‎We define hyperbolic harmonic $omega$-$alpha$-Bloch space‎ ‎$mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}‎},$$ where $0leq gammaleq 1$‎. ‎Similar results are extended to‎ ‎little $omega$-$alpha$-Bloch and Besov spaces‎. ‎These obtained‎...

Recently, increased attention has been given to the coupling of computational fluid dynamics (CFD) with fuzzy logic control system for obtaining optimum prediction many complex engineering problems. The data provided can be obtained from accurate such Windcatcher performance achieve thermal comfort conditions in buildings, especially hot climate regions, is considered as one problem. Windcatche...

In the present work, chemotaxis-Naiver-Stokes system with rapidly decaying diffusivities \begin{document}$ \begin{eqnarray*} { \bf{(KSNS)} }\ \ \left\{ \begin{array}{llll} n_{t}+u\cdot\nabla n = \nabla\cdot(D(n)\nabla n)-\nabla\cdot(S(n)\nabla c), &&x\in\Omega, \, t>0, \\ c_{t}+u\cdot\nabla c \Delta - c+ n, u_{t}+\kappa(u\cdot\nabla)u u +\nabla P+ n\nabla\Phi, \nabla\cdot 0, t>0\ ...

The thermo-hydraulic behavior of the air flow over a two dimensional ribbed channel wasnumerically investigated in various rib-width ratio configurations (B/H=0.5-1.75) atdifferent Reynolds numbers, ranging from 6000 to 18000. The capability of differentturbulence models, including standard k-ε, RNG k-ε, standard k-ω, and SST k-ω, inpredicting the heat transfer rate was compared with the experi...

Bladeless fans are more energy efficient, safer due to the hidden blades, easier clean, and adjustable than conventional fans. This paper investigates influence of airfoil’s outlet slit thickness on discharge ratio by varying an Eppler 473 airfoil from 1.2 mm 2 in intervals 0.2 using a k-omega SST turbulence model with all y+ wall treatment used numerically simulate CFD. The computational resul...

We prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in planar domain \(\Omega\), \[f_\overline{z} = \mathcal{A}(f_z)\ a.e.\ z\in\Omega,\] when \(\mathcal{A}\) is linear at \(\infty\). Namely \(W^{1,1}_{\operatorname{loc}}(\Omega)\) are \(W^{2,2+\epsilon}_{\operatorname{loc}}(\Omega)\). Here \(\epsilon>0\) depends explicitly on ellipticity...

We define and study a spatial (infinite-dimensional) counterpart of Stirling numbers. In classical combinatorics, the Pochhammer symbol $(m)_n$ can be extended from natural number $m\in\mathbb N$ to falling factorials $(z)_n=z(z-1)\dotsm (z-n+1)$ an argument $z$ $\mathbb F=\mathbb R\text{ or }\mathbb C$, numbers first second kinds are coefficients expansions $(z)_n$ through $z^k$, $k\leq n$ vic...

We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spec...

In this work, we consider the nonlocal obstacle problem with a given $\psi$ in bounded Lipschitz domain $\Omega$ $\mathbb{R}^{d}$, such that $\mathbb{K}\_\psi^s={v\in H^s\_0(\Omega):v\geq\psi \text{ a.e. }\Omega}\neq\emptyset$, by $$ u\in\mathbb{K}\_\psi^s:\quad\langle\mathcal{L}au,v-u\rangle\geq\langle F,v-u\rangle\quad\forall v\in\mathbb{K}^s\psi, for $F$ $H^{-s}(\Omega)$, dual space of fract...