Related papers: One example about the relationship between the CD …
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…
We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero.…
In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.
We provide an overview of the connections between Bell's inequalities and algebraic structure.
In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
In this paper, we propose a generalization of a congruence due to Carlitz.
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…
We extend Freiman's inequality on the cardinality of the sumset of a $d$ dimensional set. We consider different sets related by an inclusion of their convex hull, and one of them added possibly several times.
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…
The relations between Bell's inequality and quantum probability trees are explained against the background offered by the concept of a quantum probability tree built in others works. It is shown that f we use a concept of probability tree…
Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
Some extensions of an inequality from IMO'2001 are proven by means of the Lagrange multiplier criterion.
Recently, in a number of papers it was understood that results on sampling discretization and on the universal sampling discretization can be successfully used in the problem of sampling recovery. Moreover, it turns out that it is…