On the Numerical Range of Operator Polynomials

An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Factors controlling the efficiencies of photoinduced electron-transfer reactions

The overall efficiencies of photoinduced electron transfer reactions in polar solvents are usually determined by the efficiency with which separated radical ions are formed from the initially formed geminate radical-ion pairs. These separation efficiencies are determined by the competition between retum electron transfer and separation within the geminate pairs. A method is described for determining whether variations in the quantum yields for formation of separated radical ions are due to changes in the reorganization parameters for the return electron transfer reactions, or to other factors. The use of the method is illustrated in studies of the effects of varying steric bulk and molecular size of the donors, and also in studies of the effect of using a charged sensitizer.     

Intermolecular rhodium-catalyzed [2+2+2] carbocyclization reactions of 1,6-enynes with symmetrical and unsymmetrical alkynes

The crossed intermolecular rhodium-catalyzed [2+2+2] carbocyclization of carbon and heteroatom tethered 1,6-enynes can be accomplished with symmetrical and unsymmetrical alkynes, to afford the corresponding bicyclohexadienes in an efficient and highly selective manner.     

Electrode Kinetics and Ternary Complex Formation of Cd2+‐Antibiotics‐Vitamin‐B5 System. A Polarographic Study

Cd²⁺ complexes with antibiotics viz. neomycin, chlortetracycline, oxytetracycline, tetracycline, penicillin‐V and penicillin‐G as primary ligands and vitamin‐B₅ as secondary ligand have been reported at pH = 7.30 ± 0.01 and μ = 1.0 M KNO₃ at 298 K by polarographic technique.¹ Cd²⁺ formed 1:1:1, 1:1:2, and 1:2:1 complexes with a stability constants trend of neomycin < chlortetracycline < oxytetracycline < tetracycline < penicillin‐V < penicillin‐G can be explained on the basis of the nature of ligands, bonding, and steric hindrance of these drugs. The nature of electrode processes were reversible and diffusion controlled. The values of stability constants showed that these drugs can be used to reduce the toxicity of Cd.     

A novel class of amide-derived air-stable P,O-ligands for Suzuki cross-coupling at low catalyst loading

The benzamide-derived P,O-ligands efficiently promoted the Pd-catalyzed Suzuki cross-coupling reactions of aryl bromides with phenylboronic acid at 0.01 mol % of Pd loading at 60-80 °C to form biaryls in excellent yields. A sterically hindered arylboronic acid gave a quantitative yield of the coupling product at 110 °C with 1 mol % Pd.     

Mimicking photosynthesis in a computationally designed synthetic metalloprotein

While advances in protein design have made possible the construction of protein architectures with nativelike properties and predictable structures and function, there are as of yet no examples of functional, protein-based, solar energy conversion systems. This communication describes the design and characterization of an artificial reaction center (RC) protein that closely resembles the function of the natural photosynthetic RC. The synthetic protein, designed by the protein design program CORE, participates in multiple reduction/oxidation cycles with exogenous acceptors/donors following photoexcitation. The designed metalloprotein, aRC, consists of a tetrahelical bundle functionalized with two bis-histidine bound metal cofactors: a Ru(bpy)2 moiety and a heme group. Two distinct bis-histidine binding sites were engineered for each of these metal centers. Photoexcitation of aRC results in rapid ET from the RuII complex to the heme group (kET >/= 5 x 1010 s-1) yielding a long-lived (70 ns) charge-separated state (CSS), RuIII/FeII. This long-lived CSS participates in subsequent ET reactions with exogenous donors and acceptors in multiple photocycles, thus mimicking the basic function of native photosynthetic RCs. This study illustrates the successful design and construction of a protein-based functional charge separation device using a combination of automated computational protein design and knowledge of the engineering principles of biological electron tunneling extracted from natural electron-transfer systems. To our knowledge, this represents the first example of a functional protein-based artificial reaction center.     

Electron beam coater for reduction of charging in ice-embedded biological specimens using Ti(88)Si(12) alloy.

Biological macromolecules embedded in vitreous ice are known to suffer from charging while being imaged in an electron transmission cryomicroscope. We developed an electron beam coater that deposits conductive films onto the surface of frozen-hydrated specimens. The conductive films help to dissipate charge during electron irradiation of poorly conductive ice-embedded biological samples. We observed significant reduction in charging of ice-embedded catalase crystals suspended over holes in a holey carbon film after coating them with a 30-A-thick layer of an amorphous alloy, Ti(88)Si(12). Images of the crystals after coating showed diffraction spots of up to 3 A resolution.