Piecewise suboptimal control laws for differential games

This paper is concerned with optimal parameter selection in differential games. Necessary and sufficient conditions are derived for the existence of a saddle point for a general two-person zero-sum differential game when one or both the players use suboptimal control laws of specified form. The specified forms for the controls consist of weighted sums of the state variables, the weighting factors being products of known time-varying functions and of piecewise-constant functions to be determined in an optimal manner. The controls which are formed in this way are referred to as piecewise control laws. The time intervals associated with the piecewise control laws can be different for each player. The general results are applied to linear-quadratic games, and for this class of differential games, an additional development is given to obtain piecewise control law parameters that are independent of initial conditions, so that a saddle point with respect to the expected value of the performance index is obtained. Consideration has also been given to the problem of optimizing the gain change points. The results are applied to scalar and vector dynamic systems, and numerical solutions are presented.     

Air-breathing laminar flow-based microfluidic fuel cell

This communication reports the design and characterization of an air-breathing laminar flow-based microfluidic fuel cell (LFFC). The performance of previous LFFC designs was cathode-limited due to the poor solubility and slow transport of oxygen in aqueous media. Introduction of an air-breathing gas diffusion electrode as the cathode addresses these mass transfer issues. With this design change, the cathode is exposed to a higher oxygen concentration, and more importantly, the rate of oxygen replenishment in the depletion boundary layer on the cathode is greatly enhanced as a result of the 4 orders of magnitude higher diffusion coefficient of oxygen in air as opposed to that in aqueous media. The power densities of the present air-breathing LFFCs are 5 times higher (26 mW/cm2) than those for LFFCs operated using formic acid solutions as the fuel stream and an oxygen-saturated aqueous stream at the cathode ( approximately 5 mW/cm2). With the performance-limiting issues at the cathode mitigated, these air-breathing LFFCs can now be further developed to fully exploit their advantages of direct control over fuel crossover and the ability to individually tailor the chemical composition of the cathode and anode media to enhance electrode performance and fuel utilization, thus increasing the potential of laminar flow-based fuel cells.     

Substituent effects in polymerization reactions in terms of generalized substituent constants F and R and generalized weighting factors f and r

In this investigation an approach to correlate the composite rate constants of some redox polymerization reactions [acrylonitrile-Ce(IV)-organic substrate] with a new type of multiparameter equation is described. The multiparameter equation is based on Swain and Lupton's F and R, the field and resonance components of the substituents, respectively, and the unique positional weighting factors f and r suggested by Williams and Norrington. The statistical parameters of the correlation involving the substituent constants (fF and rR) and the rate data have been found to be quite satisfactory, the average coefficient of determination being 0.91. The significance levels of the correlation also indicate that the present model is applicable to the kinetics of redox polymerization. The sign and magnitude of the reaction-dependent regression constants α and β suggest that three different types of reaction mechanisms are operative for the substrates benzaldehyde, phenylthiourea, acetophenone, and toluene.     

Radiation stabilization of U5+ in CaO matrix and its thermal stability: Electron paramagnetic resonance and thermally stimulated luminescence studies

Electron paramagnetic resonance (EPR) evidence is presented for the radiation stabilization of pentavalent uranium in CaO matrix. From the theoretical predictions ofg value for U⁵⁺ in axial symmetries, it was concluded that U⁵⁺ at Ca²⁺ site is associated with a second neighbour charge compensating Ca²⁺ vacancy. EPR measurements also revealed the presence of Mn²⁺, Mn⁴⁺ and Cu²⁺ impurities in the samples. The thermal stability of U⁵⁺ was investigated using EPR and thermally stimulated luminescence (TSL) techniques. The TSL and EPR studies on gamma irradiated uranium doped calcium oxide samples had shown that the intense glow peak at 540 K is associated with the reduction in the intensity of EPR signal of U⁵⁺ ion around this temperature. This peak is associated with the process U⁵⁺+hole→U^6+*→U⁶⁺+hv. The activation energy for this process was determined to be 1.4eV.     

