4:1椭球体分离流动湍流特性的试验研究

使用六线涡量探头,对α=30°条件下绕（4:1）椭球体分离流动的湍动能u’2,v’2,w’2,雷诺应力u’v’和涡量Ωx等进行了详尽的测量.应用频谱分析的方法揭示了绕（4:1）椭球体分离流内主附着涡外缘剪切层上的离散小涡的特性.     

非线性左手材料中的二次谐波

基于电磁场理论，推导了无耗非线性左手材料中二次谐波的曼利－诺关系，及相位匹配条件下正向基波与逆向二次谐波的能量转换过程及其空间分布.验证了可将无耗非线性左手材料的入射面作为反射镜，把能量以二次谐波的形式反射.同时分别给出有限厚度介质板中基波和二次谐波的场强分布数值结果，验证了结论的正确性.最后从相位失配角度说明了相位匹配是分析非线性左手材料二次谐波的重要条件.这为研究左手材料的非线性理论奠定了基础.     

荧光寿命的正弦调制测量法及分析

设计并制作了光强调制度和频率可调的发光二极管驱动电路,应用这种激励源激发荧光样品Eu₂L′3·nH₂O(L′=C₄H₄O₄),测量了激发光和Eu3+离子的5D₀—7F₂发射光的波形。实验得到的数据用按照相位法测量荧光寿命的原理用非线性最小平方曲线拟合,得到Eu3+离子激发态5D₀的寿命约为0.680 ms。讨论了光源调制中的高次谐波分量对测量结果的影响以及寿命具有一定分布的多指数衰减体系的测量和处理方式,提出应用傅里叶级数展开处理数据的修正方法,以扩大相位法测量荧光寿命的适用范围,得到更准确的荧光寿命值。     

Expansion of potential 1/r12 of c‐spherical harmonics

The expansion coefficient C^D_|L| of Coulomb potential 1/r₁₂ of atomic system in hyper‐spherical harmonics is derived and the explicit expression is given.     

Broadening-independent demodulation for wavelength modulation spectroscopy based on even-order harmonics

The line broadening of gas absorption spectrum is a significant but unknown factor in traditional demodulation of wavelength modulation spectroscopy, which is a kind of tunable diode laser absorption spectroscopy in weak absorption cases. In this paper, another signal demodulation method based on some simple algebraic operations with the amplitudes of the zero-, second-, and fourth-order harmonics was proposed. With this method the effect of spectrum broadening could be selfeliminated. That makes the amplitude of the demodulated signal is irrelevant to the broadening, and enables the direct and fast measurement without complex simulations and curve fittings in traditional method.     

Impact of sideband harmonic pattern on losses in laminated non-oriented steel

Losses in laminated non-oriented steel under the effect of two high harmonic clusters, caused by voltage excitation typical of two-level pulse-with-modulated (PWM) DC-link and space-vector modulated (SVM) matrix converters, were analyzed. The predicting method proposed, which incorporates anisotropy of loss K_a and grain size g_s, describes the magnetizing process within the steel by the means of Poisson statistical distribution. Results are then compared to losses determined by Bertotti's model. The two methods confirmed that spreading of sideband harmonics in the kilohertz range can reduce harmonic losses by up to 40% at low power frequencies.     

Strong Convergence of Spherical Harmonic Expansions on H1(Sd-1)

Let $\sigma_k^\delta$ denote the Cesaro means of order $\delta > -1$ of the spherical harmonic expansions on the unit sphere $S^{d-1}$, and let $E_j(f, H^1)$ denote the best approximation of $f$ in the Hardy space $H^1(S^{d-1})$ by spherical polynomials of degree at most $j$. It is known that $\lambda:= (d-2)/2$ is the critical index for the summability of the Cesaro means on $H^1(S^{d-1})$. The main result of this paper states that, for $ f\in H^1(S^{d-1})$, $$\sum_{j=0}^N \f 1{j+1} \|\sigma_j^\lambda (f) -f\|_{H^1}\approx \sum_{j=0}^N \f 1{j+1} E_j(f, H^1),$$ where “$\approx$” means that the ratio of both sides lies between two positive constants independent of $f$ and $N$.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.     

Perturbed kernel approximation on homogeneous manifolds

Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.