In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

It is well known that classical theta series which are attached to positive definite rational quadratic forms yield elliptic modular forms, and linear combinations of theta series attached to lattices in a fixed genus can yield both cusp forms and Eisenstein series whose weight is one-half the rank of the quadratic form. In contrast, generalized theta series—those augmented with a spherical har...

The isoforms of the highly conserved and ubiquitously expressed 14-3-3 family of proteins function primarily as adapters that modulate interactions between components of various cellular signaling and cell cycle regulatory pathways. Low levels of 14-3-3 isoforms appear to be expressed in most tissues, but specific isoforms or combinations have been shown to be overexpressed in a cell-specific m...

Theta and gamma rhythms synchronize neurons within and across brain structures. Both rhythms are widespread within the hippocampus during exploratory behavior and rapid-eye-movement (REM) sleep. How synchronous are these rhythms throughout the hippocampus? The present study examined theta and gamma coherence along the septotemporal (long) axis of the hippocampus in rats during REM sleep, a beha...

Hippocampal place cells that fire together within the same cycle of theta oscillations represent the sequence of positions (movement trajectory) that a rat traverses on a linear track. Furthermore, it has been suggested that the encoding of these and other types of temporal memory sequences is organized by gamma oscillations nested within theta oscillations. Here, we examined whether gamma-rela...

Theta frequency oscillations are a predominant feature of rhythmic activity in the hippocampus. We demonstrate that hippocampal area CA1 generates atropine-resistant theta population oscillations in response to metabotropic glutamate receptor activation under conditions of reduced AMPA receptor activation. This activity occurred in the absence of inputs from area CA3 and extra-ammonic areas. Fi...

On microscopic picture of cirrhosis and allied disorders, "degree of nodular separation" rho theta was established to measure the advancement of cirrhotic change. Based on mathematical treatment of the curvature of linear boundaries between the parenchymal and interstitial areas, rho theta is defined as: rho theta = theta A (net)/theta A (abs) (-1 smaller than or equal to rho theta smaller than...

Theta oscillations in the local field potential of neural ensembles are considered key mediators of human working memory. Theoretical accounts arising from animal hippocampal recordings propose that the phase of theta oscillations serves to instantiate sequential neuronal firing to form discrete representations of items held online. Human evidence of phase relationships in visual working memory...

Recently, a novel numerical computation on quantum mechanics by using bootstrap method was proposed Han, Hartnoll, and Kruthoff. We consider whether this works in systems with $\ensuremath{\theta}$-term, where the standard Monte-Carlo may fail due to sign problem. As starting point, we study of charged particle circle which constant gauge potential is counterpart $\ensuremath{\theta}$-term. fin...

Given a finite alphabet $\mathbb{A}$ and primitive substitution $\theta:\mathbb{A}\to\mathbb{A}^\lambda$ (of constant length $\lambda$), let $(X_\theta,S)$ denote the corresponding dynamical system, where $X_{\theta}$ is closure of orbit via left shift $S$ fixed point natural extension $\theta$ to self-map $\mathbb{A}^{\mathbb{Z}}$. The main result paper that all continuous observables in are o...