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Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks
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作者 Levente Simon Anna Soós 《Applied Mathematics》 2016年第4期365-374,共10页
We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph model... We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks. 展开更多
关键词 Cantor Set Fixed Set Iterated function systems Iterated Multifunction systems Self-Similar Graphs
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Robust digital image watermarking against shearing based on Haar orthogonal function system 被引量:1
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作者 DENGMing-hui HAOYan-ling SHENDong-hui 《Journal of Marine Science and Application》 2004年第1期75-80,共6页
In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogon... In this paper, a robust digital watermarking method against shearing based on Haar orthogonal function system was introduced. The proposed method adopted the complete generalized orthogonal properties of Haar ortbogonal function system to achieve the piece-based orthogonal transform on the image. The significant middle frequency coefficients in the transformation matrix are picked up, based on characteristics of the image visual system and the Haar orthogonal transform. The watermark is adoptively weighed to the middle frequency matrix. The method improves the validity of watermarking and shows excellent advantage against shearing attack. Experimental results show that the Haar orthogonal function system based watermark approach can provide an excellent protection under geometric attacks. 展开更多
关键词 digital watermarking Haar orthogonal function system shearing attack
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ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS
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作者 吴享哲 卢英花 吉元君 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第4期465-469,共5页
A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems... A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too. 展开更多
关键词 iterated function system invariant measure ergodic theorem random iterating algorithm
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AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS
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作者 XIONG Yong(熊勇) +1 位作者 SHI Ding-hua(史定华) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第7期820-826,共7页
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th... Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach. 展开更多
关键词 FRACTAL random iterated function system affine transformation
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SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS
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作者 Shaoyuan Xu Wangbin Xu Dingxing Zhong 《Analysis in Theory and Applications》 2012年第3期269-277,共9页
Iterated function systems (IFS) were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function... Iterated function systems (IFS) were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings. 展开更多
关键词 iterated function system ATTRACTOR generalized contractive mapping completemetric space fixed point
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Fixed Point Theorems of the Iterated Function Systems
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作者 Ji You-qing Liu Zhi Ri Song-il 《Communications in Mathematical Research》 CSCD 2016年第2期142-150,共9页
In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function s... In this paper, we present some fixed point theorems of iterated function systems consisting of α-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of generalized metric space, which is Mso extensively applied in topological dynamic system. 展开更多
关键词 fixed point α-ψ-contractive mapping iterated function system gener-alized metric space
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Mean Dimension for Non-autonomous Iterated Function Systems
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作者 Meng Deyu Zhao Cao 《数学理论与应用》 2024年第3期119-129,共11页
In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations... In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension. 展开更多
关键词 Non-autonomous iterated function system Mean dimension Metric mean dimension
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Generalized Product of Iteration Function System
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作者 ZHAO Ting-ting WEI Xiao-peng XIA Jun-tian SANG Lin 《Computer Aided Drafting,Design and Manufacturing》 2005年第2期44-49,共6页
The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS)... The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system (IFS) are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition. 展开更多
关键词 FRACTAL iteration function system product of fractal semi-product of fractal generalized product of fractal
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Simulation for chaos game representation of genomes by recurrent iterated function systems 被引量:1
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作者 Zu-Guo Yu Long Shi +1 位作者 Qian-Jun Xiao Vo Anh 《Journal of Biomedical Science and Engineering》 2008年第1期44-51,共8页
Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequen... Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures. The parameters estimated in the RIFS model reflect information on species classification. 展开更多
关键词 GENOMES CHAOS GAME REPRESENTATION RECURRENT ITERATED function systems.
