Dirichlet problems with double resonance and an indefinite potential

We consider semilinear Dirichlet problems with an unbounded and indefinite potential and with a Carathéodory reaction. We assume that asymptotically at infinity the problem exhibits double resonance. Using variational methods, together with Morse theory and flow invariance arguments, we prove multiplicity theorems producing three, five, six or seven nontrivial smooth solutions. In most multiplicity theorems, we provide precise sign information for all the solutions established.     

Simple Dip-Coating Process for the Synthesis of Small Diameter Single-Walled Carbon Nanotubes-Effect of Catalyst Composition and Catalyst Particle Size on Chirality and Diameter

We report on a dip-coating method to prepare catalyst particles (mixture of iron and cobalt) with a controlled diameter distribution on silicon wafer substrates by changing the solution's concentration and withdrawal velocity. The size and distribution of the prepared catalyst particles were analyzed by atomic force microscopy. Carbon nanotubes were grown by chemical vapor deposition on the substrates with the prepared catalyst particles. By decreasing the catalyst particle size to below 10 nm, the growth of carbon nanotubes can be tuned from few-walled carbon nanotubes, with homogeneous diameter, to highly pure single-walled carbon nanotubes. Analysis of the Raman radial breathing modes, using three different Raman excitation wavelengths (488, 633, and 785 nm), showed a relatively broad diameter distribution (0.8-1.4 nm) of single-walled carbon nanotubes with different chiralities. However, by changing the composition of the catalyst particles while maintaining the growth parameters, the chiralities of single-walled carbon nanotubes were reduced to mainly four different types, (12, 1), (12, 0), (8, 5), and (7, 5), accounting for about 70% of all nanotubes.     

Photoisomerizations of N4-hydroxycytosines

A series of N4-hydroxycytosines, unsubstituted or substituted with methyl groups at N3 or C5 atoms of the heterocyclic ring, was studied using the matrix-isolation method. Depending on the absence or presence of the methyl substituent at N3 or C5 atoms (or at both of them) the syn or anti form of the compounds (or a mixture of both forms) was trapped from the gas phase into a low-temperature matrix. Upon UV (lambda > 295 nm) irradiation of the matrixes the syn --> anti as well as the anti --> syn photoisomerization reactions were observed. The syn and anti isomers of N4-hydroxycytosines were identified by comparing their experimental IR spectra with the theoretical spectra calculated at the DFT(B3LYP)/6-31G(d,p) level. For the majority of the studied compounds, the UV induced reactions led to a photostationary state. The position of the final photostationary state was found to be a sensitive function of weak interactions of a studied N4-hydroxycytosine with the matrix environment: solid argon or solid nitrogen. However, not all of the studied photoisomerizations led to a classical photostationary state. For some of the investigated N4-hydroxycytosines, the position of the photostationary state was shifted very strongly in favor of the photoproduct, whereas for some others the position was shifted so strongly in favor of the starting isomer that no photoisomerization was observed. These experimental findings were elucidated by theoretical investigations of the potential energy surfaces of the ground (S0) and first excited (S1) electronic states of N4-hydroxycytosine. The crucial result of these calculations (carried out at the CASSCF level) was the localization of a conical intersection between S0 and S1 at a structure with perpendicular orientation of the hydroxylimino group with respect to the heterocyclic ring.     

Experimental and theoretical studies on corals. I. Toward understanding the origin of color in precious red corals from Raman and IR spectroscopies and DFT calculations

An attempt to explain the origin of the vivid red color in precious pink and red corals was undertaken. Raman and IR spectroscopies were applied to characterize white, pink and red corals. The position of the Raman signal near 1500 cm⁻¹ of some corals and pearls was associated by several authors with the presence of the mixture of all‐trans‐polyenic pigments, containing 6–16 conjugated CC bonds or β‐carotenoids. This hypothesis was examined theoretically by performing extensive B3LYP‐DFT calculations of vibrational spectra of the model polyenic compounds. The B3LYP/6‐311++G** predicted positions of the dominating Raman mode depend on the number of CC units (Cn parameter) and can be accurately predicted for larger systems from a simple nonlinear fit. The DFT‐predicted Raman activities of these modes are extremely sensitive to Cn, and sharply increase with the number of double bonds. This implies a presence of only—two to three polyenes differing slightly in the number of CC units as the source of color in pink and red corals. Copyright © 2009 John Wiley & Sons, Ltd.     

