Related papers: A short proof and a generalization of the BKR-ineq…
We present an alternative, short proof of a recent discrete version of the Brunn-Minkowski inequality due to Lehec and the second named author. Our proof also yields the four functions theorem of Ahlswede and Daykin as well as some new…
In this article we discuss a generalized Wirtinger inequality.
The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.
The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.
TThe paper had many errors.
The achievement of this paper is a confutation of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out after establishing properties of two related sequences. One of them is the product…
We present a direct proof of the cutoff Sobolev inequality on the Sierpi\'nski gasket, which has long been regarded as highly non-trivial in the context of heat kernel estimates.
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…
In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…
In this note a far extension of the Banach fixed point theorem is proved.
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt 2$,…
Certain new inequalities for the sums of factorials are presented.
There are some problems with this paper, and it is being withdrawn.
In this correspondence, we correct an erroneous result on the achievability part of the R\'enyi common information with order $1+s\in(1,2]$ in [1]. The new achievability result (upper bound) of the R\'enyi common information no longer…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
In this short note, we point out a mistake in G.Cybenko's proof of his version of the universal approximation theorem which has been widely cited. This mistake might not be easily fixable along the idea of his proof and it also leads to an…
In this short note, we improve the famous Reid Inequality related to linear operators.
By using the properties of the uniformly distributed sequences of real numbers on $(0,1)$, a short proof of a certain version of Kolmogorov strong law of large numbers is presented which essentially differs from Kolmogorov's original proof.
We obtain a global version and a twisted version (in the sense of \cite{bp05}) of the main theorem of \cite{bkr}.