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ITERATED FUNCTION SYSTEM AND GALTON-WATSON TREE
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作者 余旌胡 谢南瑞 《Acta Mathematica Scientia》 SCIE CSCD 2007年第3期456-464,共9页
Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported... Given a system {S1,…, SN} of N contractive similarities satisfying some strong separation condition, it has an invariant Set K for the system. In this article, the authors construct some random measure μω supported on random subset Kω of K, μω having some "non-standard" multifractal structure, which contrasts the well-knoWn multifractal formalism for the invariant measure of system {S1,.., SN} may possess. The main tool is the multifractal structures of a Galton-Watson tree, which are obtained by Liu [9], Shieh-Taylor [14], and MSrters-Shieh [12]. 展开更多
关键词 Multifractal structure iterated function stysem Galton-Watson tree
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Iterated Function System-Based Crossover Operation for Real-Coded Genetic Algorithm
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作者 S. H. Ling 《Journal of Intelligent Learning Systems and Applications》 2015年第2期37-41,共5页
An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity character... An iterated function system crossover (IFSX) operation for real-coded genetic algorithms (RCGAs) is presented in this paper. Iterated?function system (IFS) is one type of fractals that maintains a similarity characteristic. By introducing the IFS into the crossover operation, the RCGA performs better searching solution with a faster convergence in a set of benchmark test functions. 展开更多
关键词 GENETIC ALGORITHM ITERATED function system CROSSOVER Operation
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Functional central nervous system regeneration:Challenges from axons to circuits
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作者 Apolline Delaunay Mickael Le Boulc’h +1 位作者 Stephane Belin Homaira Nawabi 《Neural Regeneration Research》 2026年第5期1983-1984,共2页
The mature central nervous system(CNS,composed of the brain,spinal cord,olfactory and optic nerves)is unable to regenerate spontaneously after an insult,both in the cases of neurodegenerative diseases(for example Alzh... The mature central nervous system(CNS,composed of the brain,spinal cord,olfactory and optic nerves)is unable to regenerate spontaneously after an insult,both in the cases of neurodegenerative diseases(for example Alzheimer's or Parkinson's disease)or traumatic injuries(such as spinal cord lesions).In the last 20 years,the field has made significant progress in unlocking axon regrowth. 展开更多
关键词 parkinsons disease unlocking axon regrowth neurodegenerative diseases central nervous system cnscomposed functional regeneration axon regrowth spinal cord lesions central nervous system
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The complex role of protocadherin-19 in brain function:a focus on the oxytocin system
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作者 Sara Mazzoleni Marta Busnelli Silvia Bassani 《Neural Regeneration Research》 SCIE CAS 2025年第11期3211-3212,共2页
Mutations in the protocadherin-19(PCDH19)gene(Xq22.1)cause the X-linked syndrome known as developmental and epileptic encephalopathy 9(DEE9,OMIM#300088)(Dibbens et al.,2008).DEE9 is characterized by early-onset cluste... Mutations in the protocadherin-19(PCDH19)gene(Xq22.1)cause the X-linked syndrome known as developmental and epileptic encephalopathy 9(DEE9,OMIM#300088)(Dibbens et al.,2008).DEE9 is characterized by early-onset clustering epilepsy associated with intellectual disability ranging from mild to profound,autism spectrum disorder,and other neuropsychiatric features including schizophrenia,anxiety,attentiondeficit/hyperactivity,and obsessive or aggressive behaviors.While seizures may become less frequent in adolescence,psychiatric comorbidities persist and often worsen with age(Dibbens et al.,2008;Kolc et al.,2020). 展开更多
关键词 EPILEPSY function system
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Accumulative-Error-Based Event-Triggered Control for Discrete-Time Linear Systems:A Discrete-Time Looped Functional Method 被引量:1
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作者 Xian-Ming Zhang Qing-Long Han +1 位作者 Xiaohua Ge Bao-Lin Zhang 《IEEE/CAA Journal of Automatica Sinica》 2025年第4期683-693,共11页
This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat... This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method. 展开更多
关键词 Discrete-time linear systems event-triggered control input saturation looped functional method
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Microglia overexpressing brain-derived neurotrophic factor promote vascular repair and functional recovery in mice after spinal cord injury 被引量:2
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作者 Fanzhuo Zeng Yuxin Li +6 位作者 Xiaoyu Li Xinyang Gu Yue Cao Shuai Cheng He Tian Rongcheng Mei Xifan Mei 《Neural Regeneration Research》 2026年第1期365-376,共12页
