The paper presents a two-layer,disturbance-resistant,and fault-tolerant affine formation maneuver control scheme that accomplishes the surrounding of a dynamic target with multiple underactuated Quadrotor Unmanned Aer...The paper presents a two-layer,disturbance-resistant,and fault-tolerant affine formation maneuver control scheme that accomplishes the surrounding of a dynamic target with multiple underactuated Quadrotor Unmanned Aerial Vehicles(QUAVs).This scheme mainly consists of predefinedtime estimators and fixed-time tracking controllers,with a hybrid Laplacian matrix describing the communication among these QUAVs.At the first layer,we devise predefined time estimators for leading and following QUAVs,enabling accurate estimation of desired information.In the second layer,we initially devise a fixed-time hybrid observer to estimate unknown disturbances and actuator faults.Fixedtime translational tracking controllers are then proposed,and the intermediary control input from these controllers is used to extract the desired attitude and angular velocities for the fixed-time rotational tracking controllers.We employ an exact tracking differentiator to handle variables that are challenging to differentiate directly.The paper includes a demonstration of the control system stability through mathematical proof,as well as the presentation of simulation results and comparative simulations.展开更多
纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图...纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图的整数标记定义的单变量多项式。本文主要计算一类特殊虚拟纽结的Affine index多项式。按照Cheng着色的规则,对虚拟纽结图的每一段弧进行整数标记,计算每个经典交叉点的指标值,进而得到这类特殊虚拟纽结的Affine index多项式的表达式。Knot theory is an important branch of topology. Virtual knot theory is a generalization of classical knot theory, and its research is carried out through a graphic theory. The virtual knot polynomial refers to a class of virtual knot invariant expressed by polynomials, such as the Arrow polynomial and the Wriggle polynomial. The affine index polynomial is a univariate polynomial defined by the integer label of a virtual knot graph. In this paper, we mainly calculate affine index polynomials for a special class of virtual knots. According to the rules of Cheng coloring, we will integer label each arc of the virtual knot graph and calculate the index value of each classical crossings, and then get the expression of the affine index polynomial of this special virtual knot.展开更多
The inherent challenges arising from variations in user-captured viewpoints and object orientation disparities in real-world scenarios pose significant difficulties in establishing robust correspondence relationships ...The inherent challenges arising from variations in user-captured viewpoints and object orientation disparities in real-world scenarios pose significant difficulties in establishing robust correspondence relationships between image pairs.Methods based on geometric transformation estimation usually perform affine transformation of the global image for viewpoint correction,which not only increases the time complexity but also generates a large number of redundant features.To solve this problem,this paper proposes an adaptive affine transformation model(AATM)to achieve robust image matching by dividing special regions with pixel information and employing feature extraction algorithms with different granularities.First,the input image is divided into significant and non-significant regions by an adaptive algorithm.Second,for the salient region,the feature point extraction is accelerated by optimizing the longitude angle sampling algorithm and constructing the affine invariant nonlinear scale space,introducing the Hessian integral image and box filter.Then,for the non-significant region of the weak texture scene through the uniform step sampling algorithm,a dense feature description can be obtained in the weak texture scenes,so that more robust features are extracted for both significant and non-significant regions.The results of extensive experiments on two datasets show that the AATM algorithm outperforms similar algorithms in terms of the number of correctly matched pairs,elapsed time,and root mean square error(RMSE),indicating that the AATM can obtain more robust matches in scenes with large angle tilting and scale transformations.展开更多
In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg gro...In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.展开更多
During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in unc...During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than those obtained using the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Therefore,the proposed algorithm has good suitability and does not require iterative calculations,resulting in a significant improvement in computational speed compared to the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Furthermore,the proposed algorithm can provide more reliable analysis and calculation results,improving the safety and stability of power systems.展开更多
We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and ...This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.展开更多
As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* ...As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.展开更多
An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local ...An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.展开更多
Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representati...Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.展开更多
In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length tim...In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.展开更多
The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as ...The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.展开更多
According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequali...According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.展开更多
