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
The present study investigates the flow,heat,and mass transfer analysis in the bioconvection of nanofluid containing motile gyrotactic microorganisms through a semi-porous curved oscillatory channel with a magnetic fi...The present study investigates the flow,heat,and mass transfer analysis in the bioconvection of nanofluid containing motile gyrotactic microorganisms through a semi-porous curved oscillatory channel with a magnetic field.These microorganisms produce density gradients by swimming,which induces macroscopic convection flows in the fluid.This procedure improves the mass and heat transfer,illustrating the interaction between biological activity and fluid dynamics.Furthermore,instead of considering traditional Fourier's and Fick's law the energy and concentration equations are developed by incorporating Cattaneo-Christov double diffusion theory.Moreover,to examine the influence of thermophoresis and Brownian diffusions in the fluid we have adopted the Buongiorno nanofluid model.Due to the oscillation of the surface of the channel,the mathematical development of the considered flow problem is obtained in the form of partial differential equations via the curvilinear coordinate system.The convergent series solution of the governing flow equations is obtained after applying the homotopy analysis method(HAM).The effects of different pertinent flow parameters on velocity,motile microorganism density distribution,concentration,pressure,temperature,and skin friction coefficient are examined and discussed in detail with the help of graphs and tables.It is observed during the current study that the density of microorganisms is enhanced for higher values of Reynolds number,Peclet number,radius of curvature variable,and Lewis number.展开更多
A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order ...A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order time derivatives.The proposed scheme attains third-order temporal accuracy and is rigorously validated through stability and convergence analyses for both scalar and coupled systems.Its effectiveness is demonstrated by simulating unsteady Eyring-Prandtl non-Newtonian nanofluid flow over a Riga plate with coupled heat and mass transfer under electromagnetic actuation.The physical model accounts for Brownian motion and thermophoresis,and the nanofluid considered is a Prandtl-type non-Newtonian base fluid containing suspended nanoparticles,with heat and mass transport governed by coupled momentum,energy,and concentration equations.Numerical simulations are performed over practically relevant parameter ranges,with the Reynolds number fixed at Re=5 and the Prandtl number set to Pr=3 to represent moderate inertial and thermal diffusion effects typical of nanofluid transport systems.To enhance computational efficiency,an artificial neural network(ANN)-based surrogate model is developed to predict the skin friction coefficient and local Sherwood number as functions of Reynolds number,Prandtl number,Schmidt number,Brownian motion,and thermophoresis parameters.The training dataset is generated entirely from high-fidelity numerical simulations produced by the proposed hybrid scheme.The data are systematically partitioned into 70%for training,15%for validation,and 15%for testing,ensuring reliable generalization.Regression analysis yields a near-unity correlation coefficient(R≈0.99),while error histograms exhibit tightly clustered residuals around zero,confirming high predictive accuracy.Furthermore,a benchmark convergence study using Stokes’first problem demonstrates that the proposed scheme consistently achieves lower global error norms than the classical Runge–Kutta method for identical spatial and temporal resolutions.Overall,this study introduces a novel computational intelligence framework that integrates high-order numerical solvers with machine learning,offering a robust and time-efficient tool for advanced modeling and real-time prediction of non-Newtonian nanofluid transport phenomena under electromagnetic flow control.展开更多
Efficient thermal management in porous media is essential for advanced engineering applications,including solar energy systems,electronic cooling,and aerospace thermal control.This study presents a comprehensive analy...Efficient thermal management in porous media is essential for advanced engineering applications,including solar energy systems,electronic cooling,and aerospace thermal control.This study presents a comprehensive analysis of ternary hybrid nanofluids,TiO_(2)-CdTe-MoS_(2) dispersed in water,flowing over a vertical stretching or shrinking surface in a Darcy-Brinkman porous medium.The investigation accounts for the combined effects of magnetohydrodynamics,thermal radiation,viscous dissipation,and internal heat generation.In contrast to previous studies that predominantly focused on single or binary nanofluids,the present work systematically examines the thermal and hydrodynamic performance of ternary hybrid nanofluids,highlighting their enhanced heat transport capabilities in porous structures.The governing momentum and energy equations are formulated in nondimensional form and solved numerically using the shifted Legendre collocation method.The results show that increasing the magnetic parameter,M=0-4,suppresses the fluid velocity by up to 28%,while stronger thermal radiation,R=0-5,raises the near-surface temperature by approximately 32%.Viscous dissipation and internal heat generation further enhance the Nusselt number,indicating improved heat transfer performance.Overall,the findings demonstrate the synergistic influence of the three nanoparticles in optimizing flow behavior and thermal characteristics,offering valuable insights for the design of high-performance thermal management systems in energy and aerospace applications.展开更多
