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.     

Electronic effect on the regioselectivity in the ring opening of para-substituted phenyloxiranes by acetylides

The electronic effect on the regioselectivity in the alkynylation of phenyloxiranes was investigated using three kinds of metal acetylides. BF₃ mediated lithium acetylide provided either the α- or β-alkynylated products by controlling the effect of the para-substituents of the phenyloxiranes. LiClO₄ mediated lithium acetylide and titanium acetylide, on the other hand, afforded predominantly the β- and α-products, respectively.     

Heteroatom-guided torquoselective olefination of alpha-oxy and alpha-amino ketones via ynolates

Ynolates were found to react with alpha-alkoxy-, alpha-siloxy-, and alpha-aryloxyketones at room temperature to afford tetrasubstituted olefins with high Z selectivity. Since the geometrical selectivity was determined in the ring opening of the beta-lactone enolate intermediates, the torquoselectivity was controlled by the ethereal oxygen atoms. From experimental and theoretical studies, the high Z selectivity is induced by orbital and steric interactions rather than by chelation. In a similar manner, alpha-dialkylamino ketones provided olefins with excellent Z selectivity. These products can be easily converted into multisubstituted butenolides and gamma-butyrolactams in good yield.     

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.     

Enantiospecific synthesis of 1,3-disubstituted allenes by palladium-catalyzed coupling of propargylic compounds with arylboronic acids

An enantiospecific coupling of propargylic esters and carbonates with arylboronic acids has been developed using a palladium catalyst. Optically active 1,3-disubstituted allenes were synthesized with high enantiomeric excesses by carrying out the reactions under basic aqueous conditions.