Spinal cord injury represents a severe form of central nervous system trauma for which effective treatments remain limited.Microglia is the resident immune cells of the central nervous system,play a critical role in s... Spinal cord injury represents a severe form of central nervous system trauma for which effective treatments remain limited.Microglia is the resident immune cells of the central nervous system,play a critical role in spinal cord injury.Previous studies have shown that microglia can promote neuronal survival by phagocytosing dead cells and debris and by releasing neuroprotective and anti-inflammatory factors.However,excessive activation of microglia can lead to persistent inflammation and contribute to the formation of glial scars,which hinder axonal regeneration.Despite this,the precise role and mechanisms of microglia during the acute phase of spinal cord injury remain controversial and poorly understood.To elucidate the role of microglia in spinal cord injury,we employed the colony-stimulating factor 1 receptor inhibitor PLX5622 to deplete microglia.We observed that sustained depletion of microglia resulted in an expansion of the lesion area,downregulation of brain-derived neurotrophic factor,and impaired functional recovery after spinal cord injury.Next,we generated a transgenic mouse line with conditional overexpression of brain-derived neurotrophic factor specifically in microglia.We found that brain-derived neurotrophic factor overexpression in microglia increased angiogenesis and blood flow following spinal cord injury and facilitated the recovery of hindlimb motor function.Additionally,brain-derived neurotrophic factor overexpression in microglia reduced inflammation and neuronal apoptosis during the acute phase of spinal cord injury.Furthermore,through using specific transgenic mouse lines,TMEM119,and the colony-stimulating factor 1 receptor inhibitor PLX73086,we demonstrated that the neuroprotective effects were predominantly due to brain-derived neurotrophic factor overexpression in microglia rather than macrophages.In conclusion,our findings suggest the critical role of microglia in the formation of protective glial scars.Depleting microglia is detrimental to recovery of spinal cord injury,whereas targeting brain-derived neurotrophic factor overexpression in microglia represents a promising and novel therapeutic strategy to enhance motor function recovery in patients with spinal cord injury. 展开更多
关键词 ANGIOGENESIS apoptosis brain-derived neurotrophic factor colony stimulating factor 1 receptor inflammation MICROGLIA motor function spinal cord injury vascular endothelial growth factor
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Linking starch particle physicochemical properties to functionality in medicinal plants:Insights from Polygonum multiflorum and Smilax glabra 被引量:1
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作者 Nan Wang Lingling Wu +2 位作者 Yaya Su Haifeng Tang Hailong Yuan 《Chinese Chemical Letters》 2026年第1期487-491,共5页
This study investigates the properties of high-purity starches extracted from Polygonum multiflorum(PMS)and Smilax glabra(SGS).The starches were characterized by scanning electron microscopy,Fouriertransform infrared ... This study investigates the properties of high-purity starches extracted from Polygonum multiflorum(PMS)and Smilax glabra(SGS).The starches were characterized by scanning electron microscopy,Fouriertransform infrared spectroscopy,X-ray diffraction,high-performance anion-exchange chromatography,and differential scanning calorimetry.Significant differences were observed in their morphological,physicochemical,and functional properties.PMS had a smaller particle size(13.68 μm),irregular polygonal shape,A-type,lower water absorption(62.67 %),and higher oil absorption(51.17 %).In contrast,SGS exhibited larger particles(31.75 μm),a nearly spherical shape,B-type,higher crystallinity(50.66 %),and greater amylose content(21.54 %),with superior thermal stability,shear resistance,and gelatinization enthalpy.SGS also contained higher resistant starch(83.28 %) and longer average chain length(20.58 %),but showed lower solubility,swelling power,light transmittance,and freeze-thaw stability.The physicochemical properties differences in crystal pattern and particle morphology between PMS and SGS lead to distinct behaviors during in vitro digestion and fermentation.These findings highlight the potential of medicinal plant starches in functional ingredients and industrial processes. 展开更多
关键词 Starch particle Physicochemical properties Starch function Resistant starch Starch extraction
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Parameter identification of magnetic levitation system based on modulation function method
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作者 Tingchen Du Xueling Fan Sheng Feng 《Control Theory and Technology》 2025年第4期602-617,共16页
A novel parameter identification method for magnetic levitation bearing rotor systems is proposed,based on the modulation function method.The fundamental principle of the modulation function method for parameter ident... A novel parameter identification method for magnetic levitation bearing rotor systems is proposed,based on the modulation function method.The fundamental principle of the modulation function method for parameter identification is derived on the basis of the characteristics of the modulation function.The transformation of the differential equation model of a continuous system into a general algebraic equation model is effectively achieved,thereby avoiding the influence of errors introduced by the initial value and differential derivation of the system.Modulation function method parameter identification models have been established for single-degree-of-freedom and multi-degree-of-freedom magnetic levitation bearing rotor systems.The influence of different parameters of Hartley modulation function on the accuracy of system parameter identification has been investigated,thus providing a basis for the design of Hartley modulation function parameters.Simulation and experimental results demonstrate that the modulation function method can effectively identify system parameters despite the presence of system noise. 展开更多
