In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vert...A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.展开更多
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke se...This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke semantics to axiomatize lattice structures,we focus on the modal characterization of bounded lattices and their extensions relevant to logical systems.By introducing nullary modalities 1(maximum element)and 0(minimum element),we first establish a modal axiomatic system for bounded lattices.Subsequently,we provide pure formula characterizations of complementation and orthocomplementation relations in lattices,along with corresponding completeness results.As key applications,we present modal characterizations of fundamental logical algebraic structures:Boolean algebras,orthomodular lattices,and Heyting algebras.The last section develops novel axiomatization results for atomic lattices and atomless lattices.Throughout this work,all axiomatic systems are shown to be strongly complete via pureformula extensions,demonstrating how hybrid modal languages with nullary operators can uniformly capture boundary elements,complementation properties,and latticetheoretic operations central to both classical and nonclassical logics.展开更多
Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using c...Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.展开更多
Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic c...Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic consumption and better real-time performance. In this paper,a direct thrust controller design approach for gas turbine engine based on parameter dependent model is proposed. In order to ensure the stability of DTC control system based on parameter dependent model, there are usually conservatism detects. For the purpose of reducing the conservatism in the solution process of filter and controller, an Equilibrium Manifold Expansion(EME) model with bounded parameter variation of engine is established. The design conditions of Kalman filter for discrete-time EME system are introduced, and the proposed conditions have a certain suppression effect on the input noise of the system with bounded parameter variation.The engine thrust estimator stability and H∞filtering problems are solved by the polytopic quadratic Lyapunov function based on the Linear Matrix Inequalities(LMIs). To meet the performance requirements of thrust control, the Grey Wolf Optimization(GWO) algorithm is applied to optimize the PID control parameters. The proposed method is verified on a Hardware-in-Loop(HIL) platform. The simulation results demonstrate that the DTC framework can ensure the stability of engine closed-loop system in large range deviation tests. The filter and controller solution method considering the parameter variation boundary can obtain a solution that makes the system have better performance parameters. Moreover, the proposed filter has better thrust estimation performance than the traditional Kalman filter under the condition of sensor noise. Compared with Augmented Linear Quadratic Regulator(ALQR) controller, the PID controller optimized by GWO has a faster response in simulation.展开更多
Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a netwo...Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a network, the delay is with epistemic uncertainty, which makes the traditional routing scheme based on deterministic theory or probability theory not applicable. Motivated by this problem, the MCN with epistemic uncertainty is first summarized as a dynamic uncertain network based on uncertainty theory, which is widely applied to model epistemic uncertainties. Then by modeling the uncertain end-toend delay, a new delay bounded routing scheme is proposed to find the path with the maximum belief degree that satisfies the delay threshold for the dynamic uncertain network. Finally, a lowEarth-orbit satellite communication network(LEO-SCN) is used as a case to verify the effectiveness of our routing scheme. It is first modeled as a dynamic uncertain network, and then the delay bounded paths with the maximum belief degree are computed and compared under different delay thresholds.展开更多
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
We suggest and develop a novel approach to determine edge/surface states in bounded systems based on the bulk Hamiltonian of their corresponding unbounded counterparts,where the k-space is extended to the complex k-on...We suggest and develop a novel approach to determine edge/surface states in bounded systems based on the bulk Hamiltonian of their corresponding unbounded counterparts,where the k-space is extended to the complex k-one.This approach allows us to obtain simple conditions for the existence of edge/surface states in bounded systems.Our analysis also demonstrates that the emergence of such edge/surface states,which are intrinsically linked to the characteristics of system boundaries,cannot manifest without appropriate boundary conditions dictated by the necessity for wave function convergence.In order to demonstrate our method in action,we apply it to study some examples of non-topological and topological edge/surface states.We hope our discussion helps you gain a clearer and more intuitive understanding of the bulk–boundary correspondence.展开更多
This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution un...This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.展开更多
In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish crit...In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish criteria for(h0,h)-uniform boundedness and(h0,h)-uniform ultimate boundedness in terms of two measures for impulsive differential equations.展开更多
In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forci...In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.展开更多
The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently ...The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.展开更多
In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge...In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.展开更多
This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial ra...This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
文摘A nowhere-zero k-flow on a graph G=(V(G),E(G))is a pair(D,f),where D is an orientation on E(G)and f:E(G)→{±1,±2,,±(k-1)}is a function such that the total outflow equals to the total inflow at each vertex.This concept was introduced by Tutte as an extension of face colorings,and Tutte in 1954 conjectured that every bridgeless graph admits a nowhere-zero 5-flow,known as the 5-Flow Conjecture.This conjecture is verified for some graph classes and remains unresolved as of today.In this paper,we show that every bridgeless graph of Euler genus at most 20 admits a nowhere-zero 5-flow,which improves several known results.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
基金supported by China Postdoctoral Science Foundation(2024M750225).
