Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Correlation between amplitude and phase noise in a mode-locked Cr:LiSAF laser

The coherence function between the amplitude and phase fluctuations of a mode-locked Cr:LiSAF laser has been measured with a time-domain demodulation technique. A relatively large correlation has been found for the noise components that originate in the pump-power fluctuation. Through an examination of the modulation-induced change in the noise power spectral densities, the influences of pump-power and cavity-length variations on these fluctuations have been investigated.     

Control of the optical properties of CdTe nanocrystals by selective exchange of Te with thiolate: effect of organic ligands on the formation of core-shell structures

Changes in the optical properties of CdTe nanocrystals through selective surface exchange reaction with thiolate molecules in the organic phase are studied with an aim to investigate the mechanism and the role of organic ligands. The reaction was mediated by dissociation of Te anions via oxidation in air from CdTe nanocrystals, followed by attachment of thiolate molecules in a 1:1 stoichiometric manner. This results in a gradual shell formation and a corresponding decrease in the size of the fluorescent CdTe cores, which induces a blue shift of both the absorption edge and emission wavelength in the visible region. A systematic study including the addition of ligands at different concentrations revealed that Te dissociation is the rate-determining step for the process and the degree of blue shift is significantly dependent on the amount of organic ligands present. The process could also be kinetically controlled through the addition of an excess amount of thiolate ligands, allowing systematic tuning of the emission properties of nanocrystals under ambient conditions.     

Convectional,sedimentation, and drying dissipative patterns of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass

Direct observation of the convectional dissipative patterns was successful during the course of dryness of colloidal crystals of poly (methyl methacrylate) spheres on a cover glass. Formation processes of the convectional patterns of spoke-like lines were observed as a function of sphere size and also sphere concentration. During dryness of the suspensions, the brilliant iridescent colors changed beautifully. Macro- and microscopic drying patterns and thickness profiles of the dried film were observed. Sharp broad rings were observed especially at low sphere concentrations. The water evaporation accompanied with the convectional flow of water and the colloidal spheres played an important role for these dissipative structure formation.     

Protein nanotubes comprised of an alternate layer-by-layer assembly using a polycation as an electrostatic glue

We present the synthesis and structure of various protein nanotubes comprised of an alternate layer-by-layer (LbL) assembly using a polycation as an electrostatic glue. The nanotubes were fabricated by sequential LbL depositions of positively charged polycations and negatively charged proteins into a porous polycarbonate (PC) membrane, followed by release of the cylindrical core by quick dissolution of the template with CH(2)Cl(2). This procedure provides a variety of protein nanotubes without interlayer cross-linking. The three-cycle depositions of poly-L-arginine (PLA) and human serum albumin (HSA, M(w)=66.5 kDa) into the porous PC template (pore diameter, D(p)=400 nm) yielded well-defined (PLA/HSA)(3) nanotubes with an outer diameter of 419+/-29 nm and a wall thickness of 46+/-8 nm, revealed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) observations. The outer diameter of the tubules can be controlled by the pore size of the template (200-800 nm), whereas the wall thickness is always constant, independent of the D(p) value. The (PEI/HSA)(3) (PEI: polyethylenimine) nanotubes showed a slightly thin wall of 39+/-5 nm. CD spectra of the multilayered (PEI/HSA)(n) film on a flat quartz plate suggested that the secondary structure of HSA between the polycations was almost the same as that in aqueous solution. The three-cycle LbL depositions of PLA and ferritin (M(w)=460 kDa) or myoglobin (Mb, M(w)=1.7 kDa) into the porous PC membrane also gave cylindrical hollow structures. The wall thickness of the (PLA/ferritin)(3) and (PLA/Mb)(3) nanotubes were 55+/-5 nm and 31+/-4 nm; it depends on the globular size of the protein (ferritin>HSA>Mb). The individual ferritin molecule was clearly seen in the tubular walls by SEM and TEM measurements.     

Synthesis and catalysis of di- and tetranuclear metal sandwich-type silicotungstates [(gamma-SiW10O36)2M2(mu-OH)2]10- and [(gamma-SiW10O36)2M4(mu4-O)(mu-OH)6]8- (M = Zr or Hf)

