Black Hole Entropies of the Thin Film Model and the Membrane Model Without Cutoffs

Taking into account the effect of the generalized uncertainty principle on the generalized black hole entropy and tacking the thin film brick-wall model, we calculate the entropy of the quantum scalar field in generalized static black hole. The Bekenstein–Hawking entropies of all well-known static black holes are obtained. The entropy of 2-D membrane just at the event horizon of static black hole is also calculated, and the result of the black hole entropy proportional to the event horizon area can be obtained more easily and generally. This discussion shows that black hole entropy is just identified with the entropy of the quantum field on the event horizon. The difference from the original brick-wall model is that the present result is convergent without any cutoff and the little mass approximation is removed. With residue theorem, the integral difficulty in the calculation of black hole entropy is overcome.     

On Decaying Rate of Quantum States

The survival amplitude of a quantum state (wave function) under the Schrödinger evolution can be expressed as the Fourier transform of the probability density induced by the wave function in the energy representation. In particular, the first zero of the survival amplitude is a fundamental quantity in characterizing the decaying rate of the quantum state. A basic problem in quantum mechanics is to study how fast the survival amplitude can fall. We present a general estimation of the decaying rate of a quantum state in terms of a moment of any order. The result is established by integrating an inequality which involves controlling trigonometric sums by power functions. This inequality is of independent interest in estimating exponential sums.     

Iolite Based Bulk Normalization as 100% (m/m) Quantification Strategy for Reduction of Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry Transient Signal

Iolite package draw more attention in laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) community in recent years due to its powerful data-handling capacity, excellent signal visualization and open source of calculation codes. In this study, the application of Iolite package was investigated for LA-ICP-MS elemental quantification, and a calculation code for the bulk normalization as 100% (m/m) strategy was compiled. We found that the spline interpolation approach was better than that of linear one for the correction of time-dependent instrument drift. BCR-2G as the quality material was used to assess the proposed code, and the results revealed that the code was practical and reliable. The analytical accuracy was influenced by the used calibration materials. TiO₂, MgO, K₂O and rare earth elements in BCR-2G were slightly off (5%–10%) when NIST SRM 610 as the calibrator. Cr and Mo were higher (10%–30%) than the recommended values when StHs6/80-G was used as the calibrator. The phenomena would be attributed to the matrix effect or the inaccurate values of corresponding calibrators. Three main sources for the LA-ICP-MS combined uncertainty were recognized, including the uncertainty of recommended values of analytes in calibration material, the uncertainty of measured intensity ratios in sample and the error in bulk normalization as 100% (m/m) strategy. A total of 50 elements in CGSG glass reference materials were quantified based on the proposed Iolite code. Major elements (except MnO, CaO and P₂O₅) matched well with the recommended values with a discrepancy of 5%, and the trace elements (except Cr, Ni, Zn, Ga, Mo and Sb) were agreement with the recommended values in 10%. The dataset reported in this study was helpful for the value certification of CGSG reference materials. Overall, the proposed Iolite code broadened the application of Iolite package in the reduction of LA-ICP-MS transient signal for the elemental determination.     

Robust aircraft conflict resolution under trajectory prediction uncertainty

In air traffic control, aircraft velocity may be perturbed due to weather effects or measurements errors and affect trajectory prediction. We address the aircraft conflict resolution problem in the presence of such perturbations. We consider polyhedral uncertainty sets on aircraft velocity, develop a budgeted robust optimization approach and show that it is amenable to mixed-integer optimization. Numerical experiments reveal that perturbations of the order of 5% on aircraft velocities can be accounted for without significantly impacting performance.     

