An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems

This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Association of preschool children behavior and emotional problems with the parenting behavior of both parents

BACKGROUND Parental behaviors are key in shaping children’s psychological and behavioral development,crucial for early identification and prevention of mental health issues,reducing psychological trauma in childhood.AIM To investigate the relationship between parenting behaviors and behavioral and emotional issues in preschool children.METHODS From October 2017 to May 2018,7 kindergartens in Ma’anshan City were selected to conduct a parent self-filled questionnaire-Health Development Survey of Preschool Children.Children’s Strength and Difficulties Questionnaire(Parent Version)was applied to measures the children’s behavioral and emotional performance.Parenting behavior was evaluated using the Parental Behavior Inventory.Binomial logistic regression model was used to analyze the association between the detection rate of preschool children’s behavior and emotional problems and their parenting behaviors.RESULTS High level of parental support/participation was negatively correlated with conduct problems,abnormal hyperactivity,abnormal total difficulty scores and abnormal prosocial behavior problems.High level of maternal support/participation was negatively correlated with abnormal emotional symptoms and abnormal peer interaction in children.High level of parental hostility/coercion was positively correlated with abnormal emotional symptoms,abnormal conduct problems,abnormal hyperactivity,abnormal peer interaction,and abnormal total difficulty scores in children(all P<0.05).Moreover,paternal parenting behaviors had similarly effects on behavior and emotional problems of preschool children compared with maternal parenting behaviors(all P>0.05),after calculating ratio of odds ratio values.CONCLUSION Our study found that parenting behaviors are associated with behavioral and emotional issues in preschool children.Overall,the more supportive or involved the parents are,the fewer behavioral and emotional problems the children experience;conversely,the more hostile or controlling the parents are,the more behavioral and emotional problems the children face.Moreover,the impact of fathers’parenting behaviors on preschool children’s behavior and emotions is no less significant than that of mothers’parenting behaviors.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Problems and Development Suggestions of Nature Education in Jiangxi Province

The forest coverage rate of Jiangxi Province ranks second in China.It has rich natural resources,a long history of ancient color culture and rich red culture.In the development of nature education,Jiangxi Province has great potential and advantages.This paper introduces the development conditions of nature education in Jiangxi Province,summarizes the problems existing in the development of nature education in Jiangxi Province from the aspects of the types of nature education and the construction of nature education base,such as simple content and single form,imperfect infrastructure and lack of professionals,and puts forward some suggestions on the development of nature education in Jiangxi Province.

Prevalence of emotional and behavioral problems among schoolchildren in Herat City,Afghanistan

Background:The prevalence of pediatric mental illnesses has been increasing in recent years,with a great potential to impact on individual's functionality and adaptation in adulthood.Objective:This study aims to assess emotional and behavioral problems among schoolchildren in Herat City of Afghanistan.Methods:This cross-sectional study was conducted on schoolchildren(grade 5-10),between September and November 2021.Sociodemographic data was collected using a paper-based 14-item structured questionnaire.Data on emotional and behavioral problems was collected using the Strengths and Difficulties Questionnaire(SDQ)based on teachers'and children's report.Statistical analyses were performed in IBM SPSS Statistics(version 27).Results:A total of 418 students,including 190(45.5%)males and 228(54.5%)females with a mean age of 14.1±1.7(11-<18)years were included in the study.The prevalence of students*self-reported total difficulties and prosocial problem were 5.7%and 1.2%,respectively.An insignificant difference was observed between mean total difficulties scores between students'self-reported and teachers'reported SDQ.Gender,grade,concern about shortage of food,and concern about losing house were significantly predicting students'self-reported total difficulties scores.Conclusion:This is the first study to report the prevalence of emotional and behavioral problems among schoolchildren in Herat City,Afghanistan.This,together with relevant global literature,highlight the need to address pediatric mental health,and provide services aimed at preventing,and treating children with these prob­lems around the world.

Use the Power of a Genetic Algorithm to Maximize and Minimize Cases to Solve Capacity Supplying Optimization and Travelling Salesman in Nested Problems

Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.

Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data

This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data.A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems.Existing methods either focus on single-modal ormultimodal problems,and they cannot fit each other.A general geometry problem solver shouldobviouslybe able toprocess variousmodalproblems at the same time.Inthispaper,a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image,which can solve the heterogeneity issue between multimodal geometry problems.A contrastive learning model of multimodal data enhances the semantic relevance betweenmultimodal features and maps them into a unified semantic space,which can effectively adapt to both single-modal and multimodal downstream tasks.Based on the feature extraction and fusion of multimodal data,a proposed geometry problem solver uses relation extraction,theorem reasoning,and problem solving to present solutions in a readable way.Experimental results show the effectiveness of the method.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

Existing Problems and Countermeasures of Rural Industry Development in Bijie Experimental Area

The development of rural industries in Bijie City of Guizhou Province leads the comprehensive rural revitalization with industrial revitalization,takes high-quality development as the overall guide,focuses on industrial scale,standardization,branding,and marketization,and strives to extend the industrial chain and enhance the value chain to achieve the prosperity of rural industries.In this study,it investigated the current situation of rural industry development in Bijie City(improving the quality and efficiency of characteristic industries,expanding the quantity and efficiency of agricultural products processing industry,recruiting and cultivating large business entities,expanding and strengthening the brand of agricultural products,and upgrading the rural tourism).Through analysis,it found that there are problems such as small scale of production enterprises,insufficient cultivation of independent brands,short industrial chain,low added value,weak market expansion ability,imperfect interest connection mechanism,and insufficient participation of farmers.Finally,it came up with countermeasures for the development of rural industries in Bijie City,including improving supporting facilities and building an extension base;strengthening leading enterprises and focus on deep processing;highlighting regional characteristics and paying close attention to the docking of production and marketing;enhancing the characteristic brand and strengthening the support of science and technology;promoting collaboration and support,and making innovation in the connection of interests.

Problems of Hazardous Waste Storage Facilities in Coal-fired Power Plants and Countermeasures

The hazardous waste produced by coal-fired power plants are large in quantity and variety. It is important for ecological environment protection to properly store hazardous waste in coal-fired power plants. The environmental management of hazardous waste in coal-fired power plants started late, and there are many problems in the construction and management of their storage facilities. In this paper, taking eight typical coal-fired power plants as examples, the present problems of hazardous waste storage facilities in coal-fired power plants are analyzed, and corresponding countermeasures are put forward to solve the main common problems.

Construction of Legal System of China's Farmland Protection under the Coexistence of Multiple Objectives:Historical Logic,Practical Problems and Optimization Paths

[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system.

The coupled deep neural networks for coupling of the Stokes and Darcy–Forchheimer problems

We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples.Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.

Research on the Therapeutic Effect of Sandplay Intervention on Emotional and Behavioral Problems of a Primary School Student

With the aim to explore the therapeutic effect of sandplay therapy on children with emotional and behavioral problems,in this study,a primary school student with emotional and behavioral problems was selected as the research object undergoing 12 times sandplay intervention,combining the methods of observation,interview,and questionnaire.It turns out that:(1)The traumatic theme indicates an overall downward trend in the process of intervention,while the cure theme indicates an overall upward trend.(2)The results of“strengths and difficulties questionnaire”were found to be consistent with the results of descriptive evaluation before and after sandplay intervention.(3)Based on the interview,sandplay,and questionnaire analysis,it is found that sandplay therapy shows a better therapeutic effect on children with emotional and behavioral problems.

Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

A class of Sturm-Liouville problems with discontinuity is studied in this paper.The oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are obtained.The main method used in this paper is based on Prufer transformation,which is different from the classical ones.Moreover,we give two examples to verify our main results.

Problems and Strategies:A Case Study of Translation of the Introduction of Xianda College of Economics and Humanities,SISU

The present paper takes the English translation of the introduction of Xianda College of Economics and Humanities,SISU as an example to explore the translation problems of proper nouns and differences in English and Chinese language expressions in the construction of English introductions in Chinese institutions of higher education with the intention to propose corresponding solutions.It is hoped that this paper will provide some tips for the English translation of international publicity materials for other institutions of higher education.