On spectrums of certain harmonic functions attached to the Riemann zeta-function

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.     

Algebraic structure of association schemes of prime order

Finite groups of prime order must be cyclic. It is natural to ask what about association schemes of prime order. In this paper, we will give an answer to this question. An association scheme of prime order is commutative, and its valencies of nontrivial relations and multiplicities of nontrivial irreducible characters are constant. Moreover, if we suppose that the minimal splitting field is an abelian extension of the field of rational numbers, then the character table is the same as that of a Schurian scheme.     

Polybenzimidazoles containing anthracene photodimer

Polybenzimidazoles that contained anthracene photodimer were prepared. The molecular weights of the polymers prepared by the photopolymerization of bis-anthrylbenzimidazoles were limited by the precipitation of the resulting polymers from the reaction organic solvents. Higher molecular weight polymers were obtained by the photopolymerization of bis-anthryl-Schiff's bases, followed by the oxidation of the resulting polymers. These polymers were soluble in acidic solvents such as formic and sulfuric acids but were insoluble in organic solvents.     

Crosslinked poly(N-isopropylacrylamide) gel for electrophoretic separation and recovery of substances

Crosslinked poly(N-isopropylacrylamide) gel was tested on the feasibility for a preparative electrophoretic matrix. Horse heart myoglobin and bovine hemoglobin were well separated on the gel matrix electrophoretically by molecular sieving effect of the gel network. Relative mobilities of those proteins in the gel were larger than those in a crosslinked polyacrylamide gel of the same polymer concentration. After the separation, the protein-containing portion of the gel underwent swelling at 4°C and deswelling at 37°C, alternatively. As a result of the deswelling, each protein was recovered in a discharged solution out of the gel at almost 100% yield.     

Control of the bioluminescence starting time by inoculated cell density.

In this study, we attempted to control the timing of light-emission from bioluminescent bacteria, by changed cell numbers inoculated into medium. Luminous bacteria express bioluminescence when the number of cells reached a threshold. Inoculated cell density had an effect on the time of bioluminescence starting. Samples were prepared by varying cell density of inoculation. In the results, all the vials showed different luminescence profiles in the order of inoculated cell population.     

n-sigma charge-transfer interaction and molecular and electronic structural properties in the hydrogen-bonding systems consisting of p-quinone dianions and methyl alcohol

Molecular and electronic structural properties of the hydrogen-bonded complexes of p-quinone dianions (PQ(2)(-)) were investigated by electrochemistry and spectroelectrochemistry of PQ in MeCN combined with ab initio MO calculations. Hydrogen bonding between PQ(2)(-) and MeOH was measured as the continuous positive shift of the apparent second half-wave reduction potentials with increasing concentrations of MeOH. Detailed analyses of the behavior reveal that PQ(2)(-) forms the 1:2 hydrogen-bonded complexes at low concentrations of MeOH and the 1:4 complexes at high concentrations, yielding the formation constants. Temperature dependence of the formation constants allows us to yield the formation energy as 76.6 and 118.9 kJ mol(-)(1) for the 1:2 and 1:4 complex formation of the 1,4-benzoquinone dianion (BQ(2)(-)) with MeOH, respectively. These results show that the pi-dianions involving the quinone carbonyl groups exhibit very strong hydrogen-accepting ability. The longest wavelength band of the spectra of BQ(2)(-) and the chloranil dianion (CL(2)(-)) is assigned to the (1)B(3u) <-- (1)A(g) band mainly contributed from an intramolecular charge-transfer (CT) configuration. Hydrogen bonding allows the band of BQ(2)(-) and CL(2)(-) to be blue-shifted, depending on the strength of the hydrogen bonds. CNDO/S-CI calculations reveal that the blue shift is ascribed to stabilization of the ground state by the hydrogen bonding involving strong n-sigma-type CT interaction. The HF/6-31G(d) calculation results show that the structure of PQ(2)(-) is characterized by a lengthening of the C=O bonds and a benzenoid ring. The geometrical properties of the hydrogen-bonded complexes of PQ(2)(-) are a slight lengthening of the C=O bonds and a short distance of the hydrogen bonds. It is demonstrated that this situation is due to the strong n-sigma CT interaction in the hydrogen bonds. The results suggest that the differing functions and properties of biological quinones are conferred by the n-sigma CT interaction through hydrogen bonding of the dianions with their protein environment.