For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

Let P , where |P| ≥ 2, be a set of points in d-dimensional space with a given metric ρ. For a point p ∈ P , let rp be the distance of p with respect to ρ from its nearest neighbour in P . Let B(p, rp) be the open ball with respect to ρ centered at p and having the radius rp. We define the sphere-of-influence graph (SIG) of P as the intersection graph of the family of sets {B(p, rp) | p ∈ P}. Gi...

We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaterni...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well...

If one thinks of a Riemannian metric, $g_1$, analogously as the gradient corresponding distance function, $d_1$, with respect to background $g_0$, then natural question arises whether theory Sobolev inequalities exists between metric and its function. In this paper we study sub-critical case $p < \frac{m}{2}$ show inequality where an $L^{\frac{p}{2}}$ bound on implies $L^q$ We use result state ...

in this paper, a common fixed point theorem for $psi$-weakly commuting maps in l-fuzzy metric spaces is proved.

in this paper, we study projective randers change and c-conformal change of p-reduciblemetrics. then we show that every p-reducible generalized landsberg metric of dimension n  2 must be alandsberg metric. this implies that on randers manifolds the notions of generalized landsberg metric andberwald metric are equivalent.

APA is a computer program, written in C, designed to determine the three-dimensional structure of proteins using distance geometry. We present the sampling and convergence properties of APA, as tested on bovine pancreatic trypsin inhibitor (BPTI). The results con®rm the program's earlier success with poly-L-alanine, albeit with some complications. The correct overall orientation of the BPTI con...

The Griffiths conjecture asserts that every ample vector bundle $E$ over a compact complex manifold $S$ admits hermitian metric with positive curvature in the sense of Griffiths. In this article we give sufficient condition for on $\mathcal{O}_{\mathbb{P}(E^*)}(1)$ to induce $L^2$-metric $E$. This result suggests study relative K\ahler-Ricci flow fibration $\mathbb{P}(E^*)\to S$. We define and ...