Annular Functions and Gap Series

If f(z) = c_kz^nk, where n_k+1/n_k q > 1, and f(z) is analyticin |z| < 1, the f(z) is an annular function if and only ifsup |c_k| = . This answers a question posed by L. R. Sons andD.M. Campbell simplifies the proofs of many known examples ofannular functions. Present address: Dept. of Mathematical Sciences, McMaster University,Hamilton, Ontario, Canada L8S4K1     

Development of β-hydroxyamide/titanium complexes for catalytic enantioselective silylcyanation of aldehydes

A highly enantioselective addition of trimethylsilylcyanide to aldehydes catalyzed by chiral titanium complexes is described. The chiral titanium complexes were prepared in situ from Ti(OⁱPr)₄ and β-hydroxyamide ligands, that could easily be synthesized from ketopinic acid and C₂ symmetrical chiral diamines in a small number of steps.     

Mechanism and nanosize products of the sol-gel reaction using diphenylsilanediol and 3-methacryloxypropyltrimethoxysilane as precursors

We use a first-principles calculation and small-angle neutron scattering (SANS) to investigate the mechanism and the nanosize products of the sol-gel reaction with diphenylsilanediol (DPD) and 3-methacryloxypropyltrimethoxysilane (MEMO) precursors in synthesizing a hybrid waveguide material. It is predicted that switching between a DPD hydroxyl and a MEMO methoxy with a reaction rate of 6.8 x 10(-6) s(-1) at 300 K is the fastest process for the first reaction step, thus generating diphenylmethoxysilanol (DPM) and 3-methacryloxypropyldimethoxysilanol (MEDO) as products. However, we determine that this reaction pathway could be modified by the presence of the H2O released from a catalyst such as Ba(OH)2.H2O. Next, switching between the DPM hydroxyl and the MEDO methoxy is followed to generate diphenyldimethoxysilane (DPDM) and 3-methacryloxypropylmethoxysilanediol (MEMDO). However, condensation between a MEMDO hydroxyl and a DPDM methoxy is found to be most favorable for the third reaction step, which generates the DPDM-MEMDO dimer and CH3OH molecule as products. In a similar fashion, a DPDM methoxy of the DPDM-MEMDO dimer can condense with a MEMDO hydroxyl of the second DPDM-MEMDO dimer to increase the chain, but its reaction rate of 2.8 x 10(-11) s(-1) is predicted to be about 5 times smaller than that between a DPDM methoxy and a MEMDO hydroxyl. This implies that the reaction rate for the larger nanostructures becomes smaller. Additionally, our SANS measurements determine that the final products from our sol-gel reaction are on the nanometer scale, at sizes from 1.76 to 2.36 nm.     

Molecular structure of meso-tetraphenylporphyrinatothallium(III) cyanide: Tl(tpp) (CN)

meso-Tetraphenylporphyrinatothallium(III) cyanide, Tl(tpp)(CN), was previously assumed to be monomeric and has been confirmed by X-ray analysis to exist as two independent molecules in one asymmetric unit. This unit displays two square-pyramidal coordination geometries for the thallium atoms with the cyano ligand coordinated to both Tl atoms. It crystallizes in the triclinic space group P , with a 10.003(3), b 16.231(7), c 21.277(8) Å, 89.98(3), β 90.57(3), γ 90.31(3)°' and z = 4. The structure was solved by direct methods. A total of 7995 unique reflections having I > 3σ(I) was measured with an automated diffractometer and used to refine the crystal structure to a conventional R factor of 6.05 %. The thallium-cyanide distances are 2.140(14) Å (for thallium(I)) and 2.277(14) Å (for thallium(2)) respectively, with thallium(1) situated 0.908 Å above the porphyrin ring and thallium(2) located 1.027 Å below the ring. IR and NMR spectroscopy p rovide complementary methods for investigation of the CN ligand. The characteristic band observed at 2160 cm⁻¹ in the FTIR spectrum is assigned to the CN stretching in the Tl(tpp)(CN) complex. The ¹³C resonance of axial cyano ligand is observed with a pulse delay of 3.5 s at 24°C at 139.2 ppm (with ¹J(²⁰⁵Tl-¹³C) 5394 and ¹J(²⁰³Tl-¹³C) 5344 Hz). This observation disagrees with the conclusion, drawn from previous work, in that an exchange process involving the apical ligand explains the invisibility due to line broadening at 35°C of the ¹³C signal.     

