Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic...Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.展开更多
In this paper,we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations(PDEs).The main idea is to use a neural netwo...In this paper,we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations(PDEs).The main idea is to use a neural network to learn the solution map of the PDEs and to do so in an element-wise fashion.This map takes input of the element geometry and the PDE’s parameters on that element,and gives output of two operators:(1)the in2out operator for inter-element communication,and(2)the in2sol operator(Green’s function)for element-wise solution recovery.A significant advantage of this approach is that,once trained,this network can be used for the numerical solution of the PDE for any domain geometry and any parameter distribution without retraining.Also,the training is significantly simpler since it is done on the element level instead on the entire domain.We call this approach element learning.This method is closely related to hybridizable discontinuous Galerkin(HDG)methods in the sense that the local solvers of HDG are replaced by machine learning approaches.Numerical tests are presented for an example PDE,the radiative transfer or radiation transport equation,in a variety of scenarios with idealized or realistic cloud fields,with smooth or sharp gradient in the cloud boundary transition.Under a fixed accuracy level of 10^(−3) in the relative L^(2) error,and polynomial degree p=6 in each element,we observe an approximately 5 to 10 times speed-up by element learning compared to a classical finite element-type method.展开更多
Parkinson’s disease remains a major clinical issue in terms of early detection,especially during its prodromal stage when symptoms are not evident or not distinct.To address this problem,we proposed a new deep learni...Parkinson’s disease remains a major clinical issue in terms of early detection,especially during its prodromal stage when symptoms are not evident or not distinct.To address this problem,we proposed a new deep learning 2-based approach for detecting Parkinson’s disease before any of the overt symptoms develop during their prodromal stage.We used 5 publicly accessible datasets,including UCI Parkinson’s Voice,Spiral Drawings,PaHaW,NewHandPD,and PPMI,and implemented a dual stream CNN–BiLSTM architecture with Fisher-weighted feature merging and SHAP-based explanation.The findings reveal that the model’s performance was superior and achieved 98.2%,a F1-score of 0.981,and AUC of 0.991 on the UCI Voice dataset.The model’s performance on the remaining datasets was also comparable,with up to a 2–7 percent betterment in accuracy compared to existing strong models such as CNN–RNN–MLP,ILN–GNet,and CASENet.Across the evidence,the findings back the diagnostic promise of micro-tremor assessment and demonstrate that combining temporal and spatial features with a scatter-based segment for a multi-modal approach can be an effective and scalable platform for an“early,”interpretable PD screening system.展开更多
The purpose of the study was to evaluate Jamaican early childhood pre-service teachers’attitudes towards mathematics.The study is designed according to the quantitative survey model in the descriptive type.In this st...The purpose of the study was to evaluate Jamaican early childhood pre-service teachers’attitudes towards mathematics.The study is designed according to the quantitative survey model in the descriptive type.In this study,a modified version of the Fennema-Sherman mathematics attitude scale was used to measure the mathematics attitude of 144 early childhood pre-service teachers in four different categories of the attitude scale(mathematics usefulness,confidence in learning mathematics,mathematics anxiety,and mathematics motivation).The data were collected from participants in the five teachers’colleges that offer the early childhood education program in Jamaica.The findings revealed that Jamaican early childhood pre-service teachers generally have a more positive attitude towards mathematics.A comparison among the different year groups revealed that a significantly greater percentage of the Year two group of participants possessed a more positive mathematics attitude than the other year groups.A significantly higher percentage of the Year three group indicated that they do not want to teach the subject in the future.The findings have implications for the teaching and learning of mathematics in the early childhood education program in Jamaica and,by extension,the teaching and learning of mathematics at the early childhood level of the education system.展开更多
This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualita...This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.展开更多
The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the pla...The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the plate are controlled by graphene content and the degree of origami folding,which are graded across the thickness of the plate.Thematerial properties of the GOAM plate are evaluated using genetic micro-mechanicalmodels.Governing nonlinear eigenvalue problems for the post-buckling response of the GOAM composite plate are derived using the virtual work principle and a four-variable nonlinear shear deformation theory.A novel differential quadrature method(DQM)algorithm is developed to solve the nonlinear eigenvalue problem.Detailed parametric studies are presented to explore the effects of graphene content,folding degree,and GO distribution patterns on the post-buckling responses of GOAM plates.Results show that high tunability in post-buckling characteristics can be achieved by using GOAM.FunctionallyGradedGraphene OrigamiAuxeticMetamaterials(FG-GOAM)plates can be used in aerospace structures to improve their structural performance and response.展开更多
This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations ove...This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.展开更多
The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,w...The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,which has significant applications in heat exchangers and engineering devices.To optimize heat transfer,a liquid film of Cu and TiO_(2)hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its importance.The nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid film.The solution of the problem is acquired using the homotopy analysis method HAM,and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve analysis.HAM data is utilized to train the ANN in this study,which uses Cu and TiO_(2)hybrid nanofluids in a variable porous space for unsteady thin film flow,and it is used to train the ANN.The results indicate that Cu and TiO_(2)play a greater role in boosting the rate.展开更多
A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical pro...A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.展开更多
While the significant role of technological innovation in promoting renewable energy has been extensively explored in the literature,limited attention has been paid to the impact of energy patents,particularly clean e...While the significant role of technological innovation in promoting renewable energy has been extensively explored in the literature,limited attention has been paid to the impact of energy patents,particularly clean energy patents and fossil fuel patents.This study pioneers an investigation into the effects of energy patents and energy prices on renewable energy consumption.The study utilizes data from 2000Q1 to 2023Q4 and,due to the nonlinear nature of the series,applies wavelet quantile-based methods.Specifically,it introduces the wavelet quantile cointegration approach to evaluate cointegration across different quantiles and time horizons,along with the wavelet quantile-on-quantile regression method.The results confirm cointegration across different periods and quantiles,highlighting the significant relationships between energy patents,economic factors,and renewable energy consumption.Furthermore,we found that fossil energy patents negatively affect renewable energy consumption,while clean energy patents have a similar but weaker effect,especially in the short term.In addition,higher energy prices promote renewable energy adoption while economic growth positively influences renewable energy consumption,particularly in the short term.The study formulates specific policies based on these findings.展开更多
This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro...This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.展开更多
This comprehensive research examines the dynamics of magnetohydrodynamic(MHD)flow and heat transfer within a couple stress fluid.The investigation specifically focuses on the fluid’s behavior over a vertical stretchi...This comprehensive research examines the dynamics of magnetohydrodynamic(MHD)flow and heat transfer within a couple stress fluid.The investigation specifically focuses on the fluid’s behavior over a vertical stretching sheet embedded within a porous medium,providing valuable insights into the complex interactions between fluid mechanics,thermal transport,and magnetic fields.This study accounts for the significant impact of heat generation and thermal radiation,crucial factors for enhancing heat transfer efficiency in various industrial and technological contexts.The research employs mathematical techniques to simplify complex partial differential equations(PDEs)governing fluid flow and heat transfer.Specifically,suitable similarity transformations are applied to convert the PDEs into a more manageable system of ordinary differential equations(ODEs).The homotopy perturbation method(HPM)is employed to derive approximate analytical solutions for the problem.The influences of key parameters,such as magnetic field strength,heat generation,thermal radiation,porosity,and couple stress,on velocity and temperature profiles are analyzed and discussed.Findings indicate that the mixed convection parameter positively affects flow velocity,while the magnetic field parameter significantly alters the flow dynamics,exhibiting an inverse relationship.Further,this type of flow behavior model is relevant to real-world systems like cooling of nuclear reactors and oil extraction through porous formations,where magnetic and thermal effects are significant.展开更多
