Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation     

NLS-tupe equations in 2+1 dimensions: New type of solutions and non-isospectral problems

Integrable systems of NLS type in 2+1 dimensions are studied in three ways: their special solutions by Lie point symmetries, breaking-solutions by the ISM, as well as the non-isospectral problems.Department of Mathematics, Statistics and Computing Science, University of New England, Armidale N.S.W. 2351, Australia. E-mail: zhuhan@neumann.une.edu.au, xhe@metz.une.edu.au Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 382–389, June, 1994.     

Production of fast evaporation residues by the reaction20Ne+208Pb at projectile energies of 8.6, 11.4 and 14.9 A.MeV

Velocity distributions and production cross sections of evaporation residues have been measured in the reaction²⁰Ne+²⁰⁸Pb at projectile energies of 8.6, 11.4, 14.9 A.MeV. Essential deviations from statistical model of deexcitation have been observed. Monte Carlo simulations involving emission of non-equilibrium particles have been used in order to reproduce experimental velocity, charge and mass distributions of evaporation residues and to estimate indirectly multiplicities of pre-equilibrium particles. Communicated by V. Metag     

Bahadur efficiency and robustness of studentized score tests

We derive the exact Bahadur slopes of studentized score tests for a simple null hypothesis in a one-parameter family of distributions. The Student's t-test is included as a special case for which a recent result of Rukhin (1993, Sankhy Ser. A, 55, 159–163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample location models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asymptotic null distribution free of the scale parameter, and the optimality of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and breakdown point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicating certain degree of robustness of validity, but a bounded score function is needed to cap the influence from below and to ensure a high power breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very competitive in global efficiency at a variety of location models.     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction: