Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fib...

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...

We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan’s tau function which involves t-cores and a new class of partitions which we call (m, k)-capsids. The same method can be applied in conjunction with other related identities yielding alternative combinatorial interpretations of the tau function.

This document describes a new approach of the di-tau selection presented. The method is based on the identiication of speciic tau decay channel and on the estimation of their corresponding background. The selection of data taken from 181 to 184 GeV is detailed and cross-sections as well as asymmetries are derived :