The Third-Order Singular-Perturbation Expansion of the Planar Cold-Fluid Magnetron Equations

The singular-perturbation expansion of the plasma cold-fluid equations for crossed fields in a planar geometry is presented. The general expansion is carried out to third order. Various instabilities that occur in the first, second, and third orders are discussed.     

Determination of total ammonium-nitrogen and free ammonia in a fermentation medium by sequential injection analysis

Summary Automated methods for the determination of ammonium and ammonia are reviewed, and techniques based on gas diffusion using a semi-permeable membrane were selected for the determination of both total ammonium-nitrogen and free ammonia in fermentation samples. A simple and robust instrument based on sequential injection analysis (SIA) consisting of a piston pump and two selector valves was used. Two different methods of ammonia detection, the Berthelot method and detection using pH-indicators, have been evaluated and compared. The indicator method showed higher reproducibility and the range of determination could easily be adjusted to match the concentrations of the samples. The range of determination could be adjusted from 0.05 mmol/l to 350 mmol/l, depending on choice of acceptor solution. This method has been evaluated with fermentation medium samples and tested on-line in a yeast fermentation process.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Complementary spectroscopic techniques to model the association of contaminant uranium with structural surfaces

Contaminant uranium poses unique problems for decontamination of former weapons processing and nuclear power facilities, as well as chemical plants, waste storage sites and former mining facilities. In addition, dealing with the possibility of intentional (i.e., a terrorist act) or accidental release of radioactive material in a populated area requires an accurate understanding of the nature of the association of such material with structural surfaces. These surfaces must also be considered in the context of repeated contamination, and the importance of atmospheric exposure, interaction with other possible contaminants, and corrosion or surface degradation due to such exposure must be taken into account. Complementary spectroscopic techniques, especially surface spectroscopies, are essential in developing models for the interaction of contaminants with surfaces and interfaces. In this review (which also presents new data on uranium association with corroding steel surfaces), we collect models of this association as determined by spectroscopic techniques, assess the important considerations in the development of more accurate models, and address some of the questions which remain.     

Ammonium violurate: a compact structure with extensive hydrogen bonding in three dimensions

The title compound [systematic name: ammonium pyrimidine‐2,4‐5,6(1H,3H)‐tetrone 5‐oximate], NH₄⁺·C₄H₂N₃O₄⁻, crystallizes from water in the triclinic space group P and is ismorphous with a known rubidium complex [Gillier (1965). Bull. Soc. Chim. Fr. pp. 2373–2384]. The principal feature of the structure is hydrogen bonding; each ammonium H atom acts as a bifurcated donor and three of the four violurate O atoms are bifurcated acceptors, with the fourth acting as a trifurcated acceptor. The pattern of hydrogen bonding around the cation is very similar to the rubidium coordination environment in the related structure. The violurate anions pack as hydrogen‐bonded crinkled tapes, which are linked and separated by the ammonium cations to give a compact three‐dimensional structure.     

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.     

The effect of multiple optima on the simple GA run-time complexity

Genetic algorithms are stochastic search algorithms that have been applied to optimization problems. In this paper we analyze the run-time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions. One such case occurs when multiple optima exist. We define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest.     

Hölder continuity of the gradient of solutions of uniformly parabolic equations with conormal boundary conditions

Summary We study solutions of the conormal derivative problem for uniformly parabolic equations in divergence form. Under weak regularity hypotheses on the operator, the global Hölder continuity of the gradient of a weak solution is established. The method of proof is based on [5] and the results extend those in [7, Section V.7].Sponsored by the National Science Foundation under Grant DMS-8315545.