On small zeros of quadratic forms over finite fields (II)

Let be a quadratic form with integer coefficients and letp denote a prime. Cochrane^[1] proved that ifn≥4 then has a solution satisfying , where . The aim of the present paper is to generalize the above result to finite fields.     

Spectroscopic studies on 2,3,4,5-tetraphenylpyrylium salts with and without silver (I)-bridged structures

Two novel phenylated pyrylium compounds, silver (I)-bridged 2,3,4,5-tetraphenylpyrylium perchlorate (P1) and its silver (I)-free pyrylium ligand (P2) were prepared from 1,2,3,4-tetraphenylcyclopentadiene to examine their spectroscopic behaviors. The UV/vis absorption and fluorescent emission spectra of P1 and P2, measured in three solvents (acetonitrile, dichloromethane and toluene), reveal that the photophysical behaviors are closely related to silver (I) fragment, and strongly dependent on solvent polarity. In polar acetonitrile, P1 displays longer absorption wavelength and much lower fluorescent emission intensity than P2, although they exhibit much similarity in shape. In contrast, in nonpolar toluene, while P2 shows an apparent absorption band at 338 nm, P1 displays a tail-like line without absorption band observed. All the spectra obtained indicate a better coplanarity and a stronger intra-molecular charge transfer in P1 due to the effect of silver (I) fragment. Additionally, the 1H NMR spectra of P1 and P2, which were recorded under the same conditions, indicate that the silver (I) fragment reinforces pyrylium ring's capacity to localize the formal positive charge within the heterocyclic ring.     

Dynamics of photodissociation of 3,3,3-d(3)-propene at 157 nm: site effect and hydrogen migration

In a preceding paper [Lee et al., J. Chem. Phys. 119, 827 (2003)], we measured the kinetic-energy distributions P(E(t)) and branching ratios of products from photolysis of propene at 157 nm using time-of-flight spectroscopy combined with photoionization. In the present work, hydrogen migration before fragmentation and a site effect on P(E(t)) and branching ratios were revealed from the photodissociation of CD(3)CHCH(2). Labeling of the methyl group with deuterium enabled us to differentiate between elimination of atomic and molecular hydrogen from the vinyl moiety and from the methyl moiety; the P(E(t)) and relative yields for the formation of H, D, H(2), HD, and D(2) were measured. Deuterium labeling allowed us to also differentiate the fragmentation after hydrogen transfer from that before hydrogen migration. The observation of isotopic variants of CD(3) and C(2)H(3) radicals in the C-C bond cleavage provides evidence for hydrogen transfer of propene because of site specificity. The fraction of fragmentation after hydrogen transfer is estimated to be 25%. The isotope-specific branching ratios for five dissociation pathways of CD(3)CHCH(2) were evaluated.     

Sol-gel derived carbon ceramic electrode containing methylene blue-intercalated α-zirconium phosphate micro particles

Methylene blue-intercalated alpha-zirconium phosphate (MBZrP) micro particles in deionized water were deposited onto the surface of graphite powder to prepare graphite powder-supported MBZrP, which was subsequently dispersed into methyltrimethoxysilane-derived gels to yield a conductive composite. The composite was used as electrode material to fabricate a surface-renewable, rigid, leak-free carbon ceramic composite electrode, bulk-modified with methylene blue (MB). In the configuration, alpha-zirconium phosphate was employed as a solid host for MB, which acted as a catalyst. Graphite powder ensured conductivity by percolation, the silicate provided a rigid porous backbone and the methyl groups endowed hydrophobicity and thus limited the wetting section of the modified electrode. Peak currents of the MBZrP-modified electrode were surface-confined at low scan rates but diffusion-controlled at high scan rates. Square-wave voltammetric study revealed that MBZrP immobilized in carbon ceramic matrix presented a two-electron, three-proton redox process in acidic aqueous solution with pH ranged from 0.44 to 2.94. In addition, the chemically modified electrode showed an electrocatalytic activity toward nitrite reduction at +0.15 V ( vs. Ag/AgCl) in acidic aqueous solution (pH=0.44). The linear range and detection limit are 1x10(-6)-4x10(-3) mol x L(-1) and 1.5x10(-7) mol x L(-1), respectively.     

