一类四阶方程边值问题正解的存在性与多重行

本文得到了四阶方程边值问题u(4)=f(u(x)),u'(0)=u″(0)=u″'(0)=0,ku(1)=u″'(1)相应的Green函数G(x,t).从而将该问题转化为Hammerstein型积分方程,并利用锥拉伸与锥压缩不动点定理,讨论了其正解的存在性与多重性,得到了相应的结论.     

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     

Banach空间中二元非线性算子方程的迭代求解

在Banach空间中，利用锥理论和混合单调算子性质，研究了更为一般的非线性算子方程u=A（u,u)解的存在与唯一性，给出了逼近解的迭代序列和误差估计。     

两点边值问题的双向迭加法

考虑二阶线性常微分方程的两点边值问题:(a_1~2+a_2~2≠0 b_1~2+b_2~2≠0)不失一般性,算子L可看作 Lu=u"(x)-q(x)u(x) (3)众所周知,方程(1)的通解具有如下迭加结构: u(x)=c_1u_1(x)+c_2u_2(x)+u_f(x) (4)其中u_1,u_2为对应(1)的齐次方程     

二阶非线性Volterra型积分微分方程周期边值问题的最大、最小解

考虑了二阶非线性Vo1tera型积分微分方程的周期边值题：“-u”=f(t,u,Tu,u’)，u(0)=u(2x),u'(0)=u'(2x)”。应用上下解方法及单调迭代技巧得到了上述问题的最大、最小解．     

La^3＋、Li^1＋对CaTiO3微波介电性能的影响

研究了La^3＋、Li^1＋取代对CaTiO3微波介电性能的影响。在1400℃以下烧结制备Ca1-xLa2x/3TiO3（简称CLT）微波陶瓷，分析了容差因子τ对谐振频率温度系数τf的影响。在1350℃烧结4h，可制备出εr=118，τf=＋2．95×10^-4/℃，Qf=10360GHz的CLT（x=0．4）微波陶瓷。以（1叫）Ca0.6La0.2667TiO3-yLi1/2Nd1/2TiO3为代表，对（1-y）Ca1-xLa2x/3TiO3叫-yLi1/2Nd1/2TiO3（简称CLLNT）系列材料的微波介电性能进行了探讨。随着烧结温度的提高，CLLNT（x=0．4）的εr略有下降，而Q·f值略有上升。随着y值的增加，CLLNT（x=0．4）的即Q·f、τf都下降。与CLT（X=0．4）相比，虽然CLLNT（x=0．4）的Q·f值下降了，但τf得到较大的改善，同时ε仍很高，保持在100以上。     

铌掺杂Ba（ZrxTi1-x）O3弛豫铁电陶瓷介电性质的研究

采用传统的固相反应法制备了Ba（Zr0.25Ti0.75）03＋xat％Nb2O5（x=0，0．05，0．1，0．15）弛豫铁电陶瓷，研究了Nb2O5加入量对Ba（Zr，Ti）03（BZT）基电容器陶瓷性能的影响，得到了Nb2O5影响其性能的规律。结果表明：当x=0．15时介电常数最大，当x=0．10时介电损耗最小；适量Nb2O5能使材料的介温曲线更加平缓，移峰作用明显。     

La1.5Mg0.5Ni7-xCux(x=0.1～1.2)贮氢合金电化学性能的研究

研究了Ce2Ni7型贮氢合金La1.5Mg0.5Ni7-xCux（x=0.1-1.2）的组织结构和电化学性能。当X=0．1—0．6时Cu元素部分替代Ni后可形成La2Ni7型相，x≥0．9时，合金中则有少量的未知相析出。合金MH电极电化学研究表明，随Cu元素量的增加，合金电极的最大放电容量从380mAh／g（x=0．1）下降至340mAh／g（x=1．2）；当x=0．3～0．9时合金电极的循环寿命较x=0．1时有一定的改善，合金电极交换电流密度（I0）和极限电流密度（I1）均以x=0．6为转折点先减小后增大。电极反应的动力学性能依Cu0．1〉Cu0．3〉Cu1．2〉Cu0．9〉Cu0．6的次序递减。     

一类非线性椭圆边值问题的极大值原理

寻找非线性椭圆型方程（g(u)u,i),i f(x,u)=0解的适当泛函的极大值原理是多年来的一个遗留问题，本文导出了该方程在混合和罗宾边界条件下某些泛函的极大值原理。利用这些结果，可导出感兴趣的物理问题中一些重要量的界。     

Synthesis, Characterization and Electromagnetic Studies on Nanocrystalline Nickel Zinc Ferrite by Polyacrylamide Gel

Nanocrystalline nickel zinc ferrite powders （Ni=Zn1-xFe2O4, A for x=0, B for x=0.2, C for x=0.5, D for x= 0.8 and E for x= 1） were synthesized by polyacrylamide gel method. X-ray diffraction （XRD）, transmission electron microscopy （TEM） and wave-guide were used to characterize the composition. The XRD results show that the dried gel powders are amorphous, and the characteristic peaks of the spinel Ni0.5Zn0.5Fe2O4 appear after the gel is calcined at 400℃ for 1 h. When the calcining temperatures are 600 and 800℃, the average grain sizes are identified by TEM to be 10 and 30 nm, respectively. The NixZn1-xFe2O4 powders have both dielectric loss and magnetic loss in the frequency range of 8.2-11.0GHz. With the increase of Ni^2＋ ions content, the dielectric parameters （ε′） and permeability （u′） of the NixZn1-xFe2O4 powders decrease while the dielectric loss （ε″）, magnetic loss （u″） and the reflection loss increase.     

