In this paper we state the following weighted Hardy type inequality for any functions $ \varphi in a Sobolev space and weight \mu of quite general \begin{document}$ \begin{align*} c_{N, \mu} \int_{ \mathbb{R}^N}V\, \varphi^2\mu(x)dx\le \mathbb{R}^N}|\nabla \varphi|^2\mu(x)dx +C_\mu \mathbb{R}^N}W \varphi^2\mu(x)dx, \end{align*} $\end{document} where V is multipolar potential W bounded function ...

Abstract Given a hereditary property of graphs $\mathcal{H}$ and $p\in [0,1]$ , the edit distance function $\textrm{ed}_{\mathcal{H}}(p)$ is asymptotically maximum proportion edge additions plus deletions applied to graph density p sufficient ensure that resulting satisfies . The directly related other well-studied quantities such as speed for -chromatic number random graph. Let be forbidding a...

let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

In this article, by using Moser's twist theorem, we prove that all solutions of the equation $x'' + ax^{+} - bx^{-} \varphi(x) = p(t)$ are bounded in critical situation, where $p$ is a smooth periodic function, and $\varphi$ one.

‎the purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex banach space which has a‎ ‎uniformly g^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

A way to measure the lower growth rate of φ : Ω × [ 0 , ∞ ) → $$ \varphi :\Omega \times \left[0,\infty \right)\to \right) is require t ↦ ( x − r t\mapsto \left(x,t\right){t}^{-r} be increasing in \left(0,\infty . If this condition holds with = 1 r=1 then inf u ∈ f + W ∫ | ∇ d \underset{u\in f+{W}_0^{1,\varphi}\left(\Omega \right)}{\operatorname{inf}}{\int}_{\Omega}\varphi \left(x,|\nabla u|\rig...

We elucidate the structural transitions in a helical off-lattice homopolymer induced by crowding agents, as a function of the number of monomers (N) and volume fraction (varphi c) of crowding particles. At varphic=0, the homopolymer undergoes transitions from a random coil to a helix, helical hairpin HH, and helix bundle HB structures depending on N, and temperature. Crowding induces chain comp...

The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates Lp([0, T ]) and uniform approximations of φ-sub-Gaussian random processes by finite time sampling sums. Explicit truncation error upper bounds are established. Some specifications of the general results for wh...

We consider a complete Riemannian manifold, which consists of compact interior and one or more $\varphi$-cusps: infinitely long ends type that includes cylindrical hyperbolic cusps. Here $\varphi$ is function the radial coordinate describes shape such an end. Given action by Lie group on we obtain equivariant index theorem for Dirac operators, under conditions $\varphi$. These hold in cases In ...

In this paper we consider the (ray) representations of group $\mathrm{Aut}$ biholomorphisms Siegel upper half-space $\mathcal U$ defined by $U_s(\varphi) f=(f\circ \varphi^{-1}) (J \varphi^{-1})^{s/2}$, $s\in\mathbb R$, and characterize semi-Hilbert spaces $H$ holomorphic functions on satisfying following assumptions: (a) is strongly decent; (b) $U_s$ induces a bounded ray representation $\math...