On the concept of solution for fractional differential equations with uncertainty

We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.     

高能激光能量计溯源问题研究北大核心

由于高能激光能量计标定过程中没有标准的能量测量装置和标准的激光源,无法采用常规方法对其进行标校。提出了一种利用现有小能量计从低到高逐级多次传递不确定度的方法,以及一种利用能量等效原理对激光能量计进行标校的方法。不确定度传递法方法简单,但环节较多导致不确定度较大。等效标定法包括电标法和光标法,电标法对设计要求较高,但求解过程相对简单。光标法工程实现难度要低得多,但必须事先对灯组余热及热损失进行测算。等效法的三个条件与误差大小关系紧密,在结构设计中必须严格考虑,它是提高测量准确性的根本,其次要尽量减少不确定度传递的中间环节,最后需要对误差项进行科学分析和测定,在此基础上对这些项进行相应的修正和补偿。     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩——2腔模总数与压缩阶数两者之积取奇数的情形

构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}〉q和多模虚共轭相干态的相反态|{-Z_j^(b)*}〉q的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ(ab)Ⅱ〉q.利用多模压缩态理论,研究了态|Ψ(ab)Ⅱ〉q的等阶N次方H压缩特性.结果发现,在腔模总数与压缩阶数这两者之积取奇数,则当各对应模的初始相位、各对应模的初始相位差,态间的初始相位差、以及光子干涉项的幅度之和等分别满足一定的量子化条件时,态|Ψ(ab)Ⅱ〉q的第一及第二正交分量可分别呈现出周期性变化的等阶N次方H压缩效应.这与现有报道的结果截然不同.     

Evaluation of uncertainty utilising the component by component approach

 This paper reviews the so-called "component by component approach" of evaluating measurement uncertainty. An overview of the evaluation process is given followed by an in-depth discussion of some of the differences between this approach and the approach of utilising validation data. Some of the advantages and disadvantages of using the component by component approach are outlined at the end. Received: 4 August 1999 · Accepted: 11 November 1999     

Karl Menger's contributions to social thought

The work of Karl Menger in social science is briefly surveyed, in particular in the areas of marginal utility and diminishing value, utility, and uncertainty, a logic of imperatives based on deterrence, and a theory of voluntary associations in which cohesive groups are studied combinatorially.     

On the incoherent scattering of an acoustic or electromagnetic wave

A random configuration of objects in space, or a stochastically rough boundary, is considered to scatter an incident acoustic or electromagnetic wave having harmonic time dependencee ^iwt . In the case of a stochastic surface, Beckmann has compared the Kirchhoff solution with his approach, which employs random walk. The latter approach is used to demonstrate the Rayleigh-distributed amplitude of a field scattered by a very rough surface. This demonstration requires the conjecture that large standard deviations in the random phases of the scattered elementary waves result in an incoherent scattered field. Beckmann's conjecture has not been rigorously proven. However, in this paper, incoherence of the scattered field and broad distributions, over many cycles, in the phases of the elementary waves are both shown to be implied by a third condition, which is defined. Furthermore, the random phase of an incoherent field is shown to be statistically independent of its amplitude and uniformly distributed on a 2-rad interval.     

Generalized Uncertainty Principle in a Simple Varying Speed of Light Model

In this paperwewill derive a generalized uncertainty principle (GUP) in a simple varying speed of light (VSL) model. First we will show that VSL is an immediate consequence of GUP. Then, within the framework of a simple VSL model, we will show that GUP can be expressed as a function of cosmological scale factor. This expression gives two main results: uncertainties in position and momentum are actually cosmological models dependent and these uncertainties depend on mass and momentum of the particle under consideration. The relationship between matter content of the Universe and the values of uncertainties in early stages of the evolution of the Universe will be discussed in a mini-superspace approach.     

The generation of stable project plans

This text summarises the PhD thesis that Roel Leus presented to obtain the degree of Doctor in Applied Economics at the Katholieke Universiteit Leuven, in September 2003. The promotor of the thesis was professor Willy Herroelen. The thesis is written in English and is available from the authors website. The goal of the thesis was to provide recommendations for the detailed scheduling of multi-project organisations, when a certain degree of uncertainty exists about a number of characteristics of the project. Up till now, the majority of the literature on project scheduling has consisted of deterministic models for planning a single project: both the uncertainty aspect as well as the intrinsic difficulty of coordination of a portfolio of projects have been largely ignored.Received: October 2003, MSC classification: 09B35, 90B36     

Traceability without uncertainty: current situation in the pharmaceutical industry

The current situation in the pharmaceutical industry is discussed, when the traceability of measurement (analytical) results to certified values of pharmacopoeial reference standards is required, without evaluating their uncertainties. It is shown that the evaluation of measurement uncertainty is necessary for understanding the level of confidence of the analytical results and their comparability, particularly during preparation and characterisation of the reference standards.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher. Apart from exceptional circumstances, they are not submitted to the usual referee procedure and go essentially unaltered.