Dynamics Aggregation in Stochastic Control Problems

For stochastic control problems with mixed state-control constraints, we develop a dynamics aggregation method which replaces the stochastic differential or difference equation with a simpler constraint. Solutions of such simplified problems are used to construct a sequence of approximations to the original problem. Convergence properties of the method for both discrete-time and continuous-time models are analyzed in detail.     

Available output of two-dimensional surface-emitting laser arrays

The efficient performance of two-dimensional surface-emitting laser arrays is analysed with the aid of a comprehensive fully self-consistent three-dimensional thermal–electrical model. Maximal available output of the closely packed arrays is considered as a function of their spacing and the emitter size. The superior thermal behaviour of arrays composed of small-size emitters is found to be questionable. This revised version was published online in June 2006 with corrections to the Cover Date.     

APPROXIMATE ANALYTICAL SOLUTIONS FOR PRIMARY CHATTER IN THE NON-LINEAR METAL CUTTING MODEL

This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates.     

DETECTION OF DNA-PSORALEN PHOTOADDUCTS in situ

Abstract— An immunological method, with the use of specific immune serum, has been developed for detection of 8-methoxypsoralen (8-MOP) photoadducts to DNA, formed in situ in cell nuclei, after combined treatment with 8MOP and UV-A irradiation (Zarçbska et al. , 1978). Lymphocytes fixed on slides or in suspension, and cryostat sections of different mammalian tissues, served as antigenic substrate, after treatment with 8-MOP and UV-A in vitro. Specific fluorescence in these substrates was detected in the nuclei after treatment with 30 ˜ 140 kJ/m² UV-A in the presence of 0.1-0.3 μg/cm² 8-MOP. PHA-stimulated-lymphocytes appeared to be the most sensitive substrate.
However, hairless mice treated with high doses of UV-A in vivo , 70 ˜ 360 kJ/m² did not reveal a specific fluorescence of epidermal nuclei, unless a high local concentration of 8-MOP was attained.
The apparent discrepancy in the level of photoadduct detection between the in vitro and in vivo treated specimens was explained by the low number of DNA-8-MOP-photoadducts formed in vivo under these experimental conditions. The relevance of these findings to the role of DNA-8-MOP-photoadducts formed during PUVA photochemotherapy is discussed.     

On duality between observation and control for implicit linear discrete-time systems

Some results concerning the problem of duality between observationand control for implicit linear discrete-time systems are presented.It is not assumed that the considered systems are regular. Inthis case, some new concepts of observability and controllabilityturn out to be necessary for studying the problem of duality.     

Insights into enzyme catalysis from QM/MM modelling: transition state stabilization in chorismate mutase

Chorismate mutase provides an important test of theories of enzyme catalysis, and of modelling methods. The Claisen rearrangement of chorismate to prephenate in the enzyme has been modelled here by a combined quantum mechanics/molecular mechanics (QM/MM) method. Several pathways have been calculated. The sensitivity of the results to details of model preparation and pathway calculation is tested, and the results are compared in detail to previous similar studies and experiments. The potential energy barrier for the enzyme reaction is estimated at 24.5—31.6 kcal mol^?1 (AMl/CHARMM), and 2.7—11.9 kcal mol^?1 with corrections (e.g. B3LYP/6-31 + G(d)). In agreement with previous studies, the present analysis of the calculated paths provides unequivocal evidence of significant transition state stabilization by the enzyme, indicating that this is central to catalysis by the enzyme. The active site is exquisitely complementary to the transition state, stabilizing it more than the substrate, so reducing the barrier to reaction. A number of similar pathways for reaction exist in the protein, as expected. Small structural differences give rise to differences in energetic contributions. Major electrostatic contributions to transition state stabilization come in all cases from Arg90, Arg7, one or two water molecules, and Glu78 (Glu78 destabilizes the transition state less than the substrate), while Arg63 contributes significantly in one model.     

Demixing of a binary mixture in slit-like pores at high temperatures

We investigate the fluid—fluid demixing transitions in the case of adsorption of so-called symmetric binary mixtures in slit-like pores at temperatures higher than the bulk gas—liquid critical temperature. The aim of the study is to determine how the demixing of such mixtures in the pores depends on the bulk phase composition and on the parameters characterizing the pore. The calculations have been carried out by means of a density functional theory. In the case of an equimolar bulk mixture, the demixing transition inside the pore occurs only when the adsorption potentials of both species are identical. The occurrence of this transition is manifested by a cusp in the adsorption isotherm. For nonequimolar bulk phase compositions, the transition can also take place if the adsorption energies of both components are different. However, the difference in the adsorption energies should be small enough, otherwise a continuous demixing takes place. For non-equimolar compositions two branches of the grand canonical potential intersect, whereas for equimolar bulk composition they meet tangentially. We have determined phase behaviour for several model systems.     

Complex monodromy and the topology of real algebraic sets

A relation between the Euler characteristics of the Milnorfibres of a real analytic function is derived from a simple identity involvingcomplex monodromy and complex conjugation. A corollary is the result of Costeand Kurdyka that the Euler characteristic of the local link of an irreduciblealgebraic subset of a real algebraic set is generically constant modulo 4. Asimilar relation for iterated Milnor fibres of ordered sets of functions isused to define topological invariants of ordered collections of algebraicsubsets.     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

New applications of the good old wavelength-dispersive X-ray fluorescence

Wavelength-dispersive X-ray fluorescence can be characterized by its advantages and drawbacks. Unbeaten spectral resolution in a range below 5 keV, good operational stability, excellent ability of making averaged analysis, and good presentation of peak shape which gives the basis for the chemical speciation are the advantages. Among the drawbacks, the following are important: system with sequential analysis of particular elements, low output of energy supplied to the device, and great cost of instrument which can be amortized only in routine operations. In routine geological and environmental analyses, the WD-XRF performs better than other simpler instrumental or wet techniques. WD-XRF is continuously improved, by applying new multilayer interference mirrors (MIM) for detection and quantification of very light elements. Bad spectral resolution of MIM noted earlier is now improved by tailoring their shape to the shape of gratings. The progress in the long wavelength spectral region joined with efficient and precise wavelength resolution systems enables the application of WD-XRF for speciation analysis. In another effort, XRF spectrometry is treated as a tool for obtaining quantitative basis for the judgement on Linnaean systematic classification of plants and opens the field to a new discipline – quantitative biology.