关键词 Modulation function method Hartley modulation function Magnetic levitation system Parameter identification
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Predefined-time controller design for a multiple space transportation robots system based on Lp-Norm-Normalized Sign Function
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作者 Ran TAO Yibo DING +1 位作者 Hanyu LI Xiaokui YUE 《Chinese Journal of Aeronautics》 2025年第2期432-444,共13页
This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firs... This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time. 展开更多
关键词 Multiple space transportation robots system On-orbit assemblyPredefined-time stability criterion Composite Lyapunov function Lp-Norm-Normalized Sign function Predefined-time controller
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Synchronous Membership Function Dependent Event-Triggered H∞Control of T-S Fuzzy Systems Under Network Communications
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作者 Bo-Lin Xu Chen Peng Wen-Bo Xie 《IEEE/CAA Journal of Automatica Sinica》 2025年第5期1041-1043,共3页
Dear Editor,This letter deals with the controller synthesis problem of networked Takagi-Sugeno(T-S)fuzzy systems.Due to the introduction of network communications,the same premise is no longer shared by fuzzy plants a... Dear Editor,This letter deals with the controller synthesis problem of networked Takagi-Sugeno(T-S)fuzzy systems.Due to the introduction of network communications,the same premise is no longer shared by fuzzy plants and fuzzy controllers.This makes the classic parallel distribution compensation(PDC)control infeasible.To overcome this situation,a novel method for reconstructing the membership functions'grades is proposed,which synchronizes the time scales.Then,the membership function dependent method is adopted to introduce asynchronous errors and detailed membership function information.For the event-triggered control strategy,a series of robust H∞stable conditions in LMI form are derived.Finally,a simulation of a practical system is used to demonstrate the method proposed in this letter can reduce conservatism. 展开更多
关键词 fuzzy plants controller synthesis problem network communicationsthe event triggered control reconstructing membership functionsgrades synchronizes time scalesthenthe synchronous membership functions membership function dependent method
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Systematic Evaluation and Meta-analysis of the Effects of Phase I Cardiac Rehabilitation on Heart Function of Patients after Percutaneous Coronary Intervention
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作者 Haojie Zhou Qiang Zhang +2 位作者 Xiaoyu Cai Yu Cheng Guifeng Zhao 《Journal of Clinical and Nursing Research》 2025年第6期56-66,共11页
Objective:To systematically evaluate the impact of phase I cardiac rehabilitation exercise prescriptions on cardiac function levels in patients after coronary intervention.Methods:Seven Chinese and English databases,i... Objective:To systematically evaluate the impact of phase I cardiac rehabilitation exercise prescriptions on cardiac function levels in patients after coronary intervention.Methods:Seven Chinese and English databases,including Cochrane Library,PubMed,Web of Science,ESC(European Society of Cardiology),and CNKI,as well as professional association websites,were searched using computers,with manual searching as a complement.Relevant literature published from the establishment of the database to February 2025 was retrieved.Two researchers independently screened the literature,extracted data,and evaluated the quality of the literature.Meta-analysis was performed using RevMan 5.3 software.Results:A total of 8 articles were included,involving 843 patients.Meta-analysis results showed that compared with routine nursing,phase I cardiac rehabilitation exercise prescriptions helped increase the 6-minute walking distance in patients after coronary intervention[MD=0.84,95%CI(0.57,1.10),P<0.001],increase the level of left ventricular ejection fraction in patients after coronary intervention[MD=0.67,95%CI(0.33,1.00),P<0.001],and cardiac rehabilitation combined with respiratory rehabilitation exercise could improve the level of left ventricular ejection fraction in patients after coronary intervention[MD=0.58,95%CI(0.40,0.76),P<0.001].Conclusion:The implementation of phase I cardiac rehabilitation exercise prescriptions can help improve cardiac function levels in patients after coronary intervention.However,the standardization of outcome evaluation indicators needs to be improved,and the long-term effects of rehabilitation still require verification through a large number of high-quality studies. 展开更多
关键词 Cardiac rehabilitation PCI EXERCISE Cardiac function systematic evaluation
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