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t...It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.展开更多
The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while ther...The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.展开更多
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearitie...The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
Thiswork explores aMagnetohydrodynamic(MHD)flowin a triangular cavitywith a thermally insulated baffle.Enclosure’s inclined wall is hotter,whereas the vertical border is adiabatic and the bottom is cooler.The study a...Thiswork explores aMagnetohydrodynamic(MHD)flowin a triangular cavitywith a thermally insulated baffle.Enclosure’s inclined wall is hotter,whereas the vertical border is adiabatic and the bottom is cooler.The study aims to clarify how geometric changes affect thermal performance and offers new perspectives on how to improve heat dissipation mechanisms.A COMSOL Multiphysics version 6.2 has been used to solve numerical solutions.Streamlines and thermal distributions are examined systematically in order to understand how the unique geometry and baffle size of triangular cavities can influence the fluid flow.This influence can result in optimized flow patterns,promoting efficient heat transfer by directing the fluid to specific areas that require more cooling.In comparison with conventional designs,this optimization results in more efficient convective heat transfer,which raises cooling efficiency and lowers thermal resistance.Furthermore,by strengthening heat transfer characteristics in heat transfer systems,these geometries increase thermal efficiency,which helps several sectors,including the production of electricity,HVAC,and the automobile industry.展开更多
In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regiona...In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.展开更多
The purpose of the present investigation is to explore the implications of Cross fluid in a Darcy-Forchheimer porousmediumdue to the tri-hybrid nanofluid past a porous cylinder.Thermal radiation,heat generation,therma...The purpose of the present investigation is to explore the implications of Cross fluid in a Darcy-Forchheimer porousmediumdue to the tri-hybrid nanofluid past a porous cylinder.Thermal radiation,heat generation,thermal convection,solutal convective and chemical reaction have been encountered in this analysis.Entropy generation has been accounted for under the fluidic friction,heat rate analysis,and porosity analysis.Three different nanoparticles of multiwall carbon nanotube(MWCNT),aluminum oxide(Al_(2)O_(3)),and silver(Ag)are utilized to illustrate the tri-hybrid nanofluid flow with Ethlene Glycol(EG)as the base fluid.The governance model,consisting of linked inadequate differential conditions,is transformed into an ordinary configuration of nonlinear coupled differential conditions by acceptable adjustments.The obtained outcomes in combination with the bvp4c approach are then used to resolve the generated ODEs.For discussion purposes,the impacts of the physical limitations on temperature profile,velocity,and concentration have also been illustrated.Numerical results have been obtained for the diffusion rate,heat transfer rate,drag force,and other factors.While the Forchheimer parameter and the inclination angle reduce the fluid flow’s velocity,the Biot number of heat and mass transfer influences the fluid’s temperature.According to the findings,hybrid nanofluid is the most effective way to improve heat transmission and may also be utilized for cooling.Three different kinds of nanofluids were used in a comparative examination to clarify the study’s conclusions.Changes in viscosity and porousness caused the nanofluids’velocity to drop by 13.12%and 15.8%,respectively;however,trihybrid nanofluids with improved convection showed a 13.12%rise.展开更多
The present investigation inspects the unsteady,incompressible MHD-induced flow of a ternary hybrid nanofluid made of SiO_(2)(silicon dioxide),ZnO(zinc oxide),and MWCNT(multi-walled carbon nanotubes)suspended in a wat...The present investigation inspects the unsteady,incompressible MHD-induced flow of a ternary hybrid nanofluid made of SiO_(2)(silicon dioxide),ZnO(zinc oxide),and MWCNT(multi-walled carbon nanotubes)suspended in a water-ethylene glycol base fluid between two perforated squeezing Riga plates.This problem is important because it helps us understand the complicated connections between magnetic fields,nanofluid dynamics,and heat transport,all of which are critical for designing thermal management systems.These findings are especially useful for improving the design of innovative cooling technologies in electronics,energy systems,and healthcare applications.No prior study has been done on the theoretical study of the flow of ternary nanofluid(SiO_(2)+ZnO+MWCNT/Water−EthylGl ycol,(60∶40))past a pierced squeezed Riga plates using the boundary value problem solver 4th-order collocation(BVP4C)numerical approach to date.So,the current work has been carried out to fill this gap,and the core purpose of this study is to explore the aspects that enhance the heat transfer of base fluids(H_(2)O/EG)suspended with three nanomaterials SiO_(2),ZnO,and MWCNT.The Riga plates introduce electromagnetic forcing through an embedded array of magnets and electrodes,generating Lorentz forces to regulate the flow.The squeezing effect introduces dynamic boundary movement,which enhances mixing;however,permeability,due to porosity,replicates the true material limits.Similarity transformations of the Navier-Stokes and energy equations result in a highly nonlinear set of ordinary differential equations that govern momentum and thermal energy transport.The subsequent boundary value problem is solved utilizing the BVP4C numerical approach.The study observes the impact of magnetic parameters,squeezing velocity,solid volume percentages of the three nanoparticles,and porous medium factors on velocity and temperature fields.Results show that magnetic fields reduce the velocity profile by 6.75%due to increased squeezing and medium effects.Tri-hybrid nanofluids notice a 9%rise in temperature with higher thermal radiation.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
Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is reveal...Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is revealed that trapezoidal fins tend to be more efficient,particularly when material optimization is critical.Motivated by the increasing need for sustainable energy management,this work analyses the thermal performance of inclined trapezoidal and rectangular porous fins utilising a unique hybrid nanofluid.The effectiveness of nanoparticles in a working fluid is primarily determined by their thermophysical properties;hence,optimising these properties can significantly improve overall performance.This study considers the dispersion of Graphene Oxide(GO)and Molybdenum Disulfide in the base fluid,engine oil.Temperature profiles are analysed by altering the radiative,porosity,wet porous,and angle of inclination parameters.Surface and contour plots are constructed by using the Lobatto IIIa Collocation Method with BVP5C solver in MATLAB and Gradient Descent Optimisation to predict the combined heat transfer rate.According to the study,fluid temperature consistently decreases when the angle of inclination,wet porous parameter,porosity parameter,and radiative parameter increase,suggesting significantly improved heat dissipation.The trapezoidal fin consistently exhibits a superior heat transfer mechanism than a rectangular fin.It is found that the trapezoidal fin transmits heat at a rate that is 0.05%higher than that of the rectangular fin.Validation of the present study is done through the comparison of previous studies.This research provides useful design insights for sophisticated engineering uses,including electrical cooling devices,heat exchangers,radiators,and solar heaters.展开更多
Marginal seas,as transitional zones,are closely connected to the open ocean and adjacent coastal systems.Their circulations often exhibit strong oscillatory behavior that shapes heat and salt transport,nutrient cyclin...Marginal seas,as transitional zones,are closely connected to the open ocean and adjacent coastal systems.Their circulations often exhibit strong oscillatory behavior that shapes heat and salt transport,nutrient cycling,and regional ocean-atmosphere interactions.However,the characteristics and underlying dynamics of these oscillations remain insufficiently understood.Using the unique three-layer alternating circulation in the South China Sea as an example,we show that the system undergoes a pronounced regime transition from 1993-2008 to 2009-2018.This transition is closely linked to the phase change of the Pacific Decadal Oscillation.Specifically,upper-layer cyclonic circulation intensifies during the pre-2009 but weakens during the post-2009 period,while the middle-layer anticyclonic circulation exhibits the opposite pattern.In contrast,the deep-layer circulation strengthens substantially during the post-20o9 period.These regime transitions arise from the interplay of surface wind forcing,the external exchanging current with the Pacific,and topographically modulated internal vertical coupling.The decadal trend of the upper-layer circulation is primarily wind-driven.The weakening of middle-layer circulation during pre-2oo9 is governed by pressure torque influenced by the upperlayer,whereas its post-2009 strengthening is attributed to vortex stretching associated with enhanced deep intrusion from the Pacific and a stronger deep-layer circulation.The findings clarify the oscillatory nature of South China Sea layered circulation under climate variability and highlight its role in regulating regional mass transport and ocean-atmosphere interaction.展开更多
In recent years,fog computing has become an important environment for dealing with the Internet of Things.Fog computing was developed to handle large-scale big data by scheduling tasks via cloud computing.Task schedul...In recent years,fog computing has become an important environment for dealing with the Internet of Things.Fog computing was developed to handle large-scale big data by scheduling tasks via cloud computing.Task scheduling is crucial for efficiently handling IoT user requests,thereby improving system performance,cost,and energy consumption across nodes in cloud computing.With the large amount of data and user requests,achieving the optimal solution to the task scheduling problem is challenging,particularly in terms of cost and energy efficiency.In this paper,we develop novel strategies to save energy consumption across nodes in fog computing when users