The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq systems helps gain insight into certain weather phenomena. 2D system focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain ...

Let $A_\Phi$ be a matrix valued truncated Toeplitz operator -- the compression of multiplication to vector model space $H^2(E)\ominus \Theta H^2(E)$, where $\Theta$ is non constant inner function. Under supplementary assumptions, we find necessary and sufficient condition that product $A_\Phi A_\Psi$ itself operator.

Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations separately synchronize with task-relevant sensory...

The combined effect of mean and thermal particle motion on Doppler line shape is evaluated. Optical radiation transverse to the axis of a source flow with semi-angle theta(e) is considered in the limit theta(2)(e) <<1. Expressions for gain and anomalous index of refraction are deduced in terms of radiation frequency and a parameter X(e) which characterizes the ratio of mean to thermal motion in...

Impulsivity is a personality trait within the normal population, but also a feature of many psychiatric disorders that have been associated with poor inhibitory control. The aim of the present study was to examine the relation between subjective impulsivity, theta/beta EEG ratio, and inhibitory control in healthy individuals. In 15 high and 14 low impulsive healthy volunteers (as assessed by th...

This study investigated behavioral, anatomical and electrophysiological effects produced by electrical stimulation of posterior hypothalamic (PH) or median raphe (MR) nuclei, independently and during combined stimulation of both PH and MR. These three stimulation conditions were applied during spontaneous behavior in an open field and during PH stimulation-induced wheel running, while simultane...

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the multiplicative periods. This paper shows that for a certain subclass of period lattices (compatible with the quantization form), quantum thetas satisfy an analog of ano...

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 1. Notation and terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 2. Modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 3. Discrim...

Motivated by the discovery that the eighth root of the theta series of the E 8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ Z[[x]]

Tke theta function of a sphere packing gives the number of centers at each distance from the origin. The theta functions of a number of important packings (An, D, , E,, the Leech lattice, and others) and tables of the first fifty or so of their coefficients are given in this paper.