Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Efficient preparation of chiral diamines via Red-Al reduction of N-Boc-protected amino acid-derived secondary amides

Conditions have been developed for the selective reduction of N-Boc-protected amino acid-derived secondary amides, avoiding the formation of overreduction and cyclic urea byproducts. The method is showcased by the efficient formal synthesis of NK-1 antagonist LY303870.     

Complex systems and human movement

Human movement reveals the hall mark characteristics of complex systems: namely, many interacting subsystems, multiple interactions within and between levels of analysis, emergence of movement coordination modes, and the exhibition of varying levels of the complexity of system output that continually evolve with learning and development over the life span. Here we outline how this high or infinitely dimensional complex dynamical system can be modeled by an epigenetic landscape framework—in the sense of Waddington—that captures the key features of the adaptive qualitative and quantitative properties of coordination modes (“order parameters”), the degeneracy of movement organization and the time scales of change. The framework provides some new ways to consider old problems in motor learning and development—such as an explicit and quantitative approach to exploring the concept of motor programs and developmental pathways—and yields new results and insights into the organization of learning during practice and rest times. For instance along one dimension of the landscape most of the changes occur between practice sessions. © 2006 Wiley Periodicals, Inc. Complexity 12: 40–51, 2006     

Intense Molar Circular Dichroism in Fully Conjugated All-Carbon Macrocyclic 1,3-Butadiyne Linked pseudo-meta [2.2]Paracyclophanes**

The synthetic access to macrocyclic molecular topologies with interesting photophysical properties has greatly improved thanks to the successful implementation of organic and inorganic corner units. Based on recent reports, we realized that pseudo-meta [2.2]paracyclophanes (PCPs) might serve as optimal corner units for constructing 3D functional materials, owing to their efficient electronic communication, angled substituents and planar chirality. Herein, we report the synthesis, characterization and optical properties of four novel all-carbon enantiopure macrocycles bearing three to six pseudo-meta PCPs linked by 1,3-butadiyne units. The macrocycles were obtained by a single step from enantiopure, literature-known dialkyne pseudo-meta PCP and were unambiguously identified and characterized by state of the art spectroscopic methods and in part even by x-ray crystallography. By comparing the optical properties to relevant reference compounds, it is shown that the pseudo-meta PCP subunit effectively elongates the conjugated system throughout the macrocyclic backbone, such that already the smallest macrocycle consisting of only three subunits reaches a polymer-like conjugation length. Additionally, it is shown that the chiral pseudo-meta PCPs induce a remarkable chiroptical response in the respective macrocycles, reaching unprecedented high molar circular dichroism values for all-carbon macrocycles of up to 1307 L mol⁻¹ cm⁻¹.     

Morphology of dry solid-supported protein monolayers dependent on the substrate and protein surface properties

The morphologies of dry MrgA protein monolayers on different solid substrates prepared by a three-step procedure (adsorption from an incubation solution, rinsing to remove excess salt and protein, and drying) were investigated using atomic force microscopy. MrgA is a dodecameric iron-storage protein which can form hexagonal, two-dimensional (2D) crystalline monolayers on hydrophilic surfaces at low supersaturation. The formation of such two-dimensional crystals is heavily dependent on the pH and the salinity of the incubation solution as well as on the surface properties. Correlation of surface coverage with substrate charge, ionic strength, and pH indicates the dominance of electrostatic effects in adsorption, with the balance shifting between intermolecular repulsion and protein-substrate attraction. Close to the isoelectric point (pI) of MrgA, adsorption to the surface and the formation of 2D crystals are favored. By preparation of self-assembled monolayers of thiols with different end groups on template-stripped gold, the surface properties can be varied easily from high to very low protein affinity. The resulting patterns of the crystalline protein structures are novel and could be a starting point for further scientific study, e.g., solid-supported cocrystallization with DNA, and indeed developments with technological applications, such as mesostructured deposition of MrgA-caged nanoparticles.     

Preparation of 3-arylmethylindoles as selective COX-2 inhibitors

The 3-arylmethylation of indoles using TMSOTf/Et₃SiH with a wide variety of substituted benzaldehydes has been accomplished. Under these mild Lewis acid mediated reductive conditions, it was demonstrated that indoles bearing both 6-MeSO₂ and 2-methyl substituents could be 3-arylmethylated in good to excellent yields to afford the corresponding 3-arylmethyl indoles, effective as selective COX-2 inhibitors. In addition, the viability of this method for the reductive alkylation of indoles by ketones was demonstrated and shown to be C-3 regioselective. For indoles bearing both a 6-MeSO₂ and 2-cyano substituent where this indole reductive alkylation methodology was unsuccessful, an unprecedented Pd(0) mediated arylorganozinc coupling with the requisite substituted 3-methylcarbonatomethylindole proved successful in affording the desired 2-cyano-6-MeSO₂-3-arylmethylindoles effective as selective COX-2 inhibitors.     

Iron complexes of terdentate nitrogen ligands: formation and X-ray structure of three new dicationic complexes

Dicationic iron complexes were obtained upon complexation of the ligands 6,6″-di(p-tolyl)-2,2′:6′,2″-terpyridine (L¹) or 2,6-bis-(3-mesitylpyrazol-1-yl)pyridine (L²) with iron dichloride or iron trichloride. They were characterized by X-ray diffraction and FT-IR spectroscopy. Single crystal structure determinations of , and all show six-coordinate metal center. These complexes were obtained from L¹FeCl₂ and L²FeCl₂ during recrystallization attempts. (L¹)₂Fe²⁺ was shown to be a high-spin complex, whereas (L²)₂Fe²⁺ was shown to be low-spin. For , two independent dications of very similar geometry but with distinctive distortion were observed by X-ray analysis.     

A theoretical study of bond energies in model Si–H–Cl molecules using density functional approaches for representing Si surface chemistry

The reliability of density functional theory (DFT) methods for calculating Si(SINGLE BOND)2H, Si(SINGLE BOND)Cl, and Si(SINGLE BOND)Si bond energies is examined in reactions involving molecules and small clusters representing various surface sites appropriate for Si surface chemistry. Results are presented for systematic studies using a valence double-zeta polarization basis for both all-electron calculations and valence–electron calculations employing effective core potentials (ECPs). All-electron DFT results are comparable to much more demanding MP4, G2, and MC–SCF–CI calculations for computed bond energies. Whereas the use of ECPs introduces systematic energy differences of ca. 3–5 kcal/mol compared to AE results, depending on the type of bond involved, the use of ECPs for carrying out calculations on larger clusters is discussed where AE calculations become more computationally demanding. The convergence of Si bond energies as a function of replacing hydrogens with silyl groups is examined. In constructing models to describe etching processes involving Cl species on Si surfaces, the need for incorporating differences in thermochemistries for one-, two-, and three-coordinate Si surface sites is emphasized. Comparisons of semiempirical approaches for thermochemistries of Si-containing species find these methods somewhat less reliable for obtaining reliable bond energies compared to computationally more demanding DFT and ab initio correlated models. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2075–2085, 1997