Rayleigh波方程解的渐近理论

在Sobolov空间中．对具初值问题的Rayleigh波方程．给出了一个浙近方法．初值问题的适定性及形式近似解的合理性都在时间变量0≤t≤O│ε│^-1时成立．和Horssen于1988年提出的结果,0≤t≤O(│ε│^-1/2)比较．它的近似程度较好一些,从而在Sobolov空间C^1(JL,H^1-1(R^1))中部分地回答了Blom在1994文[2]中关于具初值问题RayIeigh波方程是否存在O(O│ε│^-1)近似解的问题．     

一类半线性波动方程解的渐近理论

研究了三维空间中如下半线性波动方程的初值问题　　 utt =Δu - b24 u+εF(u ,ε) ,　　t >0 ,x∈R3,u(0 ,x ,ε) =u0 (x ,ε) ,ut(0 ,x ,ε) =u1(x ,ε) ,x∈R3,解的渐近理论。其中Δ = 3i=1 2 x2 i,常数b≥ 0。在古典空间C2 中得到了形式近似解的合理性在长时间t∈〔0 ,｜ε｜- 12 -k( p- 1) 〕(ε充分小 ,0 <2 -k(p- 1) <1,0 3)内成立     

具有阻尼项受迫Hill方程的渐近解

本文讨论具有阻尼项受迫Hill方程: +c+(δ+εP(t))x=f(t) (1)的渐近解。其中P(t)为周期偶函数,f(t)为周期函数。方程(1)的研究在振动理论中占有重要地位,许多实践振动问题最后也归结为解此方程。为了避免繁杂的计算过程,在不失一般性原则下,我们只要考虑如下问题: 作变换: x(t)=e~(-1/2et)y(t) (2)式能化为:     

基于分治的属性约简相对核计算

针对信息表中相对核的计算采用分治策略提出了一个新的属性约简方法，将在计算整个全域上的属性约简问题转化为计算在相应划分的子区域上属性约简问题．将原有计算POS X0(y)的算法复杂度O(|A||U|^2)，降为O(|A|(|Y1|^2 |Y2|^2 … |Yn|^2))，对于一般比较大的|U|说，效率提高非常明显，提高了属性约简的可计算性.     

一类非Lipschitz条件的BSDE解的存在唯一性

本文讨论了倒向随机微分方程Yt=ξ+l∫tf(s,Ys,Zs)ds-l∫tZsdWs在f(t,y,z)满足(A)N＞0,(E)CN＞0,LN＞0,使得对任意y1,y2∈Rn,z1,z2∈Rn×d,当0≤|y1|,|y2|,|z1|,|z2|≤N时,有|f(s,y1,z1)-f(s,y2,z2)|2≤ CNK(t,|y1-y2|2)+LN|z1-z2|2的非Lipschitz条件时解的存在性和唯一性.2003年,王赢、王向荣证明了一类倒向随机微分方程解的存在唯一性,我们使用函数逼近法,得到一列满足王赢,王向荣文中条件的倒向随机微分方程,因而每个方程均有唯一解,然后通过取极限的方法证明我们所讨论的方程有唯一解(Y Z),从而推广了他们的结果.     

小周期复合材料波传播问题的一个多尺度渐近展开式及其收敛性分析

利用渐近展开和均匀化思想讨论了小周期复合材料的波传播问题,得到了高阶振荡系数的双曲型波动方程的渐近展开式.对R2中的光滑凸区域Ω,证明了渐近解在L∞(0,T;H10(Ω))中具有较好的收敛性,收敛阶为O(ε).     

一类拟线性椭圆型方程带平边值问题解的存在性

建立了边值问题｛div(|Du|^p-2Du) a(|x|f(|x|,u)=0,在B属于R^Nδu／δ λu=-α 在δB｝正对称解的存在性和唯一性,这里B是R^N中的以原点为圆心的单位图。     

高维抛物型方程的一个高精度恒稳定的交替方向格式

本文对高维抛物型方程构造了一个高精度恒稳定的交替方向格式.当2≤p≤4时,格式的局部截断误差阶可达到O(τ2+h4),当p=3时,将Richardson外推法应用于本文格式,得到了O(τ3+h6)阶精度的近似解.最后通过数值实例验证了我们对所得格式所作的理论分析是正确的.     

