Shear-induced crystallization of polypropylene. Growth enhancement and rheology in the crystallization range

Crystallization under shear of many different polypropylenes has been studied using a fiber pull-out device. It appears that growth can be considerably enhanced by flow. The best correlation is obtained with weight average molecular weight. Modeling the flow pattern gives access to the mechanical parameters at the growth front (shear rate and shear stress) as well as to the total strain applied to the polymer. The residual strain can be calculated taking into account relaxation processes.     

Catalytic Antibodies by Fluorescence Screening

A series of eleven immunizations against transition-state analogs were carried out to improve the catalytic properties of Ab 9D9, a catalytic antibody that catalyzes a fluorogenic retro-Diels-Alder reaction liberating nitroxyl. By a direct fluorescence assay of cell-culture supernatant, eight new hybridoma cell lines producing catalytic antibodies for the reaction were readily identified among more than 14000 individual samples. Our results demonstrate that early catalysis screening by fluorescence allows an efficient survey of large antibody libraries, and may lead to rapid and significant improvement in catalysis.     

Enantioselective Fluorogenic Assay of Acetate Hydrolysis for Detecting Lipase Catalytic Antibodies

An enantioselective fluorogenic assay for the kinetic resolution of chiral alkyl acetates is demonstrated with 7-(3-acetoxybutoxy)-2H-1-benzopyran-2-ones (R)- and (S)- 4 or 7-(3-acetoxy-2-methylpropoxy)-2H-1-benzopyran-2-ones (R)- 4 and (S)- 6 . The alcohols released by hydrolysis of these acetates are oxidized by horse-liver alcohol dehydrogenase to unstable β-(aryloxy)carbonyl compounds, which undergo β-elimination of the strongly fluorescent product umbelliferone (=7-hydroxy-2H-1-benzopyran-2-one; 3 ) (λ_em=460±20 nm, λ_ex=360±20 nm). Enantioselectivities are calculated from the reaction rates for each enantiomeric acetate. For a series of representative lipases, the reactivities and enantioselectivities under preparative conditions are predicted accurately. This highly sensitive enantioselective assay detects as little as 10 μg/ml of hydrolytic enzyme, can be carried out in 96-well microtiter plates, and is compatible with cell-culture media. It is, therefore, suited for screening libraries of antibodies for enantioselective lipase catalytic antibodies.     

Finite and infinite Born-von Kármán regions

An attempt is made to present the connection between periodic boundary conditions and discrete wave vectors in a systematic fashion, with the continuous wave vectors as an extreme special case. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 223–227, 1997     

Chern–Weil map for principal bundles over groupoids

The theory of principal G-bundles over a Lie groupoid is an important one unifying various types of principal G-bundles, including those over manifolds, those over orbifolds, as well as equivariant principal G-bundles. In this paper, we study differential geometry of these objects, including connections and holonomy maps. We also introduce a Chern–Weil map for these principal bundles and prove that the characteristic classes obtained coincide with the universal characteristic classes. As an application, we recover the equivariant Chern–Weil map of Bott–Tu. We also obtain an explicit chain map between the Weil model and the simplicial model of equivariant cohomology which reduces to the Bott–Shulman map when the manifold is a point. P. Xu Research partially supported by NSF grant DMS-03-06665.     

A matrix generation approach for eigenvalue optimization

We study the extension of a column generation technique to nonpolyhedral models. In particular, we study the problem of minimizing the maximum eigenvalue of an affine combination of symmetric matrices. At each step of the algorithm a restricted master problem in the primal space, corresponding to the relaxed dual (original) problem, is formed. A query point is obtained as an approximate analytic center of a bounded set that contains the optimal solution of the dual problem. The original objective function is evaluated at the query point, and depending on its differentiability a column or a matrix is added to the restricted master problem. We discuss the issues of recovering feasibility after the restricted master problem is updated by a column or a matrix. The computational experience of implementing the algorithm on randomly generated problems are reported and the cpu time of the matrix generation algorithm is compared with that of the primal-dual interior point methods on dense and sparse problems using the software SDPT3. Our numerical results illustrate that the matrix generation algorithm outperforms primal-dual interior point methods on dense problems with no structure and also on a class of sparse problems. This work has been completed with the partial support of a summer grant from the College of Business Administration, California State University San Marcos, and the University Professional Development/Research and Creative Activity Grant     

Homology stability for orthogonal groups over algebraically closed fields

We give the best ranges of stability, for homology of orthogonal groups and special orthogonal groups, over an algebraically closed field, of characteristic different from 2. This answers affirmatively a conjecture asserted in a previous paper. We find distinct ranges of stability for orthogonal and special orthogonal groups, and Milnor K-theory appears as an obstruction to stability for special orthogonal groups. The main results are formulated, more generally, for infinite Pythagorean fields.     

Primitive du cocycle de Maslov généralisé

Résumé Soit un espace hermitien symétrique de type tube, de frontière de Shilov S. Nous décrivons une réalisation du revêtement universel de S. Nous construisons ensuite sur une primitive du cocycle de Maslov généralisé. C’est l’analogue de l’indice de Souriau pour la variété lagrangienne. Une variante de cette construction généralise l’indice d’Arnold-Leray-Maslov. Enfin, nous utilisons cette primitive pour généraliser la notion de nombre de rotation symplectique.     

Dyadic Hermite interpolation on a rectangular mesh

Given f and ∇f at the vertices of a rectangular mesh, we build an interpolating function f by a subdivision algorithm. The construction on each elementary rectangle is independent of any disjoint rectangle. From the Hermite data associated with the vertices of a rectangle R, the function f is defined on a dense subset of R. Sufficient conditions are found in order to extend f to a C ¹ function. Moreover, infinite products and generalized radii of matrices are used to study the convergence to a C ¹ function. This convergence depends on the five parameters introduced in the algorithm. This revised version was published online in June 2006 with corrections to the Cover Date.