A nonoscillation theorem for superlinear Emden-Fowler equations with near-critical coefficients

We are interested in the oscillatory behavior of solutions of the Emden-Fowler equation y^″+a(x)|y|^γ−1y=0, γ>1, where a(x) is a positive continuous function on (0,∞). In the special case when the coefficient a(x) is a power of x, i.e. a(x)=xα for some constant α, the value α^∗=−(γ+3)/2 plays a critical role: The equation has both oscillatory and nonoscillatory solutions if α>α^∗, while all solutions are nonoscillatory if α<α^∗. When a(x) is close to the critical exponent, one of the known results is that if a(x)=x−(γ+3)/2log−σ(x), where σ>0, then all solutions are nonoscillatory. In this paper, this result is further extended to include a class of coefficients in which the above condition with log(x) can be replaced by loglog(x), or logloglog(x) and so on.     

Synthesis and crystal structure of a novel butterfly-like complex, [WOS3Cu2(PPh3)2(Py)2] (Py = pyridine)

A new butterfly-like cluster [WOS3Cu2(PPh3)2(Py)2] was obtained by reacting [WOS3Cu2(PPh3)3] with pyridine. The crystal structure of the cluster has been determined by X-ray diffraction. The compound shows an unusual folded structure, in which two 4-coordinate Cu atoms are bound to the WOS3 moiety via two S–S edges.     

Indium tin oxide surface treatments for improvement of organic light-emitting diode performance

We have systematically investigated the influence of UV ozone and acid (HCl) treatments (separate and combined) of the surface of indium tin oxide (ITO) on the ITO parameters and the performance of organic light-emitting diodes (OLEDs) fabricated on the treated substrates. The ITO substrates were characterized by Hall measurements, Seebeck coefficient measurements and surface-probe microscopy. After ITO characterization, two types of devices (ITO/NPB/rubrene/Alq₃/LiF/Al and ITO/TPD/rubrene/Alq₃/LiF/Al) were fabricated on the differently treated substrates. It was found that in both cases the optimal treatment was HCl followed by UV ozone, which resulted in the lowest turn-on voltage and the highest luminous efficiency. The maximum luminous efficiency in the ITO/NPB/rubrene/Alq₃/LiF/Al OLED with HCl followed by UV ozone treatment was 2.15 lm/W compared to 1.46 lm/W with UV ozone treatment only. PACS 81.65Cf; 85.60.Jb     

Conversion of egg shell membrane to inorganic porous CexZr1−xO2 fibrous network

The binary system CeO₂–ZrO₂ is thermally stable and has superior reduction–oxidation properties. It has been commonly used in the three-way catalytic converters for automobiles. In this work, an inorganic biomorphic porous Ce_xZr_1−xO₂ fibrous network was successfully synthesized by using the egg shell membrane (ESM) as templates, and its morphology was a perfect replica of the original ESM. The synthesis involved a simple infiltration and calcination process. A fresh ESM was peeled from a chicken egg shell. It was soaked in a Ce(NO₃)₃ and Zr(NO₃)₄ mixture before it was calcined at 700 °C in ambient environment. The fibers in the biomorphic network had diameter ranged from 1 to 4 μm, and they were composed of Ce_xZr_1−xO₂ nanocrystallites having an average grain size of 10 nm.     

On the <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">s</Emphasis></Superscript> Theory of Hydrostatic Euler Equations

In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of H ^s solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness, mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based on weighted H ^s a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity.     

Self-assembled periodical polycrystalline-ZnO/a-C nanolayers on Zn nanowire

Zn nanowires with an epitaxial thin surface layer of zinc oxide were dispersed onto amorphous carbon films and stored at room temperature. After 1500 h, a self-organized equal-spaced zinc oxide (approximately 2 nm)/carbon (approximately 2.5 nm) multilayer structure was found to form outside the Zn nanowire, taking the place of the original ZnO surface layer. We carried a systematic study to clarify the self-formation mechanism of the periodical multilayers outside the Zn nanowire and found out that such a configuration originated from a chemical reaction between Zn and CO2 and were formed via a gas phase diffusion-interfacial chemical reaction-phase separation process.     

Syntheses, structures, photoluminescence, and theoretical studies of d(10) metal complexes of 2,2'-dihydroxy-[1,1']binaphthalenyl-3,3'-dicarboxylate

The free solvated ligand, H(2)bna.CH(3)OH.H(2)O (1), and its dimeric complex, [Cd(2)(bna)(2)(H(2)O)(6)] (2) (bna = 2,2'-dihydroxy-[1,1']-binaphthalene-3,3'-dicarboxylate), were obtained by evaporation of the solutions, while two new d(10) metal-hydroxy cluster-based coordination polymers, namely [Cd(8)(OH)(4)(H(2)O)(10)(bna)(6)].17H(2)O (3) and [Hpy](2)[Zn(4)(OH)(2)(H(2)O)(2)(bna)(4)].2H(2)O.2CH(3)CN (4), were obtained by a hydrothermal route. All the compounds have been characterized by X-ray crystallography and photoluminescence measurements. Compound 1 consists of a three-dimensional, hydrogen-bonded supramolecular array, 2 exhibits a dimeric molecule featuring a square motif organized by two Cd(II) atoms and two bna ligands each at the corner, and 3 contains unprecedented [Cd(8)(micro(3)-OH)(2)(micro-OH)(2)(micro-H(2)O)(2)](12+) octanuclear metallacrown cores which are interlinked through bna to afford a two-dimensional structure, while 4 features layers with butterfly-shaped [Zn(4)(micro(3)-OH)(2)](6+) clusters. All the complexes display photoluminescent properties in the blue/green range. The manifestation of photoluminescence, as probed by molecular orbital calculations performed on the complexes and also on hypothetical multinuclear complexes, is attributed to a ligand-to-metal charge-transfer mechanism. In addition to presenting a new approach for the study of the photoluminescent properties of metal-cluster-based coordination polymers by using simple model compounds, the study also reveals the dominant role of the structure of the ligand over that of the d(10) metal-hydroxy (or oxy) cluster and the presence of the cluster significantly increasing the emission lifetime.     

Distortionless light pulse delay in quantum-well Bragg structures

We describe a reflection scheme that allows Bragg-spaced semiconductor quantum wells to be used to trap, store, and release light. We study the temporal and spectral distortion of delayed light pulses and show that this geometry allows multibit delays and offers a high degree of distortion compensation.     

Spectroscopic ellipsometry of 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA)

The optical functions of PTCDA have been determined by spectroscopic ellipsometry. The samples were prepared by thermal evaporation of PTCDA on glass substrates. The influence of the substrate temperature on the properties of PTCDA films has also been investigated. The lowest substrate temperature investigated here was room temperature. At room temperature and higher substrate temperatures, we have not observed ordering of the evaporated films, which would result in high anisotropy, as reported for PTCDA films grown by organic molecular-beam deposition at very low temperatures (so-called quasi-epitaxial growth). Therefore, the samples have been assumed to be isotropic. The obtained imaginary part of the dielectric function exhibits the expected features: a low-magnitude peak around 370 nm and a higher magnitude, two-peak structure in the 400–600 nm spectral region. PACS 78.20.Ci; 78.66.Qn