Gnaphalium affine D. Don, a medicinal and edible plant, has been used to treat gout in traditional Chinese medicine and popularly consumed in China for a long time. A detailed phytochemical investigation on the aerial...Gnaphalium affine D. Don, a medicinal and edible plant, has been used to treat gout in traditional Chinese medicine and popularly consumed in China for a long time. A detailed phytochemical investigation on the aerial part of G. affine led to the isolation of two new esters of caffeoylquinic acid named(-) ethyl 1, 4-di-O-caffeoylquinate(1) and(-) methyl 1, 4-di-O-caffeoylquinate(2), together with 35 known compounds(3-37). Their structures were elucidated by spectroscopic data and first-order multiplet analysis. All the isolated compounds were tested for their xanthine oxidase inhibitory activity with an in vitro enzyme inhibitory screening assay. Among the tested compounds, 1(IC_(50) 11.94 μmol·L^(-1)) and 2(IC_(50) 15.04 μmol·L^(-1)) showed a good inhibitory activity. The current results supported the medical use of the plant.展开更多
This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods,the adopted two-layer network structure in...This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods,the adopted two-layer network structure in this paper is generally directed, which is suitable for practical space missions. Firstly, distributed finite-time sliding-mode estimators and formation controllers in both layers are designed separately to improve the flexibility of the formation control system. By introducing the properties of affine transformation into formation control protocol design,the controllers can be used to track different time-varying target formation patterns. Besides, multilayer time-varying encirclements can be achieved with particular shapes to surround the moving target. In the sequel, by integrating adaptive neural networks and specialized artificial potential functions into backstepping controllers, the problems of uncertain Euler-Lagrange models, collision avoidance as well as formation reconfiguration are solved simultaneously. The stability of the proposed controllers is verified by the Lyapunov direct method. Finally, two simulation examples of triangle formation and more complex hexagon formation are presented to illustrate the feasibility of the theoretical results.展开更多
Objective To evaluate the inhibitory effect of Gnaphalium affine extracts on xanthine oxidase(XO) activity in vitro and to analyze the mechanism of this effect. Methods In this in vitro study, Kinetic measurements wer...Objective To evaluate the inhibitory effect of Gnaphalium affine extracts on xanthine oxidase(XO) activity in vitro and to analyze the mechanism of this effect. Methods In this in vitro study, Kinetic measurements were performed in 4 different inhibitor concentrations and 5 different xanthine concentrations(60, 100, 200, 300, 400 μmol/L). Dixon and Lineweaver-Burk plot analysis were used to determine Ki values and the inhibition mode for the compounds isolated from Gnaphalium affine extract. Results Four potent xanthine oxidase inhibitors were found in 95% ethanolic(v/v) Gnaphalium affine extract. Among them, the f lavone Eupatilin exhibited the strongest inhibitory effect on XO with a inhibition constant(Ki) of 0.37 μmol/L, lower than the Ki of allopurinol(4.56 mol/L), a known synthetic XO inhibitor. Apigenin(Ki of 0.56 μmol/L, a proportion of 0.0053‰ in Gnaphalium affine), luteolin(Ki of 2.63 μmol/L, 0.0032‰ in Gnaphalium affine) and 5-hydroxy-6,7,3',4'-tetramethoxyflavone(Ki of 3.15 μmol/L, 0.0043‰ in Gnaphalium affine) also contributed to the inhibitory effect of Gnaphalium affine extract on XO activity. Conclusions These results suggest that the use of Gnaphalium affine in the treatment of gout could be attributed to its inhibitory effect on XO. This study provides a rational basis for the traditional use of Gnaphalium affine against gout.展开更多
The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this prob...The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.展开更多
The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bo...The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.展开更多
Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m)...Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m),Γ (m)(E)∩Γ (m)(F) is studied.In particular,sizes of maximal cliques in Γ (m) are determined and it is shown that Γ (m) is not edge-regular when m<n-1.展开更多
基金supported by Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-QN-0733)Guangdong Basic and Applied Basic Research Foundation,China(No.2022A1515110753)+2 种基金China Postdoctoral Science Foundation(No.2022M722583)China Industry-UniversityResearch Innovation Foundation(No.2022IT188)National Key Laboratory of Air-based Information Perception and Fusion and the Aeronautic Science Foundation of China(No.20220001068001)。
文摘The paper presents a two-layer,disturbance-resistant,and fault-tolerant affine formation maneuver control scheme that accomplishes the surrounding of a dynamic target with multiple underactuated Quadrotor Unmanned Aerial Vehicles(QUAVs).This scheme mainly consists of predefinedtime estimators and fixed-time tracking controllers,with a hybrid Laplacian matrix describing the communication among these QUAVs.At the first layer,we devise predefined time estimators for leading and following QUAVs,enabling accurate estimation of desired information.In the second layer,we initially devise a fixed-time hybrid observer to estimate unknown disturbances and actuator faults.Fixedtime translational tracking controllers are then proposed,and the intermediary control input from these controllers is used to extract the desired attitude and angular velocities for the fixed-time rotational tracking controllers.We employ an exact tracking differentiator to handle variables that are challenging to differentiate directly.The paper includes a demonstration of the control system stability through mathematical proof,as well as the presentation of simulation results and comparative simulations.
