ON A FAMILY OF CHEBYSHEV-HALLEY TYPE METHODS IN BANACH SPACE UNDER WEAKER SMALE CONDITION

In this paper, we discuss local convergence of a family of Chebychev Halley type methods with a parameter θ∈[0,1] in Banach space using Smale type δ criterion under 2 th γ condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.

New Ninth Order J-Halley Method for Solving Nonlinear Equations

In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.

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.

An Inexact Halley's Method

An inexact Halley＇s method-Halley-PCG（preconditioned conjugate gradient） method is proposed for solving the systems of linear equations for improved Halley method either by Cholesky factorization exactly or by preconditioned conjugate gradient method approximately. The convergence result is given and the efficiency of the method compared to the improved Halley＇s method is shown.

2021年9月16日四川泸县M_(S)6.0地震前地磁扰动异常特征分析

选取四川地区3个地磁扰动台站的观测数据,利用基于脉冲幅度法的地磁垂直强度极化方法,对2021年9月16日四川泸县M_(S)6.0地震前的地磁扰动异常演化特征进行分析。研究结果表明:(1)在中强地震前,台站的垂直强度极化值和超阈值极化值频次逐日变化均会出现高值异常,其中频次异常呈现先增强后降低,再增强-降低的形态;(2)发生异常变化的多个台站距离震中300 km范围内,时间上属准同步变化;(3)地震多发生在异常出现的一个月后,频次异常值往往是研究时段的最高值;(4)机理上,这些异常演化形态和特征是由岩石的破裂特性决定的,一定程度上反映了地震的孕育过程;(5)这种震前的地磁扰动异常与外源场无关。

THE ERROR ESTIMATES OF HALLEY'S METHOD

In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.

The Convergences Comparison between the Halley’s Method and Its Extended One Based on Formulas Derivation and Numerical Calculations

The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.

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.

Effects of King’s Theory of Goal Attainment Combined with Teach-Back Method on Improving Patients’ Standardization Rate of Eye Drop Use

Objective:To explore the effect of King’s Theory of Goal Attainment combined with teach-back method on improving the standardization rate of eye drop use in patients.Methods:A total of 200 patients who used more than two types of eye drops in the Department of Ophthalmology of our hospital were selected as the research subjects,and were randomly divided into an observation group and a control group.The control group was given routine health education,while the observation group was given King’s Theory of Goal Attainment combined with teach-back method on the basis of the control group.The standardization rate of eye drop use,knowledge awareness rate,and nursing satisfaction were compared between the two groups before and after the intervention.Results:After the intervention,the standardization rate of eye drop use,the awareness rate of eye drop knowledge,and the nursing satisfaction of the observation group were significantly higher than those of the control group(P<0.05).Conclusion:King’s Theory of Goal Attainment combined with teach-back method can effectively improve the standardization rate of eye drop use in patients,increase their awareness of eye drop knowledge,and improve nursing satisfaction,which is worthy of clinical application.

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.

Exploration of the Methods and Insights in the Introduction to Critique of Hegel’s Philosophy of Right

Marx,as one of the founders of Marxism,experienced a significant transformation in his thought during the period of 1843-1844.The Introduction to Critique of Hegel’s Philosophy of Right(hereafter referred to as the Introduction)is one of Marx’s most representative works from this time.Lenin noted that this text,along with Marx’s On the Jewish Question,marks Marx’s transition from idealism and revolutionary democracy to materialism.In this renowned text,Marx offers a rational critique of the absolute authority of religion,articulates a vision for human emancipation,and envisages the possibility of free and comprehensive human development.During this intellectual shift,Marx absorbed the essence of German classical philosophy and,from a positivist perspective,began employing critical thinking and materialist expression.This enabled him to embark on a path of critique addressing both the religious and real social worlds.In the new era,systematically studying Marxist classic works allows for the exploration of their contemporary relevance.By aligning these classics with specific directions outlined in reports such as those from the 20th CPC Central Committee’s Third Plenary Session,the vitality of these works can be reinvigorated for the modern age.

基于谱比法的近海地震动S-net台站场地分类研究

近海台站往往难以获得台站场地资料,并且海域场地工程特性是海洋重大工程设计、建造和运维的基础,也是研究海域地震动场地放大的重要参数。为了解决这一问题,基于日本海沟区域的S-net台网的150个台站的强地震动数据,得到了埋置和未埋台站的H/V谱比曲线并进行了场地分类。结果表明:海域的H/V谱比曲线有较大谱比值;各个场地类别的埋置和未埋台站的H/V谱比曲线在谱比值和谱比形状存在着巨大差异;震级和震中距对长周期的H/V谱比曲线有较大影响,震源深度对H/V谱比曲线几乎没有影响。研究成果可为海域地震动模拟、海域场地效应研究和海洋工程建设等提供参考。

A Nonstationary Halley’s Iteration Method by Using Divided Differences Formula

This paper presents a new nonstationary iterative method for solving non linear algebraic equations that does not require the use of any derivative. The study uses only the Newton’s divided differences of first and second orders instead of the derivatives of (1).

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。

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.

解非线性方程的一族修正Chebyshev-Halley迭代方法

提出一族求解非线性方程的修正Chebyshev-Halley迭代方法.该方法避免了计算函数的二阶导数,且具有至少三阶收敛的性质,当参数选取特殊值时,可以得到四阶收敛方法.收敛性分析和数值实验结果表明,该方法与具有同阶收敛性质的算法相比效率更高.

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。