The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly couple...The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.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
In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is c...In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is considered dynamic.The contact condition on the normal plane is modeled by a unilateral constraint condition for a version of normal velocity in which the memory effect and the adhesion are considered.On the tangential plane a frictional contact condition is governed by the Clarke subdifferential of a locally Lipschitz function,and the evolution of the bonding field is governed by an ordinary differential equation.We formulate this problem as coupled system that consists of two ordinary differential equations and a variational-hemivariational inequality.Then,the existence,uniqueness and continuous dependence of the solution on the data results concerning the abstract system are established.Finally,we use the abstract results to show the existence and uniqueness of the solution to the contact problem.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
This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary cond...This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary conditions).Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained.The test function technique is performed in the proofs.It is worth observing that our results in Theorem 1.1 in this article contain the results in[6]as a special case whenθ=0.To the best of our knowledge,the results in Theorems 1.1-1.2 are new.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
Our analysis is particularly motivated by its relevance to understanding compact object instabilities,gravitational collapse thresholds,and the formation of dense structures under the influence of modified gravity the...Our analysis is particularly motivated by its relevance to understanding compact object instabilities,gravitational collapse thresholds,and the formation of dense structures under the influence of modified gravity theories.The interplay of anisotropic pressures,perturbative dynamics,and modified gravity contributions offers insight into both the stable configuration of dense fluids and the mechanisms leading to dynamical instability.Such considerations directly contribute to the aims of high energy density profiles,particularly in modeling physical systems where extreme pressure,curvature,and matter interactions co-exist.We consider an axially symmetric,dense structure with anisotropic matter content and employ a specific equation of state(EoS)to examine the interplay between static and dynamic quantities via the adiabatic index.To address the complex dynamics of the collapse process,a perturbative scheme is utilized under Newtonian and post-Newtonian approximations,enabling a detailed examination of the stability and structural evolution of the system under the influence of the considered minimally coupled gravity.Our results demonstrate that hydrostatic equilibrium is maintained when effective pressure,gravitational,and anti-gravitational forces are balanced,while deviations from this balance initiate dynamical instability.Graphical representations of stable and unstable regimes are presented,revealing how the choice of gravity functions significantly affects the outcome.This work provides insight into the behavior of dense,self-gravitating configurations under modified gravity,offering broader implications for the modeling of compact astrophysical objects and contributing to the understanding of gravitational collapse in energy density regimes.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
Building reliable intent-based,task-oriented dialog systems typically requires substantial manual effort:designers must derive intents,entities,responses,and control logic from raw conversational data,then iterate unt...Building reliable intent-based,task-oriented dialog systems typically requires substantial manual effort:designers must derive intents,entities,responses,and control logic from raw conversational data,then iterate until the assistant behaves consistently.This paper investigates how far large language models(LLMs)can automate this development.In this paper,we use two reference corpora,Let’s Go(English,public transport)and MEDIA(French,hotel booking),to prompt four LLM families(GPT-4o,Claude,Gemini,Mistral Small)and generate the core specifications required by the rasa platform.These include intent sets with example utterances,entity definitions with slot mappings,response templates,and basic dialog flows.To structure this process,we introduce a model-and platform-agnostic pipelinewith two phases.The first normalizes and validates LLM-generated artifacts,enforcing crossfile consistency andmaking slot usage explicit.The second uses a lightweight dialog harness that runs scripted tests and incrementally patches failure points until conversations complete reliably.Across eight projects,all models required some targeted repairs before training.After applying our pipeline,all reached≥70%task completion(many above 84%),while NLU performance ranged from mid-0.6 to 1.0 macro-F1 depending on domain breadth.These results show that,with modest guidance,current LLMs can produce workable end-to-end dialog prototypes directly fromraw transcripts.Our main contributions are:(i)a reusable bootstrap method aligned with industry domain-specific languages(DSLs),(ii)a small set of high-impact corrective patterns,and(iii)a simple but effective harness for closed-loop refinement across conversational platforms.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
This paper proposes an innovative form of group reduction or similarity transformation involving off-diagonal block matrices. The proposed method is applied to the Ablowitz-Kaup-Newell-Segur(AKNS) matrix spectral prob...This paper proposes an innovative form of group reduction or similarity transformation involving off-diagonal block matrices. The proposed method is applied to the Ablowitz-Kaup-Newell-Segur(AKNS) matrix spectral problem, leading to the generation of reduced matrix AKNS integrable hierarchies. As a result, a variety of reduced multiple-component integrable nonlinear Schr??dinger and modified Korteweg-de Vries models are derived from the analysis of the reduced AKNS matrix spectral problem.展开更多
