New method for measuring beam profiles using a parametric X-ray pinhole camera

We propose a new method for measuring electron beam profiles using parametric X-ray radiation. In this method, a pinhole is placed between the source of parametric X-ray radiation and a two-dimensional X-ray detector, and the beam profile can be reconstructed on the detector, i.e., based on the principle of a pinhole camera. The profiles are in good agreement with the results obtained using a standard method with optical transition radiation. This method may prove useful to measure profiles of electron beams with short bunch lengths in recent advanced linear accelerators.     

Revisiting non-degenerate parametric down-conversion

The quantum dynamics of a two-mode non-resonant parametric down-conversion process is studied by recasting the time evolution equations for the basic operators in an equivalent spin equation form with simpler exact solutions for a pump field with harmonic time dependence. Expectation values of suitable operators for studying important features such as squeezing and quantum revivals are presented in simple forms.      

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

On the credibility of insurance claim frequency: Generalized count models and parametric estimators

We analyze the concept of credibility in claim frequency in two generalized count models–Mittag-Leffler and Weibull count models–which can handle both underdispersion and overdispersion in count data and nest the commonly used Poisson model as a special case. We find evidence, using data from a Danish insurance company, that the simple Poisson model can set the credibility weight to one even when there are only three years of individual experience data resulting from large heterogeneity among policyholders, and in doing so, it can thus break down the credibility model. The generalized count models, on the other hand, allow the weight to adjust according to the number of years of experience available. We propose parametric estimators for the structural parameters in the credibility formula using the mean and variance of the assumed distributions and a maximum likelihood estimation over a collective data. As an example, we show that the proposed parameters from Mittag-Leffler provide weights that are consistent with the idea of credibility. A simulation study is carried out investigating the stability of the maximum likelihood estimates from the Weibull count model. Finally, we extend the analyses to multidimensional lines and explain how our approach can be used in selecting profitable customers in cross-selling; customers can now be selected by estimating a function of their unknown risk profiles, which is the mean of the assumed distribution on their number of claims.     

Approximation of circular arcs by parametric polynomial curves

In this paper the approximation of circular arcs by parametric polynomial curves is studied. If the angular length of the circular arc is h, a parametric polynomial curve of arbitrary degree \(n \in {\mathbb{N}}\) , which interpolates given arc at a particular point, can be constructed with radial distance bounded by h ²ⁿ . This is a generalization of the result obtained by Lyche and Mørken for odd n.     

基于观测器的一类时滞不确定非线性离散系统的鲁棒模糊控制

讨论一类基于Takagi-Sugeno(T-S)模糊模型的具有时滞的不确定非线性离散系统的模糊鲁棒控制问题。在系统状态不可测的情况下。设计模糊观测器。利用LMI方法,得到模糊控制系统鲁棒稳定的充分条件。     

Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces

We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case.     

铷原子中参量六波混频和量子拍的研究

在铷原子中实现了轴向相位匹配的参量六波混频,并探测到位于红外光谱区的六波混频信号.六波混频信号与泵浦激光进行和频,产生了位于可见光范围内的可调谐的和频信号,并从和频信号中观察到频率为608 cm 1的量子拍.结果表明,六波混频信号中的量子拍能够用于研究原子和分子的相干特性.     

Entanglement in optical parametric down-conversion with losses and noise

We show that radiation generated in optical parametric down-conversion with losses and noise is entangled for all times if the coupling coefficient is higher than half of damping constant and the product of damping constant and mean number of noise photons. For the process stimulated by means of chaotic light there is a saturable bound of its intensity for the generation of nonclassical light. Otherwise the quantum behaviour and entanglement are fully reduced. Under some restrictions for noise nonclassical light can also be generated at and below the threshold.     

Bootstrap of the offspring mean in the critical process with a non-stationary immigration

In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents α and β, respectively. We prove that 1+2α is the threshold for the validity of the bootstrap in this model. If β<1+2α, the standard bootstrap is valid and if β>1+2α it is invalid. In the case β=1+2α, the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages.