In this paper, we prove that the distance function of an open connected set in R with a C boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex. We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various impro...

A generalized complex structure may be understood as a "weakly holomorphic" Poisson structure: given an integrability condition, a generalized complex structure "integrates" to a symplectic groupoid equipped with a weak holomorphic structure, i.e., a compatible holomorphic structure on the associated stack. Similarly, generalized complex branes may be represented as weakly holomorphic coisotrop...

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

To examine individual or combined effects of static stretch and explosive contraction on quadriceps spinal-reflex excitability (the peak Hoffmann’s reflex normalized by the motor-response) latency times motor-response. Fourteen healthy young males randomly experienced four conditions (stretch, contraction, + control—no intervention). For condition, three sets a 30 s hold using modified Thomas t...

The Bollob\'as-Riordan polynomial [Math. Ann. 323, 81 (2002)] is a universal invariant for ribbon graphs. We find an extension of this particular family combinatorial objects, called rank 3 weakly-colored stranded Stranded graphs arise in the study tensor models quantum gravity physics, and generalize present seven-variable these graphs, which obeys contraction/deletion recursion relation simil...

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

This article contributes to the ongoing discussion on multiple belief change. Based on earlier work, we devise a new condition, called (K−̇F), that reduces infinite contraction to sentence contraction. Two representation results reported herein characterize (K−̇F) in terms of two well known constructive models for set contraction; namely the partial meet model and the comparative possibility mode...

We find a sufficient condition for a weakly differentiable homeomorphism in Euclidean space to have a homeomorphic extension to the boundary of its domain of definition. In a certain sense, this condition is best possible.

This study examined the influence of the elongation of attached crossbridges and residual force enhancement on joint torque enhancement by the stretch-shortening cycle (SSC). Electrically evoked submaximal tetanic plantar flexions were adopted. Concentric contractions were evoked in the following three conditions: after 2 s isometric preactivation (ISO condition), after 1 s isometric then 1 s e...

Many fixed point theorems for mapping satisfies a generalized weak contractive condition is already established. In this paper we also give a result on fixed point for mapping satisfying a weakly contractive condition of integral type.