The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.

MIXED SELF-CONFORMAL MULTIFRACTAL MEASURES

Mixed multifractal analysis studies the simultaneous scaling behavior of finitely many measures. A self-conformal measure is a measure invariant under a set of conformal mappings. In this paper, we provide a descript.ion of the mixed multifractal theory of finitely many self-conformal measures.

Nonparametric Regression Estimation with Mixed Measurement Errors

We consider the estimation of nonparametric regression models with predictors being measured with a mixture of Berkson and classical errors. In practice, the Berkson error arises when the variable X of interest is unobservable and only a proxy of X can be measured while the inaccuracy related to the observation of the proxy causes an error of classical type. In this paper, we propose two nonparametric estimators of the regression function in the presence of either or both types of errors. We prove the asymptotic normality of our estimators and derive their rates of convergence. The finite-sample properties of the estimators are investigated through simulation studies.

L^p MIXED-NORM ESTIMATES FOR CONVOLUTION OPERATOR DEFINED BY SINGULAR MEASURES

Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.

Application of Uniform Experimental Design in Optimizing Excitation Parameters for Magnetic Frequency Mixing Measurements

Excitation parameter preferences are key factors a ecting the performance of magnetic frequency mixing detection.A uniform experimental design method was used to analyze this influence.Using fuzzy theory,a comprehensive model is established for evaluating the e ect of magnetic frequency mixing.A polynomial is selected as the regression function to express explicitly the correlation between the excitation parameters and the frequency-mixing e ect.The excitation parameters were then optimized using genetic algorithm.Magnetic frequency mixing experiments were conducted to measure the surface hardness of some ferromagnetic materials.Frequency mixing is further enhanced under the optimal settings,resulting in an improvement in the measurement sensitivity.The results of this study support the application of the magnetic frequency mixing technique in non-destructive testing.

A Self-Mixing Microvibration Measurement System of a π-Phase Shifted DFB Fiber Laser

Recently, with the rapid development of precision machining, microvibration measurement is required for the manufacturing and installation of parts and components. In this paper, a self-mixing microvibration measurement system of a π-phase shifted Distributed feedback (DFB) fiber laser is introduced. An all-fiberized configuration Er3+-Yb3+ co-doped DFB fiber laser was used as light source, in which an active π-phase shifted fiber Bragg grating (FBG) was wrote on Er3+-Yb3+ co-doped fiber. Using this, it can easily get a single-mode lasing with narrow linewidth. Experimental results demonstrate that the amplitude of vibration can be achieved down to λ/5 without any modulation parts while utilizing the reflecting mirror. It is in good agreement with the theoretical analysis and very helpful in proving sensitivity and stability of the measurement system. In addition, remote vibration measurement with a distance of 20 km is also realized with this system.

Sub-external cavity effect and elimination method in laser self-mixing interference wave plate measurement system

Laser self-mixing interference（SMI） wave plate measurement method is a burgeoning technique for its simplicity and efficiency. But for the non-coated sample, the reflected light from the surface can seriously affect the measurement results.To analyze the reason theoretically, a self-consistent model for laser operation with a sub-external and an external cavity is established, and the sub-external cavity formed by the sample and a cavity mirror is proved to be the main error source.A synchronous tuning method is proposed to eliminate the sub-external cavity effect. Experiments are carried out on the synchronously tuning double external cavities self-mixing interference system, and the error of the system is in the range of -0.435°~0.387° compared with the ellipsometer. The research plays an important role in improving the performance and enlarging the application range of the laser self-mixing interference system.

重复测量数据的混合模型及其MIXED过程实现——混合线性模型及其SAS软件实现(二)

目的 重复测量数据存在自相关及随机误差分布于不同层次 ,不宜使用常规分析方法 ,本文研讨使用混合线性模型及SAS软件实现的分析方法。方法 利用MIXED对多个处理组的重复测量数据进行混合模型分析。结果 通过固定效应与随机效应及对协方差矩阵的估计 ,使重复测量数据得以合理的分析。结论 MIXED可以有效地、全面地分析重复测量数据。