execute tasks through the least-cost paths.Task scheduling is developed using modified artificial ecosystem optimization(AEO),combined with negative swarm operators,Salp Swarm Algorithm(SSA),in order to competitively optimize their capabilities during the exploitation phase of the optimal search process.In addition,the proposed strategy,Enhancement Artificial Ecosystem Optimization Salp Swarm Algorithm(EAEOSSA),attempts to find the most suitable solution.The optimization that combines cost and energy for multi-objective task scheduling optimization problems.The backpack problem is also added to improve both cost and energy in the iFogSim implementation as well.A comparison was made between the proposed strategy and other strategies in terms of time,cost,energy,and productivity.Experimental results showed that the proposed strategy improved energy consumption,cost,and time over other algorithms.Simulation results demonstrate that the proposed algorithm increases the average cost,average energy consumption,and mean service time in most scenarios,with average reductions of up to 21.15%in cost and 25.8%in energy consumption.展开更多
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times f...This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.展开更多
In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper i...In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.展开更多
It is often said that music has reached its supreme and highest level in the 18th and 19th centuries. One of the main reasons for this achievement seems to be the robust structure of compositions of music, somewhat re...It is often said that music has reached its supreme and highest level in the 18th and 19th centuries. One of the main reasons for this achievement seems to be the robust structure of compositions of music, somewhat remindful of robust structure of mathematics. One is reminded of the words of Goethe: Geometry is frozen music. Here, we may extend geometry to mathematics. For the Middle Age in Europe, there were seven main subjects in the universities or in higher education. They were grammar, logic and rhetoric—these three (tri) were regarded as more standard and called trivia (trivium), the origin of the word trivial. And the remaining four were arithmetic, geometry, astronomy and music—these four (quadrus) were regarded as more advanced subjects and were called quadrivia (quadrivium). Thus for Goethe, geometry and mathematics seem to be equivocal. G. Leibniz expresses more in detail in his letter to C. Goldbach in 1712 (April 17): Musica est exercitium arithmeticae occultum nescientis se numerari animi (Music is a hidden arithmetic exercise of the soul, which doesn’t know that it is counting). Or in other respects, J. Sylvester expresses more in detail: Music is mathematics of senses. Mathematics is music of reasons. Thus, the title arises. This paper is a sequel to [1] and examines mathematical structure of musical scales entailing their harmony on expanding and elaborating material in [2] [3] [4] [5], etc. In statistics, the strong law of large numbers is well-known which claims that This means that the relative frequency of occurrences of an event A tends to the true probability p of the occurrences of A with probability 1. In music, harmony is achieved according to Pythagoras’ law of small numbers, which claims that only the small integer multiples of the fundamental notes can create harmony and consonance. We shall also mention the law of cyclotomic numbers according to Coxeter, which elaborates Pythagoras’ law and suggests a connection with construction of n-gons by ruler and compass. In the case of natural scales (just intonation), musical notes appear in the form 2p3q5r (multiples of the basic note), where p∈Z,?q=-3, -2, -1, 0, 1, 2, 3 and r=-1, 0, 1. We shall give mathematical details of the structure of various scales.展开更多
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.
文摘The present study investigates the flow,heat,and mass transfer analysis in the bioconvection of nanofluid containing motile gyrotactic microorganisms through a semi-porous curved oscillatory channel with a magnetic field.These microorganisms produce density gradients by swimming,which induces macroscopic convection flows in the fluid.This procedure improves the mass and heat transfer,illustrating the interaction between biological activity and fluid dynamics.Furthermore,instead of considering traditional Fourier's and Fick's law the energy and concentration equations are developed by incorporating Cattaneo-Christov double diffusion theory.Moreover,to examine the influence of thermophoresis and Brownian diffusions in the fluid we have adopted the Buongiorno nanofluid model.Due to the oscillation of the surface of the channel,the mathematical development of the considered flow problem is obtained in the form of partial differential equations via the curvilinear coordinate system.The convergent series solution of the governing flow equations is obtained after applying the homotopy analysis method(HAM).The effects of different pertinent flow parameters on velocity,motile microorganism density distribution,concentration,pressure,temperature,and skin friction coefficient are examined and discussed in detail with the help of graphs and tables.It is observed during the current study that the density of microorganisms is enhanced for higher values of Reynolds number,Peclet number,radius of curvature variable,and Lewis number.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2603).
