Numerical solution of volterra functional integral equation by using cubic B‐spline scaling functions

In this article, we consider a class of nonlinear functional integral equations which has rather general form and contains a lot of particular cases such as functional equations and nonlinear integral equations of Volterra type. We use a combination of a fixed point method and cubic semiorthogonal B‐spline scaling functions to solve the integral equation numerically. We provide an error analysis for the method which shows that the approximate solution converges to the exact solution. Some numerical results for several test problems are given to confirm the accuracy and the ease of implementation of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 699–722, 2014     

关于丢番图方程x~3±1=3·2~αpD_1y~2

设D_1=multiply from i=1 to s q_i(s=1或2),q_i≡-1(mod6)(i=1,2,…,s)是彼此不同的奇素数,p≡1(mod6)为奇素数.运用初等方法讨论了丢番图方程x~3±1=3·2~αpD_1y~2(α=0或1)的正整数解的情况.     

基于时间序列与灰色拓扑的春节火灾损失预测

火灾每年给中国带来了巨大的损失,春节期间的火灾损失更是严重.根据1999-2010年春节期间火灾统计资料,火灾四项指标数据具有时序性以及随机波动性、模糊性.运用时间序列与灰色拓扑预测方法相结合预测春节期间火灾发生规律,且预测出未来3年内的火灾发生情况.结果表明,时间序列预测模型的平均绝对误差较小,且所建立的灰色拓扑预测模型的拟合精度都达到"好"的标准.因此,采用时间序列与灰色拓扑预测模型相结合对春节火灾发生情况进行预测,其结果合理可靠,可供理论研究和消防部门做出相应的预防措施参考,以达到有效控制和预防春节火灾的目的.     

Fabrication of a freestanding GaN layer by direct growth on a ZnO template using hydride vapor phase epitaxy

A new hydride vapor phase epitaxy (HVPE)-based approach for the fabrication of freestanding GaN (FS-GaN) substrates was investigated. For the direct formation of low-temperature GaN (LT-GaN) layers, the growth parameters were optimized: the polarity of ZnO, the growth temperature, and the V/III ratio. The FS-GaN layer was achieved by gas etching in an HVPE reactor. A fingerprint of Zn out-diffusion was detected in the photoluminescence measurements, especially for the thin (80 μm) FS-GaN film; however, a thicker film (400 μm) was effectively reduced by optimization of GaN growth.     

Hydride vapor phase epitaxy of GaN boules using high growth rates

The boule-like growth of GaN in a vertical AIXTRON HVPE reactor was studied. Extrinsic factors like properties of the starting substrate and fundamental growth parameters especially the vapor gas composition at the surface have crucial impact on the formation of inverse pyramidal defects. The partial pressure of GaCl strongly affects defect formation, in-plane strain, and crystalline quality. Optimized growth conditions resulted in growth rates of 300–500 μm/h. GaN layers with thicknesses of 2.6 and of 5.8 mm were grown at rates above 300 μm/h. The threading dislocation density reduces with an inverse proportionality to the GaN layer thickness. Thus, it is demonstrated that growth rates above 300 μm/h are promising for GaN boule growth.     

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.     

Two-dimensional electron transport in AlGaN/GaN heterostructures

We present a theoretical study of electron transport properties of two-dimensional electron gas in AlGaN/GaN heterostructures. By assuming a drifted Fermi–Dirac distribution and taking into account all major scattering mechanisms, including polar optical and acoustic phonons, background impurities, dislocation and interface roughness, the momentum- and energy-balance equations derived from Boltzmann equation are solved self-consistently. The dependence of the electron drift velocity and electron temperature as a function of the applied electric field are obtained and discussed.     

Photo‐capacitance spectroscopy investigation of deep‐level defects in AlGaN/GaN hetero‐structures with different current collapses

We have investigated electronic deep levels in two AlGaN/GaN hetero‐structures with different current collapses grown at 1150 and 1100 °C by a photo‐capacitance spectroscopy technique, using Schottky barrier diodes. Three specific deep levels located at ～2.07, ～2.80, and ～3.23 eV below the conduction band were found to be significantly enhanced for severe current collapse, being in reasonable agreement with photoluminescence and capacitance–voltage characteristics. These levels probably originate in Ga vacancies and residual C impurities and are probably responsible for the current collapse phenomena of the AlGaN/GaN hetero‐structures. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical model of a pine in a wind

Steady-state nonlinear differential equations govering the stem curve of a wind-loaded pine are derived and solved numerically. Comparison is made between the results computed and the data from photographs of a pine stem during strong wind. The pine breaking is solved at the end.     

A SPECIAL CUBIC SYSTEM CLOSE RELATED TOTHE GENERAL QUADRATIC SYSTEM

1NumberandDistributionofCriticalPoilltsConsiderthefollowingcubicsystem:itcontainsonlytwocubictermspx'andqx'morethanthegeneralquadraticsystem:Thecoordinatesofthecriticalpointsatinfinityof(1)mustsatisfytheequation:px'y~qx'=0.(3)SoA(P,q,0)andB(0,l,0)aretheonlycriticalpointsatinfinityof(1).Itiseasilyseenthatthetwocharacteristicrootsof(1)atAareAl=AZ=--p,soAisastable(unstable)nodewhenp>0(<0).Moreover,Bisahigherordercriticalpointatinfinityof(1)withindex0,itisthepileupof3criticalpointsontheequat…