In order to solve the problems of slow dynamic response and difficult multi-source coordination of solar electric vehicle charging stations under intermittent renewable energy,this paper proposes a hardware-algorithm ...In order to solve the problems of slow dynamic response and difficult multi-source coordination of solar electric vehicle charging stations under intermittent renewable energy,this paper proposes a hardware-algorithm co-design framework:the T-type three-level bidirectional converter(100 kHz switching frequency)based on silicon carbide(SiC)MOSFET is deeply integrated with fuzzy model predictive control(Fuzzy-MPC).At the hardware level,the switching trajectory and resonance suppression circuit(attenuation resonance peak 18 dB)are optimized,and the total loss is reduced by 23%compared with the traditional silicon-based IGBT.At the algorithm level,the adaptive parameter update mechanism and multi-objective rolling optimization are adopted,and the 5 ms level dynamic power allocation is realized by relying on edge computing.Experiments on 800 V DC microgrid(including 600 kW photovoltaic and 150 A·h energy storage)built based on MATLAB/Simulink hardware-in-the-loop(HIL)platform show that the system shortens the battery charging time from 42 to 28 min(the charging speed is increased by 33%).Through the 78%valley power utilization rate,the power purchase cost of high-priced power grids was significantly reduced,and the levelized electricity price decreased by 10.3%;Under the irradiation fluctuation,the renewable energy consumption rate increases by 10.1%,and the DC bus voltage fluctuation is stable within±10 V when the load step is±30%.The co-design provides an economically feasible and dynamically robust solution for the efficient integration of PV-ESG-EV in the smart grid.展开更多
In this paper,we investigate data-driven bright soliton solutions of the nonlocal reverse-time nonlinear Schrodinger(NLS)equation and the parameter identification using the physically informed neural networks(PINNs)al...In this paper,we investigate data-driven bright soliton solutions of the nonlocal reverse-time nonlinear Schrodinger(NLS)equation and the parameter identification using the physically informed neural networks(PINNs)algorithm.Accurate simulations and comparative analyses of relative and absolute errors are performed for two-soliton and four-soliton solutions including linear solitary waves and periodic waves.In the training process,the standard PINNs scheme is employed for linear solitary wave solutions,while the prior information is added at local sharp regions for periodic wave solutions due to the complicated collision behaviors.For the parameter identification,we accurately recognize the nonlinear coefficients of the nonlocal NLS equation from known solutions with different noises.These results reinforce the application of deep learning with the PINNs framework to successfully study nonlocal integrable systems.展开更多
In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[...In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).展开更多
This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner...This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner sector,the intermediate shell and the outer sector.Different values of the barotropic equation of state(EoS)parameter provide the mathematical basis for these regions.Field equations(FEs)are initially developed for a spherically symmetric spacetime coupled with charged matter distribution.We then use the temporal component of TolmanⅣspacetime to formulate the radial metric potential for both the inner region and intermediate shell.We also apply the matching criteria to ensure smooth matching of exterior and interior spacetimes so that the constants resulting from integrations can be determined.Afterwards,we explore various physical properties of the developed gravastar model such as the proper length,entropy,energy,and others to analyze how shell thickness and charge affect them.It is concluded that,in the background of Rastall theory,a gravastar model exists and serves as a viable alternative to the black hole.展开更多
We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces.To solve this problem,we propose two new parallel algorithms.We establish a weak convergence theor...We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces.To solve this problem,we propose two new parallel algorithms.We establish a weak convergence theorem for the first and a strong convergence theorem for the second.展开更多
Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) contain...Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.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
基金Supported by National Natural Science Foundation of China Under Grant(12401647)Supported by Fundamental Research Program of Shanxi Province(202203021212336)+2 种基金Taiyuan Institute of Technology Scientific Research Initial Funding(2023KJ057,2024KJ007,2024LJ005)Supported by Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2024L358)Youth Program of Taiyuan University(24TYQN10)。
文摘The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.
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 by the NSF of Shanxi(202303021221168)the Industry-university-research project of Shanxi Datong University(2022CXY10,2022CXY13).
文摘In this paper,our main goal is to study a new mathematical model which describes the frictional contact between a foundation and a deformable body which is composed of viscoplastic materials and where the process is considered dynamic.The contact condition on the normal plane is modeled by a unilateral constraint condition for a version of normal velocity in which the memory effect and the adhesion are considered.On the tangential plane a frictional contact condition is governed by the Clarke subdifferential of a locally Lipschitz function,and the evolution of the bonding field is governed by an ordinary differential equation.We formulate this problem as coupled system that consists of two ordinary differential equations and a variational-hemivariational inequality.Then,the existence,uniqueness and continuous dependence of the solution on the data results concerning the abstract system are established.Finally,we use the abstract results to show the existence and uniqueness of the solution to the contact problem.
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.
