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

This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.

(Withdrawn: This paper turns out incomplete and even misleading. I must apologize to all of the recipients.)

In this paper, we prove a trace inequality $\text{Tr}[ f(A) A^s B^s ] \leq \text{Tr}[ f(A) (A^{1/2} B A^{1/2} )^s ]$ for any positive and monotone increasing function $f$, $s\in[0,1]$, and positive semi-definite matrices $A$ and $B$. On the…

We prove an inequality for the Kostka-Foulkes polynomials $K_{\lambda ,\mu}(q)$. As a corollary, we obtain a nontrivial lower bound for the Kostka numbers and a new proof of the Berenstein-Zelevinsky weight-multiplicity-one-criterium.

Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

It is shown that the real part of the complementary error function is bounded below by 1 in the subset of the complex plane where the principal argument is between $3\pi/4$ and $5\pi/4$. This improves a previous result asserting that the…

In the paper it is demonstrated that Bells theorem is an unprovable theorem.

We provide an alternating proof of sharp inequalities related with Burnside's formula for $n!$

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

An error in Section 4 invalidates all the main results of the paper.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

There is a serious flaw in the proposal [arXiv:1603.06857] for the achievement of unity efficiency in SPDC. This is a replacement due to mistakes in the table of probabilities. Numbers have been corrected.

This paper has been withdrawn due to an error in the proof of the main theorem.

Withdrawn due to critical error.

A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.

In this paper, we generalize several Berezin number inequalities involving product of operators. For instance, we show that if $A, B$ are positive operators and $X$ is any operator, then \begin{align*}…

The BK inequality (\cite{BK85}) says that,for product measures on $\{0,1\}^n$, the probability that two increasing events $A$ and $B$ `occur disjointly' is at most the product of the two individual probabilities. The conjecture in…