Euler transformation formula for multiple basic hypergeometric series of type A and some applications

A multiple generalization of the Euler transformation formula for basic hypergeometric series ₂φ₁ is derived. It is obtained from the symmetry of the reproducing kernel for Macdonald polynomials by a method of multiple principal specialization. As applications, elementary proofs of the Pfaff-Saalschutz summation formula and the Gauss summation formula for basic hypergeometric series in U(n+1) due to S.C. Milne are given. Some other multiple transformation and summation formulas for very-well-poised ₁₀φ₉ and ₈φ₇ series, balanced ₄φ₃ series and ₃φ₂ series are also given.     

The Perturbation of the Quantum¶Calogero–Moser–Sutherland System¶and Related Results

The Hamiltonian of the trigonometric Calogero–Sutherland model coincides with a certain limit of the Hamiltonian of the elliptic Calogero–Moser model. In other words the elliptic Hamiltonian is a perturbed operator of the trigonometric one. In this article we show the essential self-adjointness of the Hamiltonian of the elliptic Calogero–Moser model and the regularity (convergence) of the perturbation for the arbitrary root system. We also show the holomorphy of the joint eigenfunctions of the commuting Hamiltonians w.r.t the variables (x ₁, …,x _N ) for the A _{N -1}-case. As a result, the algebraic calculation of the perturbation is justified. Received: 30 May 2001 / Accepted: 27 November 2001     

Sensing of ozone based on its quenching effect on the photoluminescence of CdSe-based core-shell quantum dots

Microchimica Acta - Thin films of CdSe-based core-shell type quantum dots (CdSe/CdZnS, CdSe/ZnS and CdSeTe/ZnS) deposited on glass substrate were found to undergo a reversible change in...     

Synthesis and characterization of water-soluble silsesquioxane-based nanoparticles by hydrolytic condensation of triethoxysilane derived from 2-hydroxyethyl acrylate

A new family of silsesquioxane-based nanoparticles was synthesized by hydrolytic condensation of a triethoxysilane precursor, R-Si(OCH2CH3)3, R = -CH2CH2CH2N(CH2CH2COOCH2CH2OH)2, derived from 2-hydroxyethyl acrylate. Condensation of the triethoxysilane precursor proceeded as a homogeneous system in methanol in the presence of hydrofluoric acid (HF) to afford water-soluble silsesquioxane-based nanoparticles, as confirmed by NMR, FT-IR, and elemental analyses. Scanning force microscopy (SFM) measurements indicated the formation of nanoparticles having a relatively narrow size distribution with an average particle diameter of less than 2.0 nm without aggregation. The size of the nanoparticles (1.7 nm) was determined by X-ray diffraction (XRD). The narrow polydispersity (Mw/Mn = 1.08) and a reasonable molecular weight (Mn = 3300), corresponding to species having 6-12 silicon atoms, were also confirmed by size-exclusion chromatography. Co-condensation of tetraethoxysilane (TEOS) with the triethoxysilane precursor was carried out under different feed ratios, and water-soluble products were obtained in the cases of TEOS molar ratios up to 70%. Thermal stability and the char yield were found to increase with increasing TEOS content in the feed, as determined by thermogravimetric analysis. The isolated nanoparticles distributed homogeneously without any aggregation were visualized by SFM, when the product was prepared at TEOS/triethoxysilane precursor = 50/50 mol %.     

Nanoscale actuation of thermoreversible polymer brushes coupled with localized surface plasmon resonance of gold nanoparticles

This paper describes the fabrication of hybrid nanoassemblies with polymer brushes and gold nanoparticles enabling detection of nanoscale optical changes based on localized surface plasmon resonance. The reversible and thermosensitive nanoscale actuation is achieved by combining stimuli-responsive polymer brushes and gold nanoparticles independently and selectively assembled on substrates. These hybrid nanoassemblies are assembled on numerous substrates and will be applicable for optoelectronics, nanoactuator, and nanosensor applications.     