基金Supported by Fundamental Research Program of Shanxi Province(20210302123045,20210302123182)National Natural Science Foundation of China(11601446)。
文摘This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions(namely,the Dirichlet,Neumann,and Robin boundary conditions).Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained.The test function technique is performed in the proofs.It is worth observing that our results in Theorem 1.1 in this article contain the results in[6]as a special case whenθ=0.To the best of our knowledge,the results in Theorems 1.1-1.2 are new.
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.
文摘Our analysis is particularly motivated by its relevance to understanding compact object instabilities,gravitational collapse thresholds,and the formation of dense structures under the influence of modified gravity theories.The interplay of anisotropic pressures,perturbative dynamics,and modified gravity contributions offers insight into both the stable configuration of dense fluids and the mechanisms leading to dynamical instability.Such considerations directly contribute to the aims of high energy density profiles,particularly in modeling physical systems where extreme pressure,curvature,and matter interactions co-exist.We consider an axially symmetric,dense structure with anisotropic matter content and employ a specific equation of state(EoS)to examine the interplay between static and dynamic quantities via the adiabatic index.To address the complex dynamics of the collapse process,a perturbative scheme is utilized under Newtonian and post-Newtonian approximations,enabling a detailed examination of the stability and structural evolution of the system under the influence of the considered minimally coupled gravity.Our results demonstrate that hydrostatic equilibrium is maintained when effective pressure,gravitational,and anti-gravitational forces are balanced,while deviations from this balance initiate dynamical instability.Graphical representations of stable and unstable regimes are presented,revealing how the choice of gravity functions significantly affects the outcome.This work provides insight into the behavior of dense,self-gravitating configurations under modified gravity,offering broader implications for the modeling of compact astrophysical objects and contributing to the understanding of gravitational collapse in energy density regimes.
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This publication is part of the TrustBoost project,that has received funding from MICIU/AEI/10.13039/501100011033,from FEDER,UEIt is a coordinated project by a multidisciplinary team from the Universidad Politécnica de Madrid(UPM)and University of Granada(UGR),with two subprojects that address TrustBoost’s objectives:“Enhancing Trustworthiness in Conversational AI through Multimodal Affective Awareness”(Trust Boost-UPM,ref.PID2023-150584OB-C21)“Breaking the Duality of Conversational AI:Going beyond Guided Conversations While Ensuring Compliance with Domain Rules and Constraints”(Trust Boost-UGR,ref.PID2023-150584OB-C22).
文摘Building reliable intent-based,task-oriented dialog systems typically requires substantial manual effort:designers must derive intents,entities,responses,and control logic from raw conversational data,then iterate until the assistant behaves consistently.This paper investigates how far large language models(LLMs)can automate this development.In this paper,we use two reference corpora,Let’s Go(English,public transport)and MEDIA(French,hotel booking),to prompt four LLM families(GPT-4o,Claude,Gemini,Mistral Small)and generate the core specifications required by the rasa platform.These include intent sets with example utterances,entity definitions with slot mappings,response templates,and basic dialog flows.To structure this process,we introduce a model-and platform-agnostic pipelinewith two phases.The first normalizes and validates LLM-generated artifacts,enforcing crossfile consistency andmaking slot usage explicit.The second uses a lightweight dialog harness that runs scripted tests and incrementally patches failure points until conversations complete reliably.Across eight projects,all models required some targeted repairs before training.After applying our pipeline,all reached≥70%task completion(many above 84%),while NLU performance ranged from mid-0.6 to 1.0 macro-F1 depending on domain breadth.These results show that,with modest guidance,current LLMs can produce workable end-to-end dialog prototypes directly fromraw transcripts.Our main contributions are:(i)a reusable bootstrap method aligned with industry domain-specific languages(DSLs),(ii)a small set of high-impact corrective patterns,and(iii)a simple but effective harness for closed-loop refinement across conversational platforms.
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supported in part by the Ministry of Science and Technology of China (G2021016032L and G2023016011L)the National Natural Science Foundation of China (12271488 and 11975145)。
文摘This paper proposes an innovative form of group reduction or similarity transformation involving off-diagonal block matrices. The proposed method is applied to the Ablowitz-Kaup-Newell-Segur(AKNS) matrix spectral problem, leading to the generation of reduced matrix AKNS integrable hierarchies. As a result, a variety of reduced multiple-component integrable nonlinear Schr??dinger and modified Korteweg-de Vries models are derived from the analysis of the reduced AKNS matrix spectral problem.
