this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

We develop and analyze a model for particle transport in a stochastic ratchet with a periodic piecewise linear potential, with diffusion coefficient D, where the force is discontinuous in position and fluctuating in time via additive telegraph noise with correlation time tau. We find asymptotic formulas for the steady-state particle current J for large and small D and tau. For example, for smal...

This paper is concerned with the numerical solution of Volterra integral equations third kind non-smooth solutions based on recursive approach spectral Tau method. To this end, a new set fractional version canonical basis polynomials (called FC-polynomials) introduced. The approximate polynomial Tau-solution) expressed in terms FC-polynomials. structure Tau-solution allows recovering standard d...

We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

The detailed protein composition of the paired helical filaments (PHF) that accumulate in human neurons in aging and Alzheimer disease is unknown. However, the identity of certain components has been surmised by using immunocytochemical techniques. Whereas PHF share epitopes with neurofilament proteins and microtubule-associated protein (MAP) 2, we report evidence that the MAP tau (tau) appears...

Recent evidence has emphasized soluble species of amyloid-β (Aβ) and tau as pathogenic effectors in Alzheimer's disease (AD). Despite the fact that Aβ, tau, and α-synuclein (αSyn) can promote each other's aggregation, the potential contribution of soluble αSyn to AD pathogenesis is unknown. Here, we found an approximate twofold increase over controls in soluble αSyn levels in AD brains in the a...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

We previously developed a transgenic Caenorhabditis elegans model of human tauopathy disorders by expressing human tau in nematode worm neurons to explore genetic pathways contributing to tau-induced neurodegeneration. This animal model recapitulates several hallmarks of human tauopathies, including altered behaviour, accumulation of detergent-insoluble phosphorylated tau protein and neurodegen...