一类非参数回归函数导数估计的渐近分布

设y_1,…,y_n是在固定点x_1,…,x_n的n个观察值,适合模型y_i=g(x_i)+ε_i,1≤i≤n,这里g是R~1上的未知函数,{ε_i}为零均值、有限方差的i.i.d.序列,设O=x_o≤x_l≤…≤x_(n-1)≤x_n=1我们用作为g~(p)(x)的估计. 本文给出了的渐近分布,其中x~(1),…,x~(m)为(0,1)内的相异点。     

非谐晶体中弱阻尼非线性波吸引子

本文研究了非谐晶体中弱阻尼非线性波解的渐近性态：uxt 3/2ux^2uxx uxxxx-sinu εux=0我们首先对方程证明了在空间Hpεr^2中整体弱吸引子的存在性,然后利用能量方程方法证明了整体弱吸引子实际上是整体强吸引子。     

关于Wiener过程增量的注

本文讨论Ｗｉｅｎｅｒ过程增量的下极限结果找到正则因子ｄ（Ｔ,ｔ）,使得ｓｕｐａＴ≤ｔ≤Ｔｓｕｐｔ≤ｓ≤Ｔｄ（Ｔ,ｔ）｜ｗ（ｓ）－ｗ（ｓ－ｔ）｜与ｓｕｐｓＴ≤ｔ≤Ｔｓｕｐｔ≤ｓ≤Ｔｓｕｐ０≤ｂ≤ｔｄ（Ｔ,ｔ）｜ｗ（ｓ）－ｗ（ｓ－ｈ）｜的下极限１。     

圆波导界面电磁场的传播特性

从麦克斯韦方程及边界条件出发对含有两种不同介质的金属波导管进行了研究 ,得到特征方程 (γ1ε2 -γ2 ε1) 2 (μ1γ2 -μ2 γ1) 2 =0 ,指出当γ1ε2 =γ2 ε1,μ1γ2 ≠μ2 γ1时两区域波导模为横磁模 ,γ1ε2 ≠γ1ε2 ,μ1γ2 =μ2 γ1为横电模 ,γ1ε2 =γ2 ε1,μ1γ2 =μ2 γ1为杂交模 .并讨论了截止条件和传播特性 .     

带权最大割问题的一种基于划分技术的固定参数可解算法

运用参数计算复杂性理论和技术对带权最大割问题进行了研究。首先对该问题及其相关概念进行了参数化定义,然后对参数化带权最大割问题提出了一种基于随机划分技术的随机算法。该随机算法依次将实例图的顶点进行[1n(1/ε)]×2~k(0ε1)次随机划分,并选择其中权值最大的k-划分作为输出解,因而能在时间O~*(1n(1/ε)2~k)内以至少1-ε的概率找到目标解。接着在此基础上着重运用最新改进的(n,k)-全集划分技术对参数化带权最大割问题提出了一个时间复杂度为O~*(2~(2k+12log~2(2k))的确定性算法,表明了带权最大割问题是固定参数可解的。     

Ellipsometric study of dielectric functions of Mg(1-y)Ca(y)H(x) thin films (0.03≤y≤0.17)

Mg(1-y)Ca(y)H(x) (0.03≤y≤0.17) alloy thin films covered with thin Pd were hydrogenated using 4% H(2) in Ar under atmospheric pressure at room temperature. The complex dielectric functions (ε=ε(1) + iε(2)) in the range of 0.75 to 5.0 eV of these hydrides were evaluated with spectroscopic ellipsometry. The imaginary part of the dielectric function ε(2) was composed of one Drude and three Lorentz oscillator terms whose peak positions were about 1.2 eV (L(1)), 2.8 eV (L(2)), and 5.2 eV (L(3)). The L(3) term observed in all hydrides is attributed to optical absorption of MgH(2) with E(g)=5.16 eV. The Drude term, which may be due to unhydrogenated Mg-metal, was observed in the hydrides with a low Ca composition y of less than 0.04. The L(1) term was observed in the hydrides with a Ca composition of more than 0.05, while the L(2) term was observed for more than 0.11. These L(1) and L(2) terms were estimated from a variation with hydrogenation of ellipsometric angle Ψ which is due to optical absorption of CaH(2-α) (L(1)) and MgCaH(3.72) (L(2)).     

