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 ...

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.

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

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...

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...