Catalan and Motzkin numbers modulo 4 and 8

In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.     

New host homopolymers containing pendant triphenylamine derivatives: Synthesis,optical, electrochemical properties and its blend with Ir(ppy)3 for green phosphorescent organic light‐emitting devices

Two vinyl homopolymers poly(N‐(4‐(4‐(4‐vinylbenzyloxy)styryl)phenyl)‐N‐phenylbenzenamine) (PVST ) and poly(4‐vinyltriphenylamine) (PTPA ) containing pendant hole‐transporting triphenylamine and 4‐oxystyryltriphenylamine groups, respectively, were synthesized by radical polymerization and employed as hosts for tris(2‐phenylpyridine) iridium [Ir(ppy)₃] phosphor. Structural influences of the hole‐transporting groups upon optoelectronic properties were investigated by photophysical, electrochemical, and electroluminescent methods. The polymers were readily soluble in common organic solvents and their weight‐average molecular weights (M_w) were 5.68 × 10⁴ and 1.90 × 10⁴, respectively. The emission spectra (both photoluminescence, PL and electroluminescent, EL) of the blends [PTPA with 4 wt % Ir(ppy)₃] showed dominant green emission (517 nm) attributed to Ir(ppy)₃ due to efficient energy transfer from PTPA to Ir(ppy)₃. The HOMO levels of PVST and PTPA, estimated from onset oxidation potentials in their cyclic voltammograms, were ?5.14 and ?5.36 eV, which are much higher than ?5.8 eV of the conventional poly(9‐vinylcarbazole) (PVK) host owing to high hole‐affinity of the triphenylamine groups. The optoelectronic performances of phosphorescent EL devices, using PVST and PTPA as hosts and Ir(ppy)₃ as dopant (indium tin oxide, ITO/poly(3,4‐ethylenedioxythiophene): poly(styrene sulfonate) (PEDOT:PSS)/PVST or PTPA:Ir(ppy)₃(4 wt %):PBD(40 wt %)/BCP/Ca/Al), were investigated. The maximum luminance and luminance efficiency of the PTPA device were 9220 cd/m² and 6.1 cd/A, respectively, which were significantly improved relative to those of PVK and PVST. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7960–7971, 2008     

Miscibility and isothermal crystallization behavior of polyamide 6/poly(vinyl alcohol) blend

An investigation of miscibility and isothermal crystallization behavior of Polyamide 6 (PA6)/Poly(vinyl alcohol) (PVA) blends was conducted. Fourier transform infrared spectra (FTIR) analysis indicated that the interactions between the carbonyl groups of PA6 and hydroxyl groups of PVA increase as the weight ratios of PA6 to PVA of PA6/PVA specimens increase. This interaction between PA6 and PVA leads to their miscibility in the amorphous region and even some extent effects on their crystal phase, respectively. Further isothermal crystallization behavior of PA6/PVA indicate that the miscibility of PVA in PA6 leading difficulty in crystallization of PA6. Several kinetics equations are employed to describe the effects of PVA on the crystallization properties of PA6 in PA6/PVA blends in detail. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1360–1368, 2008     

A phenomenological theory for elastic superconductors

The purpose of the present study is to develop a phenomenological theory for elastic superconductors that is based on a rigorous thermodynamical internal variable theory in which the concept of complex internal variable is introduced to include the phase effect of quantum mechanics. Two phenomena of superconductivity, i.e., perfect conductivity and perfect diamagnetism, can be explained in the formulation. In the equilibrium state, this theory can be reduced to the well-known Ginzburg-Landau (GL) theory. Upon linearizing the field equations, boundary conditions and constitutive equations, the governing equations of the rigid-body state and the perturbed state are obtained. These equations then serve to analyze the effect of the hydrostatic deformation on the penetration depth, the GL coherence length and the critical field.     

Synthesis of polyphilic hexaazatrinaphthylenes and mesomorphic properties

Methodologies for the synthesis of polyphilic hexaazatrinaphthylenes (HATN) with reduced symmetry based on the sequential condensation reactions of 1,2-bisalkoxy-4,5-diaminobenzenes with either tetrahydroxy-1,4-quinone or hexaketocyclohexane are described. The synthesized HATN possesses improved mesogenic properties and is liquid crystalline at room temperature.     

Optically controllable and focus-tunable Fresnel lens in azo-dye-doped liquid crystals using a Sagnac interferometer

This study demonstrates a tunable Fresnel lens in an azo-dye-doped liquid crystal (ADDLC) film using an interference technique. One Fresnel-patterned green beam using a Sagnac interferometer irradiated the UV-illuminated ADDLC cell, yielding a concentric zone plate distribution with homeotropic and isotropic structures in bright and dark regions of the green interference pattern. The proposed Fresnel lens is polarization independent, focus tunable, and the focusing efficiency of the device can be optically controlled.     

Method for modulating the wafer bow of free-standing GaN substrates via inductively coupled plasma etching

The bowing curvature of the free-standing GaN substrate significantly decreased almost linearly from 0.67 to 0.056 m⁻¹ (i.e. the bowing radius increased from 1.5 to 17.8 m) with increase in inductively coupled plasma (ICP) etching time at the N-polar face, and eventually changed the bowing direction from convex to concave. Furthermore, the influences of the bowing curvature on the measured full width at half maximum (FWHM) of high-resolution X-ray diffraction (HRXRD) in (0 0 2) reflection were also deduced, which reduced from 176.8 to 88.8 arcsec with increase in ICP etching time. Decrease in the nonhomogeneous distribution of threading dislocations and point defects as well as V_Ga–O_N complex defects on removing the GaN layer from N-polar face, which removed large amount of defects, was one of the reasons that improved the bowing of the free-standing GaN substrate. Another reason was the high aspect ratio of needle-like GaN that appeared at the N-polar face after ICP etching, which released the compressive strain of the free-standing GaN substrate. By doing so, crack-free and extremely flat free-standing GaN substrates with a bowing radius of 17.8 m could be obtained.     

Asymmetric hydrogenation using ferrocenylphosphine rhodium(I) cationic complexes

High optical yields are obtained in the hydrogenation of α-acetamidocinnamic acid using [(COD)Rh((+)PPFA)]ClO₄ and related complexes as catalysts. (+)PPFA is (S)-α-[(R)-2-diphenylphosphinoferrocenyl] ethyldimethylamine.