H^1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

Abstract. Let （R＋,＊,A） be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley g function and the Lusin area function for the Jacobi hypergroup and consider their （H^1, L^1 ） boundedness. Although the g operator for （R＋,＊,A） possesses better property than the classical g operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the （H^1,L^1） estimate for the Lusin area operator, a slight modification in its form is required.

数模—动模混合仿真系统的接口建模与稳定性分析

为满足现代电力系统实时仿真的发展需求,数模-动模混合仿真系统结合实时数字仿真和物理动态模拟仿真的优点,成为现代电力系统研究的重要仿真方法。接口系统是混合仿真系统设计中的核心与难点。为了深入分析混合仿真系统的稳定性,对接口系统各个组成环节进行建模得到系统开环传递函数,分别根据劳斯判据和奈奎斯特判据研究开环传递函数中不同参数对系统稳定性的影响。理论推导表明接口系统中滤波器截止频率、接口延时和阻抗模拟比对系统的稳定性影响较大,并通过所搭建的混合仿真系统进行实验,实验结果表明不同参数对系统的稳定性影响与理论推导一致。

实变函数中简单函数的研究

实变函数较之数学分析更加抽象复杂,是近代数学的重要基础。简单函数是实变函数中非常基础且具体的重要函数类。围绕简单函数与可测函数间的联系,及其在Lebesgue积分中的运用等问题开展研究,探讨简单函数在实变函数教学中的广泛应用,以期实现降低学习的难度提升实变函数的教学效果目的。

论高职院校房产管理系统设计实现

以包头职业技术学院为例,重点分析了房产系统的业务需求,设计系统总体功能模块及数据库表单,明确数据表逻辑关系,提出采用先进的前后端分离的体系架构模式,给出了系统主要功能的现实代码,总结了系统设计的特色。本文将为高职类院校房产管理实现信息化建设提供参考。

基于EEMD分解的阶次跟踪方法研究

摆线针轮减速器组成零部件繁多、构成复杂,工作时噪声干扰大且多在变转速、往复的复杂工况下工作,因此,难以准确提取其内部的故障特征。针对这一问题,提出了一种基于集合经验模态分解(EEMD)与阶次跟踪分析的方法,对摆线针轮减速器进行了故障诊断。首先,对采集到的时域振动信号和转速信号进行了等角度域差值采样,得到了振动信号的等角域平稳信号;然后,对等角域信号进行了集合经验模态分解,得到了若干个固有模态分量(IMFs),计算了各个固有模态分量的峭度值,选取目标模态分量进行了信号重构;接着,采用快速傅里叶变换得到了故障信号的阶次图;最后,根据减速器的传动方式、各零部件的模数,计算出了各主要部件的故障阶次,对比减速器在故障前后阶次图的能量峰值进行了故障诊断。研究结果表明:该方法能够准确提取包含故障信息的固有模态分量,实现从等时域信号到等角域信号的转换,并提取摆线针轮减速器的滚针故障阶次(8.37阶),故障准确率达到99.6%,可实现摆线针轮减速器在非平稳工况下的故障特征识别,并验证该方法的可行性和有效性。

基于改进功能共振分析法的SPO风险演化

为充分识别单一飞行员运行(SPO)模式下各子系统要素间的交互关系和耦合作用,梳理风险演化机制,使用改进功能共振分析法(FRAM)构建定量分析模型。采用模糊综合评判法评估系统功能模块的功能可变性;引入结构重要性概念,分析计算系统功能模块的上下游耦合变异性,厘清系统各功能要素间耦合作用影响机制;针对SPO特定场景案例,应用蒙特卡罗模拟法计算功能共振风险指数,分析潜在功能共振情况,并设置有效功能屏障。结果表明:改进的FRAM法可以解释SPO的非线性耦合情况,空中交通管制服务、飞行员认知状态、机长操纵等模块的功能可变性耦合变化指数较大,均超过2.5;进近着陆场景中机组技术培训、重要气象信息、空中交通管制服务、地面信息保障等8个功能容易出现功能共振情况;结合功能共振结果,设置物理、象征、功能、隐形种功能安全屏障措施,并以此得出针对性运行保障建议。

