相关论文: A Short Proof of the Poincar\'e Conjecture
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
We prove the Aharoni Berger Conjecture
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.
We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.
In this article, we obtain a recursive description of the Horn cone Horn(p,q) with respect to the integers p and q, as in the classical Horn's conjecture.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…
This is the announcement of an alternative approach to the 3-dimensional Poincar\'e Conjecture, different from Perelman's big and spectacular breakthrough. No claim concerning the other parts of the Thurston Geometrization Conjecture, come…
We prove a conjecture due to Y. Last on Jacobi matrices.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…