Interactive computer assistance with calculations arising in undergraduate laboratory experiments†

The paper describes an approach to the use of interactive computing to assist students in calculating results from their experimental data in situations where several similar sets of data have to be processed, either by numerical calculation or graphically. The computer programs require the students to show that they understand the calculations by processing one set of data correctly themselves before the remaining sets are computed for them. The detection and diagnosis, by the computer, of students' calculation errors are described. The educational problems and advantages of such an approach are discussed.     

A comparison of regularizations for an ill-posed problem

We consider numerical methods for a ``quasi-boundary value' regularization of the backward parabolic problem given by

where is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value by adding , where is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provided. We also compare the regularization used here with that from Ames and Epperson.

We consider numerical methods for a ``quasi-boundary value' regularization of the backward parabolic problem given by

where is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value by adding , where is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provided. We also compare the regularization used here with that from Ames and Epperson.

     

Principle and analytical applications of resonance lonization mass spectrometry

Resonance ionization mass spectrometry (RIMS) is a very sensitive analytical technique for the detection of trace elements. This method is based on the excitation and ionization of atoms with resonant laser light followed by mass analysis. It allows element and, in some cases, isotope selective ionization and is applicable to most of the elements of the periodic table. A high selectivity can be achieved by applying three step photoionization of the elements under investigation and an additional mass separation for an unambiguous isotope assignment.An effective facility for resonance ionization mass spectrometry consists of three dye lasers which are pumped by two copper vapor lasers and of a linear time-of-flight spectrometer with a resolution better than 2500. Each copper vapor laser has a pulse repetition rate of 6.5 kHz and an average output power of 30 W.With such an apparatus measurements with lanthanide-, actinide-, and technetium-samples have been performed. By saturating the excitation steps and by using autoionizing states for the ionization step a detection efficiency of 4 × 10^–6 and 2.5 × 10^–6 has been reached for plutonium and technetium, respectively, leading to a detection limit of less than 10⁷ atoms in the sample. Measurements of isotope ratios of plutonium samples were in good agreement with mass-spectrometric data. The high elemental selectivity of the resonance ionization spectrometry could be demonstrated.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria     

Cloning of the histidine transport genes from Salmonella typhimurium and characterization of an analogous transport system in Escherichia coli

The genes for the well-characterized high-affinity histidine transport system of S typhimurium have been cloned in lambda gt4. Genetic and physiological analyses of the analogous transport system of E coli were undertaken in order that available lambda vectors, recombinant DNA techniques, and a genetic selection for transport function might be used to isolate the Salmonella genes. The presence of the transport genes on a 12.4 Kb cloned DNA fragment has been confirmed 1) genetically, by complementation studies; 2) physiologically, by the rates of histidine uptake by bacteria containing this DNA; and 3) by demonstrating that the cloned DNA codes for the previously identified transport proteins J and P. The isolated fragment carries the entire transport operon, the argT gene and the ubiX locus, but neither the purF gene nor the ack/pta loci.     

On the soliton,invariant, and shock solutions of a fourth-order nonlinear equation

A particular transmission line containing a nonlinear capacitance is shown to satisfy the equation V_xxtt + ω₀²V_xx ? C_s^?1[VC_n(V)]_tt = 0, ω₀² = (LC_S)^?1. This equation is shown to permit the propagation of solitary waves (solitons). In addition, it admits an invariant (similar) solution under the spiral group. Lastly, we demonstrate two implicit traveling wave solutions that permit the evolution of a discontinuity in the first derivatives (shocks).     

Determination of L-alanosine in plasma and urine by reversed-phase high-performance liquid chromatography of the Dns derivative

L-Alanosine is an antitumour antibiotic that has recently been placed in clinical trial. We have developed a relatively rapid and specific assay for urinary and plasma alanosine, based on formation of the Dns derivative and separation of this from other Dns compounds by reversed-phase high-performance liquid chromatography. Dns-Alanosine is detected by its absorption at 254 nm, since alanosine is atypical in that it forms a Dns derivative with very low fluorescence. The lower limit of detection of alanosine in plasma is 0.1 microgram/ml. The assay has been used to measure the levels of alanosine in the plasma and urine of rabbits and of man.     

Implicit ad hoc methods for nonlinear partial differential equations

Several special methods including implicit separation of variables, explicit and implicit generalized traveling waves are introduced and employed to obtain solutions for nonlinear equations. Certain nonlinear wave propagation problems are shown to yield to implicit separation while generalized traveling wave concepts are applied in diffusion, fluid mechanics and wave propagation.     

Space Charge Effects in a Gas Filled Penning Trap

Mass selective buffer gas cooling is a technique used for ions that are stored in a Penning trap. The technique can be applied to all elements and the mass resolving power achieved has proven to be sufficient to resolve isobars. When not only a few but 10⁶ and more ions are stored at the same time, space charge starts to play a dominant role for the spatial distribution. In addition, the observed cyclotron frequency is shifted. This work investigates these effects by numerical calculations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Group properties of utt=[F(u)ux]x

The group properties and the associated Lie algebra are developed for the subject quasilinear wave equation, for arbitrary f[fεC²(R), f > 0, f ≠ 0]. From the resulting information sets of explicit invariant solutions are constructed for wave propagation in gases and for the transonic equation.