A topoframe, denoted by $L_{ tau}$,  is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in $L$. In this paper, we define and study the notions of a $tau $-real-continuous function on a frame $L$ and the set of real continuous functions $mathcal{R}L_tau $ as an $f$-ring. We show that $mathcal{R}L_{ tau}$ is actually a generali...

In a previous article, we have shown that the discrepancy between fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $\tau$ hadronic spectral function moments, which had affected precision of $\alpha_s$ determinations many years, may be reconciled by employing renormalon-free (RF) scheme gluon condensate (GC) matrix element. addition, convergence moments with sizeable GC...

For chemical systems involving both fast and slow scales, stiffness presents challenges for efficient stochastic simulation. Two different avenues have been explored to solve this problem. One is the slow-scale stochastic simulation (ssSSA) based on the stochastic partial equilibrium assumption. The other is the tau-leaping method. In this paper we propose a new algorithm, the slow-scale tau-le...

The spectral function ρV −A(s) is determined from ALEPH and OPAL data on hadronic tau decays using a neural network parametrization trained to retain the full experimental information on errors, their correlations and chiral sum rules: the DMO sum rule, the first and second Weinberg sum rules and the electromagnetic mass splitting of the pion sum rule. Nonperturbative QCD vacuum condensates can...

We present a method to obtain the first-order temporal correlation function, ${g}^{(1)}(\ensuremath{\tau})$, of light scattered by an assembly pointlike quantum scatterers, or equivalently its spectral power distribution. This is based on mirror-assisted backscattering interferometric setup. The contrast angular fringes was already linked convolution ${g}^{(1)}(\ensuremath{\tau})$ for different...

We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operationalmatrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinea...

Time-resolved fluorescence data was collected from a series of 23 bulk crude petroleum oils and six microscopic hydrocarbon-bearing fluid inclusions (HCFI). The data was collected using a diode laser fluorescence lifetime microscope (DLFLM) over the 460-700 nm spectral range using a 405 nm excitation source. The correlation between intensity averaged lifetimes (tau) and chemical and physical pa...

We combine ALEPH and OPAL results for the spectral distributions measured in $\tau\to\pi^-\pi^0\nu_\tau$, $\tau\to 2\pi^-\pi^+\pi^0\nu_\tau$ $\tau\to\pi^-3\pi^0\nu_\tau$ decays with (i) recent BaBar analogous K^- K^0\nu_\tau$ distribution (ii) estimates of contributions from other hadronic $\tau$-decay modes obtained using CVC electroproduction data, to obtain a new more precise non-strange, in...

Physical properties of the three main structures in young stellar objects (YSOs), envelopes, bipolar outflows, and circumstellar disks, have been studied using radio interferometers: the Berkeley-Illinois-Maryland Association (BIMA) array and the Combined Array for Research in Millimeter-wave Astronomy (CARMA). (1) Envelopes: Three Class 0 YSOs (L1448 IRS 2, L1448 IRS 3, and L1157) have been ob...

The Tau Method, by construction, produces approximate polynomial solutions of differential equations. The purpose of this paper is to extend the Tau Method to the Integro-Differential equations. An efficient error estimation for the Tau method is also introduced. Details of this method are presented and some numerical results along with estimated errors are given to clarify the method and its e...