An Approximate Probabilistic Model for Structured Gaussian Elimination

Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. Structured Gaussian elimination has been proposed as a first step in solving such sparse systems. It is a method for selecting pivots in an attempt to preserve the sparseness of the coefficient matrix. Eventually it terminates with a (smaller) residual linear system which must be solved by some other method. In many cases, the original column density is roughly proportional to the reciprocal of the of the column index. We discuss the asymptotic behavior of structured Gaussian elimination for this situation. One result is the observation that, for the column density just mentioned, the size of the residual system grows linearly with the size of the problem. This makes it possible to extrapolate the results of Monte Carlo simulation to much larger problems.     

Characterization of SIPOS films by spectroscopic ellipsometry and transmission electron microscopy

The structural and compositional properties of undoped SIPOS thin films have been studied by spectroscopic ellipsometry and transmission electron microscopy. It is shown that in most cases the former method provides fast and reliable results. The growth rate and crystallinity of SIPOS layers are studied as a function of N₂O concentration in the gas phase and annealing temperature.     

The asymptotic number of non-negative integer matrices with given row and column sums

Asymptotics are obtained for the number of m×n non-negative integer matrices subject to the following constraints: (i) each row and each column sum is specified and bounded, (ii) the entries are bounded, and (iii) a specified “sparse” set of entries must be zero. The result can be interpreted in terms of incidence matrices for labeled digraphs.     

Isotope shifts in transitions between low-lying levels of Sr I by laser-atomic-beam spectroscopy

High-resolution laser-atomic-beam spectroscopy has been used to determine isotope shifts in five transitions between low-lying states of Sr I. With these results and existing data a parametric analysis of level isotope shifts has been performed. The transition isotope shifts have been separated into field shift and mass shift contributions with a King-plot procedure using model-independent nuclear charge equivalent radiiR _k from muonic x-ray measurements. Values for the mean-square nuclear charge radiiδ〈r ₂ 〉 have been calculated from the field shifts in the optical transitions 5s ^{2 1} S ₀-5s5p ³ P ₁ and 5s5p ³ P ₀-5s6s ³ S ₁ and compared with correspondingδ〈r ² 〉 values evaluated from muonic x-ray data.     

Ligandenaustauschreaktionen von Fluoratomen mit Chloratomen bei Phosphorverbindungen der Koordinationszahl 3 und 4

Ligand-exchange reactions of fluorine versus chlorine atoms in phosphorus compounds with coordination number 3 or 4 Fluorine versus chlorine ligand-exchange reactions were carried out on the following phosphorus-based central moieties: CH₃P <, CH₃P(O)<, CH₃P(S)< and CH₃P(Se)<. The measured equilibrium distributions were shown to favour the species which result from an accumulation of like substituents on the central moieties, whereas the equilibrium distribution of chlorine vs bromine on CH₃P(O) < was found to be almost random. These fluorine exchanging systems thus represent the unusual case of large positive deviation from random distribution. It is also noteworthy that the equilibrium distributions depend only very little on the nature of the atom which is bonded to phosphorus in the “isolated” position. System CH₃PF₂/CH₃PCl₂ could not be studied quantitatively owing to the competitive dismutation of CH₃PF₂; however, evidence is given for fast initial redistribution of the halogens on the methylphosphorus moiety and for the transient formation of CH₃PFCl.     

Data analysis procedures for pulse ELDOR measurements of broad distance distributions

The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distribution with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distributions by their mean distance and variance, Hermite polynomial interpolation provides the best results. Distributions that contain both broad and narrow peaks are most difficult to analyze. In this case a high signal-to-noise ratio is strictly required and approximate Pake transformation should be applied. A procedure is given for renormalizing primary experimental data from protein preparations with slightly different degrees of spin labelling, so that they can be compared directly. Performance of all the data analysis procedures is demonstrated on experimental data for a shape-persistent biradical with a label-to-label distance of 5 nm, for a [2]catenane with a broad distance distribution, and for a doubly spin-labelled double mutant of plant light harvesting complex II     

Fe-Hydroxysulphates from Bacterial Fe2+ Oxidation

The perturbed angular correlation method (PAC) was applied to investigate the lattice location of implanted ¹¹¹In probe ions in Hf₂Ni and Zr₂Ni intermetallic compounds. It is concluded that the ¹¹¹In/¹¹¹Cd probe nuclei experiencing the highly asymmetric electric field gradient (EFG) occupy the unique hafnium or zirconium 8(h) sites in the investigated phases. Above room temperature, the EFGs decrease linearly with temperature. The results are compared with that of previous PAC measurements with ¹⁸¹Ta probes.     

Thermal analysis of apatite structure

Two types of thermal effects, caused by substitutions (Ca²⁺↔ Na⁺, ↔ CO₃ ^2-, SO₄ ^2-, OH^-↔ F^-) in synthetic precipitated apatites as well as by sorption of Cd²⁺, Zn²⁺, and Cr³⁺ ions from the solutions were studied by TG/DTA, XRD and FTIR analysis. The temperatures of exothermic effect at 330-340°C and of decomposition of carbonate and sulfate apatites at 650-950°C were shown to depend on the substitutions in the apatite structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some Examples of the Use of Simulation in U.S. and Canadian Agriculture

Mathematical simulation is a technique widely used by agricultural engineers to determine systems interactions, to evaluate technical feasibility, to determine economic feasibility, to design complex structures and to help with managing production. In the past, simulation has been used one level removed from the farmers who manage operation on a day-to-day basis. This is changing.Three completely different types of simulations are presented: (1) a static and deterministic simulation of on-farm ethanol production that models the conversion process and determines economic feasibility; (2) a dynamic and deterministic simulation of maize production, including harvest and drying that is weather dependent; (3) a static and stochastic simulation that uses Monte Carlo techniques to obtain information about strength and performance of glued-laminated beams.We believe that inexpensive computing capability will tremendously increase the use of simulation models, such as the three described, that will help farmers better manage their production systems.