A module $$M$$ is said to be distributive (resp., uniserial) if the submodule lattice of a chain) Any uniserial but ring integers non-uniserial as $$\mathbb{Z}$$ -module. Direct sums (resp. modules are called semidistributive serial) modules. If $$A$$ with automorphism $$\varphi$$ , then we denote by $$A((x,\varphi))$$ skew Laurent series coefficient in which addition naturally defined and mult...

We prove that under some mild conditions on the symbol $$\varphi ,$$ spectrum of corresponding composition operator $$C_\varphi $$ Korenblum type spaces $$A_{-}^{-\alpha }$$ and $$A_{+}^{-\alpha contains a closed ball positive radius.

This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by geometric fractional Brownian path $\boldsymbol{\omega}$ with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$. We first construct approximation $\boldsymbol{\omega}_{\delta}$ probabilistic arguments, then using theory obtain solution on any finite interval. Finally, bot...

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...

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...