Enantioselective synthesis of all-carbon quaternary stereogenic centers in acyclic systems

Most of the methods for the creation of all-carbon quaternary stereogenic centers in acyclic systems were developed in the last decade showing the contemporary interest of this field of research. Initial strategies, where chiral entities were linked to carbon skeleton, to enantioselective catalysis and finally to strategies where several carbon-carbon bonds were created in a single-pot operation, reflect the constant strive and creativity in the design and execution of synthetic sequences. This feature article summarizes these sequences and is divided into sections on substitution and additions reactions, alkylation, aldol, Mannich and rearrangements reactions. It is safe to predict that this field of chemistry will continue to grow exponentially in the coming decades and the ready availability of a wide range of these chiral entities will provide an excellent opportunity to further enrich mainstream synthetic methodologies.     

Recombinant cellulose crosslinking protein: a novel paper-modification biomaterial

Cellulose-binding domains have been isolated from various cellulases, and proteins, which lack hydrolytic activity. The hypothesis that a cellulose-binding domain can be used to alter surface and mechanical properties of paper was tested. Two cellulose-binding domains from Clostriium cellulovorans were fused to form a cellulose crosslinking protein (CCP). The recombinant bifunctional cellulose-binding protein was expressed in E. coli, appliedby immersion onto Whatman cellulose filter paper, and its mechanical properties were tested. The purified protein improved the treated paper's mechanical properties (tensile strength, brittleness, Young's modulus and energy to break). In addition, cellulose crosslinking protein treatment was shown to transform filter paper into a more water-repellent paper. The binding of cellulose-binding domains to cellulose under a wide range of envi-ronmentalconditions, without the need for chemical reactions, and its biodegradability make them attractive moieties for the design of a new class of paper-modification materials.p>     

High performance solution of the complex symmetric eigenproblem

Complex symmetric matrices often appear in quantum physics in the solution methods of partial differential equations such as the Schrödinger equation. We have recently introduced a new fast and efficient direct eigensolver for this problem in [4], and reported its performance in the eigenvalue calculation in [3]. In this paper, we further report on some benchmark tests for computing the full and partial eigenspectrum on a variety of super computing machines, i.e., the Cray J-932, the DEC Alfa 8400, and the SGI Power Challenge 8000 and 10000. We observe that in all cases the new algorithm is much faster than codes available in standard state of the art eigensolver packages such as LAPACK.     

Commuting extensions and cubature formulae

Based on a novel point of view on 1-dimensional Gaussian quadrature, we present a new approach to d-dimensional cubature formulae. It is well known that the nodes of 1-dimensional Gaussian quadrature can be computed as eigenvalues of the so-called Jacobi matrix. The d-dimensional analog is that cubature nodes can be obtained from the eigenvalues of certain mutually commuting matrices. These are obtained by extending (adding rows and columns to) certain noncommuting matrices A₁,...,A_d, related to the coordinate operators x₁,...,x_d, in R^d. We prove a correspondence between cubature formulae and “commuting extensions” of A₁,...,A_d, satisfying a compatibility condition which, in appropriate coordinates, constrains certain blocks in the extended matrices to be zero. Thus, the problem of finding cubature formulae can be transformed to the problem of computing (and then simultaneously diagonalizing) commuting extensions. We give a general discussion of existence and of the expected size of commuting extensions and briefly describe our attempts at computing them.     

Calculating multidimensional discrete variable representations from cubature formulas

Finding multidimensional nondirect product discrete variable representations (DVRs) of Hamiltonian operators is one of the long standing challenges in computational quantum mechanics. The concept of a "DVR set" was introduced as a general framework for treating this problem by R. G. Littlejohn, M. Cargo, T. Carrington, Jr., K. A. Mitchell, and B. Poirier (J. Chem. Phys. 2002, 116, 8691). We present a general solution of the problem of calculating multidimensional DVR sets whose points are those of a known cubature formula. As an illustration, we calculate several new nondirect product cubature DVRs on the plane and on the sphere with up to 110 points. We also discuss simple and potentially very useful finite basis representations (FBRs), based on general (nonproduct) cubatures. Connections are drawn to a novel view on cubature presented by I. Degani, J. Schiff, and D. J. Tannor (Num. Math. 2005, 101, 479), in which commuting extensions of coordinate matrices play a central role. Our construction of DVR sets answers a problem left unresolved in the latter paper, namely, the problem of interpreting as function spaces the vector spaces on which commuting extensions act.     

Real-space observation of spectral degeneracy breaking in a waveguide-coupled disk microresonator

We report on the real-space observation of resonant frequency splitting in a high-Q waveguide-coupled silicon-on-insulator microdisk resonator. Phase sensitive near-field analysis reveals the stationary nature of the two resonant states, and spectral investigations clearly show their orthogonality. These measurements emphasize the role of the coupling waveguide in this splitting phenomenon. The symmetry of the two stationary whispering gallery modes is clearly observed and is found to follow the axial symmetry of the waveguide-coupled microdisk as it has been reported by earlier theoretical predictions.     

Symmetrized general hopping current equation

We show that within the validity range of local thermal equilibrium--therein, however, irrespective of the magnitude of the driving force--a simple current equation can be formulated that expresses the current in terms of a product of a local nonequilibrium conductivity and a sinh function of half the electrochemical potential drop (normalized with respect to kBT) over the local hopping distance. This local current/driving force relation takes account of both electrical and compositional effects and can be generalized as to include interactions and structural variations.