The Key Renewal Theorem for a Transient Markov Chain

We consider a time-homogeneous real-valued Markov chain X _n , n≥0. Suppose that this chain is transient, that is, X _n generates a σ-finite renewal measure. We prove the key renewal theorem under the condition that this chain has jumps that are asymptotically homogeneous at infinity and asymptotically positive drift.     

On orthogonal polynomial approximation with the dimensional expanding technique for precise time integration in transient analysis

We use four orthogonal polynomial series, Legendre, Chebyshev, Hermite and Laguerre series, to approximate the non-homogeneous term for the precise time integration and incorporate them with the dimensional expanding technique. They are applied to various structures subjected to transient dynamic loading together with Fourier and Taylor approximation proposed in previous works. Numerical examples show that all six methods are efficient and have reasonable precision. In particular, Legendre approximation has much higher precision and better convergence; Chebyshev approximation is also good, but only slightly inferior to Legendre approximation. The other four approximation methods usually produce results with errors hundreds of thousands of times larger. Hermite and Laguerre approximation may be useful for some special non-homogeneous terms, but do not work sufficiently well in our numerical examples. Other contributions of this paper include, a Dynamic Programming scheme for computing series coefficients, a general formula to find the assistant matrix for any polynomial series.     

A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.

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Wavelength-switchable erbium-doped fiber ring laser combined with a Fabry-Perot laser diode and a sampled grating

We present a wavelength-switchable erbium-doped fiber ring laser consisting of an anti-reflection coated Fabry-Perot laser diode (FP-LD) and a sampled fiber Bragg grating (SFBG). The wavelength switching is obtained easily by the shift of FP mode with respect to the reflection peaks of the SFBG. The proposed laser apparatus not only simultaneously emits two wavelengths but also switches between the two wavelengths by adjusting the modes of FP-LD with a change of the injection current of the FP-LD as little as ∼1 mA. The proposed wavelength-switchable erbium-doped fiber ring laser exhibits high laser performance with side-mode suppression ratio (SMSR) ?50 dB.     

Dynamic sheath expansion and ion current in transient ion sheath experiments

Experimental results on the measurement of current collected by an electrode immersed in a plasma for a pulsed negative bias are presented. The measured current is compared with a model based on the concept of an expanding capacitor. The scaling laws predicted by the model are verified for the measured current which agree each other. The paper emphasizes the role of displacement current in an expanding ion sheath.     

一种实现部分谱的Tailored检测的简便方法

本文介绍一种利用延迟采样实现部分谱的Tailored检测的方法。文章对该方法作了理论上的分析并给出了用于强溶剂峰抑制时的实验结果,获得良好的效果。     

Numerical simulation of the horizontal Bridgman growth. Part I: Two-dimensional flow

We study the generation of periodic velocity and temperature fields in a plane horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals, although the present paper is limited to two-dimensional flows. We use transient finite difference and finite element algorithms which lead to identical results. We demonstrate the oscillatory mechanism in two different geometries.     

Transient natural convection of low-Prandtl-number fluids in a differentially heated cavity

The transient convective motion in a two-dimensional square cavity driven by a temperature gradient is analysed. The cavity is filled with a low-Prandtl-number fluid and the vertical walls are maintained at constant but different temperatures, while the horizontal boundaries are adiabatic. A control volume approach with a staggered grid is employed to formulate the finite difference equations. Numerically accurate solutions are obtained for Prandtl numbers of 0·001, 0·005 and 0·01 and for Grashof numbers up to 1 × 10⁷. It was found that the flow field exhibits periodic oscillation at the critical Grashof numbers, which are dependent on the Prandtl number. As the Prandtl number is decreased, the critical Grashof number and the frequency of oscillation decrease. Prior to the oscillatory flow, steady state solutions with an oscillatory transient period were predicted. In addition to the main circulation, four weak circulations were predicted at the corners of the cavity.     

无限阶段部分可观察马尔可夫决策规划

本文对[1,2]所考虑的无限阶段折扣费用部分可观察马尔可夫决策规划作了进一步的讨论,澄清了其中的一些模糊概念,补充或纠正了其中的疏漏和错误,特别地,在保持费用函数分片线性的原则下扩大了有限瞬时策略类,最后给出了几个新的结论,并对[1]中的策略迭代算法给出了修正及收敛估计。     

Spindle Speed Variation for the Suppression of Regenerative Chatter

Summary. A phenomenon commonly encountered during machining operations is chatter. It manifests itself as a vibration between workpiece and cutting tool, leading to poor dimensional accuracy and surface finish of the workpiece and to premature failure of the cutting tool. A chatter suppression method that has received attention in recent years is the spindle speed variation method, whereby greater widths of cut are achieved by modulating the spindle speed continuously. By adapting existing mathematical techniques, a perturbative method is developed in this paper to obtain finite-dimensional equations in order to systematically study the mechanism of spindle speed variation for chatter suppression. The results indicate both modest increase of stability and complex nonlinear dynamics close to the new stability boundary. The method developed in this paper can readily be applied to any other system with time-delay characteristics.