The number of isolated intersections between a smooth curve in Eu-clidean space and an arbitrary hyperplane can be majorized by a weighted sum of integral Frenet curvatures of the curve. In the complex Hermitian space one can derive a similar result for holomorphic curves but with much better weights. The proof of this result is based on a generalizationof the Milnor{FF ary theorem for complex ...

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...

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...

The intermediate dimensions of a set $\Lambda$, elsewhere denoted by $\dim\_{\theta}\Lambda$, interpolate between its Hausdorff and box using the parameter $\theta\in\[0,1]$. For Bedford–McMullen carpet $\Lambda$ with distinct dimensions, we show that $\dim\_{\theta}\Lambda$ is strictly less than dimension for every $\theta<1$. Moreover, derivative upper bound positive at $\theta=1$. This answe...