solutions of differential equations. The purpose of this paper is to extend the Tau Method to the Integro-Differential equations. An efficient error estimation for the Tau method is also introduced. Details of this method are presented and some numerical results along with estimated errors are given to clarify the method and its e...

We have utilized tau-assembled and tau-stabilized microtubules (MTs), in the absence of taxol, to investigate the effects of tau isoforms with three and four MT binding repeats upon kinesin-driven MT gliding. MTs were assembled in the presence of either 3-repeat tau (3R tau) or 4-repeat tau (4R tau) at tau:tubulin dimer molar ratios that approximate those found in neurons. MTs assembled with 3R...

We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan’s tau function which involves t-cores and a new class of partitions which we call (m, k)-capsids. The same method can be applied in conjunction with other related identities yielding alternative combinatorial interpretations of the tau function.

A member of the interferon-stimulated gene (ISG) family encodes a 17-kDa ubiquitin homolog called ISG17 that is induced in the bovine uterine endometrium by interferon-tau (IFN-tau) during early pregnancy. The bovine (b) ISG17 cDNA shares 30% identity with a tandem ubiquitin repeat and 70% identity with human (h) ISG15. The present experiments were designed to sequence the bISG17 gene, compare ...