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.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

Facile cyclic ammonium salt with the smallest size for high performance electric double layer capacitors

A novel cyclic ammonium salt, N,N-dimethylpyrrolidinium tetrafluoroborate (P₁₁-BF₄), was successfully synthesized for the first time. The smallest cyclic structure of P₁₁-BF₄ induced high solubility and conductivity in PC, which can easier enter the micropores of activated carbon and occupy more surface area during charge/discharge process.     

二氧化碳与环氧化物的调节共聚合反应速率

在二氧化碳和环氧化物共聚时加入特定的调节剂，生成有规定的分子量和端基官能度的产物．这种调节聚合的本质是调节剂所含活泼氢与活性中心之间的链转移反应．根据建议的历程，提出了调节共聚速率方程，计算结果与实验一致．     

π-Bindungsbeitrag in Boranen, 2. Mitt.:Ab initio- und Kraftfeld-Rechnungen von Vinyldifluorboran

Ab initio calculations on vinyldifluoroborane yield a -contribution of 23 kJ/mol (5.5 kcal/mol) mainly due to the C=C bond and not to the lone pairs of the fluorine atoms. The rotational barrier was also determined. The force field calculations favour the interpretation of the bond structure derived from the theab initio results.

     

On the calculation of expectation values and transition matrix elements by coupled cluster method

Summary Finite order expressions are derived for expectation values and transition matrix elements within the framework of the coupled cluster method.     

Electronic spectral and photophysical properties of some p-phenylenevinylene oligomers in solution and thin films

A comprehensive photophysical and spectroscopic study of a new class of p-phenylenevinylene oligomers (PPV-trimers) possessing different alkyl and alkyloxy sidechain substituents and different end groups (aldehyde, CC, phenylene and anthracene units) was undertaken in solution at room temperature (293 K), low temperature (77 K) and in thin films. The study comprises absorption, emission and triplet–triplet absorption spectra, together with quantitative measurements of quantum yields (fluorescence, intersystem crossing, internal conversion and singlet oxygen formation) and lifetimes. The data allow the determination of rate constants for all decay processes. From these, several conclusions could be drawn. Changing from alkyl to alkyloxy substituents does not change fluorescence and internal conversion yields but decreases the (already small) intersystem crossing yield. The introduction of anthracene at the terminal ends of the PPV-trimers leads to the lowest fluorescence yield reported in this study. Of particular importance is the fact that the fluorescence quantum yields in films are of the same order of magnitude as those in solution, which suggests the potential for use of these oligomers for light-emitting device applications. With one of the alkyloxy derivatives, a more detailed study of the early part of the fluorescence decay was made, and it was found that upon excitation a fast conformational relaxation process of the initially excited oligomer occurs, leading to a more planar conjugation segment.     

Force Constants and Bond Orders of Nitrogen Bonds

The force constants and the corresponding bond orders of nitrogen bonds have been calculated from the vibrational spectra (infrared and Raman spectra) of a great number of nitrogen compounds. Plotting the maximum bond order of stable nitrogen bonds against the sum of Pauling's electronegativities of the bonding partners (Σx) leads to one continuous curve for the N? X bonds where X represents elements of the first and the second short period of the periodic table. Furthermore, when the bonds formed between these elements are arranged in a coordinate system in such a way that the position of each bond is determined by the difference between the electronegativities of the bonding partners (Δx along the ordinate) and the sum of the electronegativities of the bonding partners (Σx along the abscissa), the bonding partners capable of forming multiple bonds all lie within a closed domain, where their position can be correlated with their polymerizability and other reactivities of the multiple bonds. Also discussed are the orders of bonds between nitrogen and some transition elements. In an appendix, the present methods used to calculate force constants and bond orders are surveyed.     

Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.     

Absolute Rate Constants for the Addition of the 1‐(tert‐Butoxy)carbonylethyl Radical onto Cyclic Alkenes in Solution

Absolute rate constants are reported for the addition of the 1‐[(tert‐butoxy)carbonyl]ethyl (= 2‐(1,1‐dimethylethoxy)‐1‐methyl‐2‐oxoethyl) radical ^.CHMeCO₂(t‐Bu) to several cyclic and monosubstituted alkenes in MeCN as obtained by time‐resolved electron paramagnetic resonance (EPR). The activation energies for the addition of this alkyl radical are mainly governed by the addition enthalpy but are also substantially lowered by the ambiphilic effect and by relief of cyclic strain.