AN INVESTIGATION ON TWO CRACKS PERPEN DICULAR TO THE INTERFACES IN A PIEZOE LECTRIC LAYER BONDED TO TWO HALF SPACES BY THE SCHMIDT METHOD

The behavior of two collinear anti-plane shear cracks in a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

The forecasting efficiency under different selected regions by Pattern Informatics Method and seismic potential estimation in the North-South Seismic Zone

In 2022,four earthquakes with M_(S)≥6.0 including the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes occurred in the North-South Seismic Zone(NSSZ),which demonstrated high and strong seismicity.Pattern Informatics(PI)method,as an effective long and medium term earthquake forecasting method,has been applied to the strong earthquake forecasting in Chinese mainland and results have shown the positive performance.The earthquake catalog with magnitude above M_(S)3.0 since 1970 provided by China Earthquake Networks Center was employed in this study and the Receiver Operating Characteristic(ROC)method was applied to test the forecasting efficiency of the PI method in each selected region related to the North-South Seismic Zone systematically.Based on this,we selected the area with the best ROC testing result and analyzed the evolution process of the PI hotspot map reflecting the small seismic activity pattern prior to the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes.A“forward”forecast for the area was carried out to assess seismic risk.The study shows the following.1)PI forecasting has higher forecasting efficiency in the selected study region where the difference of seismicity in any place of the region is smaller.2)In areas with smaller differences of seismicity,the activity pattern of small earthquakes prior to the Menyuan M_(S)6.9 and Luding M_(S)6.8 earthquakes can be obtained by analyzing the spatio-temporal evolution process of the PI hotspot map.3)The hotspot evolution in and around the southern Tazang fault in the study area is similar to that prior to the strong earthquakes,which suggests the possible seismic hazard in the future.This study could provide some ideas to the seismic hazard assessment in other regions with high seismicity,such as Japan,Californi,Turkey,and Indonesia.

Research on the Application of Montessori Education Method in Cognitive Training of Patients with Alzheimer’s Disease

Objective:To study the application of the Montessori education method in cognitive training in patients with Alzheimer’s disease(AD).Methods:40 cases of senile dementia patients who were admitted to our hospital from January 2022 to January 2023 were selected and randomly divided into an intervention group and a control group according to the single and double number table method,with 20 cases in each group.The intervention group used the Montessori education method,the principle of which was to implement individualized health interventions based on the individual conditions of the patients,for a period of 6 months;the control group was given conventional treatment and nursing of the disease.The Mini-Mental State Examination(MMSE)was used to compare the effects of the two groups of patients before and after health intervention and conduct statistical analysis.Results:The score of the intervention group was higher than that of the control group,and there was a statistical difference between the two(P<0.05).Conclusion:Implementing the Montessori education method for diagnosed Alzheimer’s patients can effectively improve their cognitive function and delay the progress of further dementia.

Solid Waste Management:A MADM Approach Using Fuzzy Parameterized Possibility Single-Valued Neutrosophic Hypersoft Expert Settings

The dramatic rise in the number of people living in cities has made many environmental and social problems worse.The search for a productive method for disposing of solid waste is the most notable of these problems.Many scholars have referred to it as a fuzzy multi-attribute or multi-criteria decision-making problem using various fuzzy set-like approaches because of the inclusion of criteria and anticipated ambiguity.The goal of the current study is to use an innovative methodology to address the expected uncertainties in the problem of solid waste site selection.The characteristics(or sub-attributes)that decision-makers select and the degree of approximation they accept for various options can both be indicators of these uncertainties.To tackle these problems,a novel mathematical structure known as the fuzzy parameterized possibility single valued neutrosophic hypersoft expert set(ρˆ-set),which is initially described,is integrated with a modified version of Sanchez’s method.Following this,an intelligent algorithm is suggested.The steps of the suggested algorithm are explained with an example that explains itself.The compatibility of solid waste management sites and systems is discussed,and rankings are established along with detailed justifications for their viability.This study’s strengths lie in its application of fuzzy parameterization and possibility grading to effectively handle the uncertainties embodied in the parameters’nature and alternative approximations,respectively.It uses specific mathematical formulations to compute the fuzzy parameterized degrees and possibility grades that are missing from the prior literature.It is simpler for the decisionmakers to look at each option separately because the decision is uncertain.Comparing the computed results,it is discovered that they are consistent and dependable because of their preferred properties.

