Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

A theoretical investigation of the preferred conformations of glutathione and its constituent amino acid residues

The preferred conformations of the tripeptide glutathione have been investigated by performing quantum mechanical calculations using the PCILO method. A series of model compounds representing fragments of the tripeptide has been studied as well as the complete molecule. The results are compared with the available experimental data.     

Polynuclear manganese grids and clusters—A magnetic perspective

High nuclearity paramagnetic, spin-coupled transition metal clusters and grids are fascinating chemists and physicists partly because of their structural beauty, and the challenge of creating them, but also because of their novel physical properties. Magnetic interactions between the spin centers are a primary focus. This review will examine a selection of Mn(II) polynuclear grids and clusters, with nuclearities in the range Mn₄ to Mn₉. Theoretical treatments of the magnetic properties are discussed, and approaches to solving the exchange problem for ‘large’ spin systems related to computational difficulties. A freely available software package (MAGMUN4.1) is presented as a means of dealing simply with spin-coupled clusters in general, and symmetry reduction methods are discussed briefly as a means of dealing with ‘large’ spin systems.     

Diffusion in ethylene–propylene rubber

A study of sorption in a copolymer of ethylene and propylene is presented. Long-time sorption and desorption measurements provided the actual diffusion coefficient in the limit of zero concentration gradient. An analysis of the diffusion–sorption data reinforced the Frisch hypothesis about diffusion in a polymer matrix. The better solvent deforms the microstructure, allowing a more marked dependence of the diffusivity upon concentration.     

Chemical Synthesis of Oligonucleotides Containing N6-Methyladenine Residues in the GATC Site

To investigate by NMR the effects of adenine methylation, a set of oligodeoxynucleotides has been synthesized by phosphotriester or phosphoramidite procedures on silica-gel support. The preparation of fully protected 2′-deoxy-N⁶-methyladenosine 3′-phosphate 4 and (2′-deoxy-N⁶-methyladenosin-3′-O-yl)(methoxy)morpholinophosphine 5 is described. The large-scale chemical synthesis, purification by HPLC, and characterization by MS of these molecules containing N⁶-methyladenine is reported.     

Electron-impact-induced fragmentation of aromatic cyclic diazoketones

The mass spectra of eleven diazoketones have been obtained. High resolution mass measurements of selected ions have shown initial loss of nitrogen followed by loss of carbon monoxide. In many of the spectra, flat-topped metastables were observed.     

Analytical methods used to measure acrylamide concentrations in foods

The state-of-the-art of analysis for acrylamide in food is reviewed. The majority of analytical methods adopts a similar approach: addition of internal standard to the specimen, extraction with water, purification of extract using a solid-phase extraction cartridge, and then determination using either gas chromatography coupled to mass spectroscopy (GC/MS) after bromination, or direct measurement with liquid chromatography coupled to mass spectroscopy (LC/MS). The available methods generally show good agreement and are likely to be accurate. However, improvements in precision (within-laboratory) and repeatability (between-laboratory) are needed by particular data users.     

Halogenation in Fungi: What Do We Know and What Remains to Be Discovered?

In nature, living organisms produce a wide variety of specialized metabolites to perform many biological functions. Among these specialized metabolites, some carry halogen atoms on their structure, which can modify their chemical characteristics. Research into this type of molecule has focused on how organisms incorporate these atoms into specialized metabolites. Several families of enzymes have been described gathering metalloenzymes, flavoproteins, or S-adenosyl-L-methionine (SAM) enzymes that can incorporate these atoms into different types of chemical structures. However, even though the first halogenation enzyme was discovered in a fungus, this clade is still lagging behind other clades such as bacteria, where many enzymes have been discovered. This review will therefore focus on all halogenation enzymes that have been described in fungi and their associated metabolites by searching for proteins available in databases, but also by using all the available fungal genomes. In the second part of the review, the chemical diversity of halogenated molecules found in fungi will be discussed. This will allow the highlighting of halogenation mechanisms that are still unknown today, therefore, highlighting potentially new unknown halogenation enzymes.