In this paper, we consider a problem in calculus of variations motivated by quantitative isoperimetric inequality the plane. More precisely, aim article is computation minimum variational $$\begin{aligned}\inf _{u\in {\mathcal {W}}} \frac{\displaystyle \int _{-\pi }^{\pi }[(u')^2-u^2]d\theta }{\displaystyle \left[ } |u| d\theta \right] ^2} \end{aligned}$$ where function $$u\in {W}}$$ $$H^1(-\pi...

for all $a,b>0$, the following two optimal inequalities are presented: $h^{alpha}(a,b)l^{1-alpha}(a,b)geq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ h^{alpha}(a,b)l^{1-alpha}(a,b)leq m_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. here, $h(a,b)$, $l(a,b)$, and $m_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

The paper demonstrates how second-order quantiication and nite games can be exploited for deciding complicated propositional program logics like the propositional-Calculus with converse (C ?). This approach yields a new proof that C ? is in EXP T IME. Automata-theoretic technique is a very powerful and popular approach for deciding complicated propositional program logics 19, 20, 3]. The rst pa...

‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

Abstract We study the Brownian motion on non-compact Grassmann manifold $\frac {\textbf {U}(n-k,k)} {U}(n-k)\textbf {U}(k)}$ and some of its functionals. The key point is to realize this as a matrix diffusion process, use stochastic calculus take advantage hyperbolic Stiefel fibration functional that can be understood in setting generalized area process. In particular, connection Maass Laplacia...

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to class gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via momentum map. We numerically demonstrate this time invariance map its usefulness establishing precise initia...

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...