Related papers: On Ryser's Conjecture

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…

This paper proves a conjecture proposed by Ren and Li (2015: 393, \emph{Journal of Inequalities and Applications}). Our result eliminates the constraints on the parity and size of $m$, as well as the restriction $x > 1$, required in Ren and…

In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…

We prove an improved form of an expectation of Polya and discuss several related questions

We present two new conditions to extend the Ricci flow on a compact manifold over a finite time, which are improvements of some known extension theorems.

We prove a conjecture due to Y. Last on Jacobi matrices.

Several results about the union-closed sets conjecture are presented.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We give a more strong heuristic justification of our conjecture on the excess of the odious primes.

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

The paper presents the generalized persistency of excitation conditions. They are not only valid for much broader range of applications than their classical counterparts but also elegantly prove the validity of the latter. The novelty and…

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.

Necessary and sufficient conditions are given for the existence of extended Schmidt decompositions, with more than two subspaces.

We propose a new refinement of the McKay conjecture and we prove it for symmetric groups.

We establish several sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor in this paper. The first presented sufficient condition is an extension of positive definite matrices, which states that the strong…

In this article we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method…

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.