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.     

In-situ synchrotron X-ray absorption studies of LiMn0.25Fe0.75PO4 as a cathode material for lithium ion batteries

Recently, lithium bi-metal phosphates (LiM′M″PO₄) have been synthesized for use as cathode materials in order to increase cell voltages and electrical performances. In this work, we have substituted Mn²⁺ at the 4c site of LiFePO₄ to prepare the lithium bi-metal phosphate LiMn_0.25Fe_0.75PO₄ and have found that it greatly enhances the cell voltage. At a 0.05 C discharge rate, the cell capacity was about 153 mAhg^− 1 and the average working voltage rose to 3.53 V due to the Mn substitution. However, the capacity and working voltage both decrease as the discharge rate increases. By in-situ metal K-edge absorption analysis, it reveals that the substituted metal Mn²⁺ does not work completely at a higher discharge rate, due to poor electrical conductivity and a serious Jahn–Teller effect.     

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.