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...

Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimumspanning tree construction. We give closed form expressions for the average degree of theta graphs of a homogeneous Poisson point process over the plane. We then show that essentially the same bounds—with vanishing error terms—hold for theta gr...

In this article we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application we give a purely algebraic proof of some 2-adic theta identities which describe the set of theta null points...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

Let $D$ be the open disk $|x|< R$ of a complete ultrametric algebraically closed field $\mathbb K$. We define growth order $\rho(f)$, type $\sigma(f)$ cotype $\psi(f)$ and another expression $\theta(f)$ an analytic function in we show relations between number zeros $f$ ``maximum modulus'' involving $\rho,\sigma,\psi$. Then $\rho(f)$ lies $[\theta(f)-1, \theta(f)]$. Moreover, if $0< \rho(f)< +\i...

PURPOSE Working memory (WM) represents the brain's ability to maintain information in a readily available state for short periods of time. This study examines the resting-state cortical activity patterns that are most associated with performance on a difficult working-memory task. METHODS Magnetoencephalographic (MEG) band-passed (delta/theta (1-7 Hz), alpha (8-13 Hz), beta (14-30 Hz)) and se...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R$ perturbed by a quasi-periodic time potential $V(x,\omega t)$ under following conditions, namely there is $C>0$ such that \begin{equation*} |V(x,\theta)|\le C,\quad|x\partial_xV(x,\theta)|\le C,\quad\forall~(x,\theta)\in\mathbb R\times\mathbb T_\sigma^n. \end{equation*} The corresponding perturbation matrix $(P_i^j(\the...