For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

Inspired by a question of Lovász, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lovász’s theta body of the graph. We prove that theta bodies are, up to closure, a version of Lasserre’s rela...

In this work we explore the first stages of quantum wire (QWR) formation studying the evolution of the growth front for InAs coverages below the critical thickness, theta(c), determined by reflection high energy electron diffraction (RHEED). Our results obtained by in situ measurement of the accumulated stress evolution during InAs growth on InP(001) show that the relaxation process starts at a...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

Introduction: The basic objective of this study is to investigate the effects of alpha and theta brain waves amplitude increase in occipital area on reducing the severity of symptoms of generalized anxiety disorder and to increase the global functioning level in patients with GAD. Methods: This study is a quasi-experimental study with pre-test and post-test with two groups. For this purpos...

Intermolecular interactions involving aromatic pi-electron density are widely believed to be governed by the aromatic molecular quadrupole moment, Theta(zz). Arene-cation binding is believed to occur primarily with negative Theta(zz) aromatics, and arene-anion binding is believed to occur largely with positive Theta(zz) aromatics. We have performed quantum mechanical computations that show the ...

This paper is devoted to show a couple of typicality results for weak solutions $v\in C^\theta$ the Euler equations, in case $\theta 0}W^{\frac{2\theta}{1-\theta} + \varepsilon,p}(I)$ any open $I \subset [0,T]$, are residual set $X_\theta$. This, particular, partially solves [9, Conjecture 1]. We also that smooth form nowhere dense space all $C^\theta$ solutions. The technique same and what rea...

The arithmetic complexity counts the number of algebraically independent entries in periodic continued fraction $\theta=[b_1,\dots, b_N, \overline{a_1,\dots,a_k}]$. If $\mathscr{A}_{\theta}$ is a noncommutative torus corresponding to rational elliptic curve $\mathscr{E}(K)$, then rank $\mathscr{E}(K)$ given by simple formula $r(\mathscr{E}(K))= c(\mathscr{A}_{\theta})-1$, where $c(\mathscr{A}_{...

The hippocampal theta signal reflects moment-to-moment variation in the synchrony of synaptic input to hippocampal neurons. Consistent with the topography of hippocampal afferents, the synchrony (coherence) of the theta signal varies across the septotemporal axis. Septotemporal variation in the theta signal can also be observed in relation to ongoing and past experience. Thus there is a systema...

is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg [13] for even n and by Pfetzer [9] for odd n. Shimura [14] generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta s...