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.     

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.     

A practical asymmetric synthesis of trans-4,5-benzhydrindan-1-ones as a precursor of A-nor B-aromatic steroidal compounds

The enantio-controlled synthesis of trans-4,5-benzhydrindan-1-ones was achieved by means of a stereoselective [4+2] cycloaddition of o-quinodimethanes generated by a thermal cleavage of benzocyclobutene derivatives as a key step. The chiral substrates of the thermal reaction were synthesized by a diastereoselective Grignard addition to the chiral O-isopropylideneglyceroketones connected to a benzocyclobutene ring, which were simply prepared from D-mannitol as a chiral source. This approach can provide a new efficient access to A-nor B-aromatic steroidal compounds.     

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.