文摘A high-order hybrid numerical framework is developed by coupling a three-stage exponential time integrator with a Runge–Kutta scheme for the efficient solution of partial differential equations involving first-order time derivatives.The proposed scheme attains third-order temporal accuracy and is rigorously validated through stability and convergence analyses for both scalar and coupled systems.Its effectiveness is demonstrated by simulating unsteady Eyring-Prandtl non-Newtonian nanofluid flow over a Riga plate with coupled heat and mass transfer under electromagnetic actuation.The physical model accounts for Brownian motion and thermophoresis,and the nanofluid considered is a Prandtl-type non-Newtonian base fluid containing suspended nanoparticles,with heat and mass transport governed by coupled momentum,energy,and concentration equations.Numerical simulations are performed over practically relevant parameter ranges,with the Reynolds number fixed at Re=5 and the Prandtl number set to Pr=3 to represent moderate inertial and thermal diffusion effects typical of nanofluid transport systems.To enhance computational efficiency,an artificial neural network(ANN)-based surrogate model is developed to predict the skin friction coefficient and local Sherwood number as functions of Reynolds number,Prandtl number,Schmidt number,Brownian motion,and thermophoresis parameters.The training dataset is generated entirely from high-fidelity numerical simulations produced by the proposed hybrid scheme.The data are systematically partitioned into 70%for training,15%for validation,and 15%for testing,ensuring reliable generalization.Regression analysis yields a near-unity correlation coefficient(R≈0.99),while error histograms exhibit tightly clustered residuals around zero,confirming high predictive accuracy.Furthermore,a benchmark convergence study using Stokes’first problem demonstrates that the proposed scheme consistently achieves lower global error norms than the classical Runge–Kutta method for identical spatial and temporal resolutions.Overall,this study introduces a novel computational intelligence framework that integrates high-order numerical solvers with machine learning,offering a robust and time-efficient tool for advanced modeling and real-time prediction of non-Newtonian nanofluid transport phenomena under electromagnetic flow control.
文摘Efficient thermal management in porous media is essential for advanced engineering applications,including solar energy systems,electronic cooling,and aerospace thermal control.This study presents a comprehensive analysis of ternary hybrid nanofluids,TiO_(2)-CdTe-MoS_(2) dispersed in water,flowing over a vertical stretching or shrinking surface in a Darcy-Brinkman porous medium.The investigation accounts for the combined effects of magnetohydrodynamics,thermal radiation,viscous dissipation,and internal heat generation.In contrast to previous studies that predominantly focused on single or binary nanofluids,the present work systematically examines the thermal and hydrodynamic performance of ternary hybrid nanofluids,highlighting their enhanced heat transport capabilities in porous structures.The governing momentum and energy equations are formulated in nondimensional form and solved numerically using the shifted Legendre collocation method.The results show that increasing the magnetic parameter,M=0-4,suppresses the fluid velocity by up to 28%,while stronger thermal radiation,R=0-5,raises the near-surface temperature by approximately 32%.Viscous dissipation and internal heat generation further enhance the Nusselt number,indicating improved heat transfer performance.Overall,the findings demonstrate the synergistic influence of the three nanoparticles in optimizing flow behavior and thermal characteristics,offering valuable insights for the design of high-performance thermal management systems in energy and aerospace applications.
基金supported by the NSFC(12301115)the Natural Science Foundation of Huzhou(2023YZ11,2024YZ37)the second author was supported by the NSFC(12071437).
文摘It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.
