Wide-angle one-way wave equations

A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].     

Distribution density of the norm of a stable vector

Let B be a Banach space,X be a stable B -valued random vector with exponentd(0,2), and P(·) be the distribution density of the norm of X. In this paper we study the question of the boundedness of P. In particular, we construct examples of a space B with a symmetric stable vector X with exponentd(1,2) with unbounded P and prove that if X is a nondegenerate strictly stable vector with exponentd(0,1), then P is bounded.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 105–114, 1987.The author is grateful to Yu. A. Davydov, V. I. Paulauskas, V. Yu. Bentkus, and D. Pap for stimulating discussions of the subject of this paper. When the paper was finished the author learned that similar results are found in [9].     

Superbranching processes and projections of random Cantor sets

We study sequences (X ₀, X ₁, ...) of random variables, taking values in the positive integers, which grow faster than branching processes in the sense that , for m, n0, where the X _n (m, i) are distributed as X _n and have certain properties of independence. We prove that, under appropriate conditions, X _n ^1/n almost surely and in L ¹, where =sup E(X _n )^1/n . Our principal application of this result is to study the Lebesgue measure and (Hausdorff) dimension of certain projections of sets in a class of random Cantor sets, being those obtained by repeated random subdivisions of the M-adic subcubes of [0, 1] ^d . We establish a necessary and sufficient condition for the Lebesgue measure of a projection of such a random set to be non-zero, and determine the box dimension of this projection.Work done partly whilst visiting Cornell University with the aid of a Fulbright travel grant     

Precipitation structure in an Al-2·0 at. % Zn-1·0 at. % Mg alloy within and close to the grain boundaries and its effects on mechanical properties

During ageing the Al-2·0 at. %Zn-1·0 at. % Mg alloy at elevated temperatures the width of the precipitation free zone (PFZ) at both sides of the grain boundaries (GB) is identical with that free of quenched-in dislocation loops (DL). After sufficiently long ageing a band of precipitates is growing inside the former PFZ and the DLs in the midgrain regions act as sites for the heterogeneous nucleation of the-phase. Two precipitation processes significantly affect the mechanical properties. TEM correlates grain boundary precipitate density and morphology with grain boundary misorientation.     

Influence of crystal-field on the thermal conductivity of PrNi5

The thermal conductivity of PrNi₅ in the temperature range 0·5 to 20 K is investigated. The analysis of crystalline electric field effect on the experimentally obtained temperature dependence of the thermal conductivity indicates that beside the main electronic component also other contributions (phonons, magnetic excitons) can take place in the heat transport in this intermetallic compound.The authors would like to thank Dr. G. Eska for lending the sample and Dr. . Jáno for his interest in the work and stimulating discussions.     

Effects of small external magnetic fields on the hyperfine field of iron in iron metal above the curie temperature: A new method for studying critical phenomena

By applying magnetic fields up to 2 kG, the equation of state and the critical dynamics of a spin system near its critical point can be studied with the Mössbauer effect. As an example, the equation of state near the Curie temperature of iron is investigated yielding the critical exponent =4.84±0.15.     

Three-body Coulomb effects in neutral-particle-exchange singularity

In a three-body model with Coulomb interactions the Faddeev equations for the Alt-Grassberger-Sandhas transition operators are used to find the leading term of the neutron-transfer amplitude near the exchange singularity in the cos plane. We derive formulae containing three-body Coulomb effects for the renormalization of the second-order exchange pole in the calculation of observables, such as the cross section and polarizations.     

Production of light superpartners in π0 radiative decays

The production rate of light photinos in radiative pion decay \(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma\) is calculated. Experimental constraints on masses and mass splittings of scalar quarks imply the following upper bound on the decay rate \(BR(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma ) \lesssim 10^{ - 16}\) .