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.     

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.     

New stage in living cationic polymerization: An array of effective Lewis acid catalysts and fast living polymerization in seconds

Our recent extensive research on Lewis acid catalysts with a weak base for the cationic polymerization of vinyl ethers led to unprecedented living reaction systems: fast living polymerization within 1–3 s; a wide choice of metal halides containing Al, Sn, Fe, Ti, Zr, Hf, Zn, Ga, In, Si, Ge, and Bi; and heterogeneously catalyzed living polymerization with Fe₂O₃. The use of added bases for the stabilization of the propagating carbocation and the appropriate selection of Lewis acid catalysts were crucial to the success of such new types of living polymerizations. In addition, the base‐stabilized living polymerization allowed the quantitative synthesis of star‐shaped polymers with a narrow molecular weight distribution via polymer‐linking reactions and the precision synthesis and self‐assembly of stimuli‐responsive block copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1801–1813, 2007.     

Thermosensitive biodegradable polydepsipeptide

A poly(N-isopropylacrylamide) (PNIPAAm)-like biodegradable thermosensitive polydepsipeptide, poly[Glc-Asn(N-isopropyl)], was synthesized by introducing an isopropyl amide group into poly[Glc-Asn]. Poly[Glc-Asn(N-isopropyl)] was degraded in vitro by cleavage of the ester bonds in the main chain in water at room temperature. The non-toxic nature of the polymer and its degradation products, coupled with a cloud point at 29 degrees C in water, make this polymer attractive for biomedical implant applications.     

An intramolecular diels-alder approach to quassinoids—a stereoselective construction of a-aromatic klaineanone

Thermolysis of a benzocyclobutene derivative ($\text{20}$) prepared from norcamphor produced stereoselectively a tetracyclic compound ($\text{2}$), which was converted to a lactone ($\text{21}$) having correct stereochemistry at C₇, C₈, C₉, C₁₁, C₁₃, and C₁₄ positions of (±)-klaineanone.     

Stability and vibrational spectra of toroidal isomers of C 240

To study the thermodynamic and mechanical stability of toroidal isomers of C ₂₄₀, we use a semi-empirical tight-binding theory and calculate their electronic structure, cohesive energy and vibrational spectra within the harmonic approximation. From these, we deduce their free energy at temperatures up to 1500K. The results are also compared to the isomer with icosahedral symmetry. Finally, we discuss within this approach, their stability and abundance.     

Cyclopalladation of the indole ring in palladium(II) complexes of 2N1O-donor ligands and its dependence on the O-donor properties

Synthetic, structural, spectroscopic, and kinetic studies have been carried out on the Pd(II) complexes of new 2N1O-donor ligands containing a pendent indole, 3-(N-2-pyridylmethyl-N-2-hydroxy-5-methoxybenzylamino)ethylindole (HMeO-iepp), 3-(N-2-pyridylmethyl-N-2-hydroxy-5-nitrobenzylamino)ethylindole (HNO2-iepp), and (N-2-pyridylmethyl-3-indolylethylamino)acetic acid (Hiepc) (H denotes a dissociable proton). [Pd(MeO-iepp)Cl] (2), [Pd(NO2-iepp)Cl] (3), and [Pd(iepc)Cl] (4) were prepared and revealed by X-ray analysis to have a pyridine nitrogen, an amine nitrogen, a phenolate or carboxylate oxygen, and a chloride ion in the coordination plane. UV absorption and 1H NMR spectral changes indicated that all the complexes could be converted to the indole-binding complexes where the O donor was replaced by the indole C2 atom by cyclopalladation in DMSO or DMF in the temperature range of 40-60 degrees C. Formation of the indole-binding complex species obeyed the first-order kinetics, from which the activation parameters were estimated. The formation rate was dependent on the properties of the O-donor group, a lower pKa value of its conjugate acid causing faster conversion to the indole-binding species in the order 2 (methoxyphenolate) < 3 (nitrophenolate) < 4 (carboxylate). On the other hand, the ratio of the indole-binding complex to the O-donor complex as a result of the conversion was greater for the complexes with a higher pKa value of the ligand OH group, the order being 2 > 3 > 4.     

Optimal laser control of ultrafast photodissociation of I2- in water: mixed quantum/classical molecular dynamics simulation

A linearized optimal control method in combination with mixed quantum/classical molecular dynamics simulation is used for numerically investigating the possibility of controlling photodissociation wave packets of I(2)(-) in water. Optimal pulses are designed using an ensemble of photodissociation samples, aiming at the creation of localized dissociation wave packets. Numerical results clearly show the effectiveness of the control although the control achievement is reduced with an increase in the internuclear distance associated with a target region. We introduce effective optimal pulses that are designed using a statistically averaged effective dissociation potential, and show that they semiquantitatively reproduce the control achievements calculated by using optimal pulses. The control mechanisms are interpreted from the time- and frequency-resolved spectra of the effective optimal pulses.