Related papers: A short proof and a generalization of the BKR-ineq…
We present an elementary proof of a conjecture by I. Ra\c{s}a which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive very recently by the use of stochastic convex orderings. Moreover,…
We give a sketch for an alternative proof of a recent result by J. Tseng.
In this article, the author provides full details of the proof of the concordance/isotopy problem. The first published proof, [5], accomplished this task only partially since there was an error, see the erratum [6], which damaged the main…
The generalized version of the Arthurs-Kelly inequality is derived when the initial state is a tripartite separable state. When each initial substate obeys the minimal uncertainty, the generalized version reduces to the well-known…
In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.
This paper has been withdrawn by the author due to a crucial sign error in equation 1.
We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces, and then provide a unified extension of the recent…
We give an alternative proof of a formula that generalizes Hermite's identity. Instead involving modular arithmetic, our short proof relies on the Fourier-type expansion for the floor function and on a trigonometric formula.
In this short paper, we shall provide a dynamical systems' proof of the famous Kraft-McMillan inequality and its converse. Kraft-McMillan inequality is a basic result in information theory which gives a necessary and sufficient condition…
Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…
General relativity's successes and limitations are compared to those of special relativity.
(some errors corrected, slightly extended)
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
A short and direct proof of the Gibbard-Satterthwaite theorem \`{a} la Amartya Sen's proof of Arrow's impossibility theorem is given.
The paper is withdrawn. The proof has an error and it requires a different approach.
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
A simple proof of the weighted two variable geometric-arithmetic a mean inequality based on one given earlier valid only for integer weights
The paper comments on "Quantifying long-term scientific impact". It indicates that there is a mistake of [D. S. Wang , C. Song, A. L. Barabasi, Quantifying long-term scientific impact, Science 342, 127 (2013), arXiv:1306.3293].
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
In this survey we consider generalizations for Young and Cauchy--Bunyakowsky inequalities with applications.