相关论文: Proof of the circulant Hadamard conjecture

In this article, we give two different proofs of why the Collatz Conjecture is false.

In this article, we prove a class of normal dilation matrices affirming the Marcus-de Oliveira conjecture.

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions…

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

We discuss the analytic continuation of the Hadamard product of two holomorphic functions under assumptions pertaining to Ecalle's Resurgence Theory, proving that if both factors are endlessly continuable with prescribed sets of singular…

This paper has been withdrawn by the authors due to an error in Section 7.

In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials. Namely, we determine the Fourier transforms of the polynomials multiplied by the Gaussian,…

In this note we verify the equivalent version of Huppert's conjecture for $K_3$-groups.

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erd\H{o}s-Tur\'{a}n additive base conjecture.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.

This paper gives a slight refinement of a theorem of Hamilton, which shows that the velocity of a Keplerian motion moves on a circle.

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

New cases of the multiplicity conjecture are considered.

In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We prove a conjecture by Guo-Niu Han which interpolates between two known hook expansion formulas.

This paper gives another proof of the key lemma in my recent paper which solves the optimal paper Moebius band conjecture of Halpern and Weaver, namely Lemma T. The proof here is longer but it offers more geometric intuition about what is…

We provide an alternative proof that Crosscaps are diffeomorphically stable.