Degeneracy Cases of Generalized Inverse Function-Valued Padé Approximation

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.

Orthogonal Polynomials and Padé Approximation

The diagonal Padé approximants for exp ( x ), tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on P r1 (x) is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used to find the denominators of some functions.

A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

“PAD+OBE”驱动下本科课堂教学探索与实践——以“大气污染控制工程”为例

“大气污染控制工程”是环境科学与工程专业的一门核心课程。为解决教学中现有问题,以充分调动学生主体性和积极性,采用对分课堂(PAD)和成果导向教育(OBE)混合教学,以期实现教学目标。通过重构教学体系,融入思政教育,优化反馈机制,构建完整的教学闭环,有效提升了教学效果。在课程实践中,强化学生知识体系,提高创新协作能力,从而培养高素质大气环境类人才,满足地方和国家层面大气污染防控战略需求。该教学模式为厘清大气污染成因及治污提供基础,也为推进本科“双万计划”提供经验及借鉴范例。

PAD Class教学模式对英语专业学生写作焦虑影响的实证研究

本研究以英语专业大一120名学生为实验对象,进行了为期16周的实证研究,以探讨PAD class教学模式对英语专业学生写作焦虑的影响。基于《二语写作焦虑量表》调查问卷结果表明:英语专业学生总体焦虑处于中等焦虑水平,PAD Class能有效降低学生的写作总体焦虑,其中课堂焦虑、构思焦虑、自信焦虑明显降低,但回避焦虑没有达到显著水平;PAD Class模式对高中低不同写作水平学生的写作焦虑都有影响,对中、低水平学生的写作焦虑缓解比对高水平学生的影响效果更明显。

BOPPPS教学模式结合PAD课堂在“生物化学”课程教学中的探索研究

以黄山学院生物技术专业“生物化学”课程教学为例,介绍了BOPPPS教学模式结合PAD课堂开展“生物化学”课程教学的实施过程。BOPPPS和PAD课堂实践相结合,提升了学生在课堂上的参与度、积极性和主动性;通过PAD课堂隔堂讨论的“亮考帮”环节,一定程度上提升了学生的思维创新能力;通过案例以问题的方式作为BOPPPS教学模式的导入环节,PAD课堂思考题布置作为BOPPPS的前测环节,驱动学生必须进行有效思考来剖析案例和解决问题,一定程度上提升了课程的高阶性、创新性和挑战度;把提升学生学习自主性、积极性作为课程教学目的,科学实施和评价教学过程关键环节,形成重在培养创新能力的教学模式。BOPPPS教学模式与PAD课堂进行有机结合,可以塑造以学为中心,以能力达成为目标的课程教学模式,提升“生物化学”课程的教学效果。

ON COEFFICIENT POLYNOMIALS OF CUBIC HERMITE-PADé APPROXIMATIONS TO THE EXPONENTIAL FUNCTION

The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.

BOPPPS+PAD课堂教学在诊断学理论教学中的应用研究

目的 探索BOPPPS+PAD课堂在诊断学理论教学中的教学效果。方法 选取广西中医药大学2018级中医学、2018级临床医学、2019级中医学、2019级临床医学专业的本科生共328人,随机将其分为A组(传统教学模式)、B组(BOPPPS教学模式)、C组(PAD课堂教学模式)和D组(BOPPPS+PAD课堂教学模式),每组各82人。比较各组学生的理论成绩、教学满意度和教学参与度。结果 四组学生的理论成绩比较差异有统计学意义(F=59.959,P<0.05),其中D组学生成绩最好。四组学生的教学满意度比较差异有统计学意义(Z=29.908,P<0.001),D组学生的教学满意度优于A组和C组(P<0.05)。D组和B组学生的参与度评分比较差异无统计学意义(P=0.302),D组学生的参与度评分显著高于C组和A组(P<0.05)。相比于传统教学方法,BOPPPS+PAD课堂教学模式在激发学习兴趣、提高自主学习能力、团队合作、创新力和内驱力等方面均获得较好的评价。结论 BOPPPS+PAD课堂教学模式可提高诊断学理论教学的教学质量和教学效果,提高教师对课堂的把控,激发学生的学习积极性,值得进一步推广应用。

“制药资源野外实习”课程教学改革与探索——基于OBE理念和PAD课堂

科学设计实验、合理安排实习项目、优化过程管理会影响到人才培养质量的提高。本文在深入分析现有教学模式不足的基础上,结合地方实际情况,提出并实施了切实可行的改进举措。具体包括:1.整合畲药植物资源,编写实习指导手册;2.将OBE教学理念和PAD课堂深度融入实习各个环节,发挥学生的主观能动性;3.充分挖掘课程思政元素,使课程思政深入人心。通过课程教学模式的改革与实践,我们期望本校的《制药资源野外实习》课程教学质量能得到进一步提升。

对分课堂(PAD)导引下的思政课教学创新整体设计

对分课堂是一种新型的教学模式,其核心理念是把一半课堂时间分配给教师讲授,另一半分配给学生进行交互式学习。对分课堂应用于思政课教学,能够解决思政课教学改革中教学分离、教师无奈、学生无力的问题,更加体现出学生“主体型”学习地位,有效提升思政课的教学效果和质量。反映到具体的思政课对分课堂教学设计,就是要重构教学生态,重点关注思政课教学主体的变化;重塑教学组织,重点关注思政课教学条件的变化;重整教材资源,重点关注思政课教学内容的变化;重组教学实施,重点关注思政课教学流程的变化;重建教学评价,重点关注思政课教学考核的变化。

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

PAD融合式教学改革在中医妇科学的应用

中医妇科学是中医药院校的一门专业基础课程,目前的课堂教学仍存在理论与临床未能有效衔接的教学困境。为了提高学生的学习兴趣与教学质量,作者结合对分课堂(PAD)教学模式,融入“以学生为中心”的教学理念,把教学过程分为讲授、吸收、讨论三个环节,并配合相应的作业、考核评价体系,在实际教学中进行了探索应用。通过课程问卷调查及课程考核结果发现,对分课堂融合式教学改革通过将理论知识与医案教学、临床接诊模拟相结合,极大地调动了学生学习的积极性、主动性,提高了学习效果与教学质量,表明对分课堂是提高中医妇科学教学质量有效的教学方法之一。

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.