Porphyrin boxes constructed by homochiral self-sorting assembly: optical separation, exciton coupling, and efficient excitation energy migration

meso-Pyridine-appended zinc(II) porphyrins Mn and their meso-meso-linked dimers Dn assemble spontaneously, in noncoordinating solvents such as CHCl3, into tetrameric porphyrin squares Sn and porphyrin boxes Bn, respectively. Interestingly, formation of Bn from Dn proceeds via homochiral self-sorting assembly, which has been verified by optical separations of B1 and B2. Optically pure enantiomers of B1 and B2 display strong Cotton effects in the CD spectra, which reflect the length of the pyridyl arm, thus providing evidence for the exciton coupling between the noncovalent neighboring porphyrin rings. Excitation energy migration processes within Bn have been investigated by steady-state and time-resolved spectroscopic methods in conjunction with polarization anisotropy measurements. Both the pump-power dependence on the femtosecond transient absorption and the transient absorption anisotropy decay profiles are directly associated with the excitation energy migration process within the Bn boxes, where the exciton-exciton annihilation time and the polarization anisotropy rise time are well described in terms of the F?rster-type incoherent energy hopping model by assuming a number of hopping sites of N = 4 and an exciton coherence length of L = 2. Consequently, the excitation energy hopping rates between the zinc(II) diporphyrin units have been estimated for B1 (48 ps)(-1), B2 (98 +/- 3 ps)(-1), and B3 (361 +/- 6 ps)(-1). Overall, the self-assembled porphyrin boxes Bn serve as a well-defined three-dimensional model for the light-harvesting complex.     

The indenter tip radius effect in micro- and nanoindentation hardness experiments.

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao's relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix's experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor. The project supported by the National Natural Science Foundation of China (10121202) and the Ministry of Education of China (20020003023)     

Real‐Time Measurement of the Size Distribution of Diesel Exhaust Particles using a Portable 4‐stage Electrical Low Pressure Impactor

For this study, a 4 stage electrical low pressure impactor was designed to measure the real‐time size distribution of diesel particulate matter (DPM). For the performance evaluation, sodium chloride (NaCl) particles and dioctyl sebacate (DOS) particles were used. After evaluating the collection efficiency of each stage of the impactor, the size distributions of test particles were estimated using electrical current data and their inversion algorithm, and this was found to agree with the results obtained by a scanning mobility particle sizer (SMPS). For measurement of DPM, a common‐rail direct injection (CRDI) diesel engine, for engine speeds of 1,200 rpm and 1,500 rpm at 2.7 kgf·m, was used. Therefore, it was found that the size distribution of the DPM could be easily obtained, with the currents measured by the impactor and the data inversion algorithm, in less than 5 seconds. Furthermore, the effective density of the DPM could be obtained using the calculated results and the SMPS data.     

Side-lobeless far-field spectrum of a short pulse from a circular aperture with Gaussian form of transmittance

The spectrum change of a Gaussian pulse in the far field is studied with the Fresnel diffraction integral when it is incident on an aperture with Gaussian form transmittance. It is found that the side-lobes of the diffracted spectral intensity, which exist in a normal circular aperture with unit transmittance, can be eliminated completely under such a condition. Also, the red shift and blue shift of the spectral intensity maximum of the incident pulse are presented.     

Synthesis and Study of a Sulfur Heterocycle Fused p-Phenylene Vinylene Conducting Polymer

Abstract

Poly(benzo[1,2-b:4,5-b′]dithiophene-4,8-diyl vinylene) (1) has been prepared by the pyrolysis of the precursor polymer 2 and studied. Quantum mechanical calculations on the aromatic and quinoid monomers, oligomers and polymers indicate that 1 is a planar aromatic polymer.     

Site‐specific reversible immobilization and purification of His‐tagged protein on poly(2‐acetamidoacrylic acid) hydrogel beads

Ni²⁺‐complexed poly(2‐acetamidoacrylic acid) (PAAA) hydrogel beads were developed for the site‐specific reversible immobilization and purification of the histidine‐tagged green fluorescent protein (His‐tagged GFP). PAAA hydrogel beads were prepared by photopolymerization, and significantly improved mechanical properties of PAAA hydrogel beads were observed in comparison with PAAA hydrogel from our previous study. Confocal laser scanning microscopy was used to determine the binding of His‐tagged GFP to the hydrogel beads in three‐dimensional space. Photoluminescence spectroscopy revealed 89% of binding efficiency of His‐tagged GFP to the Ni²⁺‐PAAA hydrogel beads, 51% of yielding recovery. The maximum binding capacity of His‐tagged GFP was estimated to be 0.45 µg/mg of Ni²⁺‐PAAA hydrogel beads. The recombinant His‐tagged GFP from the soluble fraction of E. coli BL21(DE3) cell lysates was purified with Ni²⁺‐PAAA hydrogel beads. The major advantage of the Ni²⁺‐PAAA hydrogel beads system was simple preparation procedures of producing the matrix, because PAAA hydrogel beads had relatively enhanced mechanical strength than soft hydrogels. Copyright © 2012 John Wiley & Sons, Ltd.