Related papers: A problem of Polya
We obtain some results related to Romanoff's theorem.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
A variation on the splitting principle
In this paper we present a new formulation of the Beurling-Malliavin density (Proposition 1). Then we consider the upper Polya density and show how its existence is connected with the concept of subadditivity; moreover, by means of some…
We improve constants in the Rademacher-Menchov inequality.
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
We give complete details on an alternative formulation of the Polya-Szego principle that was mentioned in Remark 1 of our paper "Isoperimetry and Symmetrization for Logarithmic Sobolev inequalities". We also provide an alternative proof to…
We prove several extensions of the Erdos-Fuchs theorem.
Polya Enumeration Theorem is one of the most useful tools dealing with the enumeration of patterns that are symmetric in some ways. What follows is a procedure for obtaining the results of Polya Theorem directly, bypassing the usual…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We give a new simpler proof of a theorem of Jayne and Rogers.
In this paper we prove the WALA conjecture.
We consider positivity conditions both for real-valued functions of several complex variables and for Hermitian forms. We prove a stabilization theorem relating these two notions, and give some applications to proper mappings between balls…
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
We provide new sufficient conditions under which Ryser's conjecture holds.
We present a new, short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates, can…
We improve the previuosly known bound for some vertex Folkman numbers.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this note we give some remarks and improvements on a recent paper of us [3] about an optimization problem for the $p-$Laplace operator that were motivated by some discussion the authors had with Prof. Cianchi.
We give a counterexample to a recently conjectured variant of the Penrose inequality.