Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term

We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation.

Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics

In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc. We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the exp(−τ(ξ))-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the exp(−τ(ξ))-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.

NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS

The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.

ADER Methods for Hyperbolic Equations with a Time-Reconstruction Solver for the Generalized Riemann Problem: the Scalar Case

The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years,including both methodological aspects as well as very ambitious applications.In spite of methodological progress,the issues of efficiency and ease of implementation of the solution of the associated generalized Riemann problem(GRP)remain the centre of attention in the ADER approach.In the original formulation of ADER schemes,the proposed solution procedure for the GRP was based on(i)Taylor series expansion of the solution in time right at the element interface,(ii)subsequent application of the Cauchy-Kowalewskaya procedure to convert time derivatives to functionals of space derivatives,and(iii)solution of classical Riemann problems for high-order spatial derivatives to complete the Taylor series expansion.For realistic problems the Cauchy-Kowalewskaya procedure requires the use of symbolic manipulators and being rather cumbersome its replacement or simplification is highly desirable.In this paper we propose a new class of solvers for the GRP that avoid the Cauchy-Kowalewskaya procedure and result in simpler ADER schemes.This is achieved by exploiting the history of the numerical solution that makes it possible to devise a time-reconstruction procedure at the element interface.Still relying on a time Taylor series expansion of the solution at the interface,the time derivatives are then easily calculated from the time-reconstruction polynomial.The resulting schemes are called ADER-TR.A thorough study of the linear stability properties of the linear version of the schemes is carried out using the von Neumann method,thus deducing linear stability regions.Also,via careful numerical experiments,we deduce stability regions for the corresponding non-linear schemes.Numerical examples using the present simplified schemes of fifth and seventh order of accuracy in space and time show that these compare favourably with conventional ADER methods.This paper is restricted to the one-dimensional scalar case with source term,but preliminary results for the one-dimensional Euler equations indicate that the time-reconstruction approach offers significant advantages not only in terms of ease of implementation but also in terms of efficiency for the high-order range schemes.

Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers Equations

The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.

EXTENSION TO THE DIRECT METHODS AND APPLICATIONS TO THE GENERALIZED BURGERS EQUATION

A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.

An Application of Generalized Entropy Optimization Methods in Survival Data Analysis

In this paper, survival data analysis is realized by applying Generalized Entropy Optimization Methods (GEOM). It is known that all statistical distributions can be obtained as distribution by choosing corresponding moment functions. However, Generalized Entropy Optimization Distributions (GEOD) in the form of distributions which are obtained on basis of Shannon measure and supplementary optimization with respect to characterizing moment functions, more exactly represent the given statistical data. For this reason, survival data analysis by GEOD acquires a new significance. In this research, the data of the life table for engine failure data (1980) is examined. The performances of GEOD are established by Chi-Square criteria, Root Mean Square Error (RMSE) criteria and Shannon entropy measure, Kullback-Leibler measure. Comparison of GEOD with each other in the different senses shows that along of these distributions (MinMaxEnt)4 is better in the senses of Shannon measure and of Kullback-Leibler measure. It is showed that, (MinMaxEnt)3 ((MaxMaxEnt)4) is more suitable for statistical data among (MinMaxEnt)m,m=1,2,3,4(MaxMaxEnt)m,m=1,2,3,4. Moreover, (MinMaxEnt)3 is better for statistical data than (MaxMaxEnt)4 in the sense of RMSE criteria. According to obtained distribution (MinMaxEnt)3 (MaxMaxEnt)4 estimator of Probability Density Function?f^?(t), Cumulative Distribution Functio?F^ (t) , Survival Function Ŝ(t) and Hazard Rate ĥ(t) are evaluated and graphically illustrated. The results are acquired by using statistical software MATLAB.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

Generalized Maximum Fuzzy Entropy Methods with Applications on Wind Speed Data

This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.

