On the ε-expansion procedure in the RNG theory of turbulence

Rescaling the equations of eliminating small scales, the physical justification for the-expansion procedure in the RNG theory of turbulence is proposed, in terms of that the inertial effects are small comparing with the viscous effects at the vicinity of the Kolmogorov dissipation wavenumber.We are grateful to Professor Chao-Hao Gu for numerous helpful suggestions. We would also like to acknowledge Professor Ke-Lin Wang and Bing-Hong Wang for many stimulating discussions of these problems.     

表面效应对γ-Fe2O3微粉饱和磁化强度的影响

我们制备了直径为80—700A的γ-Fe₂O₃微粉,测量了它的比饱和磁化强度σ_s和比表面积S_a,得出经验公式:σ_s(s=σ_s(∞)(1—aS_a)。假定微粉由两部分组成:第一部分是表面层,在磁场的作用下,它的磁矩只能转到与磁场成某个角度;第二部分是内部,它的磁矩可以转到磁场的方向。从这个简单的模型出发,上述的经验公式可以得到较好的解释。 关键词：     

关于《强大数定律成立的充要条件》一文的补正

In this note we point out a mistake of the article ＜The sufficient and necessary condition of SLLN＞.     

相位—啁啾调控对高次谐波光谱的影响

理论研究了在激光相位和啁啾调控共同影响下高次谐波光谱的变化。结果表明：当激光相位为0时,一阶啁啾调控使谐波能量延伸。二阶啁啾调控会呈现高强度谐波平台区。当激光相位为0.5π时,一阶啁啾调控可以获得连续平台区,但是强度较弱。在二阶啁啾调控下,谐波能量得到明显增大。通过谐波时频分析给出了不同激光波形下产生高次谐波光谱的原因。     

多周期激光相位对H2+谐波频移的影响

理论研究了多周期激光相位角对H2+谐波频移的影响。结果表明,在多周期激光驱动下H2+谐波光谱在零相位时呈现蓝移现象。随着激光相位增大,谐波光谱由蓝移转向红移。随着激光相位进一步增大,谐波红移减弱。理论分析表明谐波频移是由激光上升和下降区域谐波辐射强度变化引起的。并且谐波辐射强度变化对激光相位比较敏感。     

The Generalized Uncertainty Principle

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit of the measurement precision of incompatible observables. Here it is shown that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed.     

一种生物柴油代用品在HZSM-5分子筛催化剂上的催化热解

为了深入了解生物柴油在ZSM-5沸石上的催化反应机理,在常压的流动反应器中进行了生物柴油代用品丁酸甲酯在氢型ZSM-5(HZSM-5)催化剂上的热解和催化热解. 热解产物使用气相色谱-质谱法定性和定量测量. 动力学模型和实验表明,气相中氢提取反应是热解过程中丁酸甲酯分解的主要途径,但在HZSM-5上,丁酸甲酯则主要通过解离生成烯酮和甲醇消耗;与无催化反应相比,丁酸甲酯在HZSM-5上的初始分解温度降低了约300 K. 并且通过Arrhenius方程获得了在催化热解和均相热解条件下丁酸甲酯消耗的表观活化能. 明显降低的表观活化能证实了HZSM-5对丁酸甲酯热解的催化性能. 此外催化剂的活化温度对HZSM-5的某些催化性能具有一定的影响. 该研究对进一步的实际生物柴油燃料的催化燃烧具有一定的指导意义.     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON——PISOT NUMBERS

The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2＜λ＜1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly.     

紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。     

一类椭圆型方程Dirichlet外问题的奇摄动

§ 1 .　IntroductionSingularperturbationofDirichletproblemsforellipticequationswerediscussedbysomeauthors[1 ] -[4] ,butmostofwhathavebeenconsideredareboundeddomain .InthispapertheauthorconsiderDirichletexteriorproblemsasfollow :εL1 [u]+L2 [u]=f(x ,u ,ε) ,x∈Rn -Ω ,　　 ( 1)u(x) =g(x ,ε) ,x∈ Ω ,( 2 )whereL1 issecondorderellipticoperator:L1 [u]=∑ni,j=1aij(x) 2 u xi xj+∑ni=1ai(x) u xi +a(x ,u) ,∑ni,j=1aijζiζj ≥δ0 >0 ,x∈Rn -Ω , ζ∈Rn ,ζ≠ 0 ,L2 isfirstorderdifferentialopera…