We calculate the large-volume and small-mass dependences of the quark condensate in quenched QCD using Neuberger's operator. We find good agreement with the predictions of quenched chiral perturbation theory, enabling a determination of the chiral lagrangian parameter Σ, up to a multiplicative renormalization.

Bound state perturbation theory applies to the bound states of perturbed systems, for which the energy levels are discrete and separated from one another. The system may also have a continuous spectrum, but the interest is attached to the discrete states. The effects of perturbations on states of the continuous spectrum, or on discrete states imbedded in the continuum, require different techniq...

The experimental status of stable bound states made out of heavy quarks is reviewed. The need for a way to deal with the non-perturbative transitions involved calls for precision measurements on one hand, and for discovery of as yet undetected states to confirm predictions on the other. In this article, recent experimental contributions to heavy quarkonia spectroscopy and decay will be reviewed...

In this paper, we are interested in the Dirichlet boundary value problem for a multi-dimensional nonlinear conservation law with a multiplicative stochastic perturbation. Using the concept of measure-valued solutions and Kruzhkov’s semi-entropy formulations, a result of existence and uniqueness of the entropy solution is proved. © 2013 Elsevier Inc. All rights reserved.

In the setting of adjointable operators on Hilbert C∗-modules, this paper deals with polar decomposition product three operators. The relationship between decompositions associated is clarified. Based relationship, a formula for multiplicative perturbation an operator provided. addition, full characterization made Some applications are also dealt with.

A constructive perturbation bound of the Drazin inverse of a square matrix is derived using a technique proposed by G. Stewart and based on perturbation theory for invariant subspaces. This is an improvement of the result published by the authors Wei and Li [Numer. Linear Algebra Appl., 10 (2003), pp. 563–575]. It is a totally new approach to developing perturbation bounds for the Drazin invers...

We consider a family of character sums as multiplicative analogues Kloosterman sums. Using Gauss sums, Jacobi and Katz’s bound for hypergeometric we establish asymptotic formulae any real (positive) moments the above sum

In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak. This bound is a common strengthening of both Haemers' bound and the fractional chromatic number of a graph. We show that this fractional version outperforms any bound on the Shannon capacity that could be attained through Haemers' bound. We show also that this ...

We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated to a polynomial over a finite field k = Fq for two classes of polynomials which are invariant under a large abelian group of automorphisms of the affine line Ak: those invariant under translation by elements of k and those invariant under homotheties with ratios in a lar...