基金the UGC,New Delhi,India for financial assistance via the UGC-Junior Research Fellowship(CSIR-UGC NET JULY 2024)(Student ID:241610090610)。
文摘The flow of a tetra-hybrid Casson nanofluid(Al_(2)O_(3)-CuO-TiO_(2)-Ag/H_(2)O)over a nonlinear stretching sheet is investigated.The Buongiorno model is used to account for thermophoresis and Brownian motion,while thermal radiation is incorporated to examine its influence on the thermal boundary layer.The governing partial differential equations(PDEs)are reduced to a system of nonlinear ordinary differential equations(ODEs)with fully non-dimensional similarity transformations involving all independent variables.To solve the obtained highly nonlinear system of differential equations,a novel Clique polynomial collocation method is applied.The analysis focuses on the effects of the Casson parameter,power index,radiation parameter,thermophoresis parameter,Brownian motion parameter,and Lewis number.The key findings show that thermal radiation intensifies the thermal boundary layer,the Casson parameter reduces the velocity,and the Lewis number suppresses the concentration with direct relevance to polymer processing,coating flows,electronic cooling,and biomedical applications.
基金partially supported by the National Natural Science Foundation of China(Grant No.12071073)financial support by the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002).
文摘The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
文摘Thiswork explores aMagnetohydrodynamic(MHD)flowin a triangular cavitywith a thermally insulated baffle.Enclosure’s inclined wall is hotter,whereas the vertical border is adiabatic and the bottom is cooler.The study aims to clarify how geometric changes affect thermal performance and offers new perspectives on how to improve heat dissipation mechanisms.A COMSOL Multiphysics version 6.2 has been used to solve numerical solutions.Streamlines and thermal distributions are examined systematically in order to understand how the unique geometry and baffle size of triangular cavities can influence the fluid flow.This influence can result in optimized flow patterns,promoting efficient heat transfer by directing the fluid to specific areas that require more cooling.In comparison with conventional designs,this optimization results in more efficient convective heat transfer,which raises cooling efficiency and lowers thermal resistance.Furthermore,by strengthening heat transfer characteristics in heat transfer systems,these geometries increase thermal efficiency,which helps several sectors,including the production of electricity,HVAC,and the automobile industry.
文摘In this paper,we define for the trace operator,the solution of certain models of vibrating plates standards with initial data in a strategic region spaces of weak regularities.Indeed,we know that the notion of regional controllability is more adapted to systems described by dynamic systems.Regional controllability results in a strategic area were established for vibrating plates by the Hilbertian Uniqueness Method.
基金the research support through grants ANTARABANGSA(IRMG)-TEL-U/2025/FTKM/A00086.
文摘The purpose of the present investigation is to explore the implications of Cross fluid in a Darcy-Forchheimer porousmediumdue to the tri-hybrid nanofluid past a porous cylinder.Thermal radiation,heat generation,thermal convection,solutal convective and chemical reaction have been encountered in this analysis.Entropy generation has been accounted for under the fluidic friction,heat rate analysis,and porosity analysis.Three different nanoparticles of multiwall carbon nanotube(MWCNT),aluminum oxide(Al_(2)O_(3)),and silver(Ag)are utilized to illustrate the tri-hybrid nanofluid flow with Ethlene Glycol(EG)as the base fluid.The governance model,consisting of linked inadequate differential conditions,is transformed into an ordinary configuration of nonlinear coupled differential conditions by acceptable adjustments.The obtained outcomes in combination with the bvp4c approach are then used to resolve the generated ODEs.For discussion purposes,the impacts of the physical limitations on temperature profile,velocity,and concentration have also been illustrated.Numerical results have been obtained for the diffusion rate,heat transfer rate,drag force,and other factors.While the Forchheimer parameter and the inclination angle reduce the fluid flow’s velocity,the Biot number of heat and mass transfer influences the fluid’s temperature.According to the findings,hybrid nanofluid is the most effective way to improve heat transmission and may also be utilized for cooling.Three different kinds of nanofluids were used in a comparative examination to clarify the study’s conclusions.Changes in viscosity and porousness caused the nanofluids’velocity to drop by 13.12%and 15.8%,respectively;however,trihybrid nanofluids with improved convection showed a 13.12%rise.
基金funded by King Saud University,Riyadh,Saudi Arabia,through the Ongo-ing Research Funding program—Research Chairs(ORF-RC-2025-0127)funded via Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R443).
