Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

粘度国家基准装置测量结果的不确定度

分析粘度国家基准装置测量结果不确定度的来源并进行评定。影响粘度国家基准装置测量不确定度的主要因素有温度、时间、表面张力、空气浮力以及动能修正等。根据2002年粘度国家基准量值复测的结果，以及改造后新基准装置和辅助设备的状态，计算得粘度国家基准装测量结果的扩展不确定度为0.038%-0.4%。     

Estimation scheme for level-dependent uncertainty of analytical result: application for determination of 1-hydroxypyrene in urine

The estimation scheme of uncertainty of determination of 1-hydroxypyrene (1-OHP) in urine was developed analysing the main stages of the analytical procedure: (1) preparation of 1-OHP standards, (2) creation of the calibration curve for the high performance liquid chromatography (HPLC) analysis method with the evaluation of recovery, (3) measuring procedure of aliquot of urine, (4) adjusting the pH of aliquot and hydrolysis with enzyme, (5) solid phase extraction, (6) concentration of the extract, (7) injection of the extract to chromatograph and analysing by the HPLC method, (8) calculation of 1-OHP mass from the calibration curve, (9) calculation of 1-OHP concentration in urine. The evaluation of the uncertainty is based on quantification of individual components. Combined uncertainty was calculated using the law of propagation of uncertainties according to the EURACHEM/CITAC guidelines. Level dependence of the uncertainty arises from the calibration curve. The limits of detection and quantification were found to be equal to 0.03 and 0.1 ng/mL, respectively. The calculated expanded level-dependent uncertainty covers 47–27–25% within the concentration range 0.03–0.1–0.4 ng/mL with the materials and equipment used. These parameters could easily be recalculated according to the proposed scheme if there are some changes in the analysis procedure.     

Error in an approximate wave function and an error minimization scheme

An estimate of error in an approximate wave function for a stationary state is put forward that does not require any information about the exact state. The measure is sensitive and direct. Parameters embedded in a trial wave function can be varied to minimize this error as well, leading to a variational principle. Such a scheme works nicely for bound states and the more so for Siegert states, for which the standard energy minimization principle does not apply. Pilot calculations on the anharmonic oscillator system and the radial Stark effect in the hydrogen atom reveal the worth of the endeavor. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

To what extent can an uncertainty calculation be general?

 It is argued that results of uncertainty calculations in chemical analysis should be taken into consideration with some caution owing to their limited generality. The issue of the uncertainty in uncertainty estimation is discussed in two aspects. The first is due to the differences between procedure-oriented and result-oriented uncertainty assessments, and the second is due to the differences between the theoretical calculation of uncertainty and its quantication using the validation (experimental) data. It is shown that the uncertainty calculation for instrumental analytical methods using a regression calibration curve is result-oriented and meaningful only until the next calibration. A scheme for evaluation of the uncertainty in uncertainty calculation by statistical analysis of experimental data is given and illustrated with examples from the author's practice. Some recommendations for the design of corresponding experiments are formulated.     

Traceable measurements in clinical laboratories

 Reliable, traceable and comparable measurements provide the rational basis for evaluation of the quality of a result and the starting point for recognized laboratory accreditation in any national area. Modern medical diagnostics and treatment involve rapidly rising numbers and types of clinical laboratory measurements, that are reliable. Therefore, the basic principles to be followed to assure the traceability of clinical measurements as required by the Romanian Laws of Metrology are reviewed. Main sources affecting the quality of the unbroken chain of calibrations that relate the measurements back to appropriate measurement standards are discussed. Examples of how to achieve traceable measurements in clinical laboratories are presented. Details of specific uses of reference materials, measuring instruments and standard measurement methods are also discussed. Received: 8 January 1998 · Accepted: 21 April 1998     

Fast Marching Method for Calculating Reactive Trajectories for Chemical Reactions

We present a method for computing classical Newtonian trajectories that minimize the path length or transit time from reactant to product. Our approach is based on a generalization of the fast-marching method, which allows us to construct the solution of the Hamilton-Jacobi equation for the action that optimizes the desired quantity. The resulting “reactive paths” can be interpreted as reaction coordinates but, unlike more conventional choices, they contain dynamical information about the chemical system of interest.     

丙酮中除虫脲溶液标准物质研制

采用重量-容量法制备丙酮中除虫脲溶液标准物质。准确称量国家二级标准物质除虫脲溶解到色谱纯丙酮中,通过A级容量瓶定容至500 mL,摇匀后分装到2 mL安瓿瓶内共460瓶,每瓶为1 mL,保持低温迅速封口,配制过程中室温保持在(20±2)℃。采用液相色谱法进行均匀性、稳定性检验和定值结果验证。从样品中随机抽取16瓶进行均匀性检验,经F检验表明,在95%的置信区间范围内该标准物质均匀性良好;采用t检验对标准物质稳定性进行检验,标准物质在12月内稳定性良好。对该标准物质的不确定度进行了评定,研制的丙酮中除虫脲溶液标准物质定值结果为100μg/mL,相对扩展不确定度为2%(k=2)。结果表明,该标准物质均匀性与稳定性良好,量值准确,可用于日常分析检测中的方法评价和仪器校准。