A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed, left ideals in C∗-algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain le...

The differentiation of neurons and the outgrowth of neurites depends on microtubule-associated proteins such as tau protein. To study this process, we have used the model of Sf9 cells, which allows efficient transfection with microtubule-associated proteins (via baculovirus vectors) and observation of the resulting neurite-like extensions. We compared the phosphorylation of tau23 (the embryonic...

A cosmid containing eight exons of the gene coding for the microtubule-associated tau protein was subjected to the exon trapping assay. All the constitutive exons contained in the cosmid (4, 5, 7 and 9) were efficiently captured regardless of size. Of the four alternatively spliced exons, three (3, 4A and 8) were not isolated by the assay, but the behavior of exon 6 depended on the identity of ...

Alzheimer's disease (AD) is characterized by the accumulation of intraneuronal tau and extracellular amyloid-β (Aβ) peptide. A triple transgenic (Tg) mouse (3xTg-AD) was reported to develop Aβ plaques and tau inclusions as well as remarkable accumulations of intracellular Aβ that were suggested to be the initiators of AD pathogenesis. However, it was unclear whether the anti-Aβ antibodies were ...

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The solution takes the form product consisting unknown coefficients and polynomials. Our main task is compute numerical values coefficients. To achieve goal, apply initial condition problem, Tau Lagrange multiplier methods. We do error ana...

In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$  is investigated. Some new positive periodic criteria are given.  

In [5], D. Lanphier used differential operators studied by Maass [6] to prove the above van der Pol identity (2). He also obtained several van der Pol-type identities using the Maass operators and thereby obtained new congruences for the Ramanujan’s tau-function. In [9], D. Niebur derived a formula for τ(n) similar to the classical ones of Ramanujan and van der Pol, but has the feature that hig...