Related papers: Another Proof of a Famous Inequality
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
We give a very short proof of the Golden-Thompson inequality
We improve the classical discrete Hardy inequality for $ 1<p<\infty $ for functions on the natural numbers. For integer values of $ p $ the Hardy weight is an absolutely monotonic function.
We provide a simplified proof of Zagier's conjecture / Mersmann's theorem which states that of any particular weight, there are only finitely many holomorphic eta quotients, none of which is an integral rescaling of another eta quotient or…
I prove an old unsolved conjecture, the hard part of its obvious sufficiency, namely that all identically conserved symmetric two-tensors are necessarily metric variations of invariant actions, thus sparing the world more alternative…
In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…
One way to interpret smoothness of a measure in infinite dimensions is quasi-invariance of the measure under a class of transformations. Usually such settings lack a reference measure such as the Lebesgue or Haar measure, and therefore we…
In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.
In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
In this paper, we establish new an inequality of weighted Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
We give a mathematical structure on an arithmetic surface, that has algebraic meanings over finite places and can estimate the canonical norm for a relative differential form on the arithmetic surface. This will give a lower bound for the…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
Following and generalizing unpublished work of Ange, we prove a generalized version of R\'emond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective…
In 2016 we proved that for every symmetric, repetition invariant and Jensen concave mean $\mathscr{M}$ the Kedlaya-type inequality $$ \mathscr{A}\big(x_1,\mathscr{M}(x_1,x_2),\ldots,\mathscr{M}(x_1,\ldots,x_n)\big)\le \mathscr{M} \big(x_1,…
We demonstrate that it is possible to calculate not only the mean of an underlying population but also its dispersion, given only a single observation and physically reasonable constraints (i.e., that the quantities under consideration are…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
Ratios of quantiles are often computed for income distributions as rough measures of inequality, and inference for such ratios have recently become available. The special case when the quantiles are symmetrically chosen; that is, when the…
In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-S\'andor means in terms of the arithmetic, harmonic, and contra-harmonic means…