Quantized rotation of atoms from photons with orbital angular momentum

We demonstrate the coherent transfer of the orbital angular momentum of a photon to an atom in quantized units of variant Planck's over 2pi, using a 2-photon stimulated Raman process with Laguerre-Gaussian beams to generate an atomic vortex state in a Bose-Einstein condensate of sodium atoms. We show that the process is coherent by creating superpositions of different vortex states, where the relative phase between the states is determined by the relative phases of the optical fields. Furthermore, we create vortices of charge 2 by transferring to each atom the orbital angular momentum of two photons.     

Asymmetric induction during electron transfer mediated photoreduction of carbonyl compounds: role of zeolites

Photochemistry of 17 aryl alkyl ketones included within cation exchanged zeolites has been examined. In solution five of the 17 ketones undergo intramolecular hydrogen abstraction reaction even in the presence of a chiral amine and the rest are photoreduced to the corresponding alcohol. Within zeolites all 17 ketones yielded in presence of a chiral amine, the corresponding alcohol as the major product. When a chiral amine was used as the coadsorbent within alkali ion exchanged zeolites, enantiomerically enriched alcohol was formed in all cases. The best chiral induction was obtained with phenyl cyclohexyl ketone (enantiomeric excess: 68%). 1H-13C Cross Polarization Magic Angle Spinning (CP-MAS) experiments, with a model ketone (perdeuterated acetophenone) and chiral amine (pseudoephedrine) included within MY zeolites, suggested that the cation brings the reactant and the chiral amine closer. The role of the cation in such a process is also revealed by the computation results. The results presented here highlight the importance of a supramolecular structure in forcing a closer interaction between a reactant and a chiral inductor that could be used to achieve asymmetric induction in photoproducts.     

Studies in sigmatropic rearrangements of N-prenylindole derivatives--a formal enantiomerically pure synthesis of tryprostatin B

Rearrangement of N(a)-prenyl-N(b)-acetyltryptamine, induced by BF3.Et2O at low temperature, leads to a 2-prenyl derivative, and thence to the tricyclic tryptamine 7 and the indoline 8. Similarly, N(a)-prenyl-N(b)-phthaloyl-l-tryptophan methyl ester furnished the corresponding 2-prenyl derivative 16, a known advanced precursor of tryprostatin B. Density functional (B3LYP) calculations for the putative rearrangement transition state for N-prenylskatole show that prior coordination of BF3 to the indolic nitrogen changes the character of the subsequent sigmatropic pericyclic shifts from being entirely covalent to acquiring a significant degree of ionic character. The shifting prenyl group favours the endo over the exo mode of the transition state by 4.1 kcal mol(-1).     

Asymmetric induction during photocyclization of chiral and achiral alpha-oxoamides within achiral zeolites

The photochemistry of 31 alpha-oxoamides capable of undergoing gamma-hydrogen transfer has been examined within zeolites. These molecules, upon excitation, yield two products--a beta-lactam and oxazolidinone--in solution, both resulting from gamma-hydrogen transfer. While in benzene the major product is oxazolidinone, within an MY zeolite, the main product is a beta-lactam. In this investigation, we have focused our attention on asymmetric induction in the formation of the beta-lactam product. Two approaches--using a chiral inductor and chiral auxiliary--have been employed. While in solution, in the presence of chiral inductors, achiral alpha-oxoamides yield beta-lactams with zero enantioselectivity; within zeolites, an ee of up to 44% has been achieved. Alpha-oxoamides appended with a chiral auxiliary gave beta-lactams with less than 5% diastereoselectivity in solution while within zeolites, the same alpha-oxoamides gave the products with de's of up to 83%. Such a remarkable influence of zeolites is attributed to an alkali ion interaction with the reactant alpha-oxoamides and to the confined environment of the zeolite interior. At this stage, we have not been able to provide a model with predictive power and further work is needed to understand this valuable asymmetric induction strategy.     

1,3-diketones from acid chlorides and ketones: a rapid and general one-pot synthesis of pyrazoles

[reaction: see text] 1,3-Diketones were synthesized directly from ketones and acid chlorides and were then converted in situ into pyrazoles by the addition of hydrazine. This method is extremely fast, general, and chemoselective, allowing for the synthesis of previously inaccessible pyrazoles and synthetically demanding pyrazole-containing fused rings.