This study numerically investigates inclined magneto-hydrodynamic natural convection in a porous cavity filled with nanofluid containing gyrotactic microorganisms.The governing equations are nondimensionalized and sol...This study numerically investigates inclined magneto-hydrodynamic natural convection in a porous cavity filled with nanofluid containing gyrotactic microorganisms.The governing equations are nondimensionalized and solved using the finite volume method.The simulations examine the impact of key parameters such as heat source length and position,Peclet number,porosity,and heat generation/absorption on flow patterns,temperature distribution,concentration profiles,and microorganism rotation.Results indicate that extending the heat source length enhances convective currents and heat transfer efficiency,while optimizing the heat source position reduces entropy generation.Higher Peclet numbers amplify convective currents and microorganism distribution complexity.Variations in porosity and heat generation/absorption significantly influence flow dynamics.Additionally,the artificial neural network model reliably predicts the mean Nusselt and Sherwood numbers(Nu&Sh),demonstrating its effectiveness for such analyses.The simulation results reveal that increasing the heat source length significantly enhances heat transfer,as evidenced by a 15%increase in the mean Nusselt number.展开更多
Promoting the high penetration of renewable energies like photovoltaic(PV)systems has become an urgent issue for expanding modern power grids and has accomplished several challenges compared to existing distribution g...Promoting the high penetration of renewable energies like photovoltaic(PV)systems has become an urgent issue for expanding modern power grids and has accomplished several challenges compared to existing distribution grids.This study measures the effectiveness of the Puma optimizer(PO)algorithm in parameter estimation of PSC(perovskite solar cells)dynamic models with hysteresis consideration considering the electric field effects on operation.The models used in this study will incorporate hysteresis effects to capture the time-dependent behavior of PSCs accurately.The PO optimizes the proposed modified triple diode model(TDM)with a variable voltage capacitor and resistances(VVCARs)considering the hysteresis behavior.The suggested PO algorithm contrasts with other wellknown optimizers from the literature to demonstrate its superiority.The results emphasize that the PO realizes a lower RMSE(Root mean square errors),which proves its capability and efficacy in parameter extraction for the models.The statistical results emphasize the efficiency and supremacy of the proposed PO compared to the other well-known competing optimizers.The convergence rates show good,fast,and stable convergence rates with lower RMSE via PO compared to the other five competitive optimizers.Moreover,the lowermean realized via the PO optimizer is illustrated by the box plot for all optimizers.展开更多
Traffic congestion plays a significant role in intelligent transportation systems(ITS)due to rapid urbanization and increased vehicle concentration.The congestion is dependent on multiple factors,such as limited road ...Traffic congestion plays a significant role in intelligent transportation systems(ITS)due to rapid urbanization and increased vehicle concentration.The congestion is dependent on multiple factors,such as limited road occupancy and vehicle density.Therefore,the transportation system requires an effective prediction model to reduce congestion issues in a dynamic environment.Conventional prediction systems face difficulties in identifying highly congested areas,which leads to reduced prediction accuracy.The problem is addressed by integrating Graph Neural Networks(GNN)with the Lion Swarm Optimization(LSO)framework to tackle the congestion prediction problem.Initially,the traffic information is collected and processed through a normalization process to scale the data and mitigate issues of overfitting and high dimensionality.Then,the traffic flow and temporal characteristic features are extracted to identify the connectivity of the road segment.From the connectivity and node relationship graph,modeling improves the overall prediction accuracy.During the analysis,the lion swarm optimization process utilizes the concepts of exploration and exploitation to understand the complex traffic dependencies,which helps predict high congestion on roads with minimal deviation errors.There are three core optimization phases:roaming,hunting,and migration,which enable the framework to make dynamic adjustments to enhance the predictions.The framework’s efficacy is evaluated using benchmark datasets,where the proposed work achieves 99.2%accuracy and minimizes the prediction deviation value by up to 2.5%compared to other methods.With the new framework,there was a more accurate prediction of realtime congestion,lower computational cost,and improved regulation of traffic flow.This system is easily implemented in intelligent transportation systems,smart cities,and self-driving cars,providing a robust and scalable solution for future traffic management.展开更多
This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study inclu...This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study includes two configurations:a leaderless structure using Finite-Time Non-Singular Terminal Bipartite Consensus(FNTBC)and Fixed-Time Bipartite Consensus(FXTBC),and a leader—follower structure ensuring structural balance and robustness against deceptive signals.In the leaderless model,a bipartite controller based on impulsive control theory,gauge transformation,and Markovian switching Lyapunov functions ensures mean-square stability and coordination under deception attacks and communication delays.The FNTBC achieves finite-time convergence depending on initial conditions,while the FXTBC guarantees fixed-time convergence independent of them,providing adaptability to different operating states.In the leader—follower case,a discontinuous impulsive control law synchronizes all followers with the leader despite deceptive attacks and switching topologies,maintaining robust coordination through nonlinear corrective mechanisms.To validate the approach,simulations are conducted on systems of five and seventeen vehicles in both leaderless and leader—follower configurations.The results demonstrate that the proposed framework achieves rapid consensus,strong robustness,and high resistance to deception attacks,offering a secure and scalable model-based control solution for modern vehicular communication networks.展开更多
Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numeric...Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.展开更多
License plate recognition in haze-affected images is challenging due to feature distortions such as blurring and elongation,which lead to pixel displacements.This article introduces a Displacement Region Recognition M...License plate recognition in haze-affected images is challenging due to feature distortions such as blurring and elongation,which lead to pixel displacements.This article introduces a Displacement Region Recognition Method(DR2M)to address such a problem.This method operates on displaced features compared to the training input observed throughout definite time frames.The technique focuses on detecting features that remain relatively stable under haze,using a frame-based analysis to isolate edges minimally affected by visual noise.The edge detection failures are identified using a bilateral neural network through displaced feature training.The training converges bilaterally towards the minimum edges from the maximum region.Thus,the training input and detected edges are used to identify the displacement between observed image frames to extract and differentiate the license plate region from the other vehicle regions.The proposed method maps the similarity feature between the detected and identified vehicle regions.This aids in leveraging the plate recognition precision with a high F1 score.Thus,this technique achieves a 10.27%improvement in identification precision,a 10.57%increase in F1 score,and a 9.73%reduction in false positive rate compared to baseline methods under maximum displacement conditions caused by haze.The technique attains an identification precision of 95.68%,an F1 score of 94.68%,and a false positive rate of 4.32%,indicating robust performance under haze-affected settings.展开更多
文摘Let M be a compact n-manifold of positive sectional curvature.We will review classical results on the fundamental group of M,a motivation on the c(n)-cyclic conjecture that the fundamental group of M contains a cyclic subgroup of index bounded above by c(n),a constant depending only on n,and we will survey partial results(up to date)on the c(n)-cyclic conjecture.
基金partially supported by the NSF(Grant No.DMS 2324368)by the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin-Madison with funding from the Wisconsin Alumni Research Foundation.
文摘In this paper,we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations(PDEs).The main idea is to use a neural network to learn the solution map of the PDEs and to do so in an element-wise fashion.This map takes input of the element geometry and the PDE’s parameters on that element,and gives output of two operators:(1)the in2out operator for inter-element communication,and(2)the in2sol operator(Green’s function)for element-wise solution recovery.A significant advantage of this approach is that,once trained,this network can be used for the numerical solution of the PDE for any domain geometry and any parameter distribution without retraining.Also,the training is significantly simpler since it is done on the element level instead on the entire domain.We call this approach element learning.This method is closely related to hybridizable discontinuous Galerkin(HDG)methods in the sense that the local solvers of HDG are replaced by machine learning approaches.Numerical tests are presented for an example PDE,the radiative transfer or radiation transport equation,in a variety of scenarios with idealized or realistic cloud fields,with smooth or sharp gradient in the cloud boundary transition.Under a fixed accuracy level of 10^(−3) in the relative L^(2) error,and polynomial degree p=6 in each element,we observe an approximately 5 to 10 times speed-up by element learning compared to a classical finite element-type method.
基金supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/03/32440).
文摘Parkinson’s disease remains a major clinical issue in terms of early detection,especially during its prodromal stage when symptoms are not evident or not distinct.To address this problem,we proposed a new deep learning 2-based approach for detecting Parkinson’s disease before any of the overt symptoms develop during their prodromal stage.We used 5 publicly accessible datasets,including UCI Parkinson’s Voice,Spiral Drawings,PaHaW,NewHandPD,and PPMI,and implemented a dual stream CNN–BiLSTM architecture with Fisher-weighted feature merging and SHAP-based explanation.The findings reveal that the model’s performance was superior and achieved 98.2%,a F1-score of 0.981,and AUC of 0.991 on the UCI Voice dataset.The model’s performance on the remaining datasets was also comparable,with up to a 2–7 percent betterment in accuracy compared to existing strong models such as CNN–RNN–MLP,ILN–GNet,and CASENet.Across the evidence,the findings back the diagnostic promise of micro-tremor assessment and demonstrate that combining temporal and spatial features with a scatter-based segment for a multi-modal approach can be an effective and scalable platform for an“early,”interpretable PD screening system.