基于改进贝叶斯更新方法的边坡参数概率反分析及可靠度评估

某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息的高维概率反分析问题转化为等效的结构可靠度问题,但是当现场观测数据增多时,构建的似然函数值会变得非常小,甚至低于计算机浮点运算精度,会严重影响概率反分析计算效率与精度。为此,提出了一种基于并联系统可靠度分析的改进BUS方法,从基于乔列斯基分解的中点法出发,将接受率低的总失效区域分解为多个接受率高的子失效区域,从而避免因融合大量现场观测数据引起的“维度灾难”问题,实现对边坡岩土力学参数的准确概率反分析。最后,通过一不排水饱和黏土边坡案例验证了提出方法的有效性,结果表明提出的方法能够融合大量钻孔数据和边坡服役状态等观测信息高效进行岩土力学参数概率反分析及边坡可靠度评估,为高维空间变异参数概率反分析和边坡可靠度评估提供了一种有效的工具。

Diatoms as indicators of environmental change in coastal areas:a case study in Lianjiang coast of East China Sea

Owing to the significant differences in environmental characteristics and explanatory factors among estuarine and coastal regions,research on diatom transfer functions and database establishment remains incomplete.This study analysed diatoms in surface sediment samples and a sediment core from the Lianjiang coast of the East China Sea,together with environmental variables.Principal component analysis of the environmental variables showed that sea surface salinity(SSS)and sea surface temperature were the most important factors controlling hydrological conditions in the Lianjiang coastal area,whereas canonical correspondence analysis indicated that SSS and pH were the main environmental factors affecting diatom distribution.Based on the modern diatom species–environmental variable database,we developed a diatom-based SSS transfer function to quantitatively reconstruct the variability in SSS between 1984 and 2021 for sediment core HK3 from the Lianjiang coastal area.The agreement between the reconstructed SSS and instrument SSS data from 1984 to 2021 suggests that diatombased SSS reconstruction is reliable for studying past SSS variability in the Lianjiang coastal area.Three low SSS events in AD 2019,2013,and 1999,together with an increased relative concentration of freshwater diatom species and coarser sediment grain sizes,corresponded to two super-typhoon events and a catastrophic flooding event in Lianjiang County.Thus,a diatom-based SSS transfer function for reconstructing past SSS variability in the estuarine and coastal areas of the East China Sea can be further used to reflect the paleoenvironmental events in this region.

基于最优Copula相关性分析的短期风速预测方法

准确剖析变量间的关联关系,深入挖掘数据的潜在价值,是提升一系列基于统计分析原理所构建风速预测模型精度的关键。为最大程度保留数据的潜在价值并剔除冗余信息,首先将待选输入变量用概率密度函数拟合,其次建立风速与其他变量间的最优Copula函数,再次基于最优Copula函数求解相关系数,明确影响风速预测精度的关键输入变量,最后基于长短期记忆网络模型输出预测结果。基于我国某地区的实测数据集对所提方法进行了验证。实验结果表明,所提出的方法可有效选取关键输入变量,在减少模型训练时间的同时提升预测精度。

晶圆飞拍成像系统的快速均匀曝光控制

晶圆飞拍成像系统的曝光控制对成像质量具有显著影响,传统基于空间域评价的曝光控制算法计算复杂且忽视了晶粒特征的差异,易导致曝光不均匀。为此,提出一种图像分区频率域评价的曝光控制方法。该方法采用分块的双阈值分割算法,对晶粒图像的特征区域进行自适应分割;结合高通滤波器和高斯金字塔算法,在频率域内快速提取图像高频信息,并设计一种区域加权评价函数对曝光效果进行综合评价。为实现在最大曝光时间内对最优曝光参数的快速搜索,提出了基于决策树的变步长搜索算法。对比实验结果表明:该搜索算法在保证准确率的前提下,使最佳图像的平均质量指标提高了1.34%,曝光参数调整时间减少了61.3%,保证了晶圆飞拍成像过程中的成像质量。

关于函数方程的可测解

可测函数类比连续函数类包含更多的函数.已知的结果是在连续函数类内,线性函数、指数函数、余弦函数、正弦函数可以分别被一组函数方程特征刻画.利用勒贝格积分的绝对连续性、勒贝格微分定理及卢津定理,证明在可测函数类内这些特征刻画仍然成立.

题组反思式教学在实变函数教学中的应用探究

题组反思式教学研究在中小学教学研究中经常出现,但对大学数学教学的研究很少.结合当前教育部针对师范专业师范认证的指标,以实变函数课程教学为例,探究了高校数学课堂教学中使用题组反思式教学的策略与方法,通过设计题组并引导学生反思的教学模式构建,丰富题组反思式教学模式在大学数学课程教学中的应用研究.