文摘纽结理论是拓扑学的一个重要分支,虚拟纽结理论是经典纽结理论的推广,对它的研究是通过一种图解理论来展开的。虚拟纽结多项式是一类以多项式表达的虚拟纽结不变量,例如Arrow多项式和Wriggle多项式。Affine index多项式是以虚拟纽结图的整数标记定义的单变量多项式。本文主要计算一类特殊虚拟纽结的Affine index多项式。按照Cheng着色的规则,对虚拟纽结图的每一段弧进行整数标记,计算每个经典交叉点的指标值,进而得到这类特殊虚拟纽结的Affine index多项式的表达式。Knot theory is an important branch of topology. Virtual knot theory is a generalization of classical knot theory, and its research is carried out through a graphic theory. The virtual knot polynomial refers to a class of virtual knot invariant expressed by polynomials, such as the Arrow polynomial and the Wriggle polynomial. The affine index polynomial is a univariate polynomial defined by the integer label of a virtual knot graph. In this paper, we mainly calculate affine index polynomials for a special class of virtual knots. According to the rules of Cheng coloring, we will integer label each arc of the virtual knot graph and calculate the index value of each classical crossings, and then get the expression of the affine index polynomial of this special virtual knot.
基金Supported by the National Natural Science Foundation of China(No.61971162,61771186)the Natural Science Foundation of Heilongjiang Province(No.PL2024 F023)+1 种基金the Fundamental Scientific Research Funds of Heilongjiang Province(No.2022-KYYWF-1050)the Open Research Fund of National Mobile Communications Research Laboratory in Southeast University(No.2023D07).
文摘The inherent challenges arising from variations in user-captured viewpoints and object orientation disparities in real-world scenarios pose significant difficulties in establishing robust correspondence relationships between image pairs.Methods based on geometric transformation estimation usually perform affine transformation of the global image for viewpoint correction,which not only increases the time complexity but also generates a large number of redundant features.To solve this problem,this paper proposes an adaptive affine transformation model(AATM)to achieve robust image matching by dividing special regions with pixel information and employing feature extraction algorithms with different granularities.First,the input image is divided into significant and non-significant regions by an adaptive algorithm.Second,for the salient region,the feature point extraction is accelerated by optimizing the longitude angle sampling algorithm and constructing the affine invariant nonlinear scale space,introducing the Hessian integral image and box filter.Then,for the non-significant region of the weak texture scene through the uniform step sampling algorithm,a dense feature description can be obtained in the weak texture scenes,so that more robust features are extracted for both significant and non-significant regions.The results of extensive experiments on two datasets show that the AATM algorithm outperforms similar algorithms in terms of the number of correctly matched pairs,elapsed time,and root mean square error(RMSE),indicating that the AATM can obtain more robust matches in scenes with large angle tilting and scale transformations.
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.
基金This article was supported by the general project“Research on Wind and Photovoltaic Fault Characteristics and Practical Short Circuit Calculation Model”(521820200097)of Jiangxi Electric Power Company.
文摘During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than those obtained using the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Therefore,the proposed algorithm has good suitability and does not require iterative calculations,resulting in a significant improvement in computational speed compared to the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Furthermore,the proposed algorithm can provide more reliable analysis and calculation results,improving the safety and stability of power systems.
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
文摘This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.
文摘As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.
基金Specialized Research Fund for the Doctoral Program of Higher Education ( No. 20090092110051)the Key Project of Chinese Ministry of Education ( No. 108060)the National Natural Science Foundation of China ( No. 51076027, 51036002, 51106024)
文摘An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.
基金partially supported by Natural Sciences Foundation of China (10671193)
文摘Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.
文摘In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.
文摘The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.
基金Supported by the National Natural Science Foundation of China(11161019,11561020)the Science and Technology Plan of Gansu Province(145RJZG227)
文摘According to the notion of Orlicz mixed volume, in this paper, we extend L_p-dual affine surface area to the Orlicz version. Further, we obtain the affine isoperimetric inequality and the Blachke-Santaló inequality for the dual Orlicz affine surface area. Besides, we also get the monotonicity inequality for Orlicz dual affine surface area.
