Gaussian states as minimum uncertainty states

In bosonic fields, Gaussian states, which consist of a rather wide family of states including coherent states, squeezed states, thermal states, etc., have many classical-like features, and are usually defined from the mathematical perspective in terms of characteristic functions. It is well known that some special Gaussian states, such as coherent states, are minimum uncertainty states for the conventional Heisenberg uncertainty relation involving canonical pair of position and momentum observables. A natural question arises as whether all Gaussian states can be characterized as minimum uncertainty states. In this work, we show that indeed Gaussian states coincide with minimum uncertainty states for an information-theoretic refinement of the conventional uncertainty relation established in Luo (2005) [40]. This characterization puts Gaussian states on a novel basis of physical significance.     

气相色谱-质谱联用法测定乐果的不确定度评定

本文以测定样品中乐果的含量为例,评定了气相色谱-质谱联用法测定结果的不确定度.建立数学模型,分析各不确定度分量,将不确定度分量合成,并计算其测定结果的扩展不确定度.     

Quantification of copper and zinc species fractions in legume seeds extracts by SEC/ICP-MS: validation and uncertainty estimation

Fractions of Cu and Zn species in legume samples (common white bean, pea, chick pea and lentil seeds and defatted soybean flour) were analysed by on-line hyphenation of size exclusion chromatography and inductively coupled plasma-mass spectrometry. Samples were extracted by 0.02 mol l⁻¹ Tris–HCl buffer solution, pH 7.5. The extraction efficiency lay in the region 60–90 and 60–80% for Cu and Zn, respectively. Quantification of elements in the individual chromatographic fractions was carried out by isotope dilution (ID) and external calibration (EC) techniques. For ID analysis the chromatographic effluent was mixed with the flow of ⁶⁵Cu and ⁶⁸Zn isotope enriched solution and the isotope ratio values ⁶³Cu/⁶⁵Cu and (⁶⁴Zn+⁶⁶Zn)/⁶⁸Zn were measured. In the case of EC technique calibration solutions of elements were injected to the flow of mobile phase by the second injector. Prior entering detector the effluent was mixed with the flow of internal standard solution (In, 50 μg l⁻¹). Both methods have similar precision, however the behaviour of both studied elements was not the same. The chromatographic analysis itself was the main source of variability in the case of Cu. For Zn species analysis, the extraction process and the manipulation with the extract, played the significant role too. It was probably caused by lower stability of the present zinc chelates. The total amounts of Zn found in all chromatographic fractions represented 85–95% of Zn in sampled extract whereas those of Cu approached 100%. In case of small peaks the results of ID and EC were not the same. The EC results were lower then ID results. The great deal of results uncertainty accounts for the precision.     

测量不确定度的研究和应用进展

综述了测量不确定度在国内外的研究及应用的进展，发现测量不确定度是现代误差理论的重要内容，是定量描述测量结果质量的重要指标。目前由ISO等七个国际组织提出的GUM(测量不确定度表述导则)已被各国广泛接受，国内外已有大量关于不确定度应用的文献。除GUM外，还存在其它几种不确定度评定模型。我国虽然对GUM存在重大疑义，并向有关国际组织提出了一些建设性的意见，但在方法的执行上目前仍然与国际社会保持了对GUM的一致态度。     

The acoustical characterization of orchestra platforms and uncertainty estimation of the results

Measurements have been carried out on furnished orchestra platforms in four concert halls in Italy in order to describe the sound field perceived by musicians. The heterogeneous nature of the orchestra suggested a procedure able to take into account the mutual hearing between instrumental sections. The measured parameters were the early, late and total support, the reverberation time, the early decay time and the clarity index. A part of the study has been devoted to the measurement uncertainty estimation. The source directivity and the small displacements of the microphone influence the early decay time to a great extent while the on-platform spatial variability affects both the early decay time and the clarity index. Per-section early support shows differences that render the overall spatial mean inappropriate to describe the stage as a whole. For the other parameters an overall mean platform value can instead be suitable, even though, for the case of clarity a more evident group variability is observed. The values of late support, reverberation time, early decay time and clarity index, proposed in literature as suitable measures of reverberance for musicians, are not all intercorrelated, indicating that not all these parameters can be associated to the same subjective impression.     

牛顿环实验测量结果的不确定度评定及其表示

讨论了不等精度测量牛顿环曲率半径及牛顿环直径不确定度的评定及表示     

The uncertain premium principle based on the distortion function

In this paper, we discuss the premium principle in uncertain environment. First, the net premium principle for uncertain risks is presented within the framework of uncertainty theory. With the help of distortion function, a new uncertain premium principle is derived from the uncertain net premium. Some properties of uncertain distortion premium principle are proved. Furthermore, a sufficient and necessary condition that an uncertain premium principle is an uncertain distortion premium principle has been characterized. Finally, some examples are given to illustrate the calculations of the uncertain distortion premium.     

Padé–Legendre approximants for uncertainty analysis with discontinuous response surfaces

A novel uncertainty propagation method for problems characterized by highly non-linear or discontinuous system responses is presented. The approach is based on a Padé–Legendre (PL) formalism which does not require modifications to existing computational tools (non-intrusive approach) and it is a global method. The paper presents a novel PL method for problems in multiple dimensions, which is non-trivial in the Padé literature. In addition, a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities. The numerical examples include fluid dynamic problems characterized by shock waves: a simple dual throat nozzle problem with uncertain initial state, and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain. Results are presented in terms of statistics of both shock position and strength and are compared to Monte Carlo simulations.     

Risky traveling salesman problem

In this paper we introduce a methodology for optimizing the expected cost of routing a single vehicle which has a probability of breaking down or failing to complete some of its tasks. More specifically, a calculus is devised for finding the optimal order in which each site should be visited.     

Quantum black hole and the modified uncertainty principle

Recently Ali et al. (2009) [13] proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Planck length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number n which coincides with Bekenstein?s proposal. We also found that the mass of the black hole is directly proportional to the quantum number n when quantum gravity effects are taken into consideration via the modified uncertainty relation but it reduces the value of mass for a particular value of the quantum number.