Related papers: The solution of the Brannan conjecture

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We prove the Aharoni Berger Conjecture

In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the…

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.

This is a survey on Kawaguchi-Silverman conjecture.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…

We prove Serban's conjecture which simplifies greatly the expression of the advanced single-particle Green function in the Calogero-Sutherland model. The importance of proving this conjecture is that it reorganizes the form factor in terms…

In this work we study the convergence to equilibrium for a (potentially) degenerate nonlinear and nonlocal McKean-Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

The aim of this paper is to give a proof of improving of Zalcman's lemma.

The purpose of this study is to show how to get a necessary criterion for prime numbers with the help of special matrices. My special interest lies in the empirical research of these matrices and their patterns, structures and symmetries.…

In this paper we obtain a partial answer to a conjecture on the solvabilty of linear difference equations in quasianalytic Carleman classes.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…

We survey recent developments on the Restriction conjecture.

A very simple but useful almost sure convergence theorem of probability is given.