Lacunary Measures and Self-similar Probability Measures in Function Spaces

The paper deals with multifractal quantities for some types of Radon measures,especially self-similar probability measures,and their relations to Besov spaces.

Seismic fragility analysis of clay-pile-pier systems considering the optimization of ground motion intensity measures

The performance of clay-pile-pier system under earthquake shaking was comprehensively examined via three-dimensional finite element analyses,in which the complex stress-strain relationships of a clay and piled pier system were depicted by a hyperbolic-hysteretic and an equivalent elastoplastic model,respectively.One hundred twenty ground motions with varying peak accelerations were considered,along with the variations in bridge superstructure mass and pile flexural rigidity.Comprehensive comparison studies suggested that peak pile-cap acceleration and peak pile-cap velocity are the optimal ground motion intensity measures for seismic responses of the pier and the pile,respectively.Furthermore,based on two optimal ground motion intensity measures and using curvature ductility to quantify different damage states,seismic fragility analyses were performed.The pier generally had no evident damage except when the bridge girder mass was equal to 960 t,which seemed to be comparatively insensitive to the varying pile flexural rigidity.In comparison,the pile was found to be more vulnerable to seismic damage and its failure probabilities tended to clearly reduce with the increment of pile flexural rigidity,while the influence of the bridge girder mass was relatively minor.

Analytical Evaluation of Non-Elementary Integrals Involving Some Exponential, Hyperbolic and Trigonometric Elementary Functions and Derivation of New Probability Measures Generalizing the Gamma-Type and Gaussian-Type Distributions

The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, and where α,η and β are real or complex constants are evaluated in terms of the confluent hypergeometric function 1F1 and the hypergeometric function 1F2. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions 1F1 and 1F2. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (x2) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.

THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE

Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi（x） =λix ＋ bi, i = 1,2, 3, x =（x1, x2）, b1=（0, 0）, b3=（1-λ3 /2,√3/2 （1-λ3）） This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.

DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ξ 〈 θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ = θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ ahaost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.

Measurement of Characteristic Self-Similarity and Self-Diversity for Complex Mechanical Systems

Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.

Transfer of Global Measures of Dependence into Cumulative Local

We explore an idea of transferring some classic measures of global dependence between random variables Χ1, Χ2, L, Χn into cumulative measures of dependence relative at any point?(χ1, χ2, L, χn)?in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s（E∩B（x,r））≤（2r）^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.

A Note on the Product Borel Probability Measure

In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.

FOURIER TRANSFORMATION AND SINGULAR INTEGRALS ON SELF-SIMILAR MEASURE

This paper serves two purposes. One is to modify Strichartz's results with respect to the asymptotic averages of the Fourier transform of μ on , self-similar measure defined by Hutchinson. Another purpose is to consider a singular integral operator on μ and show that this op- erator is of type (p,p)(1<p<∞).

HAUSDORFF MEASURE OF UNIFORM SELF-SIMILAR FRACTALS

Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system （UIFS） on R^d. Denote by D the Hausdorff dimension, by H^D（E） the Hausdorff measure and by diam（E） the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence of a positive constant depending only on ω, such that the Hausdorff dimension is smaller than one and H^O（E） = diam（E）^D if c is smaller than this constant. We apply our result to modified versions of various classical fractals. Moreover, we present a parametrised UIFS, where ω depends on c and show the inequatily H^D（E） 〈 diam（E）^D, if c is small enough.

基于声散射统计特性的压缩感知水下目标定位与观测矩阵性能

近年来,压缩感知理论在水下目标定位领域得到了广泛的应用,压缩感知定位算法将水下目标定位问题转化为稀疏模型重构问题,具有较高的定位准确性,但定位结果受散射环境影响。该文开展水下目标定位的水池试验,对水听器阵列接收的试验数据进行处理,通过定位误差、可定位声源数量和定位信噪比分析定位结果,研究压缩感知定位算法的宽带性能、散射环境对定位结果的影响,并使用Spark系数和声散射统计特性近似分析了观测矩阵性能。水池试验结果表明,压缩感知定位算法在较宽的频率范围内有较好的适用性;随着环境散射增强,水声定位观测矩阵的列相干性减小,稀疏重构性能提升,使得定位结果更加准确;在近似分析水声定位观测矩阵性能时,声散射统计特性与Spark系数的变化趋势相似,并具有直观且计算简单的优点。

