具有p-Laplacian算子的分数阶问题共振正解的存在性

本文研究了具有p-拉普拉斯算子的分数阶微分方程在两种边界条件下的共振正解存在的问题.利用Leggett-Williams范型定理的方法,获得了一些新的存在性结果,推广了该类问题已有的研究结果.

具有脉冲效应的分数阶p-Laplacian方程耦合系统的可解性

本文研究了一类具有脉冲效应的分数阶p-Laplacian方程耦合系统的问题.利用变分方法,获得了该系统解存在的一些新结果.在证明过程中,弱化了系统中变系数和非线性项的条件,推广了已有结果.

一类p-Laplacian问题正径向解的存在性与多解性

研究了p-Laplacian问题{-div(|∇u|^(p-2)∇u)=q(|x|)f(u),|x|>1,x∈R^(N),u(x)=b,|x|=1,u(x)→a,|x|→+∞,其中,1<p<N,a,b为正参数,q∈L^(1)_(loc)((1,+∞),[0,+∞)),f∈C([0,+∞),[0,+∞))。运用锥上的不动点定理、上下解方法和拓扑度理论,获得了p-Laplacian问题正解的存在性和多解性结果。

带p-Laplacian算子的分数阶微分方程半正系统正解的存在性

对一类带有p-Laplacian算子和含有分数阶积分的奇异非线性项的Riemann-Liouville型分数阶微分方程半正系统正解的存在性进行了分析与研究,其边界条件包括不同阶的分数阶导数、Riemann-Stieltjes积分和无穷点边值条件.基于相关Green函数的性质以及不动点指数定理,得到了参数属于合适区间时,该系统至少存在一个正解的充分条件.通过具体实例验证了所得结果的实用性.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

Enhancing Critical Path Problem in Neutrosophic Environment Using Python

In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.

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.

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).

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.

Problematic Use of Video Games in Schools in Northern Benin (2023)

Objective: To study the problematic use of video games among secondary school students in the city of Parakou in 2023. Methods: Descriptive cross-sectional study conducted in the commune of Parakou from December 2022 to July 2023. The study population consisted of students regularly enrolled in public and private secondary schools in the city of Parakou for the 2022-2023 academic year. A two-stage non-proportional stratified sampling technique combined with simple random sampling was adopted. The Problem Video Game Playing (PVP) scale was used to assess problem gambling in the study population, while anxiety and depression were assessed using the Hospital Anxiety and Depression Scale (HADS). Results: A total of 1030 students were included. The mean age of the pupils surveyed was 15.06 ± 2.68 years, with extremes of 10 and 28 years. The [13 - 18] age group was the most represented, with a proportion of 59.6% (614) in the general population. Females predominated, at 52.8% (544), with a sex ratio of 0.89. The prevalence of problematic video game use was 24.9%, measured using the Video Game Playing scale. Associated factors were male gender (p = 0.005), pocket money under 10,000 cfa (p = 0.001) and between 20,000 - 90,000 cfa (p = 0.030), addictive family behavior (p < 0.001), monogamous family (p = 0.023), good relationship with father (p = 0.020), organization of video game competitions (p = 0.001) and definite anxiety (p Conclusion: Substance-free addiction is struggling to attract the attention it deserves, as it did in its infancy everywhere else. This study complements existing data and serves as a reminder of the need to focus on this group of addictions, whose problematic use of video games remains the most frequent due to its accessibility and social tolerance. Preventive action combined with curative measures remains the most effective means of combating the problem at national level.

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.

Quafu-Qcover:Explore combinatorial optimization problems on cloud-based quantum computers

We introduce Quafu-Qcover,an open-source cloud-based software package developed for solving combinatorial optimization problems using quantum simulators and hardware backends.Quafu-Qcover provides a standardized and comprehensive workflow that utilizes the quantum approximate optimization algorithm(QAOA).It facilitates the automatic conversion of the original problem into a quadratic unconstrained binary optimization(QUBO)model and its corresponding Ising model,which can be subsequently transformed into a weight graph.The core of Qcover relies on a graph decomposition-based classical algorithm,which efficiently derives the optimal parameters for the shallow QAOA circuit.Quafu-Qcover incorporates a dedicated compiler capable of translating QAOA circuits into physical quantum circuits that can be executed on Quafu cloud quantum computers.Compared to a general-purpose compiler,our compiler demonstrates the ability to generate shorter circuit depths,while also exhibiting superior speed performance.Additionally,the Qcover compiler has the capability to dynamically create a library of qubits coupling substructures in real-time,utilizing the most recent calibration data from the superconducting quantum devices.This ensures that computational tasks can be assigned to connected physical qubits with the highest fidelity.The Quafu-Qcover allows us to retrieve quantum computing sampling results using a task ID at any time,enabling asynchronous processing.Moreover,it incorporates modules for results preprocessing and visualization,facilitating an intuitive display of solutions for combinatorial optimization problems.We hope that Quafu-Qcover can serve as an instructive illustration for how to explore application problems on the Quafu cloud quantum computers.

An Immune-Inspired Approach with Interval Allocation in Solving Multimodal Multi-Objective Optimization Problems with Local Pareto Sets

In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.

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.

Using Improved Particle Swarm Optimization Algorithm for Location Problem of Drone Logistics Hub

Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.

Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.