We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...

We examined the activity of single cells of the supramammillary nucleus (SUM), the mammillary body (MB), and adjacent regions of the diencephalon with respect to the hippocampal electroencephalogram (EEG) in urethane-anesthetized rats. Twenty-nine of 170 cells were found to discharge synchronously with the theta rhythm of the hippocampus (theta-related neurons). All of the 29 theta-related cell...

Evidence has accumulated suggesting that the median raphe (MR) mediates hippocampal theta desynchronization. However, few studies have evaluated theta-related neural circuitry during MR manipulation. In urethane-anesthetized rats, we investigated the effects of MR stimulation on hippocampal field and cell activity using high-frequency (100 Hz), theta burst (TBS), and slow-frequency electrical s...

— We study a class of polyhedral functions called cone theta functions, which are closely related to classical theta functions. Each polyhedral cone K ⊂ Rd has an associated cone theta function, and we show that they encode information about the rationality of the spherical volume of K. We show that if K is a Weyl chamber for any finite Weyl group, then its cone theta function lies in a graded ...

background and aims: the aim of this study was to investigate the relationship between brain waves and beck depression inventory(bdi) score in clinical cases with depression. methods: in this study, eeg was taken using neurofeedback device at the point f4 of dorsolateral prefrontal cortex (dlpfc) of the brain of 60 depressed patients referred to psychiatric clinic. at the same time, beck depres...

The medial septum (MS) plays an essential role in rhythmogenesis in the hippocampus (HIPP); theta-rhythmic bursts of MS neurons are believed to drive theta oscillations in rats' HIPP. The MS theta pacemaker hypothesis has solid foundation but the MS-hippocampal interactions during different behavioral states are poorly understood. The MS and the HIPP have reciprocal connections and it is not cl...

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...

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...