相关论文: On Hadamard Conjecture

We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

The revised version of the claim by Hurley, Hurley and Hurley to have proved the circulant Hadamard matrix conjecture is mistaken.

Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce…

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

We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…

This paper presents our proof of the "strong Macdonald constant term conjecture" of P. Hanlon and B. Feigin.

In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.

We prove a logical implication between two old conjectures stated by Bapat and Sunder about the permanent of positive semidefinite matrices. Although Drury has recently disproved both conjectures, this logical implication yields a…

Although Hadamard matrices have been investigated since the nineteenth century, relatively little is known about their higher-dimensional analogues. In this paper, we introduce two constructions of Hadamard hypercubes. The first…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We survey the impact of Lieb's influential paper "Proofs of some conjectures on permanents" [J. Math. Mech. 16 1966, 127-134], which introduced the famous permanental dominance conjecture. This conjecture has defied all attacks for over…

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

In this paper we consider the remaining cases of Hebey-Vaugon conjecture.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

We review a combinatoric approach to the Hodge Conjecture for Fermat Varieties and announce new cases where the conjecture is true.

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.