A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Integration of GIS with the Generalized Reciprocal Method(GRM)for Determining Foundation Bearing Capacity:A Case Study in Opolo,Yenagoa Bayelsa State,Nigeria

This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region.Past research is limited and this study contributes valuable insights by integrating Geographic Information System(GIS)with the Generalized Reciprocal Method(GRM).To collect data,near-surface seismic refraction surveys were conducted along three designated lines,utilizing ABEM Terraloc Mark 6 equipment,Easy Refract,and ArcGIS 10.4.1 software.This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites.The results revealed three distinct geoseismic layers.The uppermost layer,within a depth of 0.89 to 1.50 meters,exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus,shear modulus,N-value,ultimate bearing capacity,and allowable bearing capacity.This indicates the presence of unsuitable,soft,and weak alluvial deposits for substantial structural loads.In contrast,the second layer(1.52 to 3.84 m depth)displayed favorable geotechnical parameters,making it suitable for various construction loads.The third layer(15.00 to 26.05 m depth)exhibited varying characteristics.The GIS analysis highlighted the unsuitability of the uppermost layer for construction,while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design.In summary,this study highlights the importance of geotechnical surveys in Opolo’s construction planning.It offers vital information for informed choices,addresses issues in the initial layer,and suggests secure,sustainable construction options.

智能助产术教学法——以“智能苏格拉底会话机器人”教学实践为例

当前,生成式人工智能与学生的人机会话主要是“知识讲述”型会话关系,这会影响学生的高阶思维能力发展。解决这一问题的关键是,如何将人机“知识讲述”型会话关系,转变为“知识转化”型会话关系。为此,研究者以助产术理论、ChatGPT、学习分析和腾讯QQ工具为基础,探索智能助产术教学法的学习发生机制,开发智能苏格拉底会话机器人,构建智能助产术教学模式。本研究采用准实验方法,以“远程教育学”课程为教学内容,以教育技术学专业本科生为对象,开展以智能会话机器人支持的教学实验。实验结果表明,智能助产术教学与直接使用ChatGPT的教学相比,能显著提升学生的问题解决能力、创新能力和协作学习能力,但是对学习绩效、批判性思维能力和自我效能感的影响不显著。为提高教学效果,研究者需提升计算机的系统算力,开发批判性思维学习支架,构建人机适切性互动机制,研制自我效能感提升策略。

基于结构性问题培养全科医生深度思考能力的方法研究

背景住院医师规范化培训的全科学员在各临床专科轮转时间短暂,学习内容宽泛,需要增强学习自主性。全科师资会面临不同背景学员,如5+3、转岗、专业硕士,或3+2助理全科、实习医生、公共卫生学员等,如何在培训中,使不同培训对象能各取所需,达到应有培训效果,需要认真研究。目的探索基于结构性问题的培训方式,提高学员学习主动性,培养其深度思考能力的作用。方法选取2020年江苏省全科/助理全科骨干师资培训班(骨干师资班)和基层卫生人才能力提升培训班(基层人才班)的学员作为研究对象。在每次学习活动结束,即刻组织学员讨论,要求依次回答“通过学习1.你学到了什么?2.还有哪些疑问?3.既往有什么相同或者类似的经验与大家分享?4.对今后工作的启发?”根据上述问题思路自行设计调查问卷调查培训学员对结构性问题培训方式的认同度,分为第1部分一般资料,包括性别、学历、职称、工作单位、岗位、工作年限、参与培训的项目等;第2部分是对“问题1、问题2、问题3、问题4和培训形式5”的解释性问题,5个维度共计20个条目,备选项是四等级,赋值为“1=非常同意,2=同意,3=不太同意,4=完全不同意”。结果培训对象对所有条目选择同意与非常同意的百分比均大于95%。不同性别、年龄、职称、岗位、工作年限培训学员等对结构性问题培训方法的认同程度比较,差异无统计学意义(P>0.05);不同学历、工作单位和培训项目培训学员对结构性问题培训方法的认同程度比较,差异有统计学意义(P<0.05)。相较于研究生及以上学历,本科培训对象对问题3、问题4的认同程度更高(P<0.05)。相较于三级医院,城市社区卫生服务中心(乡镇卫生院)和二级医院的培训对象对于问题1~4认同程度更高(P<0.05)。相较于骨干师资班,基层人才班的培训对象对于问题1~4及培训形式5认同程度更高(P<0.05)。结论培训实践中总结出的四个开放式问题,内容简单,含义递进,具有内在联系。运用结构性问题培训全科学员,形式灵活,能够激发被培训者的深度思考,该方法在基层卫生人才培训班获得更高的认可程度,表明适用于全科医生的培养。

5A教学模式在普通外科住院医师规范化培训中的应用

目的探讨5A教学模式在普通外科住院医师规范化培训中的应用效果。方法采用随机对照研究方法,以2020年1月至2022年12月在解放军总医院第一医学中心普通外科医学部接受住院医师规范化培训并进入本研究团队主诊组轮转学习的学员为研究对象,随机分为试验组和对照组。试验组20名,采用5A教学模式;对照组20名,采用传统教学模式。对2组学员进行理论考核、临床技能考核和综合能力考核,记录考核成绩,并比较2组的教学效果。结果相对于对照组,试验组学员在消毒铺巾、切开缝合和腔镜技能考核3个方面的成绩得到提高,差异有统计学意义(P<0.05);试验组学员在团队协作和科学研究2个方面的成绩高于对照组,差异有统计学意义(P<0.05);试验组学员带教满意度高于对照组,差异有统计学意义(P<0.05)。结论5A教学模式可以显著提高学员的临床实践操作、团队协作和科学研究能力,可作为普通外科住院医师规范化培训的有效教学方法。

Seminar教学法在《全科医学概论》课程中的应用研究

目的:在《全科医学概论》的教学中应用Seminar教学法,探讨该教学法的应用效果。方法:从开设《全科医学概论》的佳木斯大学临床医学专业四年级本科生中选取160人作为研究对象,将学生随机分为对照组、实验组各80人。其中,对照组根据教学大纲的要求实施传统教学法,实验组应用Seminar教学法进行教学。比较分析两组学生学习效果及对教学的满意度。结果:与对照组相比,实验组学生、学习效果(课堂氛围、文献检索能力、思维拓展能力、知识的接受程度、自主学习能力、对未来从事全科医疗充满兴趣)以及学生对教学满意度均高于对照组(P<0.05)。结论:在《全科医学概论》课程教学中,应用Seminar教学法进行教学,可以激发医学生自主学习、研讨的主观能动性,有效提高学习效果并增加教学满意度。

主动配电网潮流的全纯嵌入计算方法

配电网潮流计算是进行配电网规划和运行的重要基础。目前,配电网潮流求解方法主要有牛拉(Newton Raphson,NR)法和前推回代(forward backward substitution,FBS)法两大类,但NR法和FBS法在潮流收敛性和计算效率等方面均存在一定的不足。全纯嵌入法(holomorphic embedding method,HEM)是一种求解非线性潮流方程的新方法,它可以有效避免NR法和FBS法在配电网潮流求解过程中出现的上述问题,但现有HEM未充分考虑配电网中各类型分布式电源(distributed generation,DG)和智能软开关(soft open point,SOP)控制方式的多样性,且未构建计及负荷电压特性和频率特性的潮流模型,难以适用于不同运行模式下配电网潮流计算。针对上述问题,提出一种可求解含多类型DG和SOP且可运行在并网/孤岛模式的主动配电网统一全纯嵌入潮流计算方法。首先,根据负荷静态电压和频率特性,构建计及配电网频率和节点电压影响的负荷节点全纯嵌入潮流模型;其次,根据DG不同的控制方式以及配电网不同的运行模式,将DG所连节点等效为不同节点类型,构建各类DG的全纯嵌入潮流模型;再次,考虑SOP不同控制方式,构建SOP全纯嵌入潮流模型;从次,依据全纯嵌入潮流模型等式左右两侧同次幂级数系数相等原则,推导配电网各全纯函数幂级数系数的求解递推关系式,进而计算各全纯函数的各项幂级数系数,借助解析延拓理论求取电压和频率逼近值,实现配电网潮流的准确求解;最后,通过修改的IEEE-33节点测试系统和IEEE-123节点测试系统验证所提方法准确性和有效性。

Sora变革教育:基于教师角色与学习方式的洞见

生成式人工智能的发展又迎来重大飞跃,具有“通用物理世界模拟器”潜力的文生视频模型——Sora被推出。技术的革新势必对教育领域产生重大影响,Sora对教师角色的影响如何?又将为学习方式带来哪些变革?回答好这两个问题是推动Sora变革与赋能教育领域的关键。基于此,本研究在对Sora进行本质解析的基础上,分析Sora对教师角色产生的影响,包括Sora对教师角色挑战的冲击、Sora变革下教师何为的应对以及Sora与教师协同发展的共进;接着提出Sora对学习方式的变革,包括进行“可想即可见”的学习、虚实融合学习的升级、人机协同学习的革新、促进创造性学习实现以及丰富个性化学习形态等;最后对Sora变革教育进行审思与展望,包括Sora的教育边界确立、Sora的使用标准建立、Sora应用的算力需求以及开发教育专属Sora模型。研究以期促进Sora有效应用于教育领域,提升学习效果与质量。