Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Identification by high-performance liquid chromatography of tyrosine ammonia-lyase activity in purified fractions of Phaseolus vulgaris phenylalanine ammonia-lyase.

Activities of phenylalanine ammonia-lyase (PAL) and tyrosine ammonia-lyase (TAL) were assessed at each stage of a three-step purification of PAL. Assays were performed by high-performance liquid chromatographic (HPLC) separation and ultraviolet detection of reaction products. Use of HPLC permitted assay of low activities of PAL and TAL for periods up to approximately four and two days, respectively. HPLC also facilitated the accurate quantitation of the product of the TAL reaction, trans-p-coumaric acid, which was observed to isomerize readily under experimental conditions. PAL and TAL were associated throughout the purification procedure, with TAL activity at 0.6-1.3% of PAL activity. It was concluded that, contrary to previous reports, TAL and PAL activities are mediated by the same enzyme, or else by chromatographically very similar enzymes.