Related papers: On Romanoff's theorem
We prove the Remling's Theorem on canonical systems and discuss the connection between Jacobi and Schr\"odinger equation and canonical systems.
We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.
We prove some vanishing conditions on the Gromov-Witten invariants of product of P1.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
We present a short and self-contained proof of the choosability version of Brooks' theorem.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
We describe recent advances in the study of random analogues of combinatorial theorems.
We discuss five ways of proving Chernoff's bound and show how they lead to different extensions of the basic bound.
We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.
We explore some integrals associated with the Riesz function and establish relations to other functions from number theory that have appeared in the literature. We also comment on properties of these functions.
In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).
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…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We establish the preservation of the way-below relation with respect to the tensor product.