Related papers: Difference and $(\Delta)$ properties for some new …

We give a new proof of the Gromov theorem: For any $C>0$ and integer $n>1$ there exists a function $\Delta_{C,n}$ such that if the Gromov--Hausdorff distance between complete Riemannian $n$-manifolds $V$ and $W$ is not greater than…

In the present paper the new multiplier transformations $\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l)$ $(\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )}$ of multivalent functions is defined. Making use…

We use the rationality of the generalized $h^{th}$ convergent functions, $Conv_h(\alpha, R; z)$, to the infinite J-fraction expansions enumerating the generalized factorial product sequences, $p_n(\alpha, R) =…

We present an extension of the classical De Giorgi class, and then we show that functions in this new class are locally bounded and locally H\"older continuous. Some applications are given. As a first application, we give a regularity…

We prove that the Hausdorff dimension of the set of points where a function in the Zygmund class in the euclidean space has bounded divided differences, is bigger or equal to 1. A similar result for functions in the Small Zygmund class is…

We show that for any constant $\epsilon > 0$ and $p \ge 1$, it is possible to distinguish functions $f : \{0,1\}^n \to [0,1]$ that are submodular from those that are $\epsilon$-far from every submodular function in $\ell_p$ distance with a…

In a scenario in which fourth generation fermions exist, we study effects of new physics on the differential decay width, forward-backward asymmetry $A_{\text{FB}}$ and integrated branching ratio for $B\to X_s \ell^+ \ell^-$ decay with…

We study the higher fractional differentiability properties of the gradient of the solutions to variational obstacle problems of the form \begin{gather*} \min \biggl\{ \int_{\Omega} F(x,w,Dw) d x \ : \ w \in \mathcal{K}_{\psi}(\Omega)…

We show that under minimal assumptions on a class of functions $\mathcal{H}$ defined on a probability space $(\mathcal{X},\mu)$, there is a threshold $\Delta_0$ satisfying the following: for every $\Delta\geq\Delta_0$, with probability at…

We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term…

We consider a one-parameter family of functions $\{F(t,x)\}_{t}$ on $[0,1]$ and partial derivatives $\partial_{t}^{k} F(t, x)$ with respect to the parameter $t$. Each function of the class is defined by a certain pair of two square matrices…

Let $f$ be a nonnegative function of class $C^k$ ($k \geq 2$) such that $f^{(k)}$ is H\''older continuous with exponent $\alpha$ in $(0,1]$. If $f'(x) = \cdots = f^{(k)}(x) = 0$ when $f(x) = 0$, we show that $f^{\mu}$ is differentiable for…

\begin{document} \begin This paper continues work of the earlier articles with the same title. For two classes of modular forms $f$: \begin{itemize} \item para-Eisenstein series $\alpha_{k}$ and \item coefficient forms ${}_a \ell_{k}$,…

We explore the shifted $f(R) (\propto R^{1+\delta})$ model with ${\delta}$ as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and…

Sapirovskii [18] proved that $|X|\leq\pi\chi(X)^{c(X)\psi(X)}$, for a regular space $X$. We introduce the $\theta$-pseudocharacter of a Urysohn space $X$, denoted by $\psi_\theta (X)$, and prove that the previous inequality holds for…

In this paper we give a streamlined proof of an inequality recently obtained by the author: For every $\alpha \in (0,1)$ there exists a constant $C=C(\alpha,d)>0$ such that \begin{align*} \|u\|_{L^{d/(d-\alpha),1}(\mathbb{R}^d)} \leq C \|…

Let $\Omega^o$ and $\Omega^i$ be open bounded subsets of $\mathbb{R}^n$ of class $C^{1,\alpha}$ such that the closure of $\Omega^i$ is contained in $\Omega^o$. Let $f^o$ be a function in $C^{1,\alpha}(\partial\Omega^o)$ and let $F$ and $G$…

Let $\mathscr{M}$ be a finite von Neumann algebra with a faithful normal tracial state $\tau$ and $\mathfrak{A}$ be a finite subdiagonal subalgebra of $\mathscr{M}$ with respect to a $\tau$-preserving faithful normal conditional expectation…

We establish the dynamical attractor behavior in scalar-tensor theories of dark energy, providing a powerful framework to analyze classes of theories, predicting common evolutionary characteristics that can be compared against cosmological…

Here is a sample of the results proved in this paper: Let $f:{\bf R}\to {\bf R}$ be a continuous function, let $\rho>0$ and let $\omega:[0,\rho[\to [0,+\infty[$ be a continuous increasing function such that $\lim_{\xi\to…