Critical care nurses and their clinical reasoning for customizing monitor alarms:a mixed-method study

Objective:To explore the clinical rationale of critical care nurses for personalizing monitor alarms.One of the most crucial jobs assigned to critical care nurses is monitoring patients'physiological indicators and carrying out the necessary associated interventions.Successful use of equipment in the nursing practice environment will be improved by a thorough understanding of the nurse's approach to alarm configuration.Methods:A mixed-method design integrating quantitative and qualitative components was used.The sample of this study recruited a convenience sample of 60 nurses who have worked in critical care areas.This study took place at Lebanese American University Medical Center Rizk Hospital,utilizing a semi-structured interview with participants.Results:The study demonstrated the high incidence of nuisance alarms and the desensitization of critical care nurses to vital ones.According to the nurses,frequent false alarms and a shortage of staff are the 2 main causes of alarm desensitization.Age was significantly associated with the perception of Smart alarms,according to the data(P=0.03).Four interconnected themes and subcategories that reflect the clinical reasoning process for alarm customization were developed as a result of the study's qualitative component:(1)unit alarm environment;(2)nursing style;(3)motivation to customize;and(4)clinical and technological customization.Conclusions:According to this study,nurses believe that alarms are valuable.However,a qualitative analysis of the experiences revealed that customization has been severely limited since the healthcare team depends on nurses to complete these tasks independently.Additionally,a staffing shortage and lack of technical training at the start of placement have also hindered customization.

基于修正Gram-Schmidt法的双连通区域数值保角逆变换计算法

研究基于模拟电荷法的双连通区域的数值保角逆变换问题。利用修正Gram-Schmidt法求解双连通区域数值保角逆变换中的约束方程组,解得模拟电荷量和逆变换半径,构造出近似保角逆变换函数。通过数值实验验证算法的有效性。

基于Gram-Schmidt正交法的矩阵并行QR分解算法

分析了线性无关向量组的Gram-Schmidt正交化过程以及矩阵的QR分解原理。在多核架构的微机中,设计实现了一种基于Gram-Schmidt正交法的矩阵QR多核并行分解算法。新算法易于计算机编程实现,数值实验也验证了算法具有良好的并行性。

基于Schmidt正交化的快速求逆法

基于Schmidt正交化过程获得了一种计算逆矩阵的新方法.对于可逆矩阵A,有Q=MA,其中Q是酉矩阵,M是下三角矩阵.本文直接从Schmidt规范正交化出发,获得下三角矩阵M的计算公式,从而求得逆矩阵A-1=QHM=AHMTM.

基于重排S-method的多分量辐射源信号分析方法

为实现多分量辐射源信号的有效检测和识别,提出了基于重排S-method(RSM)的多分量辐射源信号分析方法.针对Wigner-Ville分布交叉项严重和计算复杂度高的问题,采用RSM分析密集、交叠的辐射源信号,给出了其算法的硬件实现和计算复杂度分析.该方法能处理线性和非线性调频信号,算法简单,易于实现.复杂体制多分量辐射源信号分析的实验结果表明,该方法能有效分析多分量辐射源信号,时频分辨率高,不受交叉项干扰,具有比Wigner-Ville分布和S-method更强的噪声抑制能力.

基于S-method的多分量雷达辐射源信号检测

针对传统时频方法在处理多分量雷达辐射源信号时存在交叉项,不能检测各分量信号时域参数,难以适应低信噪比环境的问题,提出一种基于S-method(SM)的多分量雷达辐射源信号检测新方法。该方法首先计算信号的SM时频分布,然后在时频面的基础上检测各信号分量的瞬时频率和脉冲起止时间。实验结果表明,该方法能处理线性及非线性调频信号、时频分辨率高且不受交叉项干扰,时域检测精度大于98.60%,频域检测精度大于99.48%,信噪比降低时仍然保持强检测能力。

基于Gram-Schmidt正交法的电力线背景噪声建模

噪声干扰是影响电力线通信可靠性的最主要因素之一。文章建立了实测背景噪声的AR模型,提出用Gram-Schmidt正交法进行模型参数求解,并与奇异值分解法、LD递推法所得结果进行仿真比较。结果表明:Gram-Schmidt正交法所得结果精确度与奇异值分解法所得结果相近,且计算时间较短,模型较简单,在背景噪声的离线计算及在线生成中均可广泛应用。

Comparative Analysis of Improving Effects of 12 Maize Populations with Improved S_1 Selection Method

ln this study, 12 maize populations were improved with the improved S1 selection method, aiming to increase the improvement efficiency of maize popula-tions. The results showed that number of rows per spike, number of grains per row and 100-grain weight were the three important component traits of maize yield. The highest genetic increment was found in Mengqun 2, fol owed by Mengqun 4, Mengqun 1 and other 7 maize populations. Negative genetic increment was shown in Mengqun 3 and 3 introduced foreign maize populations. Some changes were shown in spikes, plant traits and genetic diversity of maize populations. Based on our results, we concluded that Mengqun 2, Mengqun 4, Zhongzong 7, Mengqun C and Mengqun A could be directly used for the line breeding by selfing for their higher genetic increment of yield and better improvement effects of other agricultural traits. Compared with these 5 populations, the improvement potential of other maize populations was limited for their lower genetic increment.

LU分解与广义Schmidt正交化方法

利用对称内积的Schmidt正交化方法证明了各阶主子式不为零对称阵的LDLT分解.引入两个向量组关于弱内积广义正交的概念,并构造了将两组含相同个数向量的线性无关组化为广义正交组的广义Schmidt正交化方法.最后应用这一方法证明了各阶主子式不为零矩阵的LDU分解及一些相关的结果.