Fault diagnosis for a class of nonlinear uncertain hybrid systems

This paper presents a fault diagnosis architecture for a class of hybrid systems with nonlinear uncertain time-driven dynamics, measurement noise, and autonomous and controlled mode transitions. The proposed approach features a hybrid estimator based on a modified hybrid automaton framework. The fault detection scheme employs a filtering approach that attenuates the effect of the measurement noise and allows tighter mode-dependent thresholds for the detection of both discrete and parametric faults while guaranteeing no false alarms due to modeling uncertainty and mode mismatches. Both the hybrid estimator and the fault detection scheme are linked with an autonomous guard events identification (AGEI) scheme that handles the effects of mode mismatches due to autonomous mode transitions and allows effective mode estimation. Finally, the fault isolation scheme anticipates which fault events may have occurred and dynamically employs the appropriate isolation estimators for isolating the fault by calculating suitable thresholds and estimating the parametric fault magnitude through adaptive approximation methods. Simulation results from a five-tank hybrid system illustrate the effectiveness of the proposed approach.     

计及需求响应不确定性的综合能源系统多目标优化调度管理

需求响应作为电力系统的重要调节手段,可显著提升系统灵活性和经济性。利用价格弹性构建了包含价格与激励措施的需求响应模型,并在此基础上考虑需求响应的不确定性,以综合能源系统经济性和环保性为优化目标,构建了综合能源系统多目标优化调度模型。利用E约束法将多目标优化模型转化为单目标优化模型,得到Pareto最优解集,运用模糊决策法从中选取最优方案。基于实际案例进行测算,结果表明价格型与激励型需求响应手段的结合能够实现削峰填谷,有效降低系统的运行成本和碳排放量。     

Heisenberg's uncertainty relation of position and momentum in experiments without mutual disturbance

Arranging target atoms in a plane monolayer, one may produce by atomic or nuclear reaction an ensemble of particles with small initial position spread without disturbing their momentum spread. This would either allow a violation of Heisenberg's uncertainty relation, by creating a situation not described by quantum mechanics hence rendering quantum mechanics incomplete, or, if the uncertainty relation should hold also in this non-disturbative situation, it would mean a permanent violation of energy conservation. Thus an uncertainty relation for position and momentum and energy conservation appear to be mutually exclusive.1. Recently also Croca [5] proposed another way of determining a x without interfering with p_X.2. To forbid even speaking of an initial position spread smaller than that indicated by the wave function [6] would amount to circular reasoning and the denial of a falsification of quantum mechanics.     

Quantum equilibrium and the origin of absolute uncertainty

The quantum formalism is a measurement formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that anappearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by = ¦¦ ². A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.This paper is dedicated to the memory of J. S. Bell.     

Some aspects of the evaluation of measurement uncertainty using reference materials

 In practice there are three aspects that need to be considered in order to achieve the required traceability according to its definition: the 'stated reference', the 'unbroken chain of calibrations' and the "stated uncertainty". For a certain chemical result, each of these aspects highly depends on the measurement uncertainty, both on its magnitude and how it was estimated. Therefore, the paper describes the experience of the Romanian National Institute of Metrology in estimating measurement uncertainty during the certification of reference materials (RMs), in metrological activities (calibration, pattern approval, periodical verification, etc.), as well as during the analytical measurement process. Practical examples of estimation of measurement uncertainty using RMs or certified reference materials are discussed for their applicability in spectrophotometric and turbidimetric analysis. Use of the analysis of variance to obtain some additional information on the components of measurement uncertainty and to identify the magnitude of individual random effects is described. Received: 12 November 1999 / Accepted: 25 February 2000     

气相色谱–质谱法测定食用植物油中短链脂肪酸的测量不确定度评定

采用气相色谱–质谱法(GC–MS)测定食用植物油中短链脂肪酸含量,对测量结果的不确定度进行评定,探讨提高测量准确度的方法。依据方法建立数学模型,分析得出不确定度主要来源于样品制备过程、计量器具的使用、标准溶液配制、测量设备、人员读数误差、方法回收率,计算各不确定度分量,得到相对标准不确定度和扩展不确定度。结果表明,当食用植物油中短链脂肪酸测定结果为13.1 mg/kg时,其扩展不确定度为1.8 mg/kg(k=2)。测量设备、标准溶液配制过程引入的不确定度较大,应在实验过程中予以控制和关注。