Yang-Mills equations are formally linearizable

It is proved, in the framework of a recent theory of non-linear group representations elaborated by the authors, that the non-linear Yang-Mills equations are formally linearizable: there exists a formal non-linear operator which intertwins the non-linear Yang-Mills equations with their free (linear) part.     

The Malliavin calculus

The paper presents a review of the calculus of functional derivatives introduced by Malliaving and the Malliavin technique for establishing the existence of a density for the probability law of Wiener functionals. The approach of Malliavin, Stroock and Shigekawa is compared with that of Bismut.The research was supported by the fund for the promotion of research at the Technion     

On the numerical radius and its applications

We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finite- and infinite- dimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems.     

Stopping a two parameter weak martingale

Summary This paper deals with the following problem, given a two parameter stochastic process, under what conditions is it possible to stop the process at any stopping line? It is shown that the class of stoppable processes is strictly larger than the class of two parameter integrators. Sufficient conditions for a weak martingale to be stoppable are derived and the stopped r.v. is represented as a one parameter optional dual projection.Work partially supported by a grant from the Research Authority at Bar-Ilan UniversityWork supported by the fund for promotion of research at the Technion     

Some partial orderings of exchangeable random variables by positive dependence

Some partial orderings of positively dependent exchangeable random variables are introduced. The interrelations among them, the inequalities which follow from them and two models which yield such partial orderings are then discussed. Particular examples include ordering multivariate normal, t, χ², Cauchy, exponential, binomial, Poisson, gamma and Farlie-Gumbel-Morgenstern random vectors. Applications to genetic selection and choice of sampling procedures are given.     

p-adic periods and modular symbols of elliptic curves of prime conductor

Under certain assumptions, we prove a conjecture of Mazur and Tate describing a relation between the modular symbol attached to an elliptic curve with split multiplicative reduction atp, and itsp-adic period. We generalize this relation to modular forms of weight 2 with coefficients not necessarily in.Oblatum 24-XI-1993 & 8-VI-1994