Related papers: Some comments on 'Unique Bernoulli $g$-measures'
We improve and subsume the conditions of Johansson and \"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have…
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).
We show an invariance result for the L2-torsion of groups under uniform measure equivalence provided a measure-theoretic version of the determinant conjecture holds. The measure-theoretic determinant conjecture is discussed and, for…
In this paper we consider the generalized q-Bernoulli measures with weight alpha. From those measures, we derive some interesting properties on the generalized q-Bernoulli numbers with weight alpha attached to chi.
In this short note we capitalize on and complete our previous results on the regularity of the homogenized coefficients for Bernoulli perturbations by addressing the case of the Poisson point process, for which the crucial uniform local…
We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
During the course of verifying the results of Ramanujan on hypergeometric series, Berndt in his notebooks, Part II mentioned corrected forms of two of the Ramanujan's results. The aim of this short research note is to point out that one of…
Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and…
The modified Bernoulli numbers $B_{n}^{*}$ considered by Zagier are generalized to modified N\"orlund polynomials ${B_{n}^{(\ell)*}}$. For $\ell\in\mathbb{N}$, an explicit expression for the generating function for these polynomials is…
This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.
In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.
This note is based on the original proof of the shuffle conjecture by Carlsson and Mellit (arXiv:1508.06239, version 2), which seems to be too concise for the combinatorial community. James Haglund spent a semester to check through the…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
Withdrawn -- a revised version will appear in due course.
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are…