文摘The purpose of the study was to evaluate Jamaican early childhood pre-service teachers’attitudes towards mathematics.The study is designed according to the quantitative survey model in the descriptive type.In this study,a modified version of the Fennema-Sherman mathematics attitude scale was used to measure the mathematics attitude of 144 early childhood pre-service teachers in four different categories of the attitude scale(mathematics usefulness,confidence in learning mathematics,mathematics anxiety,and mathematics motivation).The data were collected from participants in the five teachers’colleges that offer the early childhood education program in Jamaica.The findings revealed that Jamaican early childhood pre-service teachers generally have a more positive attitude towards mathematics.A comparison among the different year groups revealed that a significantly greater percentage of the Year two group of participants possessed a more positive mathematics attitude than the other year groups.A significantly higher percentage of the Year three group indicated that they do not want to teach the subject in the future.The findings have implications for the teaching and learning of mathematics in the early childhood education program in Jamaica and,by extension,the teaching and learning of mathematics at the early childhood level of the education system.
文摘This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.
文摘The nonlinear post-buckling response of functionally graded(FG)copper matrix plates enforced by graphene origami auxetic metamaterials(GOAMs)is investigated in the currentwork.The auxeticmaterial properties of the plate are controlled by graphene content and the degree of origami folding,which are graded across the thickness of the plate.Thematerial properties of the GOAM plate are evaluated using genetic micro-mechanicalmodels.Governing nonlinear eigenvalue problems for the post-buckling response of the GOAM composite plate are derived using the virtual work principle and a four-variable nonlinear shear deformation theory.A novel differential quadrature method(DQM)algorithm is developed to solve the nonlinear eigenvalue problem.Detailed parametric studies are presented to explore the effects of graphene content,folding degree,and GO distribution patterns on the post-buckling responses of GOAM plates.Results show that high tunability in post-buckling characteristics can be achieved by using GOAM.FunctionallyGradedGraphene OrigamiAuxeticMetamaterials(FG-GOAM)plates can be used in aerospace structures to improve their structural performance and response.
文摘This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.
文摘The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base fluids.Enhanced heat transfer is a result of this high thermal conductivity,which has significant applications in heat exchangers and engineering devices.To optimize heat transfer,a liquid film of Cu and TiO_(2)hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its importance.The nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid film.The solution of the problem is acquired using the homotopy analysis method HAM,and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve analysis.HAM data is utilized to train the ANN in this study,which uses Cu and TiO_(2)hybrid nanofluids in a variable porous space for unsteady thin film flow,and it is used to train the ANN.The results indicate that Cu and TiO_(2)play a greater role in boosting the rate.
文摘A new extended distribution called the Odd Exponential Generalized Exponential-Exponential distribution(EOEGE-E)is proposed based on generalization of the odd generalized exponential family(OEGE-E).The statistical properties of the proposed distribution are derived.The study evaluates the accuracy of six estimation methods under complete samples.Estimation techniques include maximumlikelihood,ordinary least squares,weighted least squares,maximumproduct of spacing,Cramer vonMises,and Anderson-Darling methods.Twomethods of estimation for the involved parameters are considered based on progressively type Ⅱ censored data(PTⅡC).These methods are maximum likelihood and maximum product of spacing.The proposed distribution’s effectiveness was evaluated using different data sets from various fields.The proposed distribution provides a better fit for these datasets than existing probability distributions.
文摘While the significant role of technological innovation in promoting renewable energy has been extensively explored in the literature,limited attention has been paid to the impact of energy patents,particularly clean energy patents and fossil fuel patents.This study pioneers an investigation into the effects of energy patents and energy prices on renewable energy consumption.The study utilizes data from 2000Q1 to 2023Q4 and,due to the nonlinear nature of the series,applies wavelet quantile-based methods.Specifically,it introduces the wavelet quantile cointegration approach to evaluate cointegration across different quantiles and time horizons,along with the wavelet quantile-on-quantile regression method.The results confirm cointegration across different periods and quantiles,highlighting the significant relationships between energy patents,economic factors,and renewable energy consumption.Furthermore,we found that fossil energy patents negatively affect renewable energy consumption,while clean energy patents have a similar but weaker effect,especially in the short term.In addition,higher energy prices promote renewable energy adoption while economic growth positively influences renewable energy consumption,particularly in the short term.The study formulates specific policies based on these findings.