基金supported by the Natural Science Foundation of Shanghai(No.15ZR1440100)the National Natural Science Foundation of China(No.81603279)
文摘Gnaphalium affine D. Don, a medicinal and edible plant, has been used to treat gout in traditional Chinese medicine and popularly consumed in China for a long time. A detailed phytochemical investigation on the aerial part of G. affine led to the isolation of two new esters of caffeoylquinic acid named(-) ethyl 1, 4-di-O-caffeoylquinate(1) and(-) methyl 1, 4-di-O-caffeoylquinate(2), together with 35 known compounds(3-37). Their structures were elucidated by spectroscopic data and first-order multiplet analysis. All the isolated compounds were tested for their xanthine oxidase inhibitory activity with an in vitro enzyme inhibitory screening assay. Among the tested compounds, 1(IC_(50) 11.94 μmol·L^(-1)) and 2(IC_(50) 15.04 μmol·L^(-1)) showed a good inhibitory activity. The current results supported the medical use of the plant.
基金sponsored by National Natural Science Foundation of China (Nos. 61673327, 51606161, 11602209, 91441128)Natural Science Foundation of Fujian Province of China (No. 2016J06011)China Scholarship Council (No. 201606310153)
文摘This paper addresses a target-enclosing problem for multiple spacecraft systems by proposing a two-layer affine formation control strategy. Compared with the existing methods,the adopted two-layer network structure in this paper is generally directed, which is suitable for practical space missions. Firstly, distributed finite-time sliding-mode estimators and formation controllers in both layers are designed separately to improve the flexibility of the formation control system. By introducing the properties of affine transformation into formation control protocol design,the controllers can be used to track different time-varying target formation patterns. Besides, multilayer time-varying encirclements can be achieved with particular shapes to surround the moving target. In the sequel, by integrating adaptive neural networks and specialized artificial potential functions into backstepping controllers, the problems of uncertain Euler-Lagrange models, collision avoidance as well as formation reconfiguration are solved simultaneously. The stability of the proposed controllers is verified by the Lyapunov direct method. Finally, two simulation examples of triangle formation and more complex hexagon formation are presented to illustrate the feasibility of the theoretical results.
文摘Objective To evaluate the inhibitory effect of Gnaphalium affine extracts on xanthine oxidase(XO) activity in vitro and to analyze the mechanism of this effect. Methods In this in vitro study, Kinetic measurements were performed in 4 different inhibitor concentrations and 5 different xanthine concentrations(60, 100, 200, 300, 400 μmol/L). Dixon and Lineweaver-Burk plot analysis were used to determine Ki values and the inhibition mode for the compounds isolated from Gnaphalium affine extract. Results Four potent xanthine oxidase inhibitors were found in 95% ethanolic(v/v) Gnaphalium affine extract. Among them, the f lavone Eupatilin exhibited the strongest inhibitory effect on XO with a inhibition constant(Ki) of 0.37 μmol/L, lower than the Ki of allopurinol(4.56 mol/L), a known synthetic XO inhibitor. Apigenin(Ki of 0.56 μmol/L, a proportion of 0.0053‰ in Gnaphalium affine), luteolin(Ki of 2.63 μmol/L, 0.0032‰ in Gnaphalium affine) and 5-hydroxy-6,7,3',4'-tetramethoxyflavone(Ki of 3.15 μmol/L, 0.0043‰ in Gnaphalium affine) also contributed to the inhibitory effect of Gnaphalium affine extract on XO activity. Conclusions These results suggest that the use of Gnaphalium affine in the treatment of gout could be attributed to its inhibitory effect on XO. This study provides a rational basis for the traditional use of Gnaphalium affine against gout.
基金supported in part by the National Natural Science Foundation of China(61627811,61573274,61673126,U1701261)
文摘The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.
基金supported by the National Science Fund of China for Distinguished Young Scholars(No.60725311)
文摘The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.
基金Supported by the National Natural Science Foundation of China(1 95 71 0 2 4 ) and Hunan Provincial De-partmentof Education(0 2 C5 1 2 )
文摘Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m),Γ (m)(E)∩Γ (m)(F) is studied.In particular,sizes of maximal cliques in Γ (m) are determined and it is shown that Γ (m) is not edge-regular when m<n-1.
