In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

The original paper presents an efficient algorithm for routing an Omega -1 × Omega nonblocking network. This comment presents an extra step required to route an Omega + Omega network.

This article provides an Omega-result for the remainder term in Weyl’s law for the spectral counting function of certain rational (2l+ 1)-dimensional Heisenberg manifolds. Introduction. For M a closed n -dimensional Riemannian manifold with a metric g and Laplace-Beltrami operator ∆, let N(t) denote the spectral counting function N(t) := ∑ λ eigenvalue of ∆ λ≤t d(λ) where d(λ) is the dimension ...

We address the supervisory synthesis problem for controlling the sequential behaviors of Discrete Event Dynamical Systems (DEDS’s) under complete as well as partial information through the use of synchronous composition of the plants and the supervisors. We present the notion of complete languages, discuss some of its algebraic properties and show its close relation to ω-languages. We prove tha...

Background: Excitotoxicity is a common pathological process in neurodegenerative diseases associated with overactivity of N-methyl-D-aspartate (NMDA) and P/Q type voltage-gated calcium (Cav2.1) channels. Omega-lycotoxin-Gsp2671g is a therapeutic tool to modulate overactive Cav2.1 (P/Q type) channels. Omega-lycotoxin binds to Cav2.1 channels with high affinity and selectivity. This study aimed t...

omega-Hydroxylation of leukotriene B4 (LTB4) has been reported in human and rodent polymorphonuclear leukocytes; preliminary information indicates that this metabolism is cytochrome P-450 dependent. Therefore, these studies were initiated to characterize the cytochrome P-450-dependent metabolism of LTB4 in other tissues. LTB4 was metabolized by rat hepatic microsomes to two products, 20-hydroxy...

Various monohydroxylated fatty acids were synthesized from eicosapolyenoic acids, namely arachidonic (20:4 omega-6), timnodonic (20:5 omega-3), dihomogammalinolenic (20:3 omega-6) and mead (20:3 omega-9) acids. 12-Hydroxy derivatives, as well as 12-hydroxy-5,8,10-heptadecatrienoic acid (HHT), were produced with platelets as the enzyme source, and 15-hydroxy derivatives were produced by soya bea...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...