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Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.

We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.

Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…

In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.

Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

I review some of the main results on hard diffraction, in their relation to QCD, and indicate some of the strengths and weaknesses of the arguments. I also make some suggestions for future work.

Cheeger inequality is a classical result emerging from the isoperimetric problem in the field of geometry. In the graph theory, a discrete version of Cheeger inequality was also studied deeply and the notion was further extended for higher…

This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…

We survey and compare, mainly in the two-dimensional case, various results obtained by IST and PDE techniques for integrable equations. We also comment on what can be predicted from integrable equations on non integrable ones.

We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…

We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.

Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.

We describe some relations between the properties of the Cauchy problem for an ODE and the properties of the Cauchy problem for the associated continuity equation in the class of measures.

The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all…

A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I…