Enantiodiscrimination of racemic electrophiles by diketopiperazine enolates: asymmetric synthesis of methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates

Enolates of (S)-N,N′-bis-(p-methoxybenzyl)-3-iso-propylpiperazine-2,5-dione exhibit high levels of enantiodiscrimination in alkylations with (RS)-1-aryl-1-bromoethanes and (RS)-2-bromoesters, affording substituted diketopiperazines containing two new stereogenic centres in high de. Deprotection and hydrolysis of the resultant substituted diketopiperazines provides a route to the asymmetric synthesis of homochiral methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates in high de and ee.     

Effect of the particle size distribution on the low shear viscosity of high‐solid‐content latexes

The production of high‐solid‐content, low‐viscosity latexes is an active field in both industry and academia. The viscosity of polymer dispersions has a clear dependence on the particle size distribution (PSD). An example is the rule of thumb that a bimodal PSD enables the reduction of the viscosity with respect to monomodal systems. Despite important progress in theoretical work, not much has been done to quantitatively predict the low shear viscosity of aqueous polymer dispersions as a function of the complex PSD. In this work, the capability of a low‐shear‐viscosity equation to quantitatively account for the influence of both the PSD and the physicochemical characteristics of the dispersions is experimentally assessed. An analysis, consistent with theoretical concepts, of the data with semiempirical correlations is proposed. Next, with values of the parameters of the viscosity equation obtained experimentally, the effect of a latex with a 70% solid content on the low shear viscosity is examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3936–3946, 2004     

An algebraic representation of the affine Bäcklund transformation

In 1980 Chern and Terng defined a Bäcklund transformation for affine minimal surfaces. In this paper we show that this Bäcklund transformation can be simply represented by an involution and translation of the affine conormal.     

A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

We apply cluster expansion methods to to theN=2 Wess-Zumino models in finite volume, in two space-time dimensions. We show that in the region of convergence of the cluster expansion, a vanishing theorem holds for the supercharge of the theory; that is, the dimension of the kernel of the Hamiltonian is equal to the index of the supercharge.Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 90-07206Supported in part by National Science Foundation Mathematical Sciences Postodoctoral Research Fellowship DmS 88-07291     

Octahedral metallo-mesogens of chromium, molybdenum and tungsten with 1,4,7-trisubstituted 1,4,7-triazacyclononane and three carbonyl groups as ligands

Liquid crystalline complexes with chromium, molybdenum and with tungsten as metallic centres are reported. 1,4,7-Trisubstituted 1,4,7-triazacyclononane and three carbonyl groups are coordinated in an octahedral geometry. The observed mesophases are characterized as disordered rectangular columnar of a pyramidic type.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

Formation, isolation and characterization of an AB-biaryl atropisomer of oritavancin

Oritavancin is a semi-synthetic glycopeptide antibiotic which is structurally related to vancomycin. When oritavancin bisphosphate is dried in vacuo with heat, a new compound forms. This new compound is stable only in the solid state and reverts to oritavancin in solution. Highly enriched samples of this compound were obtained by preparative HPLC and the structure of this compound was elucidated by using one and two-dimensional (¹H and ¹³C) NMR spectroscopy in conjunction with computer-assisted molecular modeling. It has been determined that oritavancin adopts a conformation similar to that of vancomycin in solution, while the new compound is the unnatural R-AB-biaryl atropisomer of oritavancin. This is the first observation and isolation of an AB-biaryl atropisomer in an intact member of the vancomycin family of glycopeptide antibiotics.     

Vinyl‐type polymerization of norbornene by nickel(II) bisbenzimidazole catalysts

Novel nickel(II) bisbenzimidazole complexes were prepared via a three‐step synthetic procedure consisting of aniline/diacid condensation, ligand N‐alkylation, and metal complexation. The complexes were characterized by X‐ray crystallography and found to possess a pseudotetrahedral geometry. Upon activation with methylaluminoxane, these nickel bisbenzimidazoles did not polymerize simple olefins (e.g., ethylene, propylene, and 1‐butene) but were found to carry out the rapid and efficient polymerization of norbornene. The polynorbornene products were characterized by gel permeation chromatography/light scattering, ¹³C NMR, and IR, and their Mark–Houwink and dn/dc parameters were determined. The molecular weights of the polynorbornenes were very high (weight‐average molecular weight = 587,000–797,000 g/mol). ¹³C NMR suggested that the polymerization occurred via vinyl addition (i.e., a 2,3‐linked polymer); no ring‐opened product was observed. Thermogravimetric analysis indicated that the polynorbornenes were stable up to 400 °C under nitrogen. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2095–2106, 2003     

The phase structure of the two-dimensionalN=2 Wess-Zumino model

We construct a convergent cluster expansion for the two-dimensionalN=2 Wess-Zumino model, in a region of parameter space where there are multiple phase. As a result of this expansion, we are able to construct the infinite volume field theory and demonstrate exponential decay of correlations. We are also able to investigate the different phases of the model, develop the phase diagram, and show that the free energy of each phase vanishes.Supported in part by National Science Foundation grants DMS 90-08827, PHY/DMS 88-16214 and DMS 88-58073Supported in part by National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship DMS 88-07291