Regularity and Algebras of Analytic Functions in Infinite Dimensions

A Banach space is known to be Arens regular if every continuous linear mapping from to is weakly compact. Let be an open subset of , and let denote the algebra of analytic functions on which are bounded on bounded subsets of lying at a positive distance from the boundary of We endow with the usual Fréchet topology. denotes the set of continuous homomorphisms . We study the relation between the Arens regularity of the space and the structure of .

     

Compact holomorphic mappings on Banach spaces and the approximation property

Let $\text{H}$(E) be the space of complex valued holomorphic functions on a complex Banach space E. The approximation property for $\text{H}$(E), endowed with various natural locally convex topologies, is studied. For example, $\text{H}$(E) with the compact-open topology has the approximation property if and only if E has the approximation property. In order to characterize when $\text{H}$(E) has the approximation property for topologies other than the compact-open, the notion of a compact holomorphic map between Banach spaces in introduced and studied.     

Left–right and dynamic correlation

Within density functional theory, it is natural to separate the correlation energy into two parts: left–right correlation and dynamic correlation. Left–right correlation arises from the exchange part of functionals, and dynamic correlation arises from the correlation part of functionals. We examine the nature of these correlation energies as molecules are distorted. We observe that such a natural separation is not possible using the methods of quantum chemistry. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Highly Efficient and Practical Syntheses of Lavendamycin Methyl Ester and Related Novel Quinolindiones

The novel 7-(N-formyl-, 7-(N-acetyl-, and 7-(N-isobutyrylamino)-2-methylquinoline-5,8-diones were synthesized in excellent overall yields in three steps via the nitration of the commercially available 8-hydroxy-2-methylquinoline followed by a reduction-acylation step and then oxidation. Acid hydrolysis of 7-(N-acetylamino)-2-methylquinoline-5,8-dione (14a) afforded the novel 7-aminoquinoline-5,8-dione 7 in excellent yields. Due to our efficient preparation of dione 14a, we now report a short and practical method for the total synthesis of the potent antitumor agent lavendamycin methyl ester (1b) with an excellent overall yield.     

Characterization of a new tailoring domain in polyketide biogenesis: the amine transferase domain of MycA in the mycosubtilin gene cluster

We report the expression and characterization of a truncated form of MycA from the Mycosubtilin gene cluster from Bacillus subtilis. The MycA fragment contains a new amino transferase (AMT) tailoring domain, allowing the first detailed study of a PLP-dependent enzyme operating in cis within the PKS and NRPS biosynthetic paradigm. As the AMT domain acts on covalently bound beta-ketothioesters, and is therefore a single-turnover system, electrospray ionization-Fourier transform mass spectrometry (ESI-FTMS) was used to observe the amine-transfer reaction both for amine donor substrate specificity and to regiospecifically determine enzyme-bound intermediates. We confirm the function of the AMT domain, dissect the mechanistic steps of amine transfer, identify the preferred amine source, and localize the beta-ketothioester substrate during amine transfer.     

The Bishop-Phelps-Bollobás theorem for operators

We prove the Bishop-Phelps-Bollobás theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop-Phelps-Bollobás theorem holds for operators from ?₁ into Y. Several examples of classes of such spaces are provided. For instance, the Bishop-Phelps-Bollobás theorem holds when the range space is finite-dimensional, an L₁(μ)-space for a σ-finite measure μ, a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.     

Novel structural templates for estrogen-receptor ligands and prospects for combinatorial synthesis of estrogens

BACKGROUND: The development of estrogen pharmaceutical agents with appropriate tissue-selectivity profiles has not yet benefited substantially from the application of combinatorial synthetic approaches to the preparation of structural classes that are known to be ligands for the estrogen receptor (ER). We have developed an estrogen pharmacophore that consists of a simple heterocyclic core scaffold, amenable to construction by combinatorial methods, onto which are appended 3-4 peripheral substituents that embody substructural motifs commonly found in nonsteroidal estrogens. The issue addressed here is whether these heterocyclic core structures can be used to prepare ligands with good affinity for the ER. RESULTS: We prepared representative members of various azole core structures. Although members of the imidazole, thiazole or isoxazole classes generally have weak binding for the ER, several members of the pyrazole class show good binding affinity. The high-affinity pyrazoles bear close conformational relationship to the nonsteroidal ligand raloxifene, and they can be fitted into the ligand-binding pocket of the ER-raloxifene X-ray structure. CONCLUSIONS: Compounds such as these pyrazoles, which are novel ER ligands, are well suited for combinatorial synthesis using solid-phase methods.     

Stereochemistry of post-transition metal oxides: revision of the classical lone pair model

The chemistry of post transition metals is dominated by the group oxidation state N and a lower N-2 oxidation state, which is associated with occupation of a metal s(2) lone pair, as found in compounds of Tl(I), Pb(II) and Bi(III). The preference of these cations for non-centrosymmetric coordination environments has previously been rationalised in terms of direct hybridisation of metal s and p valence orbitals, thus lowering the internal electronic energy of the N-2 ion. This explanation in terms of an on-site second-order Jahn-Teller effect remains the contemporary textbook explanation. In this tutorial review, we review recent progress in this area, based on quantum chemical calculations and X-ray spectroscopic measurements. This recent work has led to a revised model, which highlights the important role of covalent interaction with oxygen in mediating lone pair formation for metal oxides. The role of the anion p atomic orbital in chemical bonding is key to explaining why chalcogenides display a weaker preference for structural distortions in comparison to oxides and halides. The underlying chemical interactions are responsible for the unique physicochemical properties of oxides containing lone pairs and, in particular, to their application as photocatalysts (BiVO(4)), ferroelectrics (PbTiO(3)), multi-ferroics (BiFeO(3)) and p-type semiconductors (SnO). The exploration of lone pair systems remains a viable a venue for the design of functional multi-component oxide compounds.