Fluorescence resonance energy transfer in a non-conjugated system of CdSe quantum dots/zinc-phthalocyanine

Energy transfer between CdSe quantum dots (QDs) as donors and Zn phthalocyanine (Zn-Pc) molecules as acceptors was studied using steady-state photoluminescence and time-correlated single photon counting techniques. With the latter technique it is evaluated that the lifetime of Zn-Pc emission increases from 4 ns to ca. 30 ns on 460 nm excitation in the presence of the QDs. The concomitant decrease in the lifetime of the QDs emission (from 23.5 to 18.4 ns) indicates that the excitation of Zn-Pc occurs not only through reabsorption but also through fluorescence resonance energy transfer.     

Only Countable Reichenbachian Common Cause Systems Exist

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.     

Experimental and quantum-chemical studies of 1H, 13C and 15N NMR coordination shifts in Pd(II) and Pt(II) chloride complexes with methyl and phenyl derivatives of 2,2'-bipyridine and 1,10-phenanthroline

1H, 13C and 15N NMR studies of platinide(II) (M=Pd, Pt) chloride complexes with methyl and phenyl derivatives of 2,2'-bipyridine and 1,10-phenanthroline [LL=4,4'-dimethyl-2,2'-bipyridine (dmbpy); 4,4'-diphenyl-2,2'-bipyridine (dpbpy); 4,7-dimethyl-1,10-phenanthroline (dmphen); 4,7-diphenyl-1,10-phenanthroline (dpphen)] having a general [M(LL)Cl2] formula were performed and the respective chemical shifts (delta1H, delta13C, delta15N) reported. 1H high-frequency coordination shifts (Delta1Hcoord=delta1Hcomplex-delta1Hligand) were discussed in relation to the changes of diamagnetic contribution in the relevant 1H shielding constants. The comparison to literature data for similar [M(LL)(XX)], [M(LL)X2] and [M(LL)XY] coordination or organometallic compounds containing various auxiliary ligands revealed a large dependence of delta1H parameters on inductive and anisotropic effects. 15N low-frequency coordination shifts (Delta15Ncoord=delta 15Ncomplex-delta15Nligand) of ca 88-96 ppm for M=Pd and ca 103-111 ppm for M=Pt were attributed to both the decrease of the absolute value of paramagnetic contribution and the increase of the diamagnetic term in the expression for 15N shielding constants. The absolute magnitude of Delta15Ncoord parameter increased by ca 15 ppm upon Pd(II)-->Pt(II) transition and by ca 6-7 ppm following dmbpy-->dmphen or dpbpy-->dpphen ligand replacement; variations between analogous complexes containing methyl and phenyl ligands (dmbpy vs dpbpy; dmphen vs dpphen) did not exceed+/-1.5 ppm. Experimental 1H, 13C, 15N NMR chemical shifts were compared to those quantum-chemically calculated by B3LYP/LanL2DZ+6-31G**//B3LYP/LanL2DZ+6-31G*, both in vacuo and in DMSO or DMF solution.     

Systematic effect of benzo-annelation on oxo-hydroxy tautomerism of heterocyclic compounds. Experimental matrix-isolation and theoretical study

Oxo-hydroxy tautomerism and phototautomerism of 2-quinolinone, 1-isoquinolinone, 3-hydroxyisoquinoline, 2-quinoxalinone, and 4-quinazolinone were studied using the matrix-isolation technique. These compounds contain a benzene ring fused with a heterocyclic ring of 2-pyridinone, 2-pyrazinone, or 4-pyrimidinone. It turned out that direct attachment of a benzene ring to a heterocycle leads to a very pronounced increase of the relative stability of oxo tautomers (in comparison with the tautomerism of the parent compounds 2-pyridinone, 2-pyrazinone, and 4-pyrimidinone). The only exception concerns 3-hydroxyisoquinoline, where fusion with a benzene ring enforces rearrangement of the double- and single-bond system in the oxo tautomer. This destabilizes substantially the oxo form with respect to the hydroxy tautomer. The ratios of population of the oxo and hydroxy tautomers observed in Ar matrixes correspond to the tautomeric equilibria of the compounds in the gas phase. These equilibria were well reproduced by theoretical calculations carried out at the QCISD and QCISD(T) levels. The combined experimental and theoretical results reveal links between aromaticity and tautomerism. Moreover, a UV-induced phototautomeric reaction transforming the oxo forms into the hydroxy tautomers was observed for all (except 3-hydroxyisoquinoline) studied compounds. This photoeffect allowed separation of the IR spectra of the tautomers in question.