Mean values with cubic characters

We investigate various mean value problems involving order 3 primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central values of the Dirichlet L-functions associated to this family, with a power saving in the error term. We also obtain a large sieve-type result for order 3 (and 6) Dirichlet characters.     

Weakly almost periodic functionals on the measure algebra

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C*-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C*-subalgebra of M(G)* = C ₀(G)**. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly compact module maps. The main technique is to adapt some of the theory of corepresentations to the setting of general reflexive Banach spaces.     

The number of harmonic frames of prime order

Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed between inequivalent harmonic frames and the orbits of a particular set. Secondarily, the symmetry group of prime order harmonic frames is shown to contain a subgroup consisting of a diagonal matrix as well as a permutation matrix, each of which is dependent on the particular harmonic frame in question.     

Algebraic independence of arithmetic gamma values and Carlitz zeta values

We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for Fq[θ] and provide complete algebraic independence results for them.     

Cobalt ultrathin film catalyzed ethanol chemical vapor deposition of single-walled carbon nanotubes

We report a simple and efficient chemical vapor deposition (CVD) process that can grow oriented and long single-walled carbon nanotubes (SWNTs) using a cobalt ultrathin film ( approximately 1 nm) as the catalyst and ethanol as carbon feedstock. In the process, millimeter- to centimeter-long, oriented and high-quality SWNTs can grow horizontally on various flat substrate surfaces, traverse slits as large as hundreds of micrometers wide, or grow over vertical barriers as high as 20 microm. Such observations demonstrate that the carbon nanotubes are suspended in the gas flow during the growth. The trace amount of self-contained water (0.2-5 wt %) in ethanol may act as a mild oxidizer to clean the nanotubes and to elongate the lifetime of the catalysts, but no yield improvement was observed at the CVD temperature of 850 degrees C. We found that tilting the substrates supporting the Co ultrathin film catalysts can grow more, longer carbon nanotubes. A mechanism is discussed for the growth of long SWNTs.     

Investigation of the excited state structure of DCM via ultrafast electronic pump/vibrational probe

Time resolved visible pump, infrared probe transient absorption measurements of the solutes 4-dicyanomethylene-2-methyl-6-(p-(dimethylamino)styryl)-4H-pyran (DCM) and its isotopomer DCM-d6 are employed to probe the dynamics of charge transfer state formation in dimethyl sulfoxide (DMSO) and acetonitrile (MeCN). We observe a two stage charge transfer (CT): the first step is an instrument-response-limited charge separation to the dicyanomethylene group, and the second involves a structural evolution of the dimethylamino group. Theoretical calculations and isotopic substitution indicate that the observed vibration is due to the dimethylamino group twisting out of plane, stabilizing the charge separation.     

High-resolution X-ray photoelectron spectroscopy of chlorine-terminated GaAs(111)A surfaces

Oxide-terminated and Cl-terminated GaAs(111)A surfaces have been characterized in the As and Ga 3d regions by high-resolution, soft X-ray photoelectron spectroscopy. The Cl-terminated surface, formed by treatment with 6 M HCl(aq), showed no detectable As oxides or As(0) in the As 3d region. The Ga 3d spectrum of the Cl-terminated surface showed a broad, intense signal at 19.4 eV and a smaller signal at 21.7 eV. The Ga 3d peaks were fitted using three species, one representing bulk GaAs and the others representing two chemical species on the surface. The large peak was well-fitted by the bulk GaAs emission and by a second doublet, assigned to surface Ga atoms bonded to Cl, that was shifted by 0.34 eV from the bulk GaAs 3d emission. The smaller peak, shifted by 2.3 eV in binding energy relative to the bulk GaAs Ga 3d signal, is assigned to Ga(OH)3. The data confirm that wet chemical etching allows for the formation of well-defined, Cl-terminated GaAs(111)A surfaces free of detectable elemental As, that can provide a starting point for further functionalization of GaAs.     

Absolute orientation of molecules at interfaces

A method to determine the absolute orientation of molecules at liquid interfaces by sum frequency generation (SFG) is reported. It is based on measurements of the orientations of two nonparallel vibrationally active chromophores in the molecule of interest combined with a rotation matrix formulation to obtain the absolute molecular orientation. We chose m-tolunitrile, a planar molecule adsorbed to the air/water interface, as a proof-of-method experiment. Quantitative analysis of different polarization sum frequency intensities facilitate unique peak assignments of the methyl and nitrile groups of m-tolunitrile. The SFG analysis of the measurement yields a nitrile group tilting at 53 degrees to the surface normal, and the C3 axis of the methyl group is almost upright at 23 degrees with respect to the surface normal. Using a rotation matrix formulation, we found that the angle between the surface plane and the m-tolunitrile molecular plane is 70 degrees.     

Efficient asymmetric synthesis of quaternary (E)-vinylglycines by deconjugative alkylation of dehydroamino acids

A two-step protocol for the asymmetric synthesis of protected quaternary (E)-vinylglycines from simple aldehydes is reported. The key step is a regiocontrolled deconjugative asymmetric alkylation of dehydroamino acids, giving the targets as single geometric isomers with high diastereoselectivity (92-96% de). The products can be converted to valuable quaternary beta-amino alcohols by chemoselective reduction. [reaction: see text].     

Regioselective synthesis of substituted pyrroles: efficient palladium-catalyzed cyclization of internal alkynes and 2-amino-3-iodoacrylate derivatives

The first efficient and regioselective palladium-catalyzed cyclization of internal alkynes and 2-amino-3-iodoacrylates to give moderate to excellent yields of highly functionalized pyrroles has been developed. This approach is applicable to a range of alkynes and affords the deacylated pyrrole under reaction conditions for most substrates. [reaction: see text]