相关论文: Proof of the circulant Hadamard conjecture
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
We present a proof of Hadamard Inverse Function Theorem by the methods of Variational Analysis, adapting an idea of I. Ekeland and E. Sere.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We study the existence and construction of circulant matrices $C$ of order $n\geq2$ with diagonal entries $d\geq0$, off-diagonal entries $\pm1$ and mutually orthogonal rows. These matrices generalize circulant conference ($d=0$) and…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
Assume that $H$ is a circulant Hadamard matrix of order $n\geq 4$. We consider an appropriate stochastic matrix $S$ of order $n$ depending on $H$. This allows us to prove that $n = 4$. Thus, there are only $10$ circulant Hadamard matrices.
In this paper, we proved a special case of the DDVV Conjecture.
In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
We settle in the affirmative the Graham-Sloane conjecture.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576
A vector variational principle is proved.
In this paper, we give a simple counter example to the famous Hodge conjecture.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
In this paper, the abc conjecture is negated under certain conditions
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We provide a proof of the Borwein Conjecture using analytic methods.
We prove that there is no circulant Hadamard matrix $H$ with first row $[h_{1},\ldots,h_{n}]$ of order $n>4$, under a condition about a sum of scalar products of rows of two other circulant matrices of size $n/2$ associated to $H.$
We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.