Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems

In this paper we introduce a new notion of infine nonsmooth functions and give several characterizations of infineness property. We prove alternative theorems with mixed constraints (i.e., inequality and equality constraints) being described by invex-infine nonsmooth functions. We establish a necessary and sufficient condition for a solution of a vector optimization problem involving mixed constraints to be a properly efficient solution.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Polymérisation anionique amorcée par les composés lamellaires du graphite et du lithium

In the present work, we use the binary insertion compound LiC₁₂ to polymerize styrene, methyl methacrylate, butadiene, isoprene, and to copolymerize isoprene and styrene in various hydrocarbon solvents (aromatics and aliphatic) and etheral solvents. We show that the styrene polymerization in aromatic solvents gives better yields than in the etheral solvents, the polymer being atactic. Methyl methacrylate does not polymerize in toluene but does so completely in DME. More generally, the yields of polymerization are better with KC₃₇ than with LiC₁₂ because of the different capacities of the monomer to get into the carbon layers. The polymerization of dienes with LiC₁₂ shows that the microstructures of the polymer obtained in π-or n-donor solvents are similar to the ones obtained by homogenous polymerization with Li cation in such solvents. However, for isoprene in cyclohexane, the results are different. The isoprene styrene copolymers are statistical ones and the mean length of styrene blocks is less than 5. The monomer interaction with the insertion compound and the growing chain geometry between the carbon layers are the facts which control either the stereospecificity of the polymerization or the selectivity of the copolymerization.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

Fine characterization of the ethylene and ethane sorption in poly(amide 12-block-tetramethylenoxide) copolymer/AgBF4 membranes

Ethylene/ethane sorption characteristics were determined for dry Pebax™ (poly(amide 12-block-tetramethylenoxide) copolymer)/AgBF₄ membranes by using an electronic microbalance. The membranes containing 0.7 and 22 wt.% AgBF₄ showed a dual-mode sorption isotherm. The ethane isotherms for all the membranes were of the Henry-type, which is the normal sorption for gases in rubbery polymers. The abnormal presence of Langmuir sorption sites only for ethylene in the rubbery copolymer, never reported sofar, is attributed to the silver-based specific complexation sites. The silver salt which dissolved in limited amounts in the rubbery copolymer had a much smaller Langmuir sorption capacity than the salt that crystallized in the copolymer. The sorption kinetics indicate that the crystallized salt did adsorb slowly ethylene according to a zeroth-order kinetics, but not ethane. The gas uptake kinetics resulting from a step of the pressure surrounding the copolymer exhibited one stage for ethane but two stages for ethylene. For the latter, there was first a fast Fickian sorption stage, then a drift of the zeroth-order sorption of ethylene on salt crystals, which contributes for a large part to the total uptake. The zeroth-order sorption suggests that the sorbed ethylene amount in the second-stage is independent of the crystal-surface coverage. The value of the Fickian diffusion coefficient calculated by fitting the kinetics with a solution of the second Fick’s law was 5 × 10⁻¹² m²/s for both ethylene (the first stage) and ethane, and is typical for small organic compounds in a rubbery material.     

Phenomenes de complexation entre un peroxyde et les monomeres vinyliques polaires etudies par resonance magnetique protonique

The self association of cumyl hydroperoxide and its complexing with polar monomers have been studied by proton magnetic resonance. These complexations are exothermic and strongly temperature dependent. It has been suggested that the complexation of cumyl hydroperoxide by polar monomers could be one of the causes of its efficiency in initiating the radical polymerization of vinyl monomers on an ethyl-zinc terminated polyethylene chain to form radical block copolymers. However, if this phenomenon has an effect on the initiation, it should not affect the propagation mechanisms, because the hydroperoxide is destroyed by ZnEt₂ during initiation. Moreover, the tacticity of radical polymethylmethacrylate, obtained at 60° with (ZnEt₂—cumyl hydroperoxide) in heptane does not differ from the conventional radical polymer.     

Conformations of luteoskyrin and rugulosin in solution

The pigments Luteoskyrin (Ls) and Rugulosin (Rg) might adopt a priori two extreme conformations, a planar and an angular one. To determine the predominant conformation in solution, the nature of the lowest energy transition of the chromophores and the presence of intramolecular H-bonding have been investigated. The solvent effects on electronic absorption and CD spectra indicated the π-π* nature of the lowest energy transition. Treatments of the electronic absorption results according to McRae and Kosower relations, IR absorption and PMR spectra suggested the presence of strong intra-molecular H-bonds. From these results it was concluded that Ls and Rg adopted in a variety of solvents the most planar conformation.     

Investigation of oligomethylmethacrylate-lithium and its donor-acceptor complexes with organometal compounds by means of infrared spectroscopy

Anionic polymerization of methyl methacrylate in THF and toluene at ?70° was studied by means of i.r. spectroscopy. The reaction mixtures show characteristic absorption at 1600–1750 cm^?1 caused by the stretching vibrations of the propagating centre as well as by the groups obtained in side reactions (metal splitting, addition to a carbonyl group, cyclization). Sec-butyllithium is more effective in THF than n-butyllithium, ethyllithium and fluorenyllithium. When polymerizing in toluene, small amounts of a donor (THF or HMPT) cause formation of active centres similar to those in pure THF. The “living” ends of oligo-MMA form 1:1 complexes with electron acceptors such as trialkylaluminium and triethylboron.