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...

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...

Objective: Zataria multiflora (ZM) is a plant with ethnopharmacological value which was recently tested to reduce symptoms of Alzheimer’s disease (AD). The aim of the present study was to determine the effect of ZM essential oil on spatial cognitive and noncognitive behavior, as well as hippocampal tau protein and tumor necrosis factor alpha (TNFα) concentrations in ra...

Tau is an intrinsically disordered protein with a central role in the pathology of a number of neurodegenerative diseases. Tau normally functions to stabilize neuronal microtubules, although the mechanism underlying this function is not well understood. Of note is that the interaction between tau and soluble tubulin, which has implications both in understanding tau function as well as its role ...

Microtubule-associated Tau proteins belong to a family of factors that polymerize tubulin dimers and stabilize microtubules. Tau is strongly expressed in neurons, localized in the axon and is essential for neuronal plasticity and network. From the very beginning of Tau discovery, proteomics methods have been essential to the knowledge of Tau biochemistry and biology. In this review, we have sum...

We propose a Clifford algebra based model, which treats both gravity and YangMills interactions as gauge fields. There are two sectors of boson fields as electroweak and Majorana bosons. The electroweak boson sector induces fermion masses via spontaneous symmetry breaking. It is composed of scalar Higgs, pseudoscalar Higgs, and antisymmetric tensor components. The Majorana boson sector contribu...

We prove the rigidity of entire graphic Lagrangian self-shrinkers in $$({\mathbb {R}}^{2n}, g_\tau )$$ , where $$g_\tau =\sin \tau \,\delta _0+\cos \,g_0$$ is a linear combination Euclidean metric $$\delta _0$$ and pseudo $$g_0=2\sum _i dx_idy_i$$ with $$\tau \in (0,\frac{\pi }{2})$$ complementing previous results for =0$$ =\frac{\pi }{2}$$ ; actually we obtain Bernstein theorems three correspo...

The neuronal microtubule-associated protein tau has been implicated as having a role in the outgrowth of neural processes and the development of neuronal polarity. In vitro, tau promotes microtubule assembly, stabilizes cellular microtubules, and affects their dynamic behavior. Antisense experiments using cultured neurons provided evidence for an essential role of tau in the development of axon...

Molecular chaperones regulate the aggregation of a number of proteins that pathologically misfold and accumulate in neurodegenerative diseases. Identifying ways to manipulate these proteins in disease models is an area of intense investigation; however, the translation of these results to the mammalian brain has progressed more slowly. In this study, we investigated the ability of one of these ...