Related papers: Lemmes de multiplicites et constante de Seshadri

The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. In this article we show that…

Given a nef and big line bundle $L$ on a projective variety $X$ of dimension $d \geq 2$, we prove that the Seshadri constant of $L$ at a very general point is larger than $(d+1)^{\frac{1}{d}-1}$. This slightly improves the lower bound $1/d$…

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous…

This paper deals with the principal eigenvalue of discrete $p$-Laplacian on the set of nonnegative integers. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequalities. The main goal is the quantitative…

On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A…

We present new sharp results concerning multipliers and distance estimates in various spaces of harmonic functions in the unit ball of $R^n$.

The present paper studies the fractional $p$-Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and sign-changing solutions by constructing the suitable…

The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…

We propose a new asymptotic expansion for the fractional $p$-Laplacian with precise computations of the errors. Our approximation is shown to hold in the whole range $p\in(1,\infty)$ and $s\in(0,1)$, with errors that do not degenerate as…

We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic…

We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain…

In this paper, we establish an improved version of a saddle point theorem ([4]) removing a weak lower semicontinuity assumption at all. We then revisit some of the applications of that theorem in the light of such an improvement. For…

This paper is essentially derived from the observation that some results used for improving constants in the Lieb-Thirring inequalities for Schrodinger operators in L2(-\infty,\infty) can be translated to the discrete Schrodinger op-…

In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…

We correct two errors in our paper [4]. First error concerns the definition of the SVI solution, where a boundary term which arises due to the Dirichlet boundary condition, was not included. The second error concerns the discrete estimate…

In 1988, Fujita conjectured that there is an effective and uniform way to turn an ample line bundle on a smooth projective variety into a globally generated or very ample line bundle. We study Fujita's conjecture using Seshadri constants,…

The purpose of this paper is to explicitly compute the Seshadri constants of all ample line bundles on fake projective planes. The proof relies on the theory of the Toledo invariant, and more precisely on its characterization of…

We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…

An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the…

This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…