Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured...Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.展开更多
Fractal assembly in discrete structures,especially for artificial supramolecular species,has attracted significantly increased interest over the past two decades.In this study,we present the precisely controlled fract...Fractal assembly in discrete structures,especially for artificial supramolecular species,has attracted significantly increased interest over the past two decades.In this study,we present the precisely controlled fractal expanding synthesis of a novel triangular prism supramolecule featuring Sierpiński triangular face,which was achieved through a module-intervened self-expansion strategy.The homoleptic S1 was firstly synthesized through the assembly of ligand L1 with Zn^(2+)ions.Based on the triangular-faced prism S1,we further introduced Sierpiński triangular faces on the section of the heteroleptic supramolecular cage S2 with an expanded inner cavity and more abundant active sites for photocatalytic properties.The topotactic architectures for both S1 and S2 were fully characterized by nuclear magnetic resonance spectroscopy,high-resolution electrospray ionization mass spectrometry,transmission electron microscopy,and atomic force microscopy.Furthermore,the enhanced photocatalytic activity of the fractal expanded S2 was performed via the superior amine oxidative efficiency over S1.This study proposes the unprecedented fractal expanding strategy for three-dimensional supramolecular species with higher complexity,potentially opening new avenues for structural regulation of artificial fractal molecules.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
As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple q...As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple quantum dot structure.Through calculation and simulation,it is found that concurrence is mainly affected by the interdot coupling strength t,Coulomb interactionU,temperature T,and electrode coupling G.Through comparative studies with parallel triple quantum dot structures,we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions.In addition,under the condition that concurrence exceeds 0.9,the functional relationship between t and U is obtained through simulation,which provides theoretical support for quantum dot regulation under high entanglement.Finally,we demonstrate the feasibility of implementing a three-qubit quantum gate,using the Toffoli gate as a representative example,under the condition that the triangular triple quantum dot system maintains high entanglement.展开更多
In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singular...In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.展开更多
The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable m...The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable measured output.In this paper,we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence,where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance.The numerical experiments are carried out to illustrate effectiveness of the proposed approach.展开更多
This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Fur...This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.展开更多
The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice ...The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.展开更多
In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be...In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be Cl, thus can be applied for backstepping design, which has extended the scope of previous nonlinear systems in the form of strict-feedback and pure-feedback. With the help of neural network approximator, H-∞ performance analysis of stability is given. The effectiveness of proposed control law is verified via simulation.展开更多
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun...This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.展开更多
Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy mo...Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).展开更多
Turing demonstrated that spatially heterogeneous patterns can be self-organized, when the two substances interact locally and diffuse randomly. Turing systems have been applied not only to explain patterns observed wi...Turing demonstrated that spatially heterogeneous patterns can be self-organized, when the two substances interact locally and diffuse randomly. Turing systems have been applied not only to explain patterns observed within the biological and chemical fields, but also to develop image information processing tools. In a twin study, to evaluate the V-shaped bundle of the inner ear outer hair, we developed a method that utilizes a reaction-diffusion system with anisotropic diffusion that exhibited triangular patterns with the introduction of a certain anisotropy strength. In this study, we explored the parameter range over which these periodic triangular patterns were obtained. First, we defined an index for triangular clearness, TC. Triangular patterns can be obtained by introducing a large anisotropy δ, but the range of δ depends on the diffusion coefficient. We found an explanatory variable that can explain the change in TC based on a heuristic argument of the relative distance of the pitchfork bifurcation point between the maximum and minimum anisotropic diffusion function values. Clear periodic triangular patterns were obtained when the distance between the minimum anisotropic function value and pitchfork bifurcation point was over 2.5 times the distance to the anisotropic diffusion function maximum value. By changing the diffusion coefficients or the reaction terms, we further confirmed the accuracy of this condition using computer simulation. Its relevance to diffusion instability has also been discussed.展开更多
This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on ther...This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.展开更多
Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relation...Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relationship between PID parameters is established to reduce the number of adjustable parameters to one.Then,based on the incremental triangular data model,a data-driven APID tracking control(DD-APIDTC)method is proposed to adjust only one controller parameter and one model parameter online,both of which have clear physical meaning.Subsequently,sufficient conditions are derived for the boundedness of the system tracking error.Finally,simulation results are given to illustrate the effectiveness of the proposed method.展开更多
Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little...Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little is known about the impact of the rate of current change on working memory.In this study,we aimed to investigate the effects of two types of tACS with different rates of current change on working memory performance and brain activity.We applied a randomized,single-blind design and divided 81 young participants who received triangular wave tACS,sinusoidal wave tACS,or sham stimulation into three groups.Participants performed n-back tasks,and electroencephalograms were recorded before,during,and after active or sham stimulation.Compared to the baseline,working memory performance(accuracy and response time)improved after stimulation under all stimulation conditions.According to drift-diffusion model analysis,triangular wave tACS significantly increased the efficiency of non-target information processing.In addition,compared with sham conditions,triangular wave tACS reduced alpha power oscillations in the occipital lobe throughout the encoding period,while sinusoidal wave tACS increased theta power in the central frontal region only during the later encoding period.The brain network connectivity results showed that triangular wave tACS improved the clustering coefficient,local efficiency,and node degree intensity in the early encoding stage,and these parameters were positively correlated with the non-target drift rate and decision starting point.Our findings on how tACS modulates working memory indicate that triangular wave tACS significantly enhances brain network connectivity during the early encoding stage,demonstrating an improvement in the efficiency of working memory processing.In contrast,sinusoidal wave tACS increased the theta power during the later encoding stage,suggesting its potential critical role in late-stage information processing.These findings provide valuable insights into the potential mechanisms by which tACS modulates working memory.展开更多
In endoscopic surgery,the limited field of view and the nonlinear deformation of organs caused by patient movement and respiration significantly complicate the modeling and accurate tracking of soft tissue surfaces fr...In endoscopic surgery,the limited field of view and the nonlinear deformation of organs caused by patient movement and respiration significantly complicate the modeling and accurate tracking of soft tissue surfaces from endoscopic image sequences.To address these challenges,we propose a novel Hybrid Triangular Matching(HTM)modeling framework for soft tissue feature tracking.Specifically,HTM constructs a geometric model of the detected blobs on the soft tissue surface by applying the Watershed algorithm for blob detection and integrating the Delaunay triangulation with a newly designed triangle search segmentation algorithm.By leveraging barycentric coordinate theory,HTMrapidly and accurately establishes inter-frame correspondences within the triangulated model,enabling stable feature tracking without explicit markers or extensive training data.Experimental results on endoscopic sequences demonstrate that this model-based tracking approach achieves lower computational complexity,maintains robustness against tissue deformation,and provides a scalable geometric modeling method for real-time soft tissue tracking in surgical computer vision.展开更多
Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an a...Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stabl...This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.展开更多
文摘Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.
基金supported by the Major Science and Technology Projects of Yunnan Province(No.202302AB080016)the National Natural Science Foundation of China(Nos.22101060,22371056,and 52303269)the Science and Technology Research Project of Guangzhou(Nos.202201020201 and 2023A03J0624)。
文摘Fractal assembly in discrete structures,especially for artificial supramolecular species,has attracted significantly increased interest over the past two decades.In this study,we present the precisely controlled fractal expanding synthesis of a novel triangular prism supramolecule featuring Sierpiński triangular face,which was achieved through a module-intervened self-expansion strategy.The homoleptic S1 was firstly synthesized through the assembly of ligand L1 with Zn^(2+)ions.Based on the triangular-faced prism S1,we further introduced Sierpiński triangular faces on the section of the heteroleptic supramolecular cage S2 with an expanded inner cavity and more abundant active sites for photocatalytic properties.The topotactic architectures for both S1 and S2 were fully characterized by nuclear magnetic resonance spectroscopy,high-resolution electrospray ionization mass spectrometry,transmission electron microscopy,and atomic force microscopy.Furthermore,the enhanced photocatalytic activity of the fractal expanded S2 was performed via the superior amine oxidative efficiency over S1.This study proposes the unprecedented fractal expanding strategy for three-dimensional supramolecular species with higher complexity,potentially opening new avenues for structural regulation of artificial fractal molecules.
