Computation of Weng's rank 2 zeta function over an algebraic number field

In this paper, we study the zeta function, named non-abelian zeta function, defined by Lin Weng. We can represent Weng's rank r zeta function of an algebraic number field F as the integration of the Eisenstein series over the moduli space of the semi-stable OF-lattices with rank r. For r=2, in the case of F=Q, Weng proved that it can be written by the Riemann zeta function, and Lagarias and Suzuki proved that it satisfies the Riemann hypothesis. These results were generalized by the author to imaginary quadratic fields and by Lin Weng to general number fields. This paper presents proofs of both these results. It derives a formula (first found by Weng) for Weng's rank 2 zeta functions for general number fields, and then proves the Riemann hypothesis holds for such zeta functions.     

Nitric oxide (NO) production inhibitory constituents of Tabebuia avellanedae from Brazil

From the water extract of Brazilian Tabebuia avellanedae, two new iridoids (1, 2) and a new phenylethanoid glycoside (3) have been isolated together with twelve known compounds (4-15). Their structures were determined based on the spectroscopic data. The isolated compounds inhibited nitric oxide (NO) production in lipopolysaccharide (LPS)-activated macrophage-like J774.1 cells. Compounds 1, 3, 10, 11, and 12 showed inhibitory activities more potent (IC50, 13.8-26.1 microg/ml) than a positive control N(G)-monomethyl-L-arginine (L-NMMA; IC50, 27.4 microg/ml).     

Atom-probe field-ion microscopy of GaAs and GaP

The atom-probe field-ion microscope (atom-probe FIM) was applied for the first time to GaAs and GaP which belong to the III–V compound semiconductors. The general character of the pulsed field-evaporation of GaAs and GaP was quite similar. Ga field-evaporated predominantly in the form of singly charged ions. As and P also field-evaporated mainly as singly charged ions, but their abundances were small compared with Ga⁺. It appears that As (or P) atoms can field-evaporate more easily in the form of AsO⁺ (or PO⁺) in the presence of oxygen on the surface. In all experiments, GaAsⁿ⁺ and GaPⁿ⁺ were rarely detected. After chemical etching the surfaces were covered with oxide films and various oxide ions were detected. The abundance of oxide ions dramatically decreased after field evaporation in hydrogen. No distinct difference between the 〈111〉 orientations of these materials which have zinc-blende structure could be observed. Most of the experimental results obtained were explained in terms of the existing theory of field evaporation. It was concluded that field penetration effects have a considerable influence on the field evaporation processes of these materials as well as on the field ionization processes.     

Extrapolation procedures for intrinsic viscosity and for Huggins constant k′

Conventional extrapolation procedures for the calculation of intrinsic viscosities and the Huggins constant k′ have been critically examined. A condition which must be satisfied by the basic equation for viscosity–concentration relations of dilute solutions of nonelectrolytic polymers has been clarified. On the basis of the comparison of the curvatures for empirical equations and for the basic equation, it is proposed to use arithmetic averages of the values calculated from a Huggins plot and those from a Martin plot for good-solvent systems, and to employ the averages of values from the former and those from a Schulz-Blaschke plot for poor-solvent systems as approximations to the correct values. Failure to confine approximations in the usual statistical treatment of experimental points to the given range of the variables as well as neglect of the fact that curvatures for the empirical and basic equations do not necessarily coincide are the usual sources of error in the conventional extrapolation procedures.     

Huggins constant k′ for flexible chain polymers

The Huggins constant k′ in the expression for the viscosity of dilute nonelectrolytic polymer solutions, η = η(1 + [η] c + k′[η]²c² + …), is calculated. For polymers in the theta condition, k′ is estimated to be 0.5 < k_θ′ ≤ 0.7. For good solvent systems, the Peterson-Fixman theory of k′ has been modified; the equilibrium radial distribution function in the original theory is replaced with a parametric distribution for interpenetrating macromolecules in the shear force field. Comparison of the modified theory with experimental k′ for polystyrenes and poly(methyl methacrylates) of different molecular weights in various solvents shows good agreement. An empirical equation which correlates the Huggins constant k′ and the viscosity expansion factor α_η for polymers has been found to coincide well with the modified theory.     

Reduction of tetrakis(trimethylsilyl)butatriene by lithium: Monomeric and dimeric structures of the dilithium butatriene dianion

Treatment of tetrakis(trimethylsilyl)butatriene (2) with lithium in tetrahydrofuran (THF) led to quantitative formation of the corresponding dianion species. Yellow crystals of the dilithium salts of 2 were isolated as an unexpected dimeric structure (4) as well as a monomeric structure (3). Both of the crystal structures, which havebeen confirmed by X-ray diffraction, reveal a doubly bridged lithium bisallylic structure. The unique dynamic behaviour of the lithium ions of the dimer 4 in toluene-d₈ is demonstrated.     

Figure-eight thermal hysteresis of aminomethylenehelicene oligomers with terminal C16 alkyl groups during hetero-double-helix formation

1 : 1 mixtures of aminomethylenehelicene (P)-tetramer and (M)-pentamer with terminal C₁₆ alkyl groups in fluorobenzene showed structural changes between hetero-double-helices B and C and random-coils 2A. Figure-eight thermal hysteresis appeared when the solution was cooled and heated at a constant rate and involved the crossing of cooling and heating curves in Δε/temperature profiles. This unusual thermal hysteresis emerged in the intermediate state between counterclockwise and clockwise thermal hystereses. This phenomenon arose from the competition between self-catalytic reactions to form B and C from 2A. Significant effects of terminal C₁₆ alkyl groups on the thermodynamic and kinetic phenomena are also described.

1 : 1 mixtures of aminomethylenehelicene (P)-tetramer and (M)-pentamer with terminal C₁₆ alkyl groups in fluorobenzene showed structural changes between hetero-double-helices B and C and random-coils 2A.     

Photoinduced Electron Transfer‐Regulated Protein Labeling With a Coumarin‐Based Multifunctional Photocrosslinker

We developed a novel diazirine‐based photolabeling agent having a (coumarin‐4‐yl)methyl ester scaffold, which exhibited multiple photochemical properties of crosslinking, fluorogenicity and cleavage. These properties can be kinetically regulated via photoinduced electron transfer between diazirine and coumarin moieties. The C?O bond of (coumarin‐4‐yl)methyl ester can be cleaved via photochemical excitation of coumarin moiety, that function has been initially quenched by the diazirine moiety. Upon diazirine photolysis with 365‐nm light, interacting protein was stably captured with photoactivatable ligand probe. Then, the unlocked cleavage function was activated with 313 nm light, and the reaction was accelerated in a weakly‐basic solution. The crosslinked protein could be selectively isolated with attachment of a small coumarin tag on the surface. This multi‐functional labeling agent has a great potential to facilitate LC‐MS/MS‐based protein identification.