Related papers: A problem of Polya
We provide a new proof of Vivinai's Theorem using what George Polya calls a 'leading particular case.' Our proof highlights the role of generalization in mathematics.
In this paper we obtain a new constant in the P\'{o}lya-Vinogradov inequality. Our argument follows previously established techniques which use the Fourier expansion of an interval to reduce to Gauss sums. Our improvement comes from…
Theory of $n$-complements with applications is presented.
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
Several open problems in algebraic logic are solved.
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
In this short note we prove a result that is an extension of an old Olympiad problem and is a very simple variant of the question of finding an approximation for $k$, where it is a nonzero constant and it satisfies the equation $a^k+b^k=c$,…
To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…
We report on numerical experiments suggesting that rank-one convexity imples quasiconvexity in the planar case. We give a simple heuristic explanation of our findings.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
The paper presents a counterexample to the Hodge conjecture.
Minor technical changes. Section 4 improved.
In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and…
In [arXiv:1906.10951 (forthcoming on Advances in Applied Probability),arXiv:2011.05933 (published on PLOS ONE)] the authors introduce, study and apply a new variant of the Eggenberger-Polya urn, called the "Rescaled" Polya urn, which, for a…
Remarks on mathematical proof and the practice of mathematics.
We give a new proof of Lucas' Theorem in elementary number theory.
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.
We proove a Bloch's theorem in an almost complex projective plane.
We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.
We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.