相关论文: On Hadamard Conjecture
In this paper, one new classes of convex functions which is called MT-convex functions are given. We also establish some Hadamard-type inequalities.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.
In [7], Higashitani, Kummer, and Micha{\l}ek pose a conjecture about the symmetric edge polytopes of complete multipartite graphs and confirm it for a number of families in the bipartite case. We confirm that conjecture for a number of new…
A review is presented of the origin and development of the atomic hypothesis from antiquity till about the first millennium of the common era.
In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
In this paper, the recently introduced M&m sequences and associated mean-median map are studied. These sequences are built by adding new points to a set of real numbers by balancing the mean of the new set with the median of the original.…
The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize…
The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that most combinatorialists, and many other mathematicians and scientists, use at least once a day, is a treasure trove of mathematical information, and, one of its…
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
A formula concerning counting of paths was conjectured by Herzog and Conca few years ago. Recently, Krattenthaler and Prohaska gave an affirmative answer to this conjecture. In this paper we generalize this formula.
In 1998, Lin presented a conjecture on a class of ternary sequences with ideal 2-level autocorrelation in his Ph.D thesis. Those sequences have a very simple structure, i.e., their trace representation has two trace monomial terms. In this…
A determinant evaluation is proven, a special case of which establishes a conjecture of Bombieri, Hunt, and van der Poorten (Experimental Math\. {\bf 4} (1995), 87--96) that arose in the study of Thue's method of approximating algebraic…
The Collatz conjecture is a famous math problem that was introduced by Lothar Collatz in 1937, and nobody has yet succeeded in proving or disproving it. In this article, I will analyze this problem with a new approach and I will discuss my…
We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28 (1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in {\em Generic…
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
There is the classical Radon theorem. Given integer $d \geq 1$ and $d+2$ points in d-dimensional space $R^d$. Then these points can be divided into two disjoint subsets whose convex hulls have a non-empty intersection. The original proof of…
The purpose of this note is to advertise an elegant algorithmic proof for the Jordan--Chevalley decomposition of a matrix, following and (slightly) revising the discussion of Couty, Esterle und Zarouf (2011). The basic idea of that method…
In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.