Spectral stochastic two‐scale convergence method for parabolic PDEs

Following the theory of two‐scale convergence method introduced by Nguetseng (SIAM J. Math. Anal. 1989; 20 :608–623) and further developed by Allaire (SIAM J. Math. Anal. 1992; 23 :1482–1518), we introduce the chaos two‐scale method as a spectral stochastic tool to tackle parabolic partial differential equations where the material properties are stochastic processes σ^ε(t, x, ω) of the form σ(t, x, t/ε^γ, x/ε, ω), oscillating in both space and time variables with different speeds. Periodicity with respect to the fast or local variables is assumed, and, stationary Gaussian material properties processes are considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Measurement of viscosities from the transient current of nematic liquid crystals with negative dielectric anisotropy

A method for measuring the complete set of the Leslie viscosity coefficients of nematic liquid crystals (NLCs) with negative dielectric anisotropy (Δε < 0) is proposed. The method is based on the analysis of the transient current, induced by step voltage excitation, in homeotropic NLC cells. It has been shown that the transient current in homeotropic NLC cells with Δε < 0 can be explained by the theory of NLCs in which the flow effects and the free-slip boundary condition are taken into account [Y. Iwata et al., Jpn. J. Appl. Phys. 43 (2004) L 1588]. It is demonstrated that the complete set of the Leslie viscosity coefficients of NLCs with Δε < 0 can be simultaneously and accurately measured by fitting the transient current calculated by the theory to the experimental data with a differential correction method.     

Dielectric and ferroelectric properties of Bi(Zn1/2Ti1/2)O3-PbTiO3-PbZrO3 ternary ceramics

Ceramics of a new ternary solid solution system, xBi(Zn(1/2)Ti(1/2))O(3-yPbTiO(3)z)PbZrO(3) (xBZT-yPT-zPZ), with compositions along the solubility limit curve are prepared by solid-state reaction and sintering technique. Two morphotropic phase boundaries (MPBs) separating the orthorhombic and tetragonal (MPB(O-T)) phases and the tetragonal and rhombohedral (MPB(T-R)) phases, respectively, are observed with increasing z (0.10 ≤ x ≤ 0.21; 0 ≤ y ≤ 0.49). It is found that the transition from the ferroelectric to paraelectric phase becomes more diffuse with the addition of BZT into the PZT solid solution. Enhanced dielectric and ferroelectric properties appear at MPB(R-T), which exists over a wide composition region (0.45 ≤ z ≤ 0.6), as revealed by X-ray diffraction and dielectric measurements. The dielectric constant reaches a maximum value (ε' = 1250) on the tetragonal majority side of the MPB. The highest remnant polarization (P(r) = 34.2 μC/cm(2)) is found in the composition at the center of the MPB, where the rhombohedral and tetragonal phases coexist in almost equal quantities.     

人工神经网络的单调序列逼近

设Nn,Ф是以Ф为激活函数的具有n+1个神经元的前向单隐层人工神经网络的全体.主要证明了,若f∈C[0,1],则对于任意的ε>0,存在两个神经网络序列{Pn,Ф}和{Qn,Ф},使得在[0,1]上Qn,Ф(x)≤Qn+1,Ф(x)≤f(x)≤Pn+1,Ф(x)≤Pn,Ф(x),而且Pn,Ф(x)-Qn,Ф(x)≤(6+4(2~(1/2)))En,Ф(f),这里的En,Ф(f)为Nn,Ф中的元对f的最佳逼近.     

Setting expansion of gypsum-bonded investment in dental casting

The values of setting expansion of investment under uniaxial stress have been determined at conditions designed to obtain the difference of setting expansion between that parallel to the loading direction and that perpendicular to the loading axis. The setting expansion curves were represented by $$a(t) = a_0 (1 - P/E')[1 - exp( - kt)]$$ along the loading direction and $$a(t) = a_0 (1 + \nu 'P/E')[1 - exp( - kt)]$$ perpendicular to the loading direction, wherea(t) is a setting expansion,a ₀ = 0.009,ν′ = 0.2,E′ = 5 kg cm^?2,k = 0.032 min^?1,P applied stress, andt the time (min). On the basis of these results, a method to estimate the value of setting expansion under restrictive force was developed. According to this method, the setting expansion of the investment could be calculated by substituting?ε/?t forε, ka ₀ exp (?kt)/E′ for 1/E, ν′ forν, andka ₀ exp (?kt) forαT in the theory of elasticity.