基于Liapunov-Schmidt方法的局部静态分叉控制

针对某一类非线性系统 (在临界情况下 ,其线性化系统具有单个的零特征根 ) ,讨论了局部静态分叉控制问题 .首先 ,证明了临界非线性系统的局部静态分叉控制和局部稳定性之间的等价性 ;然后 ,利用 LS方法对原非线性系统进行约化 ,导出一个低阶的系统 ,在一定的条件下 ,此低阶系统与原系统的稳定性一致 ;最后 ,对约化后的低阶系统实施合适的局部状态反馈 ,使其局部渐近稳定 ,易知原非线性系统也局部渐近稳定 .从而实现了非线性系统的局部静态分叉控制 .

ADASYN与类别逆比例加权法在阿尔茨海默病不平衡数据中的应用

目的利用自适应合成抽样(adaptive synthetic sampling,ADASYN)与类别逆比例加权法处理类别不平衡数据,结合分类器构建模型对阿尔茨海默病(alzheimer′s disease,AD)患者疾病进程进行分类预测。方法数据源自阿尔茨海默病神经影像学计划(Alzheimer′s disease neuroimaging initiative,ADNI),经随机森林填补缺失值,弹性网络筛选特征子集后,利用ADASYN与类别逆比例加权法处理类别不平衡数据。分别结合随机森林(random forest,RF)、支持向量机(support vector machine,SVM)构建四种模型:ADASYN-RF、ADASYN-SVM、加权随机森林(weighted random forest,WRF)、加权支持向量机(weighted support vector machine,WSVM),与RF、SVM比较分类性能。模型评价指标为宏观平均精确率(macro-average of precision,macro-P)、宏观平均召回率(macro-average of recall,macro-R)、宏观平均F1值(macro-average of F1-score,macro-F1)、准确率(accuracy,ACC)、Kappa值和AUC(area under the ROC curve)。结果ADASYN-RF的分类性能最优(Kappa值为0.938,AUC为0.980),ADASYN-SVM次之。利用ADASYN-RF预测得到的重要分类特征分别为CDRSB、LDELTOTAL、MMSE,在临床上均可得到证实。结论ADASYN与类别逆比例加权法都能辅助提升分类器性能,但ADASYN算法更优。

基于S-R和分解定理的二维几何非线性问题的虚单元法求解

应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。

基于ST-CNN的脉冲型地震动与脉冲周期融合识别方法

如何快速准确地识别脉冲型地震动是困扰学术界和工程界的关键难题,定量识别方法虽然能够克服人工识别的经验性限制,但是传统定量识别方法存在识别结果不一致、适用范围不广泛、难以同时识别脉冲周期或识别的脉冲周期部分情况下差异明显等问题。为此建立了一种问题针对性融合学习规则并结合卷积神经网络(CNN),开发出了一种新的脉冲型地震动与脉冲周期同步识别方法。该学习规则通过对基于不同识别原理的多个传统典型识别方法进行融合学习并采用全球范围的30000条任意方向地震动数据进行训练和验证,摒弃了以往繁琐的人工标记过程并得到了3个问题针对性识别模型,分别命名为Strict识别模型、General识别模型以及TP识别模型。除此之外,为解决地震动时序输入信息不足从而导致模型泛化能力较弱的问题,对CNN的输入结构进行了优化增强,提出了ST-CNN模型。其引入了S变换层以将地震动时序变换至时频,从而增加了频域分布信息并进一步提高了识别精度。结果表明:Strict识别模型能严格区分脉冲型与非脉冲型地震动,识别结果得到已有方法的一致认可;General识别模型的识别能力更强,适用范围更加广泛;TP识别模型识别的脉冲周期更加准确,并可与前述识别模型并用以同步输出识别结果。提出的问题针对性融合学习规则还可推广至其他工程领域与其他机器学习模型,建立的识别方法可为脉冲型地震动研究提供科学指导。

基于S-Method分布的微多普勒特征分析

微多普勒特征是雷达目标所具有的独特特征之一,对目标的分类、识别具有特殊的意义。研究高精度时频分析方法在分析目标微动特性中的作用,可以为后续目标识别提供很好的支撑。S-Method分布作为一种新型的时频分析方法,它基于短时傅里叶变换来实现,减少了分析过程中的运算量,同时能较好地解决交叉项问题。首先对弹道导弹弹头的微动模型进行建模,推导得到微动模型的理论微多普勒频率,然后采用S-Method分布对回波信号进行时频分析仿真实验,获得弹头目标章动的高精度的时间-微多普勒频率图。通过比较其在分析过程中的时频分辨率、交叉项,具体阐述S-Method分布在时频分析中的优势。因此可以将S-Method分布应用于雷达目标微多普勒分析中,分析实时变化的微多普勒频率特征。