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As an important index to measure the degree of entanglement in quantum systems,concurrence plays an important role in practical research.In this paper,we study the concurrence between two qubits in triangular triple quantum dot structure.Through calculation and simulation,it is found that concurrence is mainly affected by the interdot coupling strength t,Coulomb interactionU,temperature T,and electrode coupling G.Through comparative studies with parallel triple quantum dot structures,we demonstrate that the triangular geometry exhibits significantly enhanced concurrence under identical conditions.In addition,under the condition that concurrence exceeds 0.9,the functional relationship between t and U is obtained through simulation,which provides theoretical support for quantum dot regulation under high entanglement.Finally,we demonstrate the feasibility of implementing a three-qubit quantum gate,using the Toffoli gate as a representative example,under the condition that the triangular triple quantum dot system maintains high entanglement.
基金Supported by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2025L092)the National Natural Science Foundation of China(Grant No.12071120).
文摘In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring.
基金supported by the National Natural Science Foundation of China(No.61273129).
文摘The extended state observer(ESO)is the most important part of an emerging control technology known as active disturbance rejection control to this day,aiming at estimating"total disturbance"from observable measured output.In this paper,we construct a nonlinear ESO for a class of uncertain lower triangular nonlinear systems with stochastic disturbance and show its convergence,where the total disturbance includes internal uncertain nonlinear part and external stochastic disturbance.The numerical experiments are carried out to illustrate effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (Nos. 11061019,10962004,11101200,and 11026175)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia of China (No. 2010MS0110)the Cultivation of Innovative Talent of "211 Project" of Inner Mongolia University
文摘This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.
基金＊The project supported by the National Key Basic Research Development of China under Grant No. N1998030600 and National Natural Science Foundation of China under Grant No. 10072013
文摘The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems.
基金Shanghai Leading Academic Discipline Project(B504)
文摘In this paper, a neural-network-based variable structure control scheme is presented for a class of nonlinear systems with a general low triangular structure. The proposed variable structure controller is proved to be Cl, thus can be applied for backstepping design, which has extended the scope of previous nonlinear systems in the form of strict-feedback and pure-feedback. With the help of neural network approximator, H-∞ performance analysis of stability is given. The effectiveness of proposed control law is verified via simulation.
基金the National Natural Science Foundation of China under Grant Nos.61273311 and 61803247.
文摘This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.
文摘Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).
文摘Turing demonstrated that spatially heterogeneous patterns can be self-organized, when the two substances interact locally and diffuse randomly. Turing systems have been applied not only to explain patterns observed within the biological and chemical fields, but also to develop image information processing tools. In a twin study, to evaluate the V-shaped bundle of the inner ear outer hair, we developed a method that utilizes a reaction-diffusion system with anisotropic diffusion that exhibited triangular patterns with the introduction of a certain anisotropy strength. In this study, we explored the parameter range over which these periodic triangular patterns were obtained. First, we defined an index for triangular clearness, TC. Triangular patterns can be obtained by introducing a large anisotropy δ, but the range of δ depends on the diffusion coefficient. We found an explanatory variable that can explain the change in TC based on a heuristic argument of the relative distance of the pitchfork bifurcation point between the maximum and minimum anisotropic diffusion function values. Clear periodic triangular patterns were obtained when the distance between the minimum anisotropic function value and pitchfork bifurcation point was over 2.5 times the distance to the anisotropic diffusion function maximum value. By changing the diffusion coefficients or the reaction terms, we further confirmed the accuracy of this condition using computer simulation. Its relevance to diffusion instability has also been discussed.
文摘This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.
基金supported by the National Natural Science Foundation of China(62173002,62403010,52301408)the Beijing Natural Science Foundation(L241015,4222045)+1 种基金the Yuxiu Innovation Project of NCUT(2024NCUTYXCX111)the China Postdoctoral Science Foundation(2024M750192).
文摘Dear Editor,This letter investigates a low-complexity data-driven adaptive proportional-integral-derivative(APID)control scheme to address the output tracking problem of a class of nonlinear systems.First,the relationship between PID parameters is established to reduce the number of adjustable parameters to one.Then,based on the incremental triangular data model,a data-driven APID tracking control(DD-APIDTC)method is proposed to adjust only one controller parameter and one model parameter online,both of which have clear physical meaning.Subsequently,sufficient conditions are derived for the boundedness of the system tracking error.Finally,simulation results are given to illustrate the effectiveness of the proposed method.
