Analysis of long-term distributions of calibration parameters and calibration intervals for an atomic absorption spectrophotometer

 A combination of "black box" and "calendar-time" methods for the determination of calibration intervals of an analytical measuring instrument is discussed. Since the methods require information on the distributions of the calibration parameters, such information is described for an atomic absorption spectrophotometer, as an example. The hypotheses on the normal distribution of the calibration parameters are tested using the ω²-criterion and accepted at 0.90–0.95 levels of confidence. Corresponding control charts are designed for indication of warning and action limits of the calibration parameters, and diagnoses of outliers in further calibrations. Control charts indicate also when the calibration should be done according to the full program of the equipment manufacturer. Received: 15 April 2000 / Accepted: 24 July 2000     

A deterministic algorithm for constrained enumeration of transmembrane protein folds

A deterministic algorithm for enumeration of transmembrane protein folds is presented. Using a set of sparse pairwise atomic distance constraints (such as those obtained from chemical cross-linking, FRET, or dipolar EPR experiments), the algorithm performs an exhaustive search of secondary structure element packing conformations distributed throughout the entire conformational space. The end result is a set of distinct protein conformations, which can be scored and refined as part of a process designed for computational elucidation of transmembrane protein structures.     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.     

Necessary optimality conditions and regularity results for state and adjoint state of nonlinear control problems

For optimal control problems of nonlinear evolution equations of first order we derive regularity properties for the corresponding adjoint states where the proof is based on the necessary optimal conditions and smoothness properites of the optimal states. These results are used for the characterization of the optimal solution and the corresponding adjoint state of the periodic three-dimensionel NAVIER-STOKES system.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.     

Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

Time optimality and the maximum principle in infinite dimension

We present three counterexamples related to the maximum principle for the time optimal problem. The system is linear, infinite dimensional, with point target and “full” control     

What can statistical process control show us about ionization chamber stability?

PurposeStatistical process control (SPC) has been shown to be a suitable tool for medical physicists to monitor quality and keep variability low and within specifications. We report our findings regarding ionisation chamber stability in our department when using a radioactive stability check device (RSCD) and we compare them with similar previously published records, including calibration results.MethodsWe retrospectively studied the stability of a PPC 40 parallel-plate chamber, and two Farmer chambers (FC65-G and FC65-P) by checking them with dedicated RSCDs. We analysed the data following SPC methodology which includes plotting I-MR control charts, monitoring out-of-control observations, calculating process capability ratios (C_p), and estimating conformance to specifications. We also estimated the C_p and adherence to specifications of previously published data.ResultsThe PPC40 chamber hardly went out of the control limits over the whole six-year period assessed. However, Farmer chamber verifications drifted in opposite directions in phase II, and the deviations observed did not agree with their calibration records, which only increased by a maximum of 0.5%. In phase I the most unstable chamber was the FC65-P with a C_p equal to 0.9 at a specification level of ±1%. The PPC40 chamber was stable to within a maximum C_p of 1.3. Several sets of analysed data, including ours and those from other authors, fitted well within these limits: within ±1.9% and ±1.5% for a C_p of 1.5 and 1.33 respectively.ConclusionsSPC with constant long-term RSCD checking gave us a meaningful plot of the instability of our ionisation chambers. Although a period of two years between calibrations should not be surpassed, in the interim this check can conform to specifications of ±1.5%.     

Resonant control of solitons

It is shown that the effect of “scattering on resonance” can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.