Exact and heuristic formulae to compute the geodetic height from the ellipse equation

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy.The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates.This research analyzes this influence and how it can contribute to their solutions.The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation.In addition,a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed,which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %.The calculation is stable,and the cost is low.

A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.

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.

Analysis of Modeling the Influence of Electromagnetic Fields Radiated by Industrial Static Converters and Impacts on Operators Using Maxwell’s Equations

The study of Electromagnetic Compatibility is essential to ensure the harmonious operation of electronic equipment in a shared environment. The basic principles of Electromagnetic Compatibility focus on the ability of devices to withstand electromagnetic disturbances and not produce disturbances that could affect other systems. Imperceptible in most work situations, electromagnetic fields can, beyond certain thresholds, have effects on human health. The objective of the present article is focused on the modeling analysis of the influence of geometric parameters of industrial static converters radiated electromagnetic fields using Maxwell’s equations. To do this we used the analytical formalism for calculating the electromagnetic field emitted by a filiform conductor, to model the electromagnetic radiation of this device in the spatio-temporal domain. The interactions of electromagnetic waves with human bodies are complex and depend on several factors linked to the characteristics of the incident wave. To model these interactions, we implemented the physical laws of electromagnetic wave propagation based on Maxwell’s and bio-heat equations to obtain consistent results. These obtained models allowed us to evaluate the spatial profile of induced current and temperature of biological tissue during exposure to electromagnetic waves generated by this system. The simulation 2D results obtained from computer tools show that the temperature variation and current induced by the electromagnetic field can have a very significant influence on the life of biological tissue. The paper provides a comprehensive analysis using advanced mathematical models to evaluate the influence of electromagnetic fields. The findings have direct implications for workplace safety, potentially influencing standards and regulations concerning electromagnetic exposure in industrial settings.

Investigation of multinucleon transfer processes in the Langevin equation model

Multinucleon transfer in low-energy heavy-ion collisions is increasingly considered a promising approach for generating exotic nuclei.Understanding the complex mechanisms involved in multinucleon transfer processes presents significant challenges for the theoretical investigation of nuclear reactions.A Langevin equation model was developed and employed to investigate multinucleon transfer processes.The^(40)Ar+^(232)Th reaction was simulated,and the calculated Wilczyński plot was used to verify the model.Additionally,to study the dynamics of multinucleon transfer reactions,the^(136)Xe+^(238)U and^(136)Xe+^(209)Bi reactions were simulated,and the corresponding TKE-mass and angular distributions were computed to analyze the energy dissipation and scattering angles.This investigation enhances our understanding of the dynamics involved in multinucleon transfer processes.

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential EquationModel for HIV/AIDS with Treatment Compartment

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

Measurement Research Based on Bayesian Structural Equation Cognitive Model

The Bayesian structural equation model integrates the principles of Bayesian statistics, providing a more flexible and comprehensive modeling framework. In exploring complex relationships between variables, handling uncertainty, and dealing with missing data, the Bayesian structural equation model demonstrates unique advantages. Therefore, Bayesian methods are used in this paper to establish a structural equation model of innovative talent cognition, with the measurement of college students’ cognition of innovative talent being studied. An in-depth analysis is conducted on the effects of innovative self-efficacy, social resources, innovative personality traits, and school education, aiming to explore the factors influencing college students’ innovative talent. The results indicate that innovative self-efficacy plays a key role in perception, social resources are significantly positively correlated with the perception of innovative talents, innovative personality tendencies and school education are positively correlated with the perception of innovative talents, but the impact is not significant.

A practical guideline for univariate meta-analytic structural equation modelling

Background:Meta-analysis is a quantitative approach that systematically integrates results from previous research to draw conclusions.Structural equation modelling is a statistical method that integrates factor analysis and path analysis.Meta-analytic structural equation modeling(MASEM)combines meta-analysis and structural equation modeling.It allows researchers to explain relationships among a group of variables across multiple studies.Methods:We used a simulated dataset to conduct a univariate MASEM analysis,using Comprehensive Meta Analysis 3.3,Analysis of Moment Structures 24.0 software.Results:Despite the lack of concise literature on the methodology,our study provided a practical step-by-step guide on univariate MASEM.Conclusion:Researchers can employ MASEM analysis in applicable fields based on the description,principles,and practices expressed in this study and our previous publications mentioned in this study.

A Survey Study on TPACK Framework for Normal Students of English Major in Ethnic Colleges and Universities:Empirical Analysis Based on Structural Equation Modeling

With the continuous advancement of education informatization,Technological Pedagogical Content Knowledge(TPACK),as a new theoretical framework,provides a novel method for measuring teachers’informatization teaching ability.This study takes normal students of English majors from three ethnic universities as the research object,collects relevant data through questionnaires,and uses structural equation modeling to conduct data analysis and empirical research to investigate the differences in the TPACK levels of these students at different grades and the structural relationships among the elements in the TPACK structure.The technological pedagogical knowledge element of the TPACK structure was not obtained by exploratory factors analysis but through path analysis and structural equation modeling,the results show that the one-dimensional core knowledge of technological knowledge(TK),content knowledge(CK),and pedagogical knowledge(PK)have a positive effect on the two-dimensional interaction knowledge of technological content knowledge(TCK)and pedagogical content knowledge(PCK);furthermore,TCK and PCK have a positive effect on TPACK;and TK,CK,and PK indirectly affect TPACK through TCK and PCK.On this basis,suggestions are provided to ethnic colleges and universities to develop the TPACK knowledge competence of normal students of English majors.