床旁血气分析结合即时超声对急诊创伤失血性休克抢救的应用研究

目的探讨床旁血气分析结合即时超声对急诊创伤失血性休克的应用效果。方法选取2022年1月至2023年4月于福州市第二总医院急诊创伤失血性休克患者100例,随机分为对照组(50例,常规对症治疗+常规液体复苏治疗)与观察组(50例,对照组基础上采用床旁血气分析结合床旁即时超声进行液体复苏治疗)。比较两组复苏状态[平均动脉压(MAP)、每小时尿量、心率(HR)]、血气指标[脉血氧分压(PaO_(2))、动脉血二氧化碳分压(PaCO_(2))、血乳酸(BL)、剩余碱(BE)及血酸碱度(pH)]、凝血指标[凝血酶原时间(PT)、活化部分凝血活酶时间(APTT)、凝血酶时间(TT)]变化,比较两组复苏24 h补液量及液体复苏治疗1周生存率。结果两组复苏前复苏状态、血气、凝血等指标比较,差异无统计学意义(P>0.05);复苏24 h,观察组HR、PaCO_(2)、BL、BE、PT、APTT、TT低于对照组,观察组MAP、每小时尿量、pH、PaO_(2)高于对照组,观察组复苏24 h补液量少于对照组,观察组1周生存率高于对照组,差异均有统计学意义(P<0.05)。结论床旁血气分析结合即时超声应用于急诊创伤失血性休克,有利于患者状态恢复,能够改善血气指标、凝血功能,提高整体疗效。

An isogeometric approach to free vibration analysis of bi-directional functionally graded porous doubly-curved shallow microshells with variable length-scale parameters

This study uses iso-geometric investigation,which is based on the non-uniform rational B-splines(NURBS)basis function,to investigate natural oscillation of bi-directional functionally graded porous(BFGP)doublycurved shallow microshells placed on Pasternak foundations with any boundary conditions.The characteristics of the present material vary in both thickness and axial directions along the x-axis.To be more specific,a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties.One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle,Kirchhoff-Love hypothesis,and modified couple stress theory.The numerical findings are reported for thin microshells that are spherical,cylindrical,and hyperbolic paraboloidal,with a variety of planforms,including rectangles and circles.The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances.In addition,influences of length scale parameters,power-law indexes,thickness-to-side ratio,and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail.

The Interannual Variability of Summer Rainfall in the Arid and Semiarid Regions of Northern China and Its Association with the Northern Hemisphere Circumglobal Teleconnection

Using the latest daily observational rainfall datasets for the period 1961–2008, the present study investigates the interannual variability of June–September （JJAS） mean rainfall in northern China. The regional characteristics of JJAS mean rainfall are revealed by a rotated empirical orthogonal function （REOF） analysis. The analysis identifies three regions of large interannual variability of JJAS rainfall： North China （NC）, Northeast China （NEC）, and the Taklimakan Desert in Northwest China （TDNWC）. Summer rainfall over NC is shown to have displayed a remarkable dry period from the late 1990s; while over NEC, decadal-scale variation with a significant decreasing trend in the last two decades is found, and over TDNWC, evidence of large interannual variability is revealed. Results also show that the interannual variability of JJAS rainfall in northern China is closely associated with the Northern Hemisphere circumglobal teleconnection （CGT）. Correlation coefficients between the CGT index and regional-averaged JJAS mean rainfall over NC and NEC were calculated, revealing values of up to 0.50 and 0.53, respectively, both of which exceeded the 99% confidence level.

Linkage Between Winter Temperatures in the Yellow Sea and Atmospheric Circulation Indices

This study investigated the linkage between winter temperature in the Yellow Sea(YS), China, and atmospheric indices and established this linkage through statistical models. The water temperature was obtained through hindcast simulation using a global–regional nested ocean model for the period of 1958–2007. The interannual variations of the simulated temperature were validated using satellite and in-situ observations. In the YS, the winter sea surface temperature(SST) had obvious interannual variations, with the maximum SST exceeding 2℃, and a significant shift from the cold to warm phase during 1988–1989. Based on the mechanism study, statistical models for the variations of water temperature in the YS were established using suitable atmospheric indices as predictors. For the northern YS(NYS) and the coastal region of the southern YS(SYS), statistical models of SST were established using linear regression based on the December–January–February mean Arctic oscillation index(AOI), representing the dominant large-scale atmospheric variability in boreal winter. For the YS warm current(YSWC) region, statistical models were established using both the AOI and the first principal component of the local wind stress curl(PC1-Curl), derived from the empirical orthogonal functions analysis. The PC1-Curl represents the influence of the local wind stress curl on the west-to-east shifts of the YSWC pathway. The applications proved that the models presented in this study have the ability to estimate winter temperatures in the YS within the recent years.

