Related papers: On the error-sum function of Pierce expansions
Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we…
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…
We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…
We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…
We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Dawson's integral and related functions in mathematical physics that include the complex error function (Faddeeva's integral), Fried-Conte (plasma dispersion) function, (Jackson) function, Fresnel function and Gordeyev's integral are…
Let A be a subset of the real line. We study the fractal dimensions of the k-fold iterated sumsets kA, defined as kA = A+...+A (k times). We show that for any non-decreasing sequence {a_k} taking values in [0,1], there exists a compact set…
As a generalization of the sum of digits function and other digital sequences, sequences defined as the sum of the output of a transducer are asymptotically analyzed. The input of the transducer is a random integer in $[0, N)$. Analogues in…
We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the Output Function Evaluation…
This talk reviews the recent progress in the extraction of bound-state characteristics from the operator-product expansion (OPE) for field-theory correlators, which constitutes the basis of the method of QCD sum rules. This progress is…
We consider the characteristic function of linear spectral statistics of generalized Wigner matrices. We provide an expansion of the characteristic function with error $\mathcal{O} ( N^{-1})$ around its limiting Gaussian form, and identify…
In this article we establish error bound for linear complementarity problem with $P$-matrix using plus function. We introduce a fundamental quantity associated with a $P$-matrix and show how this quantity is useful in deriving error bounds…
We compute the Hausdorff, upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction…
This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…
The first three coefficients of the Taylor's series expansion of the vector pion form factor as a function of the momentum transfer are evaluated using experimental data on the pion form factor and the P-wave pi pi phase shifts. The real…
An ill-posed problem of synthesis of the Pierce electrodes for a cylindrical beam with a polygonal cross-section is considered. It is assumed that a beam of charged particles is extracted from a space-charge-limited planar diode and the…
We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We establish a formula, utilizing transfer operators arising from…
We establish several optimal estimates for exceptional parameters in the projection of fractal measures: (1) For a parametric family of self-similar measures satisfying a transversality condition, the set of parameters leading to a…