文摘This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.
文摘This comprehensive research examines the dynamics of magnetohydrodynamic(MHD)flow and heat transfer within a couple stress fluid.The investigation specifically focuses on the fluid’s behavior over a vertical stretching sheet embedded within a porous medium,providing valuable insights into the complex interactions between fluid mechanics,thermal transport,and magnetic fields.This study accounts for the significant impact of heat generation and thermal radiation,crucial factors for enhancing heat transfer efficiency in various industrial and technological contexts.The research employs mathematical techniques to simplify complex partial differential equations(PDEs)governing fluid flow and heat transfer.Specifically,suitable similarity transformations are applied to convert the PDEs into a more manageable system of ordinary differential equations(ODEs).The homotopy perturbation method(HPM)is employed to derive approximate analytical solutions for the problem.The influences of key parameters,such as magnetic field strength,heat generation,thermal radiation,porosity,and couple stress,on velocity and temperature profiles are analyzed and discussed.Findings indicate that the mixed convection parameter positively affects flow velocity,while the magnetic field parameter significantly alters the flow dynamics,exhibiting an inverse relationship.Further,this type of flow behavior model is relevant to real-world systems like cooling of nuclear reactors and oil extraction through porous formations,where magnetic and thermal effects are significant.
基金Dean ship of Scientific Research at King Khalid University,Abha,Saudi Arabia,for funding this work through the Research Group Project(Grant No.RGP.2/610/45)funded by the Princess Nourah bint Abdulrahman University Researchers Supporting Project(Grant No.PNURSP2024R102),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia。
文摘This study numerically investigates inclined magneto-hydrodynamic natural convection in a porous cavity filled with nanofluid containing gyrotactic microorganisms.The governing equations are nondimensionalized and solved using the finite volume method.The simulations examine the impact of key parameters such as heat source length and position,Peclet number,porosity,and heat generation/absorption on flow patterns,temperature distribution,concentration profiles,and microorganism rotation.Results indicate that extending the heat source length enhances convective currents and heat transfer efficiency,while optimizing the heat source position reduces entropy generation.Higher Peclet numbers amplify convective currents and microorganism distribution complexity.Variations in porosity and heat generation/absorption significantly influence flow dynamics.Additionally,the artificial neural network model reliably predicts the mean Nusselt and Sherwood numbers(Nu&Sh),demonstrating its effectiveness for such analyses.The simulation results reveal that increasing the heat source length significantly enhances heat transfer,as evidenced by a 15%increase in the mean Nusselt number.
基金supported via funding from Prince Sattam Bin Abdulaziz University project number(PSAU/2025/R/1446).
文摘Promoting the high penetration of renewable energies like photovoltaic(PV)systems has become an urgent issue for expanding modern power grids and has accomplished several challenges compared to existing distribution grids.This study measures the effectiveness of the Puma optimizer(PO)algorithm in parameter estimation of PSC(perovskite solar cells)dynamic models with hysteresis consideration considering the electric field effects on operation.The models used in this study will incorporate hysteresis effects to capture the time-dependent behavior of PSCs accurately.The PO optimizes the proposed modified triple diode model(TDM)with a variable voltage capacitor and resistances(VVCARs)considering the hysteresis behavior.The suggested PO algorithm contrasts with other wellknown optimizers from the literature to demonstrate its superiority.The results emphasize that the PO realizes a lower RMSE(Root mean square errors),which proves its capability and efficacy in parameter extraction for the models.The statistical results emphasize the efficiency and supremacy of the proposed PO compared to the other well-known competing optimizers.The convergence rates show good,fast,and stable convergence rates with lower RMSE via PO compared to the other five competitive optimizers.Moreover,the lowermean realized via the PO optimizer is illustrated by the box plot for all optimizers.