Cascade population mechanism in nitrogen lasers

The way in which a cascade mechanism from the C3Pi(u) state affects the population of the v = 0 level of the B3Pi(g) state in a N2 laser is studied. The spectra of the 0-1 IR laser band are fit by using simple theoretical calculations that account for the population of the three laser levels involved, C3Pi(u) B3Pi(g) and A3Sigma(u)+ and two excitation mechanisms, direct electron impact and cascade. The inhibition of the 0-0 UV laser band showed a strong influence on the 0-1 IR laser band output.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

High-resolution Fourier spectrometry of N(2)(+)

A new perturbation analysis of the first negative system B(2)Σ(u)(+) ? X(2)Σ(g)(+) of the (14)N(2)(+) ion is performed based on spectra excited both at low and high temperatures by the use of either a hollow-cathode or a Pointolite lamp. Preliminary results are given for a deperturbation of the B(2)Σ(u)(+) (ν = 0, ν = 1) levels. Deperturbed molecular constants and parameters that describe the B(2)Σ(u)(+) ~ A(2)∏(u) interaction are derived.     

用经典力学计算氢分子的键长键能及力常数

氢原子中1 s电子的电子云呈球形，电子的最大几率密度分布出现在玻尔半径a0的球壳内，认为几率密度分布及电子云属统计规律，意味着已经使用了宏观时标，这样就使氢分子体系中能量和时间的作用量远大于普郎克常数；根据电子云的交叠，用经典力学计算了基态氢分子的结构常数，获得键长、键能及力常数的表达式分别为采用原子单位（a.u.）时z、e及a0均为1，获得Re=1.414a.u.，De=0.177a.u.，k=0.354a.u.，这些数值与实验值的相对误差分别<1%，<2%和<4%；成键模型直观，物理意义明确，计算中不含任何人为性参数。     

Calculation of a Temperature Error by the Conjugate Equation

A temperature error depending on the error of initial information can be calculated by the conjugate problem. On estimation of the error at one time and coordinatelocal point the expenditures of the computation time and computer memory are double the expenditures for calculation of the heatconduction equation. The conjugatetemperature field obtained in this case allows calculation of the effect of the error of any parameter of the problem (initial conditions, boundary conditions, coefficients). In the linear case, the conjugatetemperature field depends on the position of the point under estimation; in the nonlinear case, it additionally depends on the temperature field. The approach considered can be applied to calculation of the error of a wide class of temperature functionals.     

Asymptotic analysis of extinction behaviour in fast nonlinear diffusion

A number of initial-boundary-value problems for the equation of fast diffusion are analysed (at varying levels of detail and completeness), i.e., $$\frac{\partial u}{\partial t} = \nabla \cdot (u^{-n} \nabla u)$$ with n > 0, in dimension N > 2 and with zero-Dirichlet boundary data, namely (i) the Cauchy problem (no boundary), mainly summarising existing results, (ii) the interior problem for a simply connected bounded domain (in large part revisiting earlier results), (iii) the problem exterior to a simply connected bounded domain and (iv) the half-space problem (for which we include N =2). The critical (borderline) case ${n = n_{s} \equiv 4/(N+2)}$ , which arises in Yamabe flow, is the subject of particular focus, in part because it provides considerable insight into both the subcritical case, 0 < n < n _s , and the supercritical one, n _s < n < 1. The results are based on formal-asymptotic analysis and suggest a range of conjectures that could be the subject of rigorous studies. The role of distinct types of similarity solutions is highlighted.     

Spin Injection and Spin Accumulation in Permalloy–Copper Mesoscopic Spin Valves

We study the electrical injection and detection of spin currents in a lateral spin valve device, using permalloy (Py) as ferromagnetic injecting and detecting electrodes and copper (Cu) as nonmagnetic metal. Our multiterminal geometry allows us to experimentally distinguish different magnetoresistance signals, being (1) the spin valve effect, (2) the anomalous magnetoresistance (AMR) effect, and (3) Hall effects. We find that the AMR contribution of the Py contacts can be much larger than the amplitude of the spin valve effect, making it impossible to observe the spin valve effect in a conventional measurement geometry. However, these contact magnetoresistance signals can be used to monitor the magnetization reversal process, of the spin injecting and detecting Py contacts. In a nonlocal spin valve measurement we are able to completely isolate the spin valve signal and observe clear spin accumulation signals at T = 4.2 K as well as at room temperature. We obtain spin diffusion lengths in Cu of 1 m and 350 nm at T = 4.2 K and room temperature respectively.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

穿孔区域中非线性波动方程解的存在性与齐次化

本文研究如下非线性波动方程的齐次化问题 uε'div(AεΔuε) g(uε') = fε in Ωε× (0,T),在Ωε× (0,T) 内,这里Ωε为一周期穿孔区域,g为一非降标量函数,我们首先证明该问题解的存在性与唯一性,然后论证该解收敛于其齐次化问题的解。