An element x of the ring R is called periodic if there exist distinct positive integers m, n such that xm = xn; and x is potent if there exists n > 1 for which xn = x. We denote the set of potent elements by P or P(R), the set of nilpotent elements by N or N(R), the center by Z or Z(R), and the Jacobson radical by J or J(R). The ring R is called periodic if each of its elements is periodic, and...

We study the problem of estimating a nonnegative density, given a finite number of moments. Such problems arise in numerous practical applications. As the number of moments increases, the estimates will always converge weak * as measures, but need not converge weakly in L, . This is related to the existence of functions on a compact metric space which are not essentially Riemann integrable (in ...

It is known that for a sequence of independent and identically distributed random variables (Xn) the regular variation condition is equivalent to weak convergence of partial maximaMn = max{X1, . . . , Xn}, appropriately scaled. A functional version of this is known to be true as well, the limit process being an extremal process, and the convergence takes place in the space of càdlàg functions e...

For each n let Y n t be a continuous time symmetric Markov chain with state space n −1 Z d. A condition in terms of the conductances is given for the convergence of the Y n t to a symmetric Markov process Yt on R d. We have weak convergence of {Y n t : t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps.

A class of Lagrange-Newton-SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order suucient optimality condition for the reference solu...

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical exa...

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semimartingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumptio...