Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Solution-Processable Low Voltage Organic Transistors of Thieno[3,2-b]thiophene-Based Conducting Polymer

A low-operating voltage and high performance polymeric field effect transistors using octadecylphosphonic acid-treated high-k AlOx and HfO₂ hybrid dielectrics were demonstrated. High-k metal oxide hybrid dielectrics were prepared by oxygen plasma treatment of deposited Al film for AlOx and by spin coating of solution-processable HfO₂ sol-gel solution for HfO₂ in combination with phosphoric acid-based self-assembled monolayer (SAM), resulting in high capacitance (10 nF/cm² for SiO₂, 600 nF/cm² for AlOx and 580 nF/cm² for HfO₂). With phosphoric acid-based SAM on high-k metal oxide and thermal annealing of thieno[3,2-b]thiophene-based conducting polymer, the device performance was significantly enhanced. The highest mobility of the transistors using ODPA-treated AlOx as a gate dielectric is 2.3 × 10^?2 cm² V^?1 s^?1 in the saturation region with the source-drain of ?2 V. In ODPA-treated HfO₂ hybrid dielectric, the saturated mobility is 1.1 × 10^?2 cm² V^?1 s^?1 and the threshold voltage was measured to be ?0.31 V, which is at least one order lower than SiO₂ hybrid dielectric (?3 V).     

Codimension reduction in symmetric spaces

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.     

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.     

Index transforms with Weber-type kernels

New index transforms with Weber-type kernels, consisting of products of Bessel functions of the first and second kind, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth-order partial differential equation.     

The stabilization of partially-premixed jet flames in the presence of high potential electric fields

Numerous research efforts have focused on flame stabilization and emissions. Based on initial experiments, specific mechanisms resulting from DC electric fields were chosen to be investigated, namely the chemical, thermal, and ionization mechanisms. Numerical simulations were performed on premixed propane-ozone-air flames to characterize ozone effects on flame speed resulting from the formation of ozone in high potential electric fields. These results were compared against partially premixed flame experiments to observe the dominant influences within leading edge stabilization within high potential electric fields. It was found that the electromagnetic or ionization influences, serve as the dominant effect on the combustion zone.     

Another characterization of homogeneous Poisson processes

For a general renewal process N (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from N by Bernoulli 0/1 thinning is characterized. This independence is well-known to hold true in the case of homogeneous Poisson processes; by way of corollary one obtains the interesting observation that, when coupled with some minimal extra conditions, it in fact already identifies them. The proof is analytic in character.     

Invariant fibrations for some birational maps of ℂ2

Abstract

In this article, we extract and study the zero entropy subfamilies of a certain family of birational maps of the plane. We find these zero entropy mappings and give the invariant fibrations associated to them.     

Stable structure and effects of sulfur in CdTe/CdS heterojunctions

Structural and electronic properties of S in the CdTe/CdS(0001) interface are studied using the density functional theory. The interstitial S atom may induce the inversion of the surface Cd atoms and sublayer Te atoms of the Cd‐terminated surface, while S atoms may adsorb at the top sites, substitute Te atoms or accumulate at the voids inside the Te‐terminated (111) CdTe surface. Isovalent substituting S for Te in the CdTe(111)/CdS(0001) heterojunctions can reduce the strain arising from lattice mismatch and cause a reduction of interface states, so it may be better for solar cells. Copyright © 2011 John Wiley & Sons, Ltd.