基于ML预测不确定性的边坡失稳时空概率评估方法与应用研究

为解决机器学习(Machine Learning,ML)边坡位移预测中的不确定性及预测信息挖掘深度不够等问题,提出基于ML预测不确定性的边坡失稳时空概率评估方法。首先,基于Bootstrap算法度量ML边坡位移预测中的不确定性,利用GRU算法预测边坡单一点位的位移时间特征、Kriging算法插值边坡位移空间分布,建立Bootstrap-GRU-Kriging边坡位移时空不确定性预测模型;接着,利用可靠度理论挖掘位移时空不确定性预测结果,建立边坡失稳时空概率评估模型,基于最不利原则提出边坡全断面位移-失稳概率二元耦合分析指标DP;最后,依托杭绍台铁路硅藻土边坡试验段验证模型的有效性。结果表明:边坡位移时空不确定性预测模型兼具ML边坡位移预测不确定性量化和时空分布预测功能,边坡失稳时空概率评估模型不仅能得到边坡失稳概率空间分布及时变特性,还能实现边坡整体安全的高效评价;所提方法构造的预测区间清晰可靠,各测点预测区间覆盖率PICP均值高于96%,DP指标可响应边坡变形过程中外界所造成的影响。研究成果可为边坡位移预测及超前评估理论研究提供参考。

基于贝叶斯滤波理论的目标命中概率估计与判决方法研究

为了降低兵器试验中目标命中概率指标的判决错误率,提出了基于贝叶斯滤波理论的目标命中概率估计和判决方法。该方法构建了目标命中概率与试验观测数据的统计数学模型,依据贝叶斯滤波理论推导了目标命中概率后验概率密度函数、后验均值估计以及均方误差的解析表达式,并给出了基于目标命中概率后验均值估计的判决方法。依据不同的真实目标命中概率生成观测数据,分别利用传统方法和所提方法进行了估计和判决试验。结果表明:所提方法判决错误率仅为传统方法的1/3,证明所提方法具有可行性。

InGaAs/InP高速正弦门控单光子探测器后脉冲抑制方案

基于量子力学基本原理的量子密钥分发(QKD)系统具有信息论安全的水平,单光子探测器是QKD系统的重要组成,其后脉冲对QKD系统的安全成码率和安全成码距离均有重要影响。文中根据InGaAs/InP高速正弦门控探测器的后脉冲概率随时间呈现指数递减分布的规律,提出了一种基于时间测量的后脉冲抑制方案,采用“Start-Stop型”时间间隔测量方式对探测脉冲进行测量,通过对探测事件进行时间标记并舍弃一段时长内探测脉冲的方法降低了后脉冲概率。实际验证了某型号单光子探测器的后脉冲概率随舍弃时长的关系,在500 ns舍弃时长条件下,后脉冲概率2.46%,增加舍弃时长至5μs可降低后脉冲至2%以下。同时,分析了100 ns舍弃时长条件下的典型探测脉冲计数分布,指出了主要后脉冲分布区域以及未过甄别阈值的雪崩脉冲引起的后脉冲机理。进一步地,指出基于时间测量方式区分探测脉冲的到达时间不仅可用于降低单光子探测的后脉冲概率,还可以根据探测脉冲的到达时间识别雪崩过渡区攻击事件、门外攻击事件,从而丢弃被攻击区域的探测脉冲来提升QKD系统抗量子黑客攻击的能力,可支撑高速正弦门控单光子探测器应用于实用化的QKD系统。

基于分数阶矩和分片Wasserstein距离的鲁棒风险度量优化模型

鲁棒风险度量优化是一类随机风险分析度量的重要问题,其对不确定分布信息的捕捉需依赖不完善的假设和估计,分布尾部的反映直接影响分布预测的精准性,尾部模型误差在实际风险管理决策中会造成严重的后果。文章以一种对尾部模型误差具有稳健性的方式建立鲁棒风险度量优化模型。在构造模型不确定集时,提出基于Wasserstein距离的分布估计方法,克服了已有参数分布无法反映真实分布尾部行为的限制。鉴于分数阶矩对分布尾部信息具有精准刻画的能力,在解析分布估计的基础上,建立分数阶矩约束的鲁棒风险度量模型。为优化Wasserstein距离忽略分布几何结构造成的尾部模型误差,基于纤维丛理论思想,提出分片Was⁃serstein距离解析约束的分片鲁棒风险度量模型。最后,通过规范数据进行仿真分析,数值实验结果显示,该模型能够精准量化突发性极端损失风险。

基于实时组分的天然气流量在线计量方法

超声波流量计采用固定天然气组分计量标况流量,为解决与实时组分偏差影响计量精度的问题,针对SCADA系统中不同的计量实时数据条件,基于质量守恒原理,结合AGA8气体物性方程,确定了天然气标准状态体积流量和能量流量计算式,以及流量累积计量误差评价方法;设计开发了在线计量软件系统,应用于某海底管道陆上计量终端,在线分析6台超声波流量计,4个月共计15万余组计量数据。结果表明:采用固定天然气组分计量流量,导致的最大相对误差为1.02%,大于A级流量计的计量不确定度(0.85%),且计量误差与实时组分和固定组分密度差值成正比。计量相对误差分布近似满足正态分布,误差在-0.5%~0.5%的概率为98.79%。因此,采用固定天然气组分计量流量,对计量精度影响较大。提出的在线计量方法,有助于提高天然气标准状态体积流量的计量精度。