INTRODUCTION In Alzheimer's disease (AD), accelerated neurofibrillary tangle formation occurs which is associated with increased tau protein release into the cerebrospinal fluid (CSF). Recent studies found significantly increased CSF tau already in patients at risk of developing AD, indicating its potential as a biochemical marker of AD. Cerebral glucose metabolism is reduced in frontotemporopa...

The paper considers a scalar differential equation of an advance-delay type \begin{equation*} \dot{y}(t)= -\left(a_0+\frac{a_1}{t}\right)y(t-\tau )+\left(b_0+\frac{b_1}{t}\right)y(t+\sigma )\,, \end{equation*} where constants $a_0$, $b_0$, $\tau $ and $\sigma are positive, $a_1$ $b_1$ arbitrary. behavior its solutions for $t\rightarrow \infty is analyzed provided that the transcendental \lambda...

Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in open unit disk $\mathbb{U}$ and given by\[f(z)=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \left( z\in \mathbb{U}\right) .\]The coefficient functional $\phi _{\lambda }\left( f\right) =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, _{1}\left( =a_{3}-a_{2}^{2}=S_{f}\left( 0\...

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...

Motived by the neutrino oscillation data, we consider the lightest tau sneutrino ν̃τ1 (which is mostly the right tau sneutrino) to be the lightest supersymmetric particle (LSP) in the framework of the minimal supersymmetric Standard Model. Both the standard and the non-standard trilinear scalar coupling terms are included for the right tau sneutrino interactions. The decay branching ratio of ν̃τ2...

We present final measurements of the Z boson-lepton coupling asymmetry parameters A(e), A(mu), and A(tau) with the complete sample of polarized Z bosons collected by the SLD detector at the SLAC Linear Collider. From the left-right production and decay polar angle asymmetries in leptonic Z decays we measure A(e) = 0.1544+/-0.0060, A(mu) = 0.142+/-0.015, and A(tau) = 0.136+/-0.015. Combined with...

‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $R$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{sigma,tau}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper‎, ‎it is shown that if charac...