Quantification problems in depth profiling of pwr steels using Ar+ ion sputtering and XPS analysis.

The oxide scales of AISI 304 formed in boric acid solutions at 300 degrees C and pH = 4.5 have been studied using X-ray photoelectron spectroscopy (XPS) depth profiling. The present focus is depth profile quantification both in depth and chemical composition on a molecular level. The roughness of the samples is studied by atomic force microscopy before and after sputtering, and the erosion rate is determined by measuring the crater depth with a surface profilometer and vertical scanning interferometry. The resulting roughness (20-30 nm), being an order of magnitude lower than the crater depth (0.2-0.5 microm), allows layer-by-layer profiling, although the ion-induced effects result in an uncertainty of the depth calibration of a factor of 2. The XPS spectrum deconvolution and data evaluation applying target factor analysis allows chemical speciation on a molecular level. The elemental distribution as a function of the sputtering time is obtained, and the formation of two layers is observed-one hydroxide (mainly iron-nickel based) on top and a second one deeper, mainly consisting of iron-chromium oxides.     

Estimating means from a non-I.I.D. Mixture of Poisson samples

In this paper, a family of estimators for estimating means when mixing two independent Poisson samples is proposed. This family is based on the probability-generating function of the Poisson distribution and is offered as an alternative to the maximum likelihood estimators, which have some drawbacks. These estimators include the method of moments estimators as a special limiting case.     

Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.     

An algebraic representation of the affine Bäcklund transformation

In 1980 Chern and Terng defined a Bäcklund transformation for affine minimal surfaces. In this paper we show that this Bäcklund transformation can be simply represented by an involution and translation of the affine conormal.     

Constructing one-parameter families of elliptic curves with moderate rank

We give several new constructions for moderate rank elliptic curves over Q(T). In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over Q using polynomials of degree two in T. While our method generates linearly independent points, we are able to show the rank is exactly 6 without having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Octahedral metallo-mesogens of chromium, molybdenum and tungsten with 1,4,7-trisubstituted 1,4,7-triazacyclononane and three carbonyl groups as ligands

Liquid crystalline complexes with chromium, molybdenum and with tungsten as metallic centres are reported. 1,4,7-Trisubstituted 1,4,7-triazacyclononane and three carbonyl groups are coordinated in an octahedral geometry. The observed mesophases are characterized as disordered rectangular columnar of a pyramidic type.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.