Unconstrained optimization based on homogeneous models

In this paper a generalized algorithm for unconstrained optimization based on homogeneous functions is presented. It is shown that this generalized algorithm reaches the minimum of a homogeneous function inn + 2 iterations and does not require finding the minimum on the one-dimensional search. The Jacobson and Oksman algorithm can be derived from this general algorithm.This work was supported by the National Research Council of Canada under grant A 7239 and by a scholarship to the author.     

On the Denominator of the Poincaré Series for Monomial Quotient Rings

Let S = 𝕜 [x ₁,…, x _n ] be a polynomial ring over a field 𝕜 and I a monomial ideal of S. It is well known that the Poincaré series of 𝕜 over S/I is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of S/I.     

A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries

In this paper, we report on a comparison of the treatment of addition and subtraction of fractions in primary mathematics textbooks used in Cyprus, Ireland, and Taiwan. To this end, we use a framework specifically developed to investigate the learning opportunities afforded by the textbooks, particularly with respect to the presentation of the content and the textbook expectations as manifested in the associated tasks. We found several similarities and differences among the textbooks regarding the topics included and their sequencing, the constructs of fractions, the worked examples, the cognitive demands of the tasks, and the types of responses required of students. The findings emphasized the need to examine textbooks in order to understand differences in instruction and achievement across countries. Indeed, we postulate that within a given country there may exist a recognizable “textbook signature.” We also draw on the results and the challenges inherent in our analysis to provide suggestions and directions for future textbook analysis studies.     

Study of DyFe12−xMx compounds by57Fe and161Dy Mössbauer spectroscopy

DyFe_12?xM_x (M=Si,Ti,Cr) were studied with⁵⁷Fe and¹⁶¹Dy Mössbauer spectroscopy. The deduced coupling constants J_RFe of these compounds are about equal. It is found that Si is substituting one particular Fe-site, while Cr is substituting Fe randomly. In DyFe₁₀Si₂ two Fe-sites favour a c-axis anisotropy, while the third one favours the basal plane.     

Muons as local probes of three-body correlations in the mixed state of type-II superconductors

The vortex glass state formed by magnetic flux lines in a type-II superconductor is shown to possess nontrivial three-body correlations. While such correlations are usually difficult to measure in glassy systems, the magnetic fields associated with the flux vortices allow us to probe these via muon-spin rotation measurements of the local field distribution. We show via numerical simulations and analytic calculations that these observations provide detailed microscopic insight into the local order of the vortex glass and more generally validate a theoretical framework for correlations in glassy systems.     

Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem

Bin-oriented heuristics for one-dimensional bin-packing problem construct solutions by packing one bin at a time. Several such heuristics consider two or more subsets for each bin and pack the one with the largest total weight. These heuristics sometimes generate poor solutions, due to a tendency to use many small items early in the process. To address this problem, we propose a method of controlling the average weight of items packed by bin-oriented heuristics. Constructive heuristics and an improvement heuristic based on this approach are introduced. Additionally, reduction methods for bin-oriented heuristics are presented. The results of an extensive computational study show that: (1) controlling average weight significantly improves solutions and reduces computation time of bin-oriented heuristics; (2) reduction methods improve solutions and processing times of some bin-oriented heuristics; and (3) the new improvement heuristic outperforms all other known complex heuristics, in terms of both average solution quality and computation time.     

Ultra trace analysis of refractory metals by solid state mass spectrometry — A comparison of GDMS,SSMS and SIMS

A high resolution glow discharge mass spectrometer (GDMS VG 9000) has been used to analyze tungsten and molybdenum. Detection limits have been shown to be typically of the order of 1 ng/g or better in these matrices for integration times of 60 s per element. The results demonstrate that precisions of approximately 10% can be obtained on trace concentrations at the 10 ng/g level.