Toeplitz Operators Associated to Unimodular Algebras

We introduce a class of function algebras, that we call unimodular, and study Toeplitz operators on the Hardy spaces associated to representing measures on these algebras.We show that our class of function algebras is very extensive and that a number of important results for Toeplitz operators and their associated C*-algebras extend to the very general setting we consider. Submitted: July 1. 2001.     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Synthesis of multiply substituted, ion channel forming octi(p-phenylene)s: theme and variations

[reaction: see text] To facilitate the access to unique models for biological processes, we examined six different synthetic routes to octi(p-phenylene) rods with lateral and terminal substituents R(L) and R(T). This systematic study allowed us to increase to overall yield for the synthesis of a new class of oligo(p-phenylene) ionophores about 20 times and to provide general insights into the practicability of synthetic routes to multiply substituted molecular rods.     

Synthesis, spectroscopy, and X-ray structure of the polymer catena-[bis(azido-N)-copper(II)-μ-bis(2-benzimidazolyl)butane]

The title compound, catena-[bis(azido-N)-copper(II)-(bis(2-benzimidazolyl)butane), [Cu(C₁₈H₁₈N₄)(N₃)₂]_n, was obtained from the reaction of the ligand bis(2-benzimidazolyl)butane and Cu(N₃)₂. The x-ray crystal structure is reported. The compound crystallizes in the monoclinic space group P2₁/c with a = 8.2524(10), b = 12.765(5), c = 9.1125(15) Å, = 106.423(12)°, Z = 2. The Cu(II) ions are square-planar coordinated with trans-oriented end-on binding azido ligands. The structure is a polynuclear chain with the benzimidazole bridging at each end. In addition a N_(ligand)-H···N_(azido) H-bridge [N_(ligand)···N_(azido) = 2.994(7) Å] is present, resulting in a pseudo 2-dimensional lattice. The characteristic azido infrared vibrations are found at 2060 and 2077 cm^–1 (_as(N₃)) and 1284 and 1297 cm^–1 ((N₃)).     

Tables of curves with many points

These tables record results on curves with many points over finite fields. For relatively small genus () and a small power of or we give in two tables the best presently known bounds for , the maximum number of rational points on a smooth absolutely irreducible projective curve of genus over a field of cardinality . In additional tables we list for a given pair the type of construction of the best curve so far, and we give a reference to the literature where such a curve can be found.

     

Polybenzoxazines from renewable diphenolic acid

The novel benzoxazine monomers, DPA‐Bz and MDP‐Bz from renewable diphenolic acid (DPA), which mimics the structure of bisphenol A (BPA), were synthesized by traditional approaches. The structure and purity of the monomers was confirmed by FTIR, ¹H NMR, and ¹³C NMR spectra. The thermally activated polymerization of the MDP‐Bz and DPA‐Bz afforded thermosetting polybenzoxazines with higher T_g's, 270 °C and 208 °C respectively, and higher crosslinking density compared to BPA‐Bz, due to the transesterification or esterification reactions occurred during curing process. These reactions are in accordance with the number of independent reactions determined analyzing by SVD the chemical rank of the IR spectra data matrices recorded along the homopolymerization reactions monitored at 200 °C. Spectral and concentration profiles of the active chemical species involved in these processes were obtained by MCR‐ALS. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

In Vitro Biomineralization and Bulk Characterization of Chitosan/Hydroxyapatite Composite Microparticles Prepared by Emulsification Cross-Linking Method: Orthopedic Use

Chitosan/hydroxyapatite composite microparticles were prepared by a solid-in-water-in-oil emulsification cross-linking method. The characteristics and activity in presence of simulated body fluid for 14 and 21?days were investigated. The size distribution, surface morphology, and microstructure of these biomaterials were evaluated. The scanning electron microscopy revealed an aggregate of microparticles with a particle size, ranged from 4 to 10???m. The deposited calcium phosphate was studied using X-ray diffraction analysis, Fourier transform infrared spectroscopy, and inductively coupled plasma/atomic emission?spectroscopy analysis of phosphorus. These results show that the mineral, formed on microparticles, was a mixture of carbonated hydroxyapatite and calcite. Scanning electron microscopy revealed that calcium phosphate crystals growth was in form of rods organized as concentric triangular packets interconnected to each other by junctions. Interaction between chitosan and growing carbonated hydroxyapatite and calcite crystals are responsible for a composite growth into triangular and spherical shapes. The results demonstrated that these microparticles were potential materials for bone repair.     

Cold Molecules: Preparation,Applications, and Challenges

Research with cold molecules has developed rapidly in recent years. There is now a variety of established methods for cooling molecules into the millikelvin range. Nevertheless, a focal point of current research is directed toward finding new ways to bring the temperature of molecules even closer to absolute zero. Samples of cold molecules offer not only important applications for high‐resolution spectroscopy, which benefit from the increased interaction time of slow molecules with electromagnetic radiation; they also promise access to an exotic regime of chemical reactivity, in which phenomena such as quantum tunneling and quantum resonances predominate. This review begins with an introduction to the methods by which cold molecules can be prepared, with special emphasis on Stark deceleration and traps. In addition to applications of cold molecules that have already been partially achieved, an important focus of the review concentrates on possible future applications, and both aspects are illustrated with selected examples.     

Comment on “Theoretical studies on the ground states in [M(terpyridine)2] and [M(4-(4-(t-butyl)phenyl)terpyridine)2] (M = Fe, Ru, Os) and excited states in [Ru(terpyridine)2] using density functional theory”

The nature of the first excited state of [Fe(terpyridine)₂]²⁺ has been reinvestigated. In contrast to previous findings, it is metal-to-ligand charge transfer in nature, thus fitting in the series of the Ru and Os complexes.