双反应变量重复测量资料分析及MIXED过程实现

目的探讨双反应变量重复测量资料的分析原理与方法及SAS软件PROCMIXED过程的应用。方法结合双反应变量重复测量数据的特点,采用SAS软件的MIXED过程对其进行分析,建立线性混合效应模型。结果该模型不仅考虑了每个变量多次重复测量结果之间的相关性,也考虑了两个变量之间的相关性,同时还引入固定效应和随机效应,结合数据特征分析,结果更为可信。结论对双反应变量非独立重复测量资料,可以把数据之间的相关性分解为重复测量间相关性和变量间相关性两部分,采用MIXED过程不仅可对其相关性做出明晰深入的分析,且可保证数据分析结果解释更符合实际。

带时依协变量的重复测量资料的混合线性模型分析及其MIXED过程实现

目的探讨混合线性模型在带有时依协变量的重复测量资料分析中的应用。方法以治疗轻、中度原发性高血压病临床试验资料为例,考虑到给药方案在各个时间点随病情而变化,利用SAS中的MIXED过程,选择合适的协方差结构来实现带有时依协变量的重复测量资料的统计分析。结果时依协变量(给药方案)对治疗轻、中度原发性高血压病有统计学意义(P<0.05);时间因素有统计学意义(P<0.05);给药方案与时间因素之间有交互效应(P<0.05)、给药方案与处理因素之间有交互效应(P<0.05)。结论采用混合线性模型对带有时依协变量的临床试验重复测量资料进行统计分析,可以更客观地进行药物疗效评价。

ON BONNESEN-STYLE SYMMETRIC MIXED ISOHOMOTHETIC INEQUALITY IN R^2

In this paper, we investigate the translative containment measure for a convex domain Ki to contain, or to be contained in the homothetic copy of another convex domain tKj(t ≥ 0). Via the formulas of translative Blaschke and Poincaré in integral formula, we obtain a Bonnesen-style symmetric mixed isohomothetic inequality. The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc. As a direct consequence, we attain an inequality which strengthen the result proved by Bonnesen, Blaschké and Flanders. Furthermore, by the containment measure and Blaschke's rolling theorem, we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities. These inequalities are the analogues of the known Bottema's result in 1933.

Assessing the influence of the minimum measured diameter on forest spatial patterns and nearest neighborhood relationships

Forest structure analysis is important for understanding the properties and development of a forest community,and its outcomes can be influenced by how trees are measured in sampled plots.Although there is a general consensus on the height at which tree diameter should be measured[1.3 m:diameter at breast height(DBH)],the minimum measureddiameter(MMD)often varies in different studies.In this study,we assumed that the outcomes of forest structure analysis can be influenced by MMD and,to this end,we applied g(r)function and stand spatial structural parameters(SSSPs)to investigate how different MMDs affect forest spatial structure analysis in two pine-oak mixed forests(30 and 57 years old)in southwest China and one old-growth oak forest(>120years old)from northwest China.Our results showed that 1)MMD was closely related to the distribution patterns of forest trees.Tree distribution patterns at each observational scale(r=0-20 m)tended tobecome random as the MMD increased.The older the community,the earlier this random distribution pattern appeared.2)As the MMD increased,neighboring trees became more regularly distributed around a reference tree.In most cases,however,nearest neighbors of a reference tree were randomly distributed.3)Tree species mingling decreased with increasing diameter,but it decreased slowly in older forests.4)No correlations can be found between individual tree size differentiation and MMD.We recommend that comparisons of spatial structures between communities would be more effective if using a unified MMD criterion.

Experimental study by online measurement of the precipitation of nickel hydroxide: Effects of operating conditions

The objective of this work is using the online measurement method to study the process of precipitation of nickel hydroxide in a single-feed semi-batch stirred reactor with an internal diameter of D = 240 mm. The effects of impeller speed, impeller type, impeller diameter and feed location on the mean particle size d43 and particle size distribution(PSD) were investigated. d43 and PSD were measured online using a Malvern Insitec Liquid Process Sizer every 20 s. It was found that d43 varied between 13 μm and 26 μm under different operating conditions,and it decreased with increasing impeller diameter. When feeding at the off-bottom distance of D/2 under lower impeller speeds, d43 was significantly smaller than that at D/3. PSDs were slightly influenced by operating conditions.

