连续时间马氏链中的两个计数过程

木文考虑连续时间齐次Markov链在(O,t]期间状态转移次数和从状态集A到B的转移次数.为计算平均转移次数,我们得到了某些在随机模型中极其有用的简便公式并引进了无限位相型(Phase Type)分布.     

超高效液相色谱-高分辨质谱法筛查婴幼儿配方奶粉中17种头孢菌素类药物残留

建立了一种快速筛查婴幼儿配方奶粉中17种头孢菌素类药物残留的超高效液相色谱-四极杆/静电场轨道阱高分辨质谱（UHPLC-Q-Orbitrap HRMS）分析方法。奶粉样品经水溶解后,使用乙腈提取除去蛋白质等杂质,经低温高速离心后可达到净化样品的目的。选用C8色谱柱对待测物进行分离,在Q Exactive高分辨质谱Full MS/dd-MS²（data-dependent MS²）扫描模式下采集数据进行定性定量分析。17种目标物在5~200 μg/L范围内线性关系良好,相关系数（r²）均大于0.99,检出限0.0060~0.040 μg/L,定量限0.71~4.6 μg/kg,平均回收率69.6%~101.4%,相对标准偏差（RSDs）均小于10%。该法操作简单,重现性好,分辨率高,适用于婴幼儿配方奶粉中17种头孢菌素类药物残留的定性、定量筛查。     

分部积分与Taylor公式

利用定积分的分部积分法由简到繁的推导得到了微分学中的Taylor公式从而给出了Taylor公式的另一种证法,并利用这种方法还可得到复变函数或泛函分析中的Taylor公式及某些函数的渐进级数和更广泛的函数展开.     

Dirichlet L-函数倒数的2k次加权均值

本文主要目的是利用经典的Ｋｌｏｏｓｔｅｒｍａｎｎ和估计及其解析方法研究Ｄｉｒｉｃｈ－ｌｅｔ Ｌ-函数倒数的 ２ｋ次加权均值,得到了一个较为精确的渐近公式．     

An almost sure scaling limit theorem for Dawson-Watanabe superprocesses

We establish a scaling limit theorem for a large class of Dawson-Watanabe superprocesses whose underlying spatial motions are symmetric Hunt processes, where the convergence is in the sense of convergence in probability. When the underling process is a symmetric diffusion with -coefficients or a symmetric Lévy process on Rd whose Lévy exponent Ψ(η) is bounded from below by cα|η| for some c>0 and α∈(0,2) when |η| is large, a stronger almost sure limit theorem is established for the superprocess. Our approach uses the principal eigenvalue and the ground state for some associated Schrödinger operator. The limit theorems are established under the assumption that an associated Schrödinger operator has a spectral gap.     

Stochastic population dynamics under regime switching II

This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population.     

Shift Harnack inequality and integration by parts formula for semilinear stochastic partial differential equations

Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.     

对一道数学分析题证明方法的改进

某文献在处理一道关于高阶导数的应用问题时,反复利用Rolle定理来证明高阶导数为零．考虑到这种做法过于繁琐,遂通过对其证明方法的改进,综合使用Lagrange中值定理和Taylor公式,使该问题的解决获得简化．     

Elliptic boundary value problems in hybrid domains

We derive asymptotic transmission conditions at points where segments are attached to a three-dimensional body. These conditions result in a formally self-adjoint problem on a hybrid set with properties similar to those of standard boundary value problems. In particular, the problem has a zero index and possesses a variational statement. If the systems of differential equations have a special form, then the operator of the problem is realized as a self-adjoint extension of the decoupled operators of the problems on the body and the segments. From this viewpoint, we interpret the results of asymptotic analysis of coupled thin and solid bodies.Dedicated to Victor Borisovich Lidskii on the occasion of his jubileeTranslated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 55–72, 2004Original Russian Text Copyright © by S. A. NazarovSupported by the Russian Foundation for Basic Research (grant No. 00-01-00835).