Critical behaviour of the two-dimensional Ising susceptibility

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hundred terms, generated in about 100 hours on an obsolete workstation. In terms of a temperature variable, \tau, linear in T/T_c-1, the short-distance terms are shown to have the form \tau^p(ln|\tau|)^q with p>=q^2. To O(\tau^14) the long-distance part divided by the leading \tau^{-7/4} singularity contains only integer powers of \tau. The presence of irrelevant variables in the scaling function is clearly evident, with contributions of distinct character at leading orders |\tau|^{9/4} and |\tau|^{17/4} being identified.Comment: 11 pages, REVTex

Solid solutions in mineral nomenclature

GUIDELINES for mineral nomenclature com-mended by the Commission on New Minerals and Mineral Names (CNMMN) of the Internationa

Bullying girls - Changes after brief strategic family therapy: A randomized, prospective, controlled trial with one-year follow-up

Background: Many girls bully others. They are conspicuous because of their risk-taking behavior, increased anger, problematic interpersonal relationships and poor quality of life. Our aim was to determine the efficacy of brief strategic family therapy (BSFT) for bullying-related behavior, anger reduction, improvement of interpersonal relationships, and improvement of health-related quality of life in girls who bully, and to find out whether their expressive aggression correlates with their distinctive psychological features. Methods: 40 bullying girls were recruited from the general population: 20 were randomly selected for 3 months of BSFT. Follow-up took place 12 months after the therapy had ended. The results of treatment were examined using the Adolescents' Risk-taking Behavior Scale (ARBS), the State-Trait Anger Expression Inventory (STAXI), the Inventory of Interpersonal Problems (IIP-D), and the SF-36 Health Survey (SF-36). Results: In comparison with the control group (CG) (according to the intent-to-treat principle), bullying behavior in the BSFT group was reduced (BSFT-G from n = 20 to n = 6; CG from n = 20 to n = 18, p = 0.05) and statistically significant changes in all risk-taking behaviors (ARBS), on most STAXI, IIP-D, and SF-36 scales were observed after BSFT. The reduction in expressive aggression (Anger-Out scale of the STAXI) correlated with the reduction on several scales of the ARBS, IIP-D, and SF-36. Follow-up a year later showed relatively stable events. Conclusions: Our findings suggest that bullying girls suffer from psychological and social problems which may be reduced by the use of BSFT. Expressive aggression in girls appears to correlate with several types of risk-taking behavior and interpersonal problems, as well as with health-related quality of life. Copyright (c) 2006 S. Karger AG, Basel

On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v