α-Glycosylation by D-glucosamine-derived donors: synthesis of heparosan and heparin analogues that interact with mycobacterial heparin-binding hemagglutinin

Numerous biomolecules possess α-D-glucosamine as structural component. However, chemical glycosylations aimed at this backbone are usually not easily attained without generating the unwanted β-isomer. We report herein a versatile approach in affording full α-stereoselectivity built upon a carefully selected set of orthogonal protecting groups on a D-glucosaminyl donor. The excellent stereoselectivity provided by the protecting group combination was found independent of leaving groups and activators. With the trichloroacetimidate as the optimum donor leaving group, core skeletons of glycosylphosphatidyl inositol anchors, heparosan, heparan sulfate, and heparin were efficiently assembled. The orthogonal protecting groups were successfully manipulated to further carry out the total syntheses of heparosan tri- and pentasaccharides and heparin di-, tetra-, hexa-, and octasaccharide analogues. Using the heparin analogues, heparin-binding hemagglutinin, a virulence factor of Mycobacterium tuberculosis, was found to bind at least six sugar units with the interaction notably being entropically driven.     

Perceived parental influence and students' dispositions to study mathematically-demanding courses in Higher Education

We explore the influence of family on adolescent students' mathematical habitus by investigating the association between students' perceptions of parental influence and their dispositions towards mathematics. A construct measuring ‘perceived parental influence’ was validated using Rasch methodology on data from 563 Cypriot students on ‘core’ and ‘advanced’ mathematics pre-university courses, and was then used to predict students' dispositions towards future study of mathematically-demanding courses at university. In most of the regression models, perceived parental influence was not associated significantly with students' dispositions towards mathematics, when other variables were included in the models. However, further statistical analysis showed that perceived parental influence is mediated by (i) the mathematics course students are studying and (ii) their mathematical inclination. We suggest that family influences on students' dispositions are significantly accounted for by students' prior choice of mathematics course and the family's inculcation of their mathematical inclination; these are important factors influencing university choices.     

The study of a homogeneous column of argon plasma at a pressure of 0.5 torr,generated by means of the Beenakker’s cavity

A homogeneous column of argon plasma at a pressure of 0.5 torr, generated by means of the Beenakker cavity, has been investigated by methods of emission spectroscopy, photography and self-consistent 3D modeling in a nonlocal approximation. It is shown that the plasma column, which spreads beyond the resonator, is spatially uniform and it represents the afterglow of the microwave discharge produced inside the cavity. The simulation data of the spatial distributions of the electron energy density and concentrations of electrons, ions and argon atoms in metastable and radiating states are presented. The results of calculations are in agreement with experimental data.     

Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions

We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions. These are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper, we focus on the case of Hilbert spaces and introduce, in particular, a version of the Hardy space. Then we define Blaschke factors and Blaschke products and consider an interpolation problem. In the second part of the paper, we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, a theorem of Shmulyan on densely defined contractive linear relations. We then study realizations of generalized Schur functions and of generalized Carathéodory functions.     

Structures and thermodynamics of biphenyl dihydrodiol stereoisomers and their metabolites in the enzymatic degradation of arene xenobiotics

A key step in the metabolic degradation of biphenyl xenobiotics is catechol formation upon dehydrogenation of cis‐ and trans‐dihydrodiols in prokaryotic and eukaryotic pathways, respectively. Structure and thermodynamics of stereoisomers of cis‐, trans‐2,3‐biphenyl‐dihydrodiols ( I ) and their dehydrogenation products (hydroxyketones, II ), as well as final catechol (2,3‐biphenyldiol, III ) are studied by means of ab initio MP2/6‐311++G(2df,2p)//MP2/6‐311G(d,p) calculations. Formation of stereoisomers I and II is exothermic and endergonic, whereas III is enthalpically and entropically driven. Dehydrogenations are endothermic (ΔH ～ 1.5–4 kcal mol^?1) and exergonic (ΔG ～ ?5 to ?7.5 kcal mol^?1) without noticeable differences between cis and trans pathways, although the same keto stereoisomer II ‐(2S) is found to be the more favored product from both cis‐ and trans‐ I . The final II → III tautomerization is thermodynamically enhanced (ΔH ～ ?27, ΔG ～ ?28 kcal mol^?1) but the process is shown to have a large activation energy if it had to occur via unimolecular path. Although this tautomerization is generally assumed to be a nonenzymatic process as it involves rearomatization of an oxygenated ring, proton transfer with an anionic intermediate might be a more probable process. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Asymptotic behavior at the boundary of a semiconductor device in two space dimensions

We study the analytic properties of the solution to a system of elliptic-parabolic equations simulating a semiconductor device. We describe the optimal regularity of the solution and its asymptotic behavior at the singular points of the problem.This paper is based on the thesis dissertation presented at the University of Chicago, Chicago, Illinois, in December 1989.     

Schwarzschild geometry,once more

Schwarzschild geometry exhibits interesting features when the field equations are decomposed with respect to a system of freely falling observers. We only use quantities behaving like tensors under a restricted group of transformations of the reference system. Moreover Lorentz transformations with non-constant velocities drastically change the physical picture of the theory.     

A-B quasiconvexity and implicit partial differential equations

The study of existence of solutions of boundary-value problems for differential inclusions where , is an open subset of , is a compact set, and B is a -valued first order differential operator, is undertaken. As an application, minima of the energy for large magnetic bodies where the magnetization is taken with values on the unit sphere is the induced magnetic field satisfying and is the anisotropic energy density, and the applied external magnetic field is given by , are fully characterized. Setting with , it is shown that E admits a minimizer with if and only if either 0 is on a face of or , where denotes the convex hull of Z. Received: 6 November 2000 / Accepted: 23 January 2001 / Published online: 23 April 2001