相关论文: A short proof and a generalization of the BKR-ineq…

We give an example to show that the main result of [1] is incorrect.

The main theorem is incorrectly stated.

A very short note, explaining the error in the original paper, which renders its central result incorrect.

A false application of Proposition 4.10 causes a mistake in the proof of Corollary 4.11

The Halting Problem is ill-conceived and ill-defined.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

Given events $A$ and $B$ on a product space $S=\prod_{i=1}^n S_i$, the set $A \Box B$ consists of all vectors ${\bf x}=(x_1,\ldots,x_n) \in S$ for which there exist disjoint coordinate subsets $K$ and $L$ of $\{1,\ldots,n\}$ such that given…

We prove two correlation inequalities .

A generalization of an inequality from IMO is proven.

A recent Comment by W. T. Kranz is shown to be plagued by a serious mathematical error which makes its conclusions invalid.

We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of B\"or\"oczky, Lutwak, Yang and Zhang.

This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).

Error in proof of theorem 10.

The BKR inequality conjectured by van den Berg and Kesten in [11], and proved by Reimer in [8], states that for $A$ and $B$ events on $S$, a finite product of finite sets $S_i,i=1,\ldots,n$, and $P$ any product measure on $S$, $$ P(A \Box…

In this work, we show that the proof of the main result in [An Application of Hayashi's Inequality for Differentiable Functions, Computers & Mathematics with Applications, 32 (6) (1996), 95--99, by R.P. Agarwal and S.S. Dragomir] was wrong.…

We give an alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables, is possible. This last…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.

We give a short proof of a slightly weaker version of the multilinear Kakeya inequality proven by Bennett, Carbery, and Tao.