On Hitting Times and Fastest Strong Stationary Times for Skip-Free and More General Chains

An (upward) skip-free Markov chain with the set of nonnegative integers as state space is a chain for which upward jumps may be only of unit size; there is no restriction on downward jumps. In a 1987 paper, Brown and Shao determined, for an irreducible continuous-time skip-free chain and any d, the passage time distribution from state 0 to state d. When the nonzero eigenvalues ν _j of the generator on {0,…,d}, with d made absorbing, are all real, their result states that the passage time is distributed as the sum of d independent exponential random variables with rates ν _j . We give another proof of their theorem. In the case of birth-and-death chains, our proof leads to an explicit representation of the passage time as a sum of independent exponential random variables. Diaconis and Miclo recently obtained the first such representation, but our construction is much simpler. We obtain similar (and new) results for a fastest strong stationary time T of an ergodic continuous-time skip-free chain with stochastically monotone time-reversal started in state 0, and we also obtain discrete-time analogs of all our results. In the paper’s final section we present extensions of our results to more general chains. Research supported by NSF grant DMS–0406104, and by The Johns Hopkins University’s Acheson J. Duncan Fund for the Advancement of Research in Statistics.     

Feynman-Kac Formula for Left Continuous Additive Functionals and Extended Kato Class Measures

The perturbation of the generator of a Borel right process by a signed measure is investigated, using probabilistic and analytic potential theoretical methods. We establish a Feynman-Kac formula associated with measures charging no polar set and belonging to an extended Kato class. A main tool of this approach is the validity of a Khas’minskii Lemma for Stieltjes exponentials of positive left continuous additive functionals.      

Simpson校正公式

给出了Simpson校正公式的截断误差,分析了复化Simpson校正公式的收敛阶.数值算例验证了理论分析的正确性.     

常息力更新场合有限时间破产概率对负相依索赔额的不敏感性

设索赔来到过程为具有常数利息力度的更新风险模型.在索赔额分布为负相依的次指数分布假定下,建立了有限时间破产概率的一个渐近等价公式.所得结果显示,在独立同分布索赔额情形,有限时间破产概率的有关渐近等价公式,在负相依场合依然成立.这表明有限时间破产概率对于索赔额的负相依结构是不敏感的.     

平移积分几何中的对偶运动公式

本文利用对偶混合体积建立平移积分几何中的对偶运动公式.这些公式是将关于均质积分的基本运动公式推广到对偶均质积分和对偶混合体积情形.     

关于SSSP（n）和SISP（n）的均值

研究了Smarandache最小平方数列和Smarandache最大平方数列的均值性质,并用初等方法得到了关于这两个数列均值的渐近公式．     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

Let H = uq（sl（2）） or u（sl（2））. By means of the standard basis of polynomial algebras, the Glebsch-Gordan formula and quantum Clebsch-Gordan formula are proved by a unified method, and the explicit formula of the decomposition of V（1）^n into the direct sum of simple modules is given in this paper.     

Measurements of the isotopic composition of water vapor using a DFG-based spectrometer at

We report on absorption measurements of the isotopic composition of water in a demineralized sample by means of wavelength modulation spectroscopy of H₂O lines in the spectral region around . The mid-IR radiation was obtained by difference-frequency mixing of the radiation of an extended cavity diode laser () and that of a diode-pumped monolithic Nd–YAG laser. Preliminary tests indicate the possibility of obtaining a precision for the ¹⁸O/¹⁶O, ¹⁷O/¹⁶O and ²H/¹⁶O isotope ratio measurements of the order of 1 per mil.     

小麦品质的太赫兹波段光学与光谱特性研究

采用太赫兹时域光谱技术(THz-TDS),以储藏小麦为研究对象,研究了霉变、虫蛀、发芽等小麦与正常小麦样品在0.2～1.6 THz波段的光学与光谱特性,采用傅里叶变换得到被测样品的频域光谱,并计算获得THz吸收系数和折射率等光学参数。结果表明,不同品质小麦具有不同的折射率和吸收系数,其中正常小麦比霉变、虫蚀和发芽小麦的吸收系数和折射率都高,且吸收系数在有效波段随频率的增加而增加,进而可以根据其在THz波段的特征谱进行判别。THz-TDS在小麦品质检测中的应用,为该技术在储粮品质检测和分析中提供新的实验方法,具有重要的应用前景。     

阈值电路特性对腔衰荡光谱测量影响的实验研究

腔衰荡光谱技术(cavity ring-down spectroscopy, CRDS)是一种高灵敏的激光吸收光谱技术,被广泛应用于镜片反射率测量、光谱分析以及痕量气体检测等研究领域。首先从理论上描述了CRDS技术的实验原理,然后基于555定时器自行设计了一种可应用于CRDS技术的阈值电路,并通过实验进行了验证。为了优化阈值电路的性能,研究了不同输入阻抗及容抗下阈值电路对衰荡事件测量的影响。通过直接接入不同值的电容与电阻,发现输入电容越大,输入阻抗越小,对衰荡事件的测量影响越大,尤其当阈值电路输入电阻小于50 Ω时,衰荡事件的线型严重扭曲。对不同输入电阻与输入电容时C₂H₂气体在6 531.780 5 cm-1处的吸收信号进行了采集与分析,发现输入电容与输入电阻的改变对测量结果有很大的影响,得到的吸收信号会失真,甚至无法进行拟合。最终给出了阈值电路的最佳设计方案,在阈值电路的设计中选取的输入阻抗越大越好,最小要在100 Ω以上,选取的容抗越小越好,最好低于1 nF,同时要保证阈值电路的时间常数远小于衰荡时间。该研究对于CRDS技术应用过程中阈值电路的设计具有重要的参考价值。