Related papers: Orderings on measures induced by higher-order mono…

We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we…

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…

We study the problem of the existence of increasing and continuous solutions $\varphi\colon[0,1]\to[0,1]$ such that $\varphi(0)=0$ and $\varphi(1)=1$ of the functional equation \begin{equation*}…

We show that there is a measure $\mu$, defined on the hyperbolic plane and with polynomial growth, such that the centered maximal operator associated to $\mu$ does not satisfy weak type $(1,1)$ bounds.

We establish new recurrence and multiple recurrence results for a rather large family $\mathcal{F}$ of non-polynomial functions which includes tempered functions defined in [11], as well as functions from a Hardy field with the property…

We observe a stochastic process $Y$ on $[0,1]^d$ ($d\geq 1$) satisfying $dY(t)=n^{1/2}f(t)dt$ + $dW(t)$, $t \in [0,1]^d$, where $n \geq 1$ is a given scale parameter (`sample size'), $W$ is the standard Brownian sheet on $[0,1]^d$ and $f…

In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity…

Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576--1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017--1054]. The general upper bound for the threshold width of…

This article investigates the role of the regularity of the test function when considering the weak error for standard discretizations of SPDEs of the form $dX(t)=AX(t)dt+F(X(t))dt+dW(t)$, driven by space-time white noise. In previous…

We write expressions connected with numerical differentiation formulas of order $2$ in the form of Stieltjes integral, then we use Ohlin lemma and Levin-Stechkin theorem to study inequalities connected with these expressions. In particular,…

The theory of uniform approximation of real numbers motivates the study of products of consecutive partial quotients in regular continued fractions. For any non-decreasing positive function $\varphi:\mathbb{N}\to [2,\infty)$, we determine…

The equality problem of the two-variable Bajraktarevi\'c means can be expressed as the functional equation $$ \left(\frac{f}{g}\right)^{-1}\bigg(\frac{f(x)+f(y)}{g(x)+g(y)}\bigg)…

We introduce completely monotonic functions of order $r>0$ and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any…

In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…

The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…

A random variable $Y_1$ is said to be smaller than $Y_2$ in the increasing concave stochastic order if $\mathbb{E}[\phi(Y_1)] \leq \mathbb{E}[\phi(Y_2)]$ for all increasing concave functions $\phi$ for which the expected values exist, and…

In arithmetic statistics and analytic number theory, the asymptotic growth rate of counting functions giving the number of objects with order below $X$ is studied as $X\to \infty$. We define general counting functions which count…

We introduce the notion of a weighted lift zonoid and show that, for properly chosen weights v, the ordering condition on a measure \mu, formulated in terms of the weighted lift zonoids of this measure, leads to certain functional…

In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on $(0,\infty)$. As applications of the necessary and…

Let $V\in C^2(\R^d)$ such that $\mu_V(\d x):= \e^{-V(x)}\,\d x$ is a probability measure, and let $\aa\in (0,2)$. Explicit criteria are presented for the $\aa$-stable-like Dirichlet form $$\E_{\aa,V}(f,f):= \int_{\R^d\times\R^d}…