Interpretation of diagnosis and treatment scheme of COVID-19 in Hunan province (the third trial version) based on three factors and measures

The similarities and differences between"Novel Coronavirus Infected pneumonia in Hunan province(trial second edition)"and"Novel Coronavirus Infected pneumonia(Trial seventh edition)"released by the National Health Commission and their ideas were interpreted based on"suiting measures to three factors".①In Hunan program,the third version of the trial adjustment more suitable for local characteristics of the disease;②The prevention program population classification is clear,support,eliminate pathogenic factors of the primary and secondary distinct;③The cause of disease is prominent,damp and toxin are mixed with dryness,and the treatment is mainly to moisten the lung and clear away heat,and the prescription is mostly Xinliang light agent.

Quantum Zeno Effect with Mixed Initial States

Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.

Study on Catalytic Cracking of VGO Derived from Kazakhstan-Russian Mixed Crude

The study on options for catalytic cracking of VGO derived from the Kazakhstan-Russian mixed crude was carried out in a small-scale riser FCC unit. The influence of several catalysts and the LCC-A additive for increasing propylene yield on the distribution and quality of FCC products was analyzed. This article sets forth the possible issues arising from processing the Kazakhstan-Russian mixed crude in FCC unit and the response measures to be adopted.

基于激光自混合效应的微角度测量实验教学研究

为了丰富大学实验教学内容,本文提出了一种新型微角度测量方法。该方法运用激光自混合干涉技术并结合直角棱镜的光学特性,具有系统结构紧凑、分辨率高等特点。实验中采用氦氖激光器为光源,测量范围可达21.49 mrad。该实验操作性及拓展性较强,可进一步培养学生的实践能力和科研思维。

基于激光自混合干涉的磁场测量方法研究

针对光纤磁流体磁场传感器易受环境干扰及磁流体薄膜制作工艺复杂的问题,激光自混合干涉具有抗干扰能力强、稳定性好的特点,提出一种基于空间光的水平偏振激光自混合干涉的磁场测量方法,在外部磁场的作用下,水平偏振自混合干涉信号幅值发生变化,在一定范围内,磁场与信号幅值变化成正比,通过用施加磁场前后信号幅值的均值比与磁场的变化关系实现对磁场的传感检测。经过实验验证,信号的幅值在1%浓度的磁流体中衰减明显,薄膜厚度为0.5 mm,减小了薄膜的制作难度。在实验结果中对5.02 mt到19.112 mt磁场强度范围内的均值比进行线性拟合,相对误差最小为0.17%。

激光回馈精密测量技术及应用

介绍了激光回馈干涉的理论模型,阐述了激光回馈测量灵敏度高、装置结构简单、可自准直、能够对非合作目标进行精密测量的技术特点。分析了激光回馈测量相较传统干涉测量的优势,探讨了激光回馈测量技术在工业和科研领域中的应用方向,包括位移、角度、振动、绝对距离测量等,指出利用频率复用、偏振复用、(准)共路等技术可提高回馈测量的实际应用性能。最后展望了激光回馈技术的发展前景,为推动回馈技术的广泛应用提供借鉴。

矿粮复合区“三生”空间冲突诊断及演化特征分析——以大冶市陈贵镇为例

[目的]促进乡镇级矿粮复合区空间结构协调稳定,为国土空间规划的合理布局及实施提供科学参考。[方法]以矿粮复合区陈贵镇为例,基于生命周期法选取1986—2020年的5个研究时间节点,通过空间现状图和转移矩阵解释空间格局变化,构建改进的空间冲突测度模型,利用ArcGIS 10.2结合Fragstats 4.2软件分析空间冲突演化特征,使用Google Earth历史影像验证了冲突结果。[结果]农业生产空间和生态空间是转入和转出面积最大的两类空间类型,“耕地—林地”互转成为最显著的土地转换方式;1986—2020年,陈贵镇“三生”空间冲突整体有上升的趋势,在矿业衰退期,较弱、中等和强空间冲突空间单元占比分别减少3.2%,3.09%,0.22%,较强空间冲突占比增加6.51%;“三生”空间的冲突等级除了生活空间,均集中在较弱空间冲突和中等空间冲突等级,两者面积占比超过70%;借助Google Earth历史影像进行对比验证,发现“三生”空间冲突结果与空间现状较吻合。[结论]矿粮复合区受城市化和工业化的影响较大,空间冲突特征明显,参考空间冲突诊断结果,可针对性地实施空间冲突缓解措施,促进地区的可持续发展。