基金Jiangsu Provincial College Student Innovation and Entrepreneurship Program(Grant No.SJCX25_2184)—“Multi-energy Complementary Optimization and Vehicle-Storage Bidirectional Interaction Technology Driven by Novel 5E Framework”(Principal Investigator:Yuan-Yuan ShiFunding Agency:Jiangsu Provincial Education Department)+3 种基金Huaian Natural Science Research Project(Grant No.HAB2024046)—“Optimal Control of Flexible Cold-Heat-Power Integrated System with Source-Grid-Load-Storage Coordination”(Principal Investigator:Jie JiFunding Agency:Huaian Science and Technology Bureau)Huaiyin Institute of TechnologyUniversity-funded Project(GrantNo.HGYK202511)—“Data-driven CooperativeOptimization Dispatch for Source-Grid-Load Systems”(Principal Investigator:Chu-Tong ZhangFunding Agency:Huaiyin Institute of Technology).
文摘In order to solve the problems of slow dynamic response and difficult multi-source coordination of solar electric vehicle charging stations under intermittent renewable energy,this paper proposes a hardware-algorithm co-design framework:the T-type three-level bidirectional converter(100 kHz switching frequency)based on silicon carbide(SiC)MOSFET is deeply integrated with fuzzy model predictive control(Fuzzy-MPC).At the hardware level,the switching trajectory and resonance suppression circuit(attenuation resonance peak 18 dB)are optimized,and the total loss is reduced by 23%compared with the traditional silicon-based IGBT.At the algorithm level,the adaptive parameter update mechanism and multi-objective rolling optimization are adopted,and the 5 ms level dynamic power allocation is realized by relying on edge computing.Experiments on 800 V DC microgrid(including 600 kW photovoltaic and 150 A·h energy storage)built based on MATLAB/Simulink hardware-in-the-loop(HIL)platform show that the system shortens the battery charging time from 42 to 28 min(the charging speed is increased by 33%).Through the 78%valley power utilization rate,the power purchase cost of high-priced power grids was significantly reduced,and the levelized electricity price decreased by 10.3%;Under the irradiation fluctuation,the renewable energy consumption rate increases by 10.1%,and the DC bus voltage fluctuation is stable within±10 V when the load step is±30%.The co-design provides an economically feasible and dynamically robust solution for the efficient integration of PV-ESG-EV in the smart grid.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171217 and 12375003)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LMS 25A010013)。
文摘In this paper,we investigate data-driven bright soliton solutions of the nonlocal reverse-time nonlinear Schrodinger(NLS)equation and the parameter identification using the physically informed neural networks(PINNs)algorithm.Accurate simulations and comparative analyses of relative and absolute errors are performed for two-soliton and four-soliton solutions including linear solitary waves and periodic waves.In the training process,the standard PINNs scheme is employed for linear solitary wave solutions,while the prior information is added at local sharp regions for periodic wave solutions due to the complicated collision behaviors.For the parameter identification,we accurately recognize the nonlinear coefficients of the nonlocal NLS equation from known solutions with different noises.These results reinforce the application of deep learning with the PINNs framework to successfully study nonlocal integrable systems.
基金supported by the Fundamental Research Program of Shanxi Province(202103021223038).
文摘In this note,we study a question introduced by Bourin[1]and extend the conclusion from[2]to the case of operators on noncommutative fully symmetric spaces.The conclusion is as follows.Let 0≤x,y∈E(M),If t∈[0,1/4]∪[3/4,1],then∥x^(t)y^(1-t)+ytx^(1-t)∥E(M)≤2^(2t-3/2)∥x+y∥E(M).
文摘This study examines the effect of charge on physical features of a gravastar model in the framework of Rastall gravity.A gravastar is an alternative model to a black hole consisting of three separate regions:the inner sector,the intermediate shell and the outer sector.Different values of the barotropic equation of state(EoS)parameter provide the mathematical basis for these regions.Field equations(FEs)are initially developed for a spherically symmetric spacetime coupled with charged matter distribution.We then use the temporal component of TolmanⅣspacetime to formulate the radial metric potential for both the inner region and intermediate shell.We also apply the matching criteria to ensure smooth matching of exterior and interior spacetimes so that the constants resulting from integrations can be determined.Afterwards,we explore various physical properties of the developed gravastar model such as the proper length,entropy,energy,and others to analyze how shell thickness and charge affect them.It is concluded that,in the background of Rastall theory,a gravastar model exists and serves as a viable alternative to the black hole.
基金supported by the Science and Technology Fund of TNU-Thai Nguyen University of Science.
文摘We study the split common solution problem with multiple output sets for monotone operator equations in Hilbert spaces.To solve this problem,we propose two new parallel algorithms.We establish a weak convergence theorem for the first and a strong convergence theorem for the second.
文摘Let n≥2 be a natural number,1≤p≤∞and X a Banach space.We prove that if X^(*)containsλ-uniformly copies of l^(k)^(p),then:P(^(n)X) contains cKλ^(n)-uniformly copies of■.in the case p^(*)>n(ii)P(^(n)X) containsλ^(n)-uniformly copies of l^(k)_(∞)in the case p^(*)≤n.This complete a result of S.Dineen’s from 1995.
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.
