相关论文: Non-sharpness of the Morton-Franks-Williams inequa…

We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.

We study invariant Seifert surfaces for strongly invertible knots, and prove that the gap between the equivariant genus (the minimum of the genera of invariant Seifert surfaces) of a strongly invertible knot and the (usual) genus of the…

A knot in a thickened surface $K$ is a smooth embedding $K:S^1 \rightarrow \Sigma \times [0,1]$, where $\Sigma$ is a closed, connected, orientable surface. There is a bijective correspondence between knots in $S^2 \times [0,1]$ and knots in…

We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…

We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.

The sharp constants in the classical John--Nirenberg inequality are found by using Bellman function approach.

The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range $1<p\leq q<\infty.$ We also calculate the precise value of…

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 generalize the Novikov inequalities for 1-forms in two different directions: first, we allow non-isolated critical points (assuming that they are non-degenerate in the sense of R.Bott), and, secondly, we strengthen the inequalities by…

We describe a procedure for creating infinite families of knots, each having the maximum degree of their HOMFLY polynomial strictly less than twice their canonical genus. These families build upon examples first found by Stoimenow.

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

Sharp error estimates in terms of the fractional Laplacian and a weighted Besov norm are obtained for Pitt's inequality by using the spectral representation with weights for the fractional Laplacian due to Frank, Lieb and Seiringer and the…

We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality. As an example application of our four…

We prove that the sharp constant in the univariate Bernstein--Nikolskii inequality for entire functions of exponential type is the limit of the sharp constant in the V. A. Markov type inequality with an exponential weight for coefficients…

Let $V\subset\R^m$ be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subsets of $aV$. We prove a limit equality as $a\to \iy$ between…

Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…

Subject to suitable boundary conditions being imposed, sharp inequalities are obtained on integrals over a region $\Omega$ of certain special quadratic functions $f(\bf{E})$ where $\bf{E}(\bf{x})$ derives from a potential $\bf{U}(\bf{x})$.…

In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a $C^2$ class bounded domain of $R^N$. This work is essentially based on…

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…

We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers.…