Detection Performance Analysis of Spectrum Sensing in Cognitive Radio Networks with Mobile Secondary Users

The majority of existing papers about spectrum sensing have the assumption that secondary users(SUs) are stationary. However,mobility is an essential feature of mobile communications networks. In this paper,the detection performance of spectrum sensing by mobile SUs was analyzed. Three performance metrics,i.e.,detection probability,miss detection probability and false alarm probability,were thoroughly investigated. In our analysis,a critical variable was the real-time received primary user signal power by a mobile SU. Its probability distribution and mathematical expectation were analytically derived. Moreover,the three performance metrics in single-node spectrum sensing and multi-node collaborative spectrum sensing systems were also derived. Extensive simulations were performed. The results are consistent with the theoretical analysis. And it is concluded that SU mobility has a significant impact on the detection probability and the miss detection probability,but not on the false alarm probability.

Subinterval Decomposition-Based Interval Importance Analysis Method

The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty.When an input variable is described by a specific interval rather than a certain probability distribution,the interval importance measure of input interval variable can be calculated by the traditional non-probabilistic importance analysis methods.Generally,the non-probabilistic importance analysis methods involve the Monte Carlo simulation(MCS)and the optimization-based methods,which both have high computational cost.In order to overcome this problem,this study proposes an interval important analytical method avoids the time-consuming optimization process.First,the original performance function is decomposed into a combination of a series of one-dimensional subsystems.Next,the interval of each variable is divided into several subintervals,and the response value of each one-dimensional subsystem at a specific input point is calculated.Then,the obtained responses are taken as specific values of the new input variable,and the interval importance is calculated by the approximated performance function.Compared with the traditional non-probabilistic importance analysis method,the proposed method significantly reduces the computational cost caused by the MCS and optimization process.In the proposed method,the number of function evaluations is equal to one plus the sum of the subintervals of all of the variables.The efficiency and accuracy of the proposed method are verified by five examples.The results show that the proposed method is not only efficient but also accurate.

Trends and Interannual Variability of Winds and Turbulent Heat Flux in the Indian Ocean Sector of Southern Ocean during 2000-2009

Using satellite-based wind and sea surface temperature (SST) observations, linear trend and inter-annual variability of wind stress, turbulent heat flux (Q) and wind stress curl are addressed for the Indian Ocean sector of the Southern Ocean (ISO, 0°E - 155°E) for the period 2000-2009. The analysis reveals that spatial mean of Q varies between 70 and 73 Wm-2 in the austral summer and winter, respectively, while the mean wind stress is nearly same at 0.22 Nm-2 for both seasons. The anticyclonic curl dominates the ISO, which increases from 0.15 × 10-7 to 0.35 × 10-7 Nm-3 during the austral summer. The detrended box-mean time series of Q, wind stress, and wind stress curl exhibits a decreasing trend of –6.3 ± 1.6 Wm-2·decade-1, -0.012 ± 0.004 Nm-2·decade-1 and -0.48 ± 0.6 × 10-8 Nm-3·decade-1, respectively. The Empirical Orthogonal Function (EOF) analysis was carried out to study inter-annual variability. EOF-1 of Q captures 25% of the total variance, which mimics the austral summer pattern;its time coefficient is highly and negatively correlated with a 2-month lagged Nino3.4 SST index (r =-0.8 at 95% confidence). EOF-1 of wind stress accounts for 35% of the total variance and its time coefficient is strongly correlated with the Antarctic Oscillation (r= 0.86 at 95% confidence). EOF-1 of wind stress curl captures 15% of the total variance;its time coefficient is correlated to the Nino3.4 SST index (r= 0.65 at 95% confidence) with the former lagging the latter by two years. The repercussions of the weakening trends of the climatic parameters on the air-sea interaction and ocean circulation are highlighted.

反例等在实变函数教学中的应用

实变函数是数学类专业最重要的专业课程之一。为提高该课程教学效果,充分发挥其育人功能,针对实变函数教学中普遍存在学生对基础知识理解不透彻、课程内涵建设不深入、学习途径单一等问题开展教学应用探索。首先,对实变函数中的反例进行分类,帮助学生更加深刻地理解基础知识。其次,增强实变函数课程的内涵建设,发挥其在提升学生数学素养和综合素养中的积极作用。最后,探索移动学习在实变函数教学中的应用,使其成为课程学习的新途径之一。教学实践表明,反例、内涵建设和移动学习在实变函数教学中发挥重要作用,取得良好的教育教学效果。