Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

Etude par spectrométrie de masse de la fragmentation du désoxy-3-di-O-isopropylidène-1,2: 5,6-méthylidène-3-α-D-hexofurannose et de quelques analogues substitués en C(3′)

Electron Impact Mass Spectrometry of the 3-Desoxy-1,2: 5,6-di-O-isopropylidene-3-methylidene-δ-D -hexofuranose and Some C(3′)-Substituted Analogues The mass spectra of the 3-desoxy-1,2:5, 6-di-O-isopropylidene-3-methylidene- α-D -ribo-hexofuranose and of some C(3′)-mono- and -disubstituted derivatives have been investigated. Deuterium labelled molecules allow fragmentation modes to be proposed.     

Oligothienylenevinylenes incorporating 3,4-ethylenedioxythiophene (EDOT) units

A new series of π-conjugated oligomers based on various combinations of thiophene and EDOT units and double bonds has been synthesized by Wittig-Horner reactions from phosphonate anions carrying EDOT or bis-EDOT units. Optical and electrochemical results evidence the crucial role of the EDOT moiety for modulating the electronic properties of the oligomers. The insertion of bis-EDOT unit in the middle of the molecule leads to a self-rigidification of the conjugated system due to non covalent S?O intramolecular interactions. The strong electron donor effect of the EDOT units explains the determining role of the relative position of the EDOT units on the localization and stabilization of the positive charges in the radical cation or dication states.     

Un théorème de représentation pour les martingales discontinues

We consider a fixed integer-valued random measure (also called a random point process). We represent any local martingale as the sum of a stochastic integral with respect to this random measure, and of a local martingale which does not jump on the support of the random measure.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

A vectorial algorithm with finite element method for prediction of powder segregation in metal injection molding

The design of the mold and the choice of the injection parameters for metal injection molding (MIM) is required to maintain homogeneity of the filled mixture. However, powder segregation is unavoidable in MIM because of the significant difference in densities of the metallic powder and the polymer binder. To achieve an effective prediction of segregation effect, a biphasic model based on mixture theory is employed. The viscous behaviors of each phase and the interaction coefficient between the flows of the two phases should be determined. The solution of two coupled Navier–Stokes equations results in a tremendous computation effort. The previous development of an explicit algorithm makes the biphasic simulation much faster than that of the classic methods. However, it is strongly desired to reduce or even eliminate the numerous global solutions for pressure fields at each time step. Hence, a new vectorial algorithm is proposed and developed to perform the simulation only by vectorial operations. It provides the anticipated efficiency in the simulation of biphasic modeling, and the advantage to use the classic elements of equal‐order interpolations. Some results produced by the two algorithms are compared with the experimental values to validate the new vectorial algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Novel Copolymers of Styrene and Alkyl and Alkoxy Ring‐Trisubstituted Methyl 2‐Cyano‐3‐phenyl‐2‐propenoates

Electrophilic trisubstituted ethylene monomers, akyl and alkoxy ring‐trisubstituted methyl 2‐cyano‐3‐phenyl‐2‐propenoates, RC₆H₂CH[dbnd]C(CN)CO₂CH_3, (where R is 2,3‐dimethyl‐4‐methoxy, 2,5‐dimethyl‐4‐methoxy‐, 2,3,4‐trimethoxy‐, 2,4,5‐trimethoxy, 2,4,6‐trimethoxy, and 2,4‐dimethoxy‐3‐methyl), were synthesized by the piperidine catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and methyl cyanoacetate, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (AIBN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 283–306°C range.