New FIR laser lines and frequency measurements for optically pumped CD3OH

Twenty new cw FIR laser lines in CD₃OH, optically pumped by a CO₂ laser, are reported. The frequencies of 39 of the stronger laser lines were measured relative to stabilized CO₂ lasers with a fractional uncertainty, as determined by the reproducibility of the FIR frequency itself, of 2 parts in 10⁷.Contribution of the U.S. Government, not subject to copyright.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Uniformity in Computable Structure Theory

We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by Kudinov and by Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and with previous work of Ash, Knight, and Slaman on uniformity in a general computable structure-theoretical setting.     

Diffusive behavior of asymmetric zero-range processes

We investigate a new interpretation for the Navier-Stokes corrections to the hydrodynamic equation of asymmetric interacting particle systems. We consider a system that starts from a measure associated with a profile that is constant along the drift direction. We show that under diffusive scaling the macroscopic behavior of the process is described by a nonlinear parabolic equation whose diffusion coefficient coincides with the diffusion coefficient of the hydrodynamic equation of the symmetric version of the process.     

关于微分熵的一类强偏差定理

利用关于乘积分布密度的相对熵和相对熵率的概念,建立了相依连续型随机变量序列关于参考微分熵的一类强偏差定理,证明中给出了将Laplace变换应用于微分熵强偏差定理的研究的一种途径．     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

无穷区间上二阶微分方程的边值问题

利用Schauder不动点定理讨论了一类非线性二阶微分方程在无穷区间上的边值问题无界解的存在性，部分改进了郭大钧教授最近得到的结果。     

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.     

Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities are developed and it is proved that these estimators are asymptotically efficient or even possess the desirable bounded relative error property. In this paper, as an illustration, we consider a simple tail probability involving geometric sums of heavy tailed random variables. This is useful in estimating the probability of large delays in M/G/1 queues. In this setting we develop an unbiased estimator whose relative error decreases to zero asymptotically. The key idea is to decompose the probability of interest into a known dominant component and an unknown small component. Simulation then focuses on estimating the latter ‘residual’ probability. Here we show that the existing conditioning methods or importance sampling methods are not effective in estimating the residual probability while an appropriate combination of the two estimates it with bounded relative error. As a further illustration of the proposed ideas, we apply them to develop an estimator for the probability of large delays in stochastic activity networks that has an asymptotically zero relative error.      

重离子治疗计划系统的构想

对重离子柬治癌的优势进行简要的回顾，并着重介绍了用于重离子放射治疗的治疗计划系统。治疗计划系统是一套软件系统，不同的硬件设施应有与其相匹配的软件系统，即治疗计划系统。在此基础上，针对兰州重离子加速器的特点提出一些关于治疗计划系统方面的构想。After a brief review concerning the advantages of heavy ions in radiotherapy, more interests are concentrated on treatment planning system （TPS） for heavy ion radiotherapy. Compared to the hardware devices such as accelerator and beam delivery system, the TPS is a set of software system, and different therapy facilities require their corresponding TPSs. Based on the specialities of the Heavy Ion Research Facility in Lanzhou （HIIRFL）, some suggestions on the TPS for tumor therapy at HIRFL finally are given.