Excitation and circular dichroism spectra of (-)-(3aS, 7aS)-2-chalcogena-trans-hydrindans(Ch = S, Se, Te): SAC and SAC-CI calculations

The ground and several electronic excited states of (3aS,7aS)-2-chalcogena-trans-hydrindans were calculated by the symmetry adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) methods. Theoretical electronic excitation spectra and natural circular dichroism (CD) spectra were obtained for these compounds, and the calculated spectra showed good agreement with the experimental ones reported by Laur (Proceedings of the Third International Symposium on Organic Selenium and Tellurium compounds, Metz, France, 1979, pp. 219-299). For all the chalcogen compounds, the first singlet excited states are assigned to n-sigma* and the other states are assigned to n-Rydberg in our calculations. It indicates that the spectra for the sulfide, selenide, and telluride are almost regarded as the analogues except for the red shifts of the band positions from the sulfide to the telluride. For the telluride, however, the experimental spectra have shapes that cannot be interpreted by the singlet excitations solely. Our calculations predict the triplet states that account for the spectral shapes, indicating importance of the spin-orbit interaction effects for the accurate reproduction of the experimental spectra of the telluride.     

The photoreaction of the photoactive yellow protein domain in the light sensor histidine kinase Ppr is influenced by the C-terminal domains

To study the role of the C-terminal domains in the photocycle of a light sensor histidine kinase (Ppr) having a photoactive yellow protein (PYP) domain as the photosensor domain, we analyzed the photocycles of the PYP domain of Ppr (Ppr-PYP) and full-length Ppr. The gene fragment for Ppr-PYP was expressed in Escherichia coli, and it was chemically reconstituted with p-coumaric acid; the full-length gene of Ppr was coexpressed with tyrosine ammonia-lyase and p-coumaric acid ligase for biosynthesis in cells. The light/dark difference spectra of Ppr-PYP were pH sensitive. They were represented as a linear combination of two independent difference spectra analogous to the PYP(L)/dark and PYP(M)/dark difference spectra of PYP from Halorhodospira halophila, suggesting that the pH dependence of the difference spectra is explained by the equilibrium shift between the PYP(L)- and PYP(M)-like intermediates. The light/dark difference spectrum of Ppr showed the equilibrium shift toward PYP(L) compared with that of Ppr-PYP. Kinetic measurements of the photocycles of Ppr and Ppr-PYP revealed that the C-terminal domains accelerate the recovery of the dark state. These observations suggest an interaction between the C-terminal domains and the PYP domain during the photocycle, by which light signals captured by the PYP domain are transferred to the C-terminal domains.     

Assessment of macrocyclic triamine ligands as synthons for organometallic 99mTc radiopharmaceuticals

In a search of coordination molecules suitable to the fac-{(99m)Tc(CO)3}(+) core as a synthon for (99m)Tc-radiopharmaceuticals, nonradioactive rhenium complexes of two macrocyclic triamine compounds with different chelate ring structures, 1,4,7-triazacyclononane (9N3) and 1,5,9-triazacyclododecane (12N3), were synthesized and characterized. (99m)Tc-labeled 9N3 and 12N3 compounds were also prepared using [(99m)Tc(OH 2)3(CO)3](+) and were characterized by both in vitro and in vivo studies. 9N3 produced a single rhenium complex, whereas 12N3 generated two major complexes. The crystallographic data and infrared absorption wavenumber assigned to the C-O stretch suggested that the coordination geometry of 9N3 would be more suitable to fac-{Re(CO)3}(+) than that of 12N3. In contrast, both 9N3 and 12N3 provided a single (99m)Tc-labeled compound. However (99m)Tc-labeled 9N3 exhibited higher stability than (99m)Tc-labeled 12N3 in rat plasma and in the presence of histidine at an elevated temperature. In biodistribution studies, both (99m)Tc-labeled compounds did not show any specific accumulation of radioactivity in any organs except for the excretory organs such as the liver and kidney. These findings showed that 9N3 would constitute a macrocyclic chelating molecule of choice to prepare (99m)Tc radiopharmaceuticals using a fac-{(99m)Tc(CO)3}(+) core.