We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove that such discrete operators extend to bounded operators from `p to `q for a certain family of kernels. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of H...

Correlations of neuronal oscillations in different brain regions are closely related to a variety of brain functions. The delta and theta oscillations in the olfactory bulb (OB), coupled with respiration rhythm, could play important roles in olfactory tasks. The correlations between the two OBs, however, are largely unknown. By simultaneously recording local field potentials from the OBs, we fo...

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 ...

Cross-talk between the thalamus and cortex has been implicated in attention but its pathogenic role in attention-deficit/hyperactivity disorder (ADHD) remains unknown. Here, I demonstrate that Git1 (-/-) mice, previously proposed as an animal model for ADHD, show abnormal theta oscillation in the thalamus. Multi-electrode recordings revealed that Git1 (-/-) mice have hyper-synchrony of neural a...

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...

For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that convex hull of $n$ independent copies $X$ contains given point $\theta$. We provide several sharp inequalities regarding and $N_X(\theta)$ denoting smallest for which X}(\theta)\ge1/2$. As main result, we derive totally general inequality $1/2 \le \alpha_X(\theta)N_X(\theta)\le 3d + 1$, where $\alpha_X(\thet...