Let S be a (discrete) semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach ...

Let S be a semigroup, and let ` (S) be the Banach algebra which is the semigroup algebra of S. We shall study the structure of this Banach algebra and of its second dual. We shall determine exactly when ` (S) is amenable as a Banach algebra, and shall discuss its amenability constant, showing that there are ‘forbidden values’ for this constant. The second dual of ` (S) is the Banach algebraM(βS...

The effect of elevated CO(2) and O(3) on apparent quantum yield (varphi), maximum photosynthesis (P(max)), carboxylation efficiency (V(cmax)) and electron transport capacity (J(max)) at different canopy locations was studied in two aspen (Populus tremuloides) clones of contrasting O(3) tolerance. Local light climate at every leaf was characterized as fraction of above-canopy photosynthetic phot...

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...