‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...

‎Let $tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$‎. ‎Let $bar{G}=G/H_{G}$ and $bar{H}=H/H_{G}$‎. ‎We say that $H$ is $Phi$-$tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $bar{T}$ of $bar{G}$ and some $tau$-subgroup $bar{S}$ of $bar{G}$ contained in $bar{H}$‎, ‎$bar{H}bar{T}$ is $S$-quasinormal in $bar{G}$ and $bar{H}capbar{T}leq bar{S}Phi(bar{H})$‎. ‎I...

Left ventricular relaxation time constant, Tau, is the best index to evaluate left ventricular diastolic function. The measurement is only available traditionally in catheter lab. In Echo lab, several methods of non-invasive measurement of Tau have been tried since 1992, however almost all the methods are still utilizing the same formula to calculate Tau as in catheter lab, which makes them inc...

BACKGROUND Cerebrospinal fluid (CSF) tau is a common biomarker for Alzheimer disease (AD). Measurements of tau have historically been performed using immunoassays. Given the molecular diversity of tau in CSF, the selectivity of these immunoassays has often been questioned. Therefore, we aimed to develop an analytically sensitive and selective immunoaffinity liquid chromatography-tandem mass spe...

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

we describe under various conditions abelian subgroups of the automorphism‎ ‎group $mathrm{aut}(t_{n})$ of the regular $n$-ary tree $t_{n}$‎, ‎which are‎ ‎normalized by the $n$-ary adding machine $tau =(e‎, ‎dots‎, ‎e,tau )sigma _{tau‎ ‎}$ where $sigma _{tau }$ is the $n$-cycle $left( 0,1‎, ‎dots‎, ‎n-1right) $‎. ‎as‎ ‎an application‎, ‎for $n=p$ a prime number‎, ‎and for $n=4$‎, ‎we prove that...

BACKGROUND Cerebrospinal fluid (CSF) biomarkers and quantitative EEG show particular patterns of change in Alzheimer's disease (AD) and reflect neuropathologic processes and cerebral function, respectively. The changes precede cognitive decline and should be visible already in preclinical stages. We therefore aimed to investigate their relationship in cognitively healthy individuals. METHOD T...

OBJECTIVE The aim of this study was to examine the relative efficacy of evidence-based treatments (EBTs) versus treatment-as-usual (TAU) in routine care for anxiety and depression in adults. METHOD A computerized search of studies that directly compared an EBT with a TAU was conducted. Meta-analytic methods were used to estimate effectiveness of EBTs relative to TAU and to model how various c...

The perforant pathway projection from the entorhinal cortex (EC) to the hippocampal dentate gyrus is critically important for long-term memory and develops tau and amyloid pathologies and progressive degeneration starting in the early stages of Alzheimer disease (AD). However, perforant pathway function has not been assessed in experimental models of AD, and a therapeutic agent that protects it...