基金supported by the Key-Area Research and Development Program of Guangdong Province(2023B0303030002)the Beijing Natural Science Foundation(IS23114,7242274)+4 种基金the China Postdoctoral Science Foundation(2023TQ0027 and 2024M754099)the STI 2030-Major Projects(2022ZD0208500)the National Natural Science Foundation of China(62336002,82071912,62406025,82202291,62373056,62306035)the Beijing Nova Program(20230484465)the Shenzhen Basic Research Program(JCYJ20241202124804007).
文摘Working memory is an executive memory process that includes encoding,maintenance,and retrieval.These processes can be modulated by transcranial alternating current stimulation(tACS)with sinusoidal waves.However,little is known about the impact of the rate of current change on working memory.In this study,we aimed to investigate the effects of two types of tACS with different rates of current change on working memory performance and brain activity.We applied a randomized,single-blind design and divided 81 young participants who received triangular wave tACS,sinusoidal wave tACS,or sham stimulation into three groups.Participants performed n-back tasks,and electroencephalograms were recorded before,during,and after active or sham stimulation.Compared to the baseline,working memory performance(accuracy and response time)improved after stimulation under all stimulation conditions.According to drift-diffusion model analysis,triangular wave tACS significantly increased the efficiency of non-target information processing.In addition,compared with sham conditions,triangular wave tACS reduced alpha power oscillations in the occipital lobe throughout the encoding period,while sinusoidal wave tACS increased theta power in the central frontal region only during the later encoding period.The brain network connectivity results showed that triangular wave tACS improved the clustering coefficient,local efficiency,and node degree intensity in the early encoding stage,and these parameters were positively correlated with the non-target drift rate and decision starting point.Our findings on how tACS modulates working memory indicate that triangular wave tACS significantly enhances brain network connectivity during the early encoding stage,demonstrating an improvement in the efficiency of working memory processing.In contrast,sinusoidal wave tACS increased the theta power during the later encoding stage,suggesting its potential critical role in late-stage information processing.These findings provide valuable insights into the potential mechanisms by which tACS modulates working memory.
基金Support by Sichuan Science and Technology Program[2023YFSY0026,2023YFH0004].
文摘In endoscopic surgery,the limited field of view and the nonlinear deformation of organs caused by patient movement and respiration significantly complicate the modeling and accurate tracking of soft tissue surfaces from endoscopic image sequences.To address these challenges,we propose a novel Hybrid Triangular Matching(HTM)modeling framework for soft tissue feature tracking.Specifically,HTM constructs a geometric model of the detected blobs on the soft tissue surface by applying the Watershed algorithm for blob detection and integrating the Delaunay triangulation with a newly designed triangle search segmentation algorithm.By leveraging barycentric coordinate theory,HTMrapidly and accurately establishes inter-frame correspondences within the triangulated model,enabling stable feature tracking without explicit markers or extensive training data.Experimental results on endoscopic sequences demonstrate that this model-based tracking approach achieves lower computational complexity,maintains robustness against tissue deformation,and provides a scalable geometric modeling method for real-time soft tissue tracking in surgical computer vision.
基金supported by the National Key R&D Program of China(Grant No.2022YFC3003601)Joint Funds of the National Natural Science Foundation of China Project on Earthquake Science(Grant No.U2239252)the program of the Innovative Research Team in China Earthquake Administration.
文摘Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
基金supported by the China Scholarship Council(CSC)(No.202206290131)。
文摘This paper presents an analysis of an equilateral triangular array formation initialization for space-based gravitational wave observatory(GWO)near Lagrange points in the circular-restricted three-body problem.A stable configuration is essential for the continuous observation of gravitational waves(GWs).However,the motion near the collinear libration points is highly unstable.This problem is examined by output regulation theory.Using the tracking aspect,the equilateral triangular array formation is established in two periods and the fuel consumption is calculated.Furthermore,the natural evolution of the formation without control input is analyzed,and the effective stability duration is quantified to determine the timing of control interventions.Finally,to observe the GWs in same direction with different frequency bands,scale reconfiguration is employed.
