The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.      

Exponential synchronization of stochastic impulsive perturbed chaotic Lur''e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

转镜式高速相机扫描速度检测装置及不确定度评定

基于光电转换基本原理，设计并研制了用于转镜式高速扫描相机扫描速度的检测装置，包括均匀脉冲光源、精密双狭缝、超快响应光电转换器以及高带宽、高采样率数字示波器等。论述了检测装置的核心部件，用该装置实测了SJZ-15型转镜扫描相机名义扫速为4．5mm／μs的扫描速度，计算出了扫速不均匀性。按照国军标GJB3756，对检测装置的测量不确定度来源进行了分析，给出了该装置的不确定度评定方法及测量不确定度，对检测结果的评定表明，该检测装置的相对测量不确定度不大于0．1%，远低于目前转镜扫描相机的最大扫速不均匀性水平。实验证明，设计的检测装置具有很高的准确度和可靠性。     

棱镜耦合法测量掺杂波导模折射率中的误差分析

讨论了棱镜耦合法测量离子交换掺Er-Yb平面光波导中传播模式的模折射率实验中的误差与不确定度,模折射率误差由耦合棱镜折射率与底角及同步入射角误差决定，得出了测量模折射率不确定度的传递公式,作为实例．用Ag^＋-Na^＋离子交换技术,在285℃下交换15min．得到了Er-Yb共掺磷酸盐玻璃平面波导，给出了波导模折射率（@632．8nm）及不确定度。     

New framework nanostructures of carbon atoms in <Emphasis Type="Italic">sp</Emphasis><Superscript>2</Superscript> and <Emphasis Type="Italic">sp</Emphasis><Superscript>3</Superscript> hybridized states

A new family of framework nanostructures including carbon atoms in _sp ² and sp ³ hybridized states is reported. Structure optimization was fulfilled using MM+ molecular mechanics and Hückel semiempirical methods. The energy characteristics of the structures have been evaluated. Comparative analysis of the stability of the title nanostructures has been performed in relation to their geometry and relative contents of sp ²/sp ³ atoms.     

Measurement uncertainty of iodine determination in radiochemical neutron activation analysis

The measurement uncertainty of iodine determination in NIST standard reference material (SRM) 1549 using radiochemical neutron activation analysis (RNAA) was studied. This method is based on ignition of the irradiated sample [¹²⁷I(n,)¹²⁸I, t_1/2=25 min, E=422.9 keV] in an oxygen atmosphere, followed by absorption of iodine in a reducing acid solution and its purification by a selective extraction–stripping–reextraction cycle. The purified solution of iodine in CHCl₃ was transferred to a well-type HPGe detector for -ray measurement of the induced radionuclide ¹²⁸I. The detection limit of the method employed under the conditions described was 1 ng/g. The reproducibility of iodine determination in the SRM was 3.6% (12 determinations within 1 month), calculated by the analysis of variance procedure. Using the commercially available software program GUM Workbench and the recommendations of the Eurachem/CITAC Guide, we evaluated the uncertainty budget for this RNAA method and the relative uncertainty obtained was 3.6%. The largest uncertainty contributions were due to the repeatability of the chemical yield determination, the count rate of the induced nuclide in the standard and sample, the mass of the carrier and the mass of the irradiation standard.     

两种特殊四态叠加多模叠加态光场的等N次幂H压缩

根据线性叠加原理,用多模相干态|{Z_j^*}〉q,|{-Z_j^*}〉q及其复共轭|{Z_j^*}〉q和|{-Z_j^*}〉q组成了两种四态叠加多模叠加态光场|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q,利用多模压缩态理论研究了它们的等N次幂H压缩,结果发现:态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q具有完全相同的等N次幂H压缩规律;当压缩幂次N与腔模总数q之积,即qN为偶数时,态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q恒处于等幂次N-H最小测不准态或呈现"半相干态效应";当qN为奇数时,在不同条件下,态|Ψ_oe⁽⁴⁾Ⅵ〉q和|Ψ(4)oeⅦ〉q可以呈现三种不同状态:第一正交分量呈现等N次幂H压缩;第二正交分量呈现等N次幂H压缩; 可呈现"半相干态效应".     

Best time localized trigonometric polynomials and wavelets

In spaces of trigonometric polynomials, the minimum of the angular variance is determined, which is a time localization measure forL ₂ ² . Wavelets and wavelet packets are constructed with the resulting polynomials.     

Uncertainty Evaluation in Multivariate Analysis – A Test Case Study

We have used different multivariate analysis methods to estimate quantities in the fields of food control and atmospheric remote sensing. In order to estimate the uncertainties in these estimates we studied analytical as well as non-parametric numerical methods. The methods have been evaluated by comparison between obtained results and independent sets of measurements. We present one test case from each field, including results, where these methods have been applied. For the food control test case reduced chi-squared of approximately unity indicate that both the analytical and numerical methods used for uncertainty estimation produce uncertainties of reasonable size. In the atmospheric remote sensing test case, a indicated that the uncertainties from the numerical method were far too small, whereas a indicate that the size of the analytically determined uncertainties can represent the size of the “true” errors.     

A Discrete-Time American Put Option Model with Fuzziness of Stock Prices

To solve a mathematical model for American put option with uncertainty, we utilize two essentials, i.e., a λ-weighting function and a mean value of fuzzy random variables simultaneously. Estimation of randomness and fuzziness as uncertainty should be important when we deal with a reasonable and natural model extended from the original optimization/decision making. Three kinds of mean values by fuzzy measures, which are based on Possibility, Necessity and Credibility, are demonstrated particularly. We consider the optimal expected price of the American put option by dynamic programming under a reasonable assumption. A numerical example is given to illustrate our idea.