Regularity properties significantly stronger than were previously known are developed for four-dimensional non-linear conformally invariant quantized fields. The Fourier coefficients of the interaction Lagrangian in the interaction representation-i.e., evaluated after substitution of the associated quantized free field-is a densely defined operator on the associated free field Hilbert space K. ...

We investigate the spatiotemporal coding of low amplitude inputs to a simple system of globally coupled phase oscillators with coupling function g(varphi)=-sin(varphi+alpha)+rsin(2varphi+beta) that has robust heteroclinic cycles (slow switching between cluster states). The inputs correspond to detuning of the oscillators. It was recently noted that globally coupled phase oscillators can encode ...

The purpose of this paper is to introduce the notion of a fuzzy H-weak contraction and prove a fixed point theorem for fuzzy H-weak contractions without exploiting the notion of continuity in M -complete fuzzy metric spaces. Examples are given to show that our result is a proper extension of some known results in the literature.

A ($2k+1$)$-$dimensional contact Lie algebra is one which admits a one-form $\varphi$ such that $\varphi \wedge (d\varphi)^k\ne0$. Such algebras have index one, but this not generally sufficient condition. Here we show index-one type-A seaweed are necessarily contact. Examples, together with method for their explicit construction, provided.

We establish curvature estimates and a convexity result for mean convex properly embedded $\[\varphi,\vec{e}{3}]$-minimal surfaces in $\mathbb{R}^3$, i.e., $\varphi$-minimal when $\varphi$ depends only on the third coordinate of $\mathbb{R}^3$. Led by works 3-manifolds, due to White minimal surfaces, Rosenberg, Souam Toubiana stable CMC Spruck Xiao translating solitons we use compactness argume...

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk $\mathbb{D}$, which satisfies following: $(1)$ biharmonic equation $\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) boundary condition $\Delta f=\varphi$ ($\varphi\in\mathcal{C}(\mathbb{T})$ and $\mathbb{T}$ denotes circle), $(3)$ $f(0)=0$. The purpose this paper to prove Lipschitz continuos, and, furthe...

During sustained maximal voluntary contractions (MVCs), most fatigue occurs within the muscle, but some occurs because voluntary activation of the muscle declines (central fatigue), and some of this reflects suboptimal output from the motor cortex (supraspinal fatigue). This study examines whether supraspinal fatigue occurs during a sustained submaximal contraction of 5% MVC. Eight subjects sus...

Let E be a vector lattice, $$\lambda _1,\lambda _2,\ldots ,\lambda _k$$ scalars and $$\varphi _1,\ldots ,\varphi pairwise independent regular linear functionals on E. We show that if $$k<m$$ then $$\sum _{j=1}^k\lambda _j\varphi _j^m$$ is orthogonally additive only _j$$ or $$-\varphi lattice homomorphism for each j, $$1\le j\le k$$ . Moreover, $$m\ge 2$$ , we provide an example to this result d...

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.