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.     

Enantioseparations by capillary electro-chromatography: differences exhibited by normal- and reversed-phase versions of polysaccharide stationary phases

The influence of using normal-phase and reversed-phase versions of four commercial polysaccharide stationary phases on chiral separations was investigated with capillary electrochromatography (CEC). Both versions of the stationary phases, Chiralcel OD, OJ, and Chiralpak AD, AS were tested for the separation of two basic, two acidic, a bifunctional, and a neutral compound. Different background electrolytes were used, two at low pH for the acid, bifunctional and neutral substances, and three at high pH for the basic, bifunctional and neutral ones. This setup allowed evaluating differences between both stationary-phase versions and between mobile-phase compositions on a chiral separation. Duplicate CEC columns of each stationary phase were in-house prepared and tested, giving information about the intercolumn reproducibility. In general, reversed-phase versions of the current commercial polysaccharide stationary phases are found to be best for reversed-phase CEC, even though at high pH no significant differences were seen between both versions. Most differences were observed at low pH. For acidic compounds, it was seen that an ammonium formate electrolyte performed best, which is also an excellent electrolyte if coupling with mass spectrometry is desired. For basic, bifunctional and neutral compounds, no significant differences between the three tested electrolytes were observed at high pH. Here, a phosphate buffer is preferred as electrolyte because of its buffering capacities. However, if coupling to mass spectrometry is wanted, the more volatile ammonium bicarbonate electrolyte can be used as an alternative.     

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.