On the additive theory of prime numbers II

The undecidability of the additive theory of primes (with identity) as well as the theory Th(N,+, n -> p\_n), where p\_n denotes the (n+1)-th prime, are open questions. As a possible approach, we extend the latter theory by adding some extra function. In this direction we show the undecidability of the existential part of the theory Th(N, +, n -> p\_n, n -> r\_n), where r\_n is the remainder of p\_n divided by n in the euclidian division

Strict pseudocontractions and demicontractions, their properties and applications

We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary and sufficient conditions under which a convex combination and composition of strict pseudocontractions as well as demicontractions that share a common fixed point is again a strict pseudocontraction or a demicontraction, respectively. Moreover, we introduce a generalized relaxation of composition of demicontraction and give its properties. We apply these properties to prove the weak convergence of a class of algorithms that is wider than the Douglas-Rachford algorithm and projected Landweber algorithms. We have also presented two numerical examples, where we compare the behavior of the presented methods with the Douglas-Rachford method.Comment: 27 pages, 3 figure

Obtuse cones and Gram matrices with nonnegative inverse

AbstractWe study some properties of Gram matrices with nonnegative inverse which lead to the constructions of obtuse cones. These constructions can find applications in optimization problems, e.g., in methods of convex feasibility problems or of convex minimization problems

The effect of information about counseling process or the counseling center on multiple measures of counseling outcome at a university counseling service

In an attempt to impact on the high incidence of premature termination which has been documented at several university counseling centers, this study was designed to investigate the effect of precounseling information on premature termination and other measures of counseling outcome. Counselor and client gender effects were also examined. Seventy-six students who sought counseling at a large university counseling center served as subjects. Prior to their initial counseling session clients viewed one of two videotapes. One videotape presented information about the counseling process with particular focus on the client role. The other videotape presented information about the services which the counseling center offers. Multiple measures of counseling outcome were used, with both clients and counselors responding. Videotape treatments failed to produce any significant differences on the dependent measures. Two isolated gender effects were found. Counselor experience level which was not considered in the initial design of the study, proved to have considerable impact on some of the counseling outcome measures