Dunkl Multiplier Operators on a Class of Reproducing Kernel Hilbert Spaces

We study some class of Dunkl multiplier operators; and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark''s uncertainty principle. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.     

多项式混沌方法在偶然不确定度量化中的应用

复杂工程建模与模拟中必然存在误差与不确定度,分析与辨识其不确定度的来源,对不确定度进行量化,对建模与模拟可信度评估具有重要意义。本文给出建模与模拟中误差与不确定度的概念及不确定度的量化过程,并以质量弹簧阻尼系统为例说明量化偶然不确定度的过程,验证了非嵌入多项式混沌方法在非光滑系统不确定度量化中的有效性,对建模与模拟中不确定度量化具有重要的参考价值。     

元素分析仪测定土壤氮、碳含量的不确定度评定

用实例对元素分析仪测定土壤氮、碳含量不确定度进行评定.分析讨论了测定过程中不确定度的来源、不确定度分量的计算.结果表明,影响土壤碳、氮含量测定不确定度的主要因素是标准物质的引入和标准曲线的绘制.     

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite‐time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well‐known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–19, 2016     

The path player game

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption undermodel uncertainty. The underlying market model consists of a risky asset, whosevolatility and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with risk aversionparameter 0 < α < 1 and a dynamically consistent coherent risk measure, whichallows for model uncertainty in the distributions of both the asset price dynamics andthe factor process. Ourmethod combines recent results by Wittmüß (Robust optimizationof consumption with random endowment, 2006) on the duality theory of robustoptimization of consumption with a stochastic control approach to the dual problemof determining a ‘worst-case martingale measure’.     

On the accuracy of micro Winkler titration procedures: a case study

Accuracy data (expressed as precision and trueness) presented by the authors of three different micro modifications of the Winkler titration procedure for dissolved oxygen concentration determination are critically evaluated. Tentative uncertainty estimates are extracted from the data based on the single-laboratory validation approach (originally published in the Nordtest Technical Report 537) and they lead to expanded uncertainty (k = 2) estimates in the range from 0.13 to 0.27 mg l⁻¹ for the three procedures. It is demonstrated that, in all cases, the authors have presented the accuracy and/or precision estimates of the procedures in a way that can lead to too optimistic conclusions about the uncertainty of their procedures. This case study demonstrates the usefulness and flexibility of the single-laboratory validation approach to uncertainty estimation, even in the case of insufficient data, and can be of interest to laboratory workers dealing with measurement procedures from the literature. It is also expected to be of interest to university instructors of analytical chemistry and metrology in chemistry as a real-life example of the critical evaluation of the literature data. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

How to revise the GUM?

The announcement of a revision of the Guide to the expression of uncertainty in measurement has renewed the debate about the topic of measurement uncertainty. In this paper the author, chairman of Working Group 1 of the Joint Committee for Guides in Metrology, replies to the theses given in two recent papers by Semion Rabinovich. His opinions are personal, and are not necessarily shared by the JCGM/WG1. They are to be intended as a further contribution to the present discussion. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Estimation of the uncertainty components associated with the measurement of radionuclides in air filters using γ-ray spectrometry

This paper discusses and assesses the major sources of uncertainty arising in measurement of radionuclide activity concentrations in air. Besides counting statistics, the main contributors to the overall uncertainty of the activity concentration of long-lived radionuclides are the heterogeneities of the calibration source and the test samples (approximately 4%). In addition, in the case of radionuclides with half-lives of the order of days or shorter, a significant uncertainty results from the variability of the source term because the peak concentration of the radionuclide might occur either at the beginning or at the end of the sampling period. For¹³¹I (T_1/28 days), for instance, the relative standard uncertainty was estimated as 17% owing to this effect. In addition, the uncertainty introduced by the software used for evaluation of the -ray spectra is discussed. Details of the uncertainty components, including their assessed probability distributions and degrees of freedom, and the conversion into standard uncertainties are reported in this paper, following the ISO Guide to the expression of uncertainty in measurement. A standard form for documenting and reporting the uncertainty budged is proposed and illustrated with an example.     

Hedging entry and exit decisions: optimizing location under exchange rate uncertainty

^** Email: alexru00{at}ms41.hinet.net^*** Email: ctlin{at}mail.yust.edu.tw The Cobb–Douglas production function with Abel's (1983,Am. Econ. Rev., 173, 228–233) model is extended herein,and real options analysis (ROA) for entry–exit decision-makingestablished utilizing Dixit's (1989b) decision model under exchangerate uncertainty. This work considers the effects of real exchangerates on strategies that determine the locations of productionby firms that are entering markets in two countries. The ROAis also adopted to evaluate the switching location between twocountries. A continuous-time model optimization problem is solvedin closed-form. This provides a useful beginning to an importantanalysis of the effects on industry of exchange rate fluctuationswhen the optimal entry (exit) trigger for transferring locationsis important for a basic global logistics model. Furthermore,a myopic solution of the optimal entry (exit) trigger, sensitivityanalysis and some characteristics of the optimal productionstrategy are sought. This paper contributes to the problem ofchoice of foreign production strategy.     

Exact uncertainty approach in quantum mechanics and quantum gravity

The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of motion to the Schrödinger equation. This ‘exact uncertainty’ approach may be generalised to ensembles of gravitational fields, where nonclassical fluctuations are added to the field momentum densities, of a magnitude determined by the uncertainty in the metric tensor components. In this way one obtains the Wheeler-DeWitt equation of quantum gravity, with the added bonus of a uniquely specified operator ordering. No a priori assumptions are required concerning the existence of wave functions, Hilbert spaces, Planck's constant, linear operators, etc. Thus this approach has greater transparency than the usual canonical approach, particularly in regard to the connections between quantum and classical ensembles. Conceptual foundations and advantages are emphasised.