‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

Metrized graphs are finite graphs equipped with a distance function on their edges. For a metrized graph Γ, the tau constant τ(Γ) is an invariant which plays important roles in both harmonic analysis on metrized graphs and arithmetic of curves. T. Chinburg and R. Rumely [CR] introduced a canonical measure μcan of total mass 1 on a metrized graph Γ. The diagonal values of the Arakelov-Green’s fu...

An unusually high frequency of atypical Parkinson syndrome has been delineated over the last 5 years in the French West Indies. Postural instability with early falls, prominent frontal lobe dysfunction and pseudo-bulbar palsy were common and three-quarters of the patients were L-dopa unresponsive. One-third of all patients seen had probable progressive supranuclear palsy (PSP). This new focus o...

the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

We present a methodology to construct efficient high-order in time accurate numerical schemes for class of gradient flows with appropriate Lipschitz continuous nonlinearity. There are several ingredients the strategy: exponential differencing (ETD), multi-step (MS) methods, idea stabilization, and technique interpolation. They synthesized develop generic $k^{th}$ order linear scheme help an art...

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.