Exploring Gender Differences in Adolescent Dissociative Symptoms via A Structural Equation Model

Adolescent dissociative disorders(ADDs)have been recognized as significant psychological issues with an estimated prevalence of 45.2%in psychiatric outpatient clinics^([1]).Previous studies have demonstrated that dissociative symptoms(DSs)manifest as early signs of dissociative disorders(DDs)^([2]).DSs are characterized as aberrations in one's feelings,experiences,and thoughts in the realm of awareness and memory^([3]).

Target-oriented Q-compensated reverse-time migration by using optimized pure-mode wave equation in anisotropic media

Research on seismic anisotropy and attenuation plays a significant role in exploration geophysics. To enhance the imaging quality for complicated structures, we develop several effective improvements for anisotropic attenuation effects in reverse-time migration (Q-RTM) on surface and vertical seismic profiling (VSP) acquisition geometries. First, to suppress pseudo-shear wave artifact and numerical instability of the commonly used anisotropic pseudo-acoustic wave equations, an optimized pure P-wave dispersion relation is derived and the corresponding pure-mode wave equation is solved by combining the finite-difference and Possion methods. Second, a simplified anisotropic pure-mode visco-acoustic wave equation (PVAWE) based on standard linear solid model is established. Third, a time-dispersion correlation strategy is applied to improve the modeling accuracy. Fourth, we extend a target-oriented scheme to anisotropic attenuated modeling and imaging. Instead of the conventional wavefield modeling and RTM, the proposed approach can extract available wavefield information near the target regions and produce high imaging resolution for target structures. Last, both anisotropic surface and VSP Q-RTMs are executed by combining optimized PVAWE, time-dispersion correlation and target-oriented algorithm. Modeling examples demonstrate the advantages of our schemes. Moreover, our modified Q-compensated imaging workflow can be regarded as a supplement to the classical anisotropic RTM.

Surrogate modeling for unsaturated infiltration via the physics and equality-constrained artificial neural networks

Machine learning(ML)provides a new surrogate method for investigating groundwater flow dynamics in unsaturated soils.Traditional pure data-driven methods(e.g.deep neural network,DNN)can provide rapid predictions,but they do require sufficient on-site data for accurate training,and lack interpretability to the physical processes within the data.In this paper,we provide a physics and equalityconstrained artificial neural network(PECANN),to derive unsaturated infiltration solutions with a small amount of initial and boundary data.PECANN takes the physics-informed neural network(PINN)as a foundation,encodes the unsaturated infiltration physical laws(i.e.Richards equation,RE)into the loss function,and uses the augmented Lagrangian method to constrain the learning process of the solutions of RE by adding stronger penalty for the initial and boundary conditions.Four unsaturated infiltration cases are designed to test the training performance of PECANN,i.e.one-dimensional(1D)steady-state unsaturated infiltration,1D transient-state infiltration,two-dimensional(2D)transient-state infiltration,and 1D coupled unsaturated infiltration and deformation.The predicted results of PECANN are compared with the finite difference solutions or analytical solutions.The results indicate that PECANN can accurately capture the variations of pressure head during the unsaturated infiltration,and present higher precision and robustness than DNN and PINN.It is also revealed that PECANN can achieve the same accuracy as the finite difference method with fewer initial and boundary training data.Additionally,we investigate the effect of the hyperparameters of PECANN on solving RE problem.PECANN provides an effective tool for simulating unsaturated infiltration.

Analysis and Numerical Computations of the Multi-Dimensional,Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation

The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.

Mechanisms Influencing Learning Gains Under Information Security: Structural Equation Modeling with Mediating Effect

With the expanding enrollments in higher education,the quality of col-lege education and the learning gains of students have attracted much attention.It is important to study the influencing factors and mechanisms of individual stu-dents’acquisition of learning gains to improve the quality of talent cultivation in colleges.However,in the context of information security,the original data of learning situation surveys in various universities involve the security of educa-tional evaluation data and daily privacy of teachers and students.To protect the original data,data feature mining and correlation analyses were performed at the model level.This study selected 12,181 pieces of data from X University,which participated in the Chinese College Student Survey(CCSS)from 2018 to 2021.A confirmatory factor analysis was conducted and a structural equation modeling was conducted using AMOS 24.0.Through hypothesis testing,this study explored the mechanisms that influence learning gains from the per-spectives of student involvement,teacher involvement,and school support.The results indicated that the quality of student involvement has an important mediat-ing effect on learning gains and that a supportive campus environment has the greatest influence on learning gains.Establishing positive emotional communica-tions between teachers and students is a more direct and effective method than improving the teaching level to improve the quality of student involvement.This study discusses the implications of these results on the research and practice of connotative development in higher education.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Some Modified Equations of the Sine-Hilbert Type

Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.

An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields

In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.

Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks

By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.