AN ALTERNATIVE SPECIFICATION FOR MODELING GROUNDWATER DYNAMICS

This research extends previous work with dynamic models to manage groundwater quality by using the consumptive nitrate use rate instead of the nitrate application rate. The analysis indicates that misspecification results in overestimation of economic benefits, and supra-optimum nitrogen fertilizer application rates and groundwater nitrate stocks at a steady state.     

Cognitive Demands and Second-Language Learners: A Framework for Analyzing Mathematics Instructional Contexts

The issues involved in teaching English language learners mathematics while they are learning English pose many challenges for mathematics teachers and highlight the need to focus on language-processing issues related to teaching mathematical content. Two realistic-type problems from high-stakes tests are used to illustrate the complex interactions between culture, language, and mathematical learning. The analyses focus on aspects of the problems that potentially increase cognitive demands for second-language learners. An analytical framework is presented that is designed to enable mathematics teachers to identify critical elements in problems and the learning environment that contribute to increased cognitive demands for students of English as a second language. The framework is proposed as a cycle of teacher reflection that would extend a constructivist model of teaching to include broader linguistic, cultural, and cognitive processing issues of mathematics teaching, as well as enable teachers to develop more accurate mental models of student learning.     

Gauge fixing, families index theory, and topological features of the space of lattice gauge fields

The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: the topological sectors, specified by the fermionic topological charge, are shown to contain noncontractible even-dimensional spheres when N3, and noncontractible circles in the N=2 case. We describe how certain obstructions to the existence of gauge fixings without the Gribov problem in the continuum setting correspond on the lattice to obstructions to the contractibility of these spheres and circles. We also point out a canonical connection on the space of lattice gauge fields with monopole-like singularities associated with the spheres.     

Chemical analysis and distribution investigation of trace elements in indium matrix by spark source mass spectrometry

Summary High-purity indium was analysed by spark source mass spectrometry, using electrical and photoplate detection. For the calibration of the differences in elemental sensitivity, a standard sample was prepared in which 10 impurities were determined by graphite furnace atomic absorption spectrometry. In this way accuracies of less than 40% were obtained for relatively homogeneous elements at ppm and sub-ppm level. About 40 elements could be determined with detection limits of 10 to 30 ppb. Two pattern recognition methods, principal component analysis and clustering analysis, were applied to obtain information on trace element distribution, which indicated that a number of elements were strongly spatially correlated in the analysed sample.

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Chemische Analyse und Verteilungsbestimmung von Spurenelementen in Indium-Matrix durch Funkenquellen-Massenspektrometrie

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On leave from: Department of Chemistry, Nanjing Normal University, Nanjing, People's Republic of China     

The minimum span of L(2,1)-labelings of certain generalized Petersen graphs

In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)-f(y)|? 2 if xand y are adjacent vertices and |f(x)-f(y)|?1 if xand y are at distance two. The goal is to determine the λ-number of G, which is defined as the minimum span over all L(2,1)-labelings of G, or equivalently, the smallest number k such that G has an L(2,1)-labeling using integers from {0,1,…,k}. Recent work has focused on determining the λ-number of generalized Petersen graphs (GPGs) of order n. This paper provides exact values for the λ-numbers of GPGs of orders 5, 7, and 8, closing all remaining open cases for orders at most 8. It is also shown that there are no GPGs of order 4, 5, 8, or 11 with λ-number exactly equal to the known lower bound of 5, however, a construction is provided to obtain examples of GPGs with λ-number 5 for all other orders. This paper also provides an upper bound for the number of distinct isomorphism classes for GPGs of any given order. Finally, the exact values for the λ-number of n-stars, a subclass of the GPGs inspired by the classical Petersen graph, are also determined. These generalized stars have a useful representation on Möebius strips, which is fundamental in verifying our results.     

Cube factorizations of complete graphs

A cube factorization of the complete graph on n vertices, K_n, is a 3‐factorization of K_n in which the components of each factor are cubes. We show that there exists a cube factorization of K_n if and only if n ≡ 16 (mod 24), thus providing a new family of uniform 3‐factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. © 2004 Wiley Periodicals, Inc.     

An embedded atom method study of the equilibrium shapes of small platinum and palladium clusters

The embedded atom method (EAM) was used to determine the equilibrium shapes of small platinum and palladium clusters (N=5–60 atoms). The stability of various polyhedral symmetries was performed at 0K. A search for the presence of any other lower energy structures was also carried out. Pt clusters reconstructed to lower energy clusters even at the magic numbers. Pd also reconstructed to lower energy structures except at the magic number sizes where the icosahedron was found to be the most stable.     

Rheological and diffusion properties of a dextran-con A polymer in the presence of Insulin and Magnesium

Previous work carried out in our laboratories has focused on the formation and investigation of a dextran and concanavalin A (con A) based gel, which has the ability to alter its conformational structure in the presence and absence of free and terminal glucoses such that a gel–sol phase transition occurs. Here we report the diffusion and rheological investigations in to the effects of the addition of insulin and varyingconcentrations of magnesium chloride hexahydrate (Mg₂Cl₂6H₂O) at 20 and 37 °C. Rheological examination of glucose-sensitive (dextran-con A) gels were conducted using a cone and plate viscometer used in continual rotation and oscillatory modes. The results are interpreted in terms of the structure of the gel network and suggest rheological assessment provides an effective method of assessing the properties of gel systems. The subsequent testing of such formulations in in-vitro diffusion experiments revealed a reduction in the rate of diffusivity in the insulin marker, poly R-478 dye. The performance of this self-regulating drug delivery system has been examined and the addition of insulin and magnesium chloride may alter the way in which the gel operates as a drug delivery device and in the delivery of insulin. This may have implications for other ligands.