文摘The present investigation inspects the unsteady,incompressible MHD-induced flow of a ternary hybrid nanofluid made of SiO_(2)(silicon dioxide),ZnO(zinc oxide),and MWCNT(multi-walled carbon nanotubes)suspended in a water-ethylene glycol base fluid between two perforated squeezing Riga plates.This problem is important because it helps us understand the complicated connections between magnetic fields,nanofluid dynamics,and heat transport,all of which are critical for designing thermal management systems.These findings are especially useful for improving the design of innovative cooling technologies in electronics,energy systems,and healthcare applications.No prior study has been done on the theoretical study of the flow of ternary nanofluid(SiO_(2)+ZnO+MWCNT/Water−EthylGl ycol,(60∶40))past a pierced squeezed Riga plates using the boundary value problem solver 4th-order collocation(BVP4C)numerical approach to date.So,the current work has been carried out to fill this gap,and the core purpose of this study is to explore the aspects that enhance the heat transfer of base fluids(H_(2)O/EG)suspended with three nanomaterials SiO_(2),ZnO,and MWCNT.The Riga plates introduce electromagnetic forcing through an embedded array of magnets and electrodes,generating Lorentz forces to regulate the flow.The squeezing effect introduces dynamic boundary movement,which enhances mixing;however,permeability,due to porosity,replicates the true material limits.Similarity transformations of the Navier-Stokes and energy equations result in a highly nonlinear set of ordinary differential equations that govern momentum and thermal energy transport.The subsequent boundary value problem is solved utilizing the BVP4C numerical approach.The study observes the impact of magnetic parameters,squeezing velocity,solid volume percentages of the three nanoparticles,and porous medium factors on velocity and temperature fields.Results show that magnetic fields reduce the velocity profile by 6.75%due to increased squeezing and medium effects.Tri-hybrid nanofluids notice a 9%rise in temperature with higher thermal radiation.
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.
基金supported by the“Regional Innovation System&Education(RISE)”through the Seoul RISE Center,funded by the Ministry of Education(MOE)and the Seoul Metropolitan Government(2025-RISE-01-027-04).
文摘Fluid dynamic research on rectangular and trapezoidal fins is aimed at increasing heat transfer by means of large surfaces.The trapezoidal cavity form is compared with its thermal and flow performance,and it is revealed that trapezoidal fins tend to be more efficient,particularly when material optimization is critical.Motivated by the increasing need for sustainable energy management,this work analyses the thermal performance of inclined trapezoidal and rectangular porous fins utilising a unique hybrid nanofluid.The effectiveness of nanoparticles in a working fluid is primarily determined by their thermophysical properties;hence,optimising these properties can significantly improve overall performance.This study considers the dispersion of Graphene Oxide(GO)and Molybdenum Disulfide in the base fluid,engine oil.Temperature profiles are analysed by altering the radiative,porosity,wet porous,and angle of inclination parameters.Surface and contour plots are constructed by using the Lobatto IIIa Collocation Method with BVP5C solver in MATLAB and Gradient Descent Optimisation to predict the combined heat transfer rate.According to the study,fluid temperature consistently decreases when the angle of inclination,wet porous parameter,porosity parameter,and radiative parameter increase,suggesting significantly improved heat dissipation.The trapezoidal fin consistently exhibits a superior heat transfer mechanism than a rectangular fin.It is found that the trapezoidal fin transmits heat at a rate that is 0.05%higher than that of the rectangular fin.Validation of the present study is done through the comparison of previous studies.This research provides useful design insights for sophisticated engineering uses,including electrical cooling devices,heat exchangers,radiators,and solar heaters.
基金supported by the National Natural Science Foundation of China(42376024and 42450181)the Science and Technology Development Fund,Macao SAR(File/Project no.001/2024/SKL)+2 种基金supported by the Centre for Regional Oceans in the University of Macao(SP2025-00005-CRO)CORE,which is a joint research center for ocean research between Laoshan Laboratory and HKUSTsubstantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(AoE/P-601/23-N and GRF 16310724).