基金Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2025-02-01641)。
文摘Traffic congestion plays a significant role in intelligent transportation systems(ITS)due to rapid urbanization and increased vehicle concentration.The congestion is dependent on multiple factors,such as limited road occupancy and vehicle density.Therefore,the transportation system requires an effective prediction model to reduce congestion issues in a dynamic environment.Conventional prediction systems face difficulties in identifying highly congested areas,which leads to reduced prediction accuracy.The problem is addressed by integrating Graph Neural Networks(GNN)with the Lion Swarm Optimization(LSO)framework to tackle the congestion prediction problem.Initially,the traffic information is collected and processed through a normalization process to scale the data and mitigate issues of overfitting and high dimensionality.Then,the traffic flow and temporal characteristic features are extracted to identify the connectivity of the road segment.From the connectivity and node relationship graph,modeling improves the overall prediction accuracy.During the analysis,the lion swarm optimization process utilizes the concepts of exploration and exploitation to understand the complex traffic dependencies,which helps predict high congestion on roads with minimal deviation errors.There are three core optimization phases:roaming,hunting,and migration,which enable the framework to make dynamic adjustments to enhance the predictions.The framework’s efficacy is evaluated using benchmark datasets,where the proposed work achieves 99.2%accuracy and minimizes the prediction deviation value by up to 2.5%compared to other methods.With the new framework,there was a more accurate prediction of realtime congestion,lower computational cost,and improved regulation of traffic flow.This system is easily implemented in intelligent transportation systems,smart cities,and self-driving cars,providing a robust and scalable solution for future traffic management.
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP.2/103/46”Deanship of Scientific Research at Northern Border University,Arar,Saudi Arabia for funding this research work through project number“NBU-FFR-2025-871-15”funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1447).
文摘This paper proposes a model-based control framework for vehicle platooning systems with secondorder nonlinear dynamics operating over switching signed networks,time-varying delays,and deception attacks.The study includes two configurations:a leaderless structure using Finite-Time Non-Singular Terminal Bipartite Consensus(FNTBC)and Fixed-Time Bipartite Consensus(FXTBC),and a leader—follower structure ensuring structural balance and robustness against deceptive signals.In the leaderless model,a bipartite controller based on impulsive control theory,gauge transformation,and Markovian switching Lyapunov functions ensures mean-square stability and coordination under deception attacks and communication delays.The FNTBC achieves finite-time convergence depending on initial conditions,while the FXTBC guarantees fixed-time convergence independent of them,providing adaptability to different operating states.In the leader—follower case,a discontinuous impulsive control law synchronizes all followers with the leader despite deceptive attacks and switching topologies,maintaining robust coordination through nonlinear corrective mechanisms.To validate the approach,simulations are conducted on systems of five and seventeen vehicles in both leaderless and leader—follower configurations.The results demonstrate that the proposed framework achieves rapid consensus,strong robustness,and high resistance to deception attacks,offering a secure and scalable model-based control solution for modern vehicular communication networks.
基金Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120funded by the Research Council of Lithuania.
文摘Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.
基金supported by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R848)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabiathe Deanship of Scientific Research at Northern Border University,Arar,Saudi Arabia for funding this research work through the project number“NBU-FFR-2025-2932-09”.
文摘License plate recognition in haze-affected images is challenging due to feature distortions such as blurring and elongation,which lead to pixel displacements.This article introduces a Displacement Region Recognition Method(DR2M)to address such a problem.This method operates on displaced features compared to the training input observed throughout definite time frames.The technique focuses on detecting features that remain relatively stable under haze,using a frame-based analysis to isolate edges minimally affected by visual noise.The edge detection failures are identified using a bilateral neural network through displaced feature training.The training converges bilaterally towards the minimum edges from the maximum region.Thus,the training input and detected edges are used to identify the displacement between observed image frames to extract and differentiate the license plate region from the other vehicle regions.The proposed method maps the similarity feature between the detected and identified vehicle regions.This aids in leveraging the plate recognition precision with a high F1 score.Thus,this technique achieves a 10.27%improvement in identification precision,a 10.57%increase in F1 score,and a 9.73%reduction in false positive rate compared to baseline methods under maximum displacement conditions caused by haze.The technique attains an identification precision of 95.68%,an F1 score of 94.68%,and a false positive rate of 4.32%,indicating robust performance under haze-affected settings.
