Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

基于L1正则化的随机梁式结构静力损伤识别方法

提出了一种结合摄动法和L1正则化方法的随机梁式结构静力损伤识别方法。考虑初始模型误差和测量误差的影响,建立了关于随机损伤指数的控制方程,并将摄动法和L1正则化方法相结合,对随机损伤指数的控制方程进行求解,进而从概率的角度对结构的损伤进行识别。损伤试验结果表明,和传统的最小二乘求解法相比,本文方法能够更为准确地识别多处局部损伤的位置及大小,对实际结构损伤检测具有较好的参考价值。     

一类改进最大熵方法的可调参数分析

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。     

有雨概率与分维数关系的初步研究

对武汉地区１９８２～１９９４年有雨分维数与有雨概率之间的关系进行了初步的分析和研究，并给出了研究结果．为今后修改降雨衰减预报模型作准备．     

新型螺旋型内包层双包层光纤吸收效率分析

提出一种新型的内包层横截面边界为螺旋曲线的双包层光纤结构,并给出一种分析双包层光纤吸收效率的新方法:它以射线法为基础,采用概率理论计算出光纤内部传播的光线每次被内包层边界反射后能够被纤芯直接吸收的概率,并以此概率来衡量内包层横截面形状对光纤吸收效率的影响.最后用这种方法对螺旋型双包层光纤进行分析,得出它比一般缺陷型双包层光纤优异的结论.     

关于非负下半连续函数最优可测耦合的存在性及其应用

本文证明了两个转移概率关于非负下半连续函数最优可测耦合的存在性定理．作为对这一结果的应用,推广了Ｓｔｒａｓｓｅｎ定理,进而证明了跳过程的随机可比性等价于保序耦合的存在性．     

概率约束规划逼近最优解集的上半收敛性

本文讨论了概率约束规划目标函数的连续收敛性,并利用概率测度弱收敛的特征给出了概率约束规划可行集的收敛性条件,得到了概率约束规划逼近最优解集的上半收敛性.     

Scenario Reduction Algorithms in Stochastic Programming

We consider convex stochastic programs with an (approximate) initial probability distribution P having finite support supp P, i.e., finitely many scenarios. The behaviour of such stochastic programs is stable with respect to perturbations of P measured in terms of a Fortet-Mourier probability metric. The problem of optimal scenario reduction consists in determining a probability measure that is supported by a subset of supp P of prescribed cardinality and is closest to P in terms of such a probability metric. Two new versions of forward and backward type algorithms are presented for computing such optimally reduced probability measures approximately. Compared to earlier versions, the computational performance (accuracy, running time) of the new algorithms has been improved considerably. Numerical experience is reported for different instances of scenario trees with computable optimal lower bounds. The test examples also include a ternary scenario tree representing the weekly electrical load process in a power management model.     

复合二项风险模型的破产概率

本文讨论了一般情形的复合二项风险模型,得出了初始资本为０时的破产概率以及初始资本为ｕ≥０的情况下的破产概率的一般公式．     

概率逻辑学基本定理的推广

通过引入生成状态集和生成概率等概念给出了概率逻辑学基本定理的简捷证明,并进一步通过引入自然合并概率的概念将概率逻辑学的基本定理推广到了更一般的形式,改进了对推理结论的不可靠度上界的估计.然后将概率逻辑学的基本方法引入计量逻辑学,得出了带参数 的有限逻辑理论相容度概念,是δ-相容度的推广.