Surface structures of adsorption layers of sodium hyaluronate and bovine serum albumin complexes on poly(γ-methyl-l-glutamate) film and their surface properties

Two-dimensional structures and characteristics of the complexes between sodium hyaluronate (NaHA) and bovine serum albumin (BSA) were studied by using a quartz crystal microbalance method and an atomic force microscope (AFM). NaHA did not adsorb on poly(-methyl-l-glutamate) (PMLG) film. On the other hand, the complexes adsorbed on it and the adsorption behaviors were found to be Langmuir types. With increasing weight ratio of BSA to NaHA, W _BSA, the adsorption constants K decreased and the saturated adsorption masses increased. The adsorbed complexes were spherical particles and at saturated adsorption states they covered compactly on the PMLG film. The mean diameters d _AFM estimated from the topographic images decreased from 70 to 54 nm with increasing W _BSA. The adhesion force F _ad and the frictional force F _f between the complex layers and the AFM tip were obtained by using the contact mode of the AFM. With increasing W _BSA, the values of F _ad decreased and the values of F _f increased. Compared with the frictional coefficient of the NaHA adsorption layer on the BSA monolayer, the values for the NaHA–BSA complex layer were found to be much higher.     

模板法制备聚乙烯咔唑及其复合物纳米管有序阵列

近十几年来,纳米管引起了人们越来越多的关注,不仅仅是由于它独特的性质,也因为它们在电、磁以及光电器件上具有广泛的应用前景。纳米管的制备方法大体上分为两种:自组装法[1￣3]和模板法[4￣7]。尽管自组装法已成功地制得了一些纳米管,但由于它对构造纳米管的材料有着较严格的     

Study on the immobilization of anti-IgG on Au-colloid modified gold electrode via potentiometric immunosensor, cyclic voltammetry, and electrochemical impedance techniques

The immobilization of anti-IgG on Au-colloid modified gold electrodes has been investigated. A cleaned gold electrode was first immersed in a mercaptoethylamine (AET) solution, and then gold nanoparticles were chemisorbed onto the thiol groups of the mercaptoethylamine. Finally, anti-IgG was adsorbed onto the surface of the gold nanoparticles. Potentiometric immunosensor, cyclic voltammetry, and electrochemical impedance techniques were used to investigate the immobilization of anti-IgG on Au colloids. In the impedance spectroscopic study, an obvious difference of the electron transfer resistance between the Au-colloid modified electrode and the bare gold electrode was observed. The cyclic voltammogram tends to be more irreversible with increased anti-IgG concentration. Using the potentiometric immunosensor, the proposed technique is based on that the specific agglutination of antibody-coated gold nanoparticles, averaging 16 nm in diameter, in the presence of the corresponding antigen causes a potential change that is monitored by a potentiometry. It is found that the developed immunoagglutination assay system is sensitive to the concentration of IgG antigen as low as 12 ng mL(-1). Experimental results showed that the developed technique is in satisfactory agreement with the ELISA method, and that gold nanoparticles can be used as a biocompatible matrix for antibody or antigen immobilization.     

Relationship between the molybdenum phases and the conversion of n-butane over Mo/HZSM-5

The conversion of n-C₄H₁₀ was undertaken on MoO₃/HZSM-5 catalyst at 773–973 K and the phases of molybdenum species were detected by XRD. The XRD results show that bulk MoO₃ on HZSM-5 can be readily reduced by n-C₄H₁₀ to MoO₂ at 773 K and MoO₂ can be gradually carburized to molybdenum carbide above 813 K. The molybdenum carbide formed from the carburization of MoO₂ with n-C₄H₁₀ below 893 K is -MoC_1−x with fcc-structure, while hcp-molybdenum carbide formed above 933 K. During the evolution of MoO₃ to MoO₂ (>773 K) or the carburization of MoO₂ to molybdenum carbide (>813 K), deep oxidation, cracking and coke deposition are serious, in particular at higher reaction temperatures, these lead to the poor selectivity to aromatics. Aromatization of n-C₄H₁₀ can proceed catalytically on both Mo₂C/HZSM-5 and MoO₂/HZSM-5, the distribution of the products for the two catalysts is similar below 813 K, but the activity for Mo₂C/HZSM-5 is much higher than that for MoO₂/HZSM-5.     

Highly effective and recyclable dendritic ligands for the enantioselective aryl transfer reactions to aldehydes

[reaction: see text] A series of chiral pyrrolidinylmethanol-based dendritic ligands were synthesized for application in enantioselective aryl transfer reactions to aldehydes with the (ArBO)3/ZnEt2 system in up to 98% ee.