Related papers: Sur le minimum de la fonction de Brjuno
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
Recently, Ivan Mihajlin and Alexander Smal proved a composition theorem of a universal relation and some function via so called xor composition, that is there exists some function $f:\{0,1\}^n \rightarrow \{0,1\}$ such that…
Minimal representations of a real reductive group G are the `smallest' irreducible unitary representations of G. We discuss special functions that arise in the analysis of L^2-model of minimal representations.
The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for the sign change counting function is given where classical…
In a previous paper, the author proved the existence of extremal function for the Moser-Trudinger inequality on a compact manifold. In the this paper, we will give a new proof of one of the key proposition.
Let $(\Sigma_A, \sigma)$ be a subshift of finite type and let $M(x)$ be a continuous function on $\Sigma_A$ taking values in the set of non-negative matrices. We extend the classical scalar pressure function to this new setting and prove…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
Finding the minimum and the minimizers of convex functions has been of primary concern in convex analysis since its conception. It is well-known that if a convex function has a minimum, then that minimum is global. The minimizers, however,…
"The Baron's omni-sequence", B(n), first defined by Khovanova and Lewis (2011), is a sequence that gives for each n the minimum number of weighings on balance scales that can verify the correct labeling of n identically-looking coins with…
Very recently, the CDF Collaboration reported the first non-zero measurement of the $B_s \rightarrow \mu^+ \mu^-$ branching fraction. The central value of this measurement is more than 5 times of that predicted in the Standard Model and, if…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
We prove a generalization of the fact that periodic functions converge weakly to the mean value as the oscillation increases. Some convergence questions connected to locally periodic nonlinear boundary value problems are also considered.
Functions of bounded deformation ($BD$) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation ($BV$), but are less well understood. We discuss here the…
We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…
We present an effective formula for the Sibony function for all Reinhardt domains.
This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse…
Given a multiplicative function f satisfying |f(n)| <= 1 for all n, the authors study the problem of obtaining explicit upper bounds on the mean-value 1/x |sum_{n <= x} f(n)|.
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We describe the morphology of the universal function for the critical (cubic) circle map at the golden mean, paying particular attention to the birth of inflection points and their reproduction. In this way one can fully understand its…