文摘Marginal seas,as transitional zones,are closely connected to the open ocean and adjacent coastal systems.Their circulations often exhibit strong oscillatory behavior that shapes heat and salt transport,nutrient cycling,and regional ocean-atmosphere interactions.However,the characteristics and underlying dynamics of these oscillations remain insufficiently understood.Using the unique three-layer alternating circulation in the South China Sea as an example,we show that the system undergoes a pronounced regime transition from 1993-2008 to 2009-2018.This transition is closely linked to the phase change of the Pacific Decadal Oscillation.Specifically,upper-layer cyclonic circulation intensifies during the pre-2009 but weakens during the post-2009 period,while the middle-layer anticyclonic circulation exhibits the opposite pattern.In contrast,the deep-layer circulation strengthens substantially during the post-20o9 period.These regime transitions arise from the interplay of surface wind forcing,the external exchanging current with the Pacific,and topographically modulated internal vertical coupling.The decadal trend of the upper-layer circulation is primarily wind-driven.The weakening of middle-layer circulation during pre-2oo9 is governed by pressure torque influenced by the upperlayer,whereas its post-2009 strengthening is attributed to vortex stretching associated with enhanced deep intrusion from the Pacific and a stronger deep-layer circulation.The findings clarify the oscillatory nature of South China Sea layered circulation under climate variability and highlight its role in regulating regional mass transport and ocean-atmosphere interaction.
基金supported and funded by theDeanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘In recent years,fog computing has become an important environment for dealing with the Internet of Things.Fog computing was developed to handle large-scale big data by scheduling tasks via cloud computing.Task scheduling is crucial for efficiently handling IoT user requests,thereby improving system performance,cost,and energy consumption across nodes in cloud computing.With the large amount of data and user requests,achieving the optimal solution to the task scheduling problem is challenging,particularly in terms of cost and energy efficiency.In this paper,we develop novel strategies to save energy consumption across nodes in fog computing when users execute tasks through the least-cost paths.Task scheduling is developed using modified artificial ecosystem optimization(AEO),combined with negative swarm operators,Salp Swarm Algorithm(SSA),in order to competitively optimize their capabilities during the exploitation phase of the optimal search process.In addition,the proposed strategy,Enhancement Artificial Ecosystem Optimization Salp Swarm Algorithm(EAEOSSA),attempts to find the most suitable solution.The optimization that combines cost and energy for multi-objective task scheduling optimization problems.The backpack problem is also added to improve both cost and energy in the iFogSim implementation as well.A comparison was made between the proposed strategy and other strategies in terms of time,cost,energy,and productivity.Experimental results showed that the proposed strategy improved energy consumption,cost,and time over other algorithms.Simulation results demonstrate that the proposed algorithm increases the average cost,average energy consumption,and mean service time in most scenarios,with average reductions of up to 21.15%in cost and 25.8%in energy consumption.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
文摘This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.
文摘In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.
文摘It is often said that music has reached its supreme and highest level in the 18th and 19th centuries. One of the main reasons for this achievement seems to be the robust structure of compositions of music, somewhat remindful of robust structure of mathematics. One is reminded of the words of Goethe: Geometry is frozen music. Here, we may extend geometry to mathematics. For the Middle Age in Europe, there were seven main subjects in the universities or in higher education. They were grammar, logic and rhetoric—these three (tri) were regarded as more standard and called trivia (trivium), the origin of the word trivial. And the remaining four were arithmetic, geometry, astronomy and music—these four (quadrus) were regarded as more advanced subjects and were called quadrivia (quadrivium). Thus for Goethe, geometry and mathematics seem to be equivocal. G. Leibniz expresses more in detail in his letter to C. Goldbach in 1712 (April 17): Musica est exercitium arithmeticae occultum nescientis se numerari animi (Music is a hidden arithmetic exercise of the soul, which doesn’t know that it is counting). Or in other respects, J. Sylvester expresses more in detail: Music is mathematics of senses. Mathematics is music of reasons. Thus, the title arises. This paper is a sequel to [1] and examines mathematical structure of musical scales entailing their harmony on expanding and elaborating material in [2] [3] [4] [5], etc. In statistics, the strong law of large numbers is well-known which claims that This means that the relative frequency of occurrences of an event A tends to the true probability p of the occurrences of A with probability 1. In music, harmony is achieved according to Pythagoras’ law of small numbers, which claims that only the small integer multiples of the fundamental notes can create harmony and consonance. We shall also mention the law of cyclotomic numbers according to Coxeter, which elaborates Pythagoras’ law and suggests a connection with construction of n-gons by ruler and compass. In the case of natural scales (just intonation), musical notes appear in the form 2p3q5r (multiples of the basic note), where p∈Z,?q=-3, -2, -1, 0, 1, 2, 3 and r=-1, 0, 1. We shall give mathematical details of the structure of various scales.