The di- and tetranuclear metal sandwich-type silicotungstates of Cs10[(gamma-SiW10O36)2{Zr(H2O)}2(mu-OH)2] x 18 H2O (Zr2, monoclinic, C2/c (No. 15), a = 25.3315(8) A, b = 22.6699(7) A, c = 18.5533(6) A, beta = 123.9000(12) degrees, V = 8843.3(5) A(3), Z = 4), Cs10[(gamma-SiW10O36)2{Hf(H2O)}2(mu-OH)2] x 17 H2O (Hf2, monoclinic, space group C2/c (No. 15), a = 25.3847(16) A, b = 22.6121(14) A, c = 18.8703(11) A, beta = 124.046(3) degrees, V = 8974.9(9) A(3), Z = 4), Cs8[(gamma-SiW10O36)2{Zr(H2O)}4(mu4-O)(mu-OH)6] x 26 H2O (Zr4, tetragonal, P4(1)2(1)2 (No. 92), a = 12.67370(10) A, c = 61.6213(8) A, V = 9897.78(17) A(3), Z = 4), and Cs8[(gamma-SiW10O36)2{Hf(H2O)}4(mu4-O)(mu-OH)6] x 23 H2O (Hf4, tetragonal, P4(1)2(1)2 (No. 92), a = 12.68130(10) A, c = 61.5483(9) A, V = 9897.91(18) A(3), Z = 4) were obtained as single crystals suitable for X-ray crystallographic analyses by the reaction of a dilacunary gamma-Keggin silicotungstate K8[gamma-SiW10O36] with ZrOCl2 x 8 H2O or HfOCl2 x 8 H2O. These dimeric polyoxometalates consisted of two [gamma-SiW10O36](8-) units sandwiching metal-oxygen clusters such as [M2(mu-OH)2](6+) and [M4(mu4-O)(mu-OH)6](8+) (M = Zr or Hf). The dinuclear zirconium and hafnium complexes Zr2 and Hf2 were isostructural. The equatorially placed two metal atoms in Zr2 and Hf2 were linked by two mu-OH ligands and each metal was bound to four oxygen atoms of two [gamma-SiW10O36](8-) units. The tertanuclear zirconium and hafnium complexes Zr4 and Hf4 were isostructural and consisted of the adamantanoid cages with a tetracoordinated oxygen atom in the middle, [M4(mu4-O)(mu-OH)6](8+) (M = Zr or Hf). Each metal atom in Zr4 and Hf4 was linked by three mu-OH ligands and bound to two oxygen atoms of the [gamma-SiW10O36](8-) unit. The tetra-nuclear zirconium and hafnium complexes showed catalytic activity for the intramolecular cyclization of (+)-citronellal to isopulegols without formation of byproducts resulting from etherification and dehydration. A lacunary silicotungstate [gamma-SiW10O34(H2O)2](4-) was inactive, and the isomer ratio of isopulegols in the presence of MOCl2 x 8 H2O (M = Zr or Hf) were much different from that in the presence of tetranuclear complexes, suggesting that the [M4(mu4-O)(mu-OH)6](8+) core incorporated into the POM frameworks acts as an active site for the present cyclization. On the other hand, the reaction hardly proceeded in the presence of dinuclear zirconium and hafnium complexes under the same conditions. The much less activity is possibly explained by the steric repulsion from the POM frameworks in the dinuclear complexes.     

IR signature of the photoionization-induced hydrophobic-->hydrophilic site switching in phenol-Arn clusters

IR spectra of phenol-Arn (PhOH-Arn) clusters with n=1 and 2 were measured in the neutral and cationic electronic ground states in order to determine the preferential intermolecular ligand binding motifs, hydrogen bonding (hydrophilic interaction) versus pi bonding (hydrophobic interaction). Analysis of the vibrational frequencies of the OH stretching motion, nuOH, observed in nanosecond IR spectra demonstrates that neutral PhOH-Ar and PhOH-Ar2 as well as cationic PhOH+-Ar have a pi-bound structure, in which the Ar atoms bind to the aromatic ring. In contrast, the PhOH+-Ar2 cluster cation is concluded to have a H-bound structure, in which one Ar atom is hydrogen-bonded to the OH group. This pi-->H binding site switching induced by ionization was directly monitored in real time by picosecond time-resolved IR spectroscopy. The pi-bound nuOH band is observed just after the ionization and disappears simultaneously with the appearance of the H-bound nuOH band. The analysis of the picosecond IR spectra demonstrates that (i) the pi-->H site switching is an elementary reaction with a time constant of approximately 7 ps, which is roughly independent of the available internal vibrational energy, (ii) the barrier for the isomerization reaction is rather low(<100 cm(-1)), (iii) both the position and the width of the H-bound nuOH band change with the delay time, and the time evolution of these spectral changes can be rationalized by intracluster vibrational energy redistribution occurring after the site switching. The observation of the ionization-induced switch from pi bonding to H bonding in the PhOH+-Ar2 cation corresponds to the first manifestation of an intermolecular isomerization reaction in a charged aggregate.     

One-pot amidation of olefins through Pd-catalyzed coupling of alkylboranes and carbamoyl chlorides

A one-pot synthesis of C1-elongated amides starting from olefins and carbamoyl chlorides has been developed. Alkylboranes, generated by hydroboration of terminal olefins with 9-BBN-H, underwent smooth coupling with carbamoyl chlorides in the presence of palladium catalyst and Cs2CO3.     

Colloidal crystals of core-shell type spheres with poly(styrene) core and poly(ethylene oxide) shell

Elastic modulus and crystal growth kinetics have been studied for colloidal crystals of core–shell type colloidal spheres (diameter = 160–200 nm) in aqueous suspension. Crystallization properties of three kinds of spheres, which have poly(styrene) core and poly(ethylene oxide) shell with different oxyethylene chain length (n = 50, 80 and 150), were examined by reflection spectroscopy. The suspensions were deionized exhaustively for more than 1 year using mixed bed of ion-exchange resins. The rigidities of the crystals range from 0.11 to 120 Pa and from 0.56 to 76 Pa for the spheres of n = 50 and 80, respectively, and increase sharply as the sphere volume fraction increase. The g factor, parameter for crystal stability, range from 0.029 to 0.13 and from 0.040 to 0.11 for the spheres of n = 50 and 80, respectively. These g values indicate the formation of stable crystals, and the values were decreased as the sphere volume fraction increased. Two components of crystal growth rate coefficients, fast and slow, were observed in the order from 10⁻³ to 10¹ s⁻¹. This is due to the secondary process in the colloidal crystallization mechanism, corresponding to reorientation from metastable crystals formed in the primary process and/or Ostwald-ripening process. There are no distinct differences in the structural, kinetic and elastic properties among the colloidal crystals of the different core–shell size spheres, nor difference between those of core–shell spheres and silica or poly(styrene) spheres. The results are very reasonably interpreted by the fact that colloidal crystals are formed in a closed container owing to long-range repulsive forces and the Brownian movement of colloidal spheres surrounded by extended electrical double layers, and their formation is not influenced by the rigidity and internal structure of the spheres.