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.

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.

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.

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).

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.

Linking 24-h Movement Behavior Guidelines to Cognitive Difficulties,Internalizing and Externalizing Problems in Preterm Youth

Background:Given the heightened risk of developmental challenges associated with preterm birth,it is crucial to explore interventions that may ameliorate potential adverse outcomes.This study aimed to examine whether meeting the 24-h movement behavior(24-HMB)guidelines,which include recommendations on physical activity(PA),screen time(ST),and sleep(SL),is related to indicators of cognitive difficulties,internalizing problems(e.g.,depression and anxiety),and externalizing problems(e.g.,difficulties in making friends and arguing)in a sample of preterm youth(children and adolescents born preterm).Methods:In this cross-sectional study,data from 3410 preterm youth(aged 6 to 17 years)were included for data analyses.Multivariable logistic regression was used to investigate associations between meeting the 24-HMB guidelines and the above-mentioned health outcomes,while controlling for sociodemographic and health-related factors.Results:The prevalence of meeting 24-HMB guidelines varied across independent and integrated components of the 24-HMB guidelines.Meeting the ST guideline alone(p<0.05)and integrated guidelines(i.e.,ST+SL and ST+SL+PA)were associated with fewer cognitive difficulties and reduced internalizing and externalizing problems(p<0.05).Specifically,meeting the SL guideline alone and integrated guidelines(i.e.,SL+ST)were associated with lower odds of depression and anxiety(p<0.01).Additionally,meeting independent,and integrated(PA and/or ST)guidelines were associated with less pronounced difficulties in making friends and arguing(p<0.05).Meeting 24-HMB guidelines in an isolated and integrated manner are linked to better cognitive performance and fewer internalizing and externalizing problems in preterm youth.Conclusion:Results suggest that advocating for the implementation of the 24-HMB guidelines may reduce cognitive challenges and behavioral issues,which is of high relevance for improving public health.Future longitudinal studies in preterm youth should investigate how modifying specific 24-HMB behaviors,especially ST,influence cognitive difficulties,internalizing and externalizing problems in this vulnerable population.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

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.

Identifying multidisciplinary problems from scientific publications based on a text generation method

Purpose:A text generation based multidisciplinary problem identification method is proposed,which does not rely on a large amount of data annotation.Design/methodology/approach:The proposed method first identifies the research objective types and disciplinary labels of papers using a text classification technique;second,it generates abstractive titles for each paper based on abstract and research objective types using a generative pre-trained language model;third,it extracts problem phrases from generated titles according to regular expression rules;fourth,it creates problem relation networks and identifies the same problems by exploiting a weighted community detection algorithm;finally,it identifies multidisciplinary problems based on the disciplinary labels of papers.Findings:Experiments in the“Carbon Peaking and Carbon Neutrality”field show that the proposed method can effectively identify multidisciplinary research problems.The disciplinary distribution of the identified problems is consistent with our understanding of multidisciplinary collaboration in the field.Research limitations:It is necessary to use the proposed method in other multidisciplinary fields to validate its effectiveness.Practical implications:Multidisciplinary problem identification helps to gather multidisciplinary forces to solve complex real-world problems for the governments,fund valuable multidisciplinary problems for research management authorities,and borrow ideas from other disciplines for researchers.Originality/value:This approach proposes a novel multidisciplinary problem identification method based on text generation,which identifies multidisciplinary problems based on generative abstractive titles of papers without data annotation required by standard sequence labeling techniques.

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.

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.

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.

THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

Riemann–Hilbert problem for the defocusing Lakshmanan–Porsezian–Daniel equation with fully asymmetric nonzero boundary conditions

The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.

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.

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.

Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems

A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid mechanics.However,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order derivatives.In this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)method.This novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending problems.In particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.

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.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.