Related papers: Remarks on Robin's and Niocolas Inequalities

In this paper, we prove that the conductor formula of Bloch implies the conjecture of Deligne on Milnor numbers of isolated singularities. In particular, thanks to the work of Bloch on his conjecture, our result implies that this so-called…

An algebraic deformation theory of coalgebra morphisms is constructed.

The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

We improve constants in the Rademacher-Menchov inequality.

Some extensions of an inequality from IMO'2001 are proven by means of the Lagrange multiplier criterion.

While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental…

We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than $1$. Our proof is…

We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.

The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

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

Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if $\sigma(n)<e^\gamma n\log\log n$ for all $n>5040$ where $\sigma(n)$ is the sum of divisors of $n$ and…

The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove \begin{eqnarray*}…

In a remarkably insightful pair of papers recently, Sica demonstrated that: dichotomic data taken in any experiment that violates Bell's inequalities ``cannot represent any data streams that could possibly exist or be imagined'' if it is to…

Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.

We translate the results of Yansong Xu into the language of~\cite{GGV1}, obtaining nearly the same formulas for the intersection number of Jacobian pairs, but with an inequality instead of an equality.

We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an…