Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.     

Dual energy time reversed elastic wave propagation and nonlinear signal processing for localisation and depth-profiling of near-surface defects: a simulation study

Nonlinear Elastic Wave Spectroscopy (NEWS) relies on the activation of defects by wave energy that propagates through the medium. In general, the response of activated defects will not scale linearly with the excitation amplitude, and the resulting nonlinear signatures can be identified and used for quality inspection. The efficiency of NEWS based inspection methods is therefore intrinsically linked to the locally deposited activation energy at the defect zone and the ability to generate nonlinear signatures that exceed the noise level of acquisition. Time Reversal techniques allow focusing of high levels of energy in small areas, and are consequently very useful for the local activation of defected zones. In this report, numerical simulations are reported showing the potential of a combination consisting of dual energy reciprocal Time Reversal and nonlinearity filtering using the Scaling Subtraction Method. The method is applied to the detection of planar near-surface defects parallel to the surface in a 2D domain. The results are evaluated for sweep excitation at different frequency ranges; for point-like receiver as well as extended transducers, and for in-plane as well as out-of-plane focusing. The observable nonlinear response at the surface is linked to an effective nonlinearity within the medium based on the defect geometry and the distribution of the local stresses.     

球面散布数据点插值的误差估计

讨论球面上散布数据点插值的误差估计问题．一方面用深刻的新概念——正规生成集对插值节点集的特性进行刻画,同时给出它与基本系统、网格范数间的关系;另一方面得到了插值误差及导数的点态估计．     

关于一个核含参数且-2齐次的Hilbert型不等式

通过估算权系数,建立一个核含2-参数且-2齐次的Hilbert型不等式及其等价式,并考虑了逆向不等式的情形．     

Integrated squared error of kernel-type estimator of distribution function

Let X ₁ ,...,X _n be a random sample drawn from distribution function F(x) with density function f(x) and suppose we want to estimate X(x). It is already shown that kernel estimator of F(x) is better than usual empirical distribution function in the sense of mean integrated squared error. In this paper we derive integrated squared error of kernel estimator and compare the error with that of the empirical distribution function. It is shown that the superiority of kernel estimators is not necessarily true in the sense of integrated squared error.     

Nuclearity of a nonnegative definite integral kernel on a separable metric space

The aim of this paper is to characterize the nuclearity of an integral operator, defined by a continuous non-negative definite square integrable kernel on a separable metric space, in terms of the integrability of the trace of the kernel function. Nuclearity here plays a role forU-statistics.     

Boundary behavior of the Bergman kernel function on pseudoconvex domains with comparable Levi form

Let Ω be a smoothly bounded pseudoconvex domain in and let be a point of finite type. We also assume that the Levi form of bΩ is comparable in a neighborhood of z₀. Then we get a quantity which bounds from above and below the Bergman kernel function in a small constant and large constant sense.     

交通流非参数回归模型

交通流宏观参数流量、速度和占有率在交通工程和管理中具有非常重要的作用 ,对这三者关系的刻划反映了道路本身特性和交通流的规律。到目前为止 ,基本上采用线性或非线性的参数模型来描述 ,此类模型在应用中具有一定的局限性 ,并交通变量时间序列进行预测 ,数据拟合表明 ,选择适当的核函数或邻近数以及窗宽 ,可以达到比较满意的效果     

Analytic continuation and identities involving heat,Poisson, wave and Bessel kernels

In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)