文摘This article extends the foundational work of Wang and Wang on modal logic over lattices.Building upon their framework using polyadic modal logic with binary modalities<sup>and<inf>under standard Kripke semantics to axiomatize lattice structures,we focus on the modal characterization of bounded lattices and their extensions relevant to logical systems.By introducing nullary modalities 1(maximum element)and 0(minimum element),we first establish a modal axiomatic system for bounded lattices.Subsequently,we provide pure formula characterizations of complementation and orthocomplementation relations in lattices,along with corresponding completeness results.As key applications,we present modal characterizations of fundamental logical algebraic structures:Boolean algebras,orthomodular lattices,and Heyting algebras.The last section develops novel axiomatization results for atomic lattices and atomless lattices.Throughout this work,all axiomatic systems are shown to be strongly complete via pureformula extensions,demonstrating how hybrid modal languages with nullary operators can uniformly capture boundary elements,complementation properties,and latticetheoretic operations central to both classical and nonclassical logics.
基金supported in part by the Science and Technology Research and Development Foundation of China Academy of Railway Sciences Corporation Limited(Grant No.2023YJ364)in part by National Key R&D Program of China(Grant No.2022YFC3803700)in part by the project of Beijing Laboratory of Advanced Information Networks.
文摘Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.
基金supported by the National Natural Science Foundation of China(No.52372371)the Science Center for Gas Turbine Project,China(Nos.P2022-B-V-002-001,P2022-B-V-001-001).
文摘Direct Thrust Control(DTC) is effective in dealing with the mismatch between thrust and rotor speed in traditional engine control. Among the DTC architecture, model-based thrust estimation method has less arithmetic consumption and better real-time performance. In this paper,a direct thrust controller design approach for gas turbine engine based on parameter dependent model is proposed. In order to ensure the stability of DTC control system based on parameter dependent model, there are usually conservatism detects. For the purpose of reducing the conservatism in the solution process of filter and controller, an Equilibrium Manifold Expansion(EME) model with bounded parameter variation of engine is established. The design conditions of Kalman filter for discrete-time EME system are introduced, and the proposed conditions have a certain suppression effect on the input noise of the system with bounded parameter variation.The engine thrust estimator stability and H∞filtering problems are solved by the polytopic quadratic Lyapunov function based on the Linear Matrix Inequalities(LMIs). To meet the performance requirements of thrust control, the Grey Wolf Optimization(GWO) algorithm is applied to optimize the PID control parameters. The proposed method is verified on a Hardware-in-Loop(HIL) platform. The simulation results demonstrate that the DTC framework can ensure the stability of engine closed-loop system in large range deviation tests. The filter and controller solution method considering the parameter variation boundary can obtain a solution that makes the system have better performance parameters. Moreover, the proposed filter has better thrust estimation performance than the traditional Kalman filter under the condition of sensor noise. Compared with Augmented Linear Quadratic Regulator(ALQR) controller, the PID controller optimized by GWO has a faster response in simulation.
基金National Natural Science Foundation of China (61773044,62073009)National key Laboratory of Science and Technology on Reliability and Environmental Engineering(WDZC2019601A301)。
文摘Delay aware routing is now widely used to provide efficient network transmission. However, for newly developing or developed mobile communication networks(MCN), only limited delay data can be obtained. In such a network, the delay is with epistemic uncertainty, which makes the traditional routing scheme based on deterministic theory or probability theory not applicable. Motivated by this problem, the MCN with epistemic uncertainty is first summarized as a dynamic uncertain network based on uncertainty theory, which is widely applied to model epistemic uncertainties. Then by modeling the uncertain end-toend delay, a new delay bounded routing scheme is proposed to find the path with the maximum belief degree that satisfies the delay threshold for the dynamic uncertain network. Finally, a lowEarth-orbit satellite communication network(LEO-SCN) is used as a case to verify the effectiveness of our routing scheme. It is first modeled as a dynamic uncertain network, and then the delay bounded paths with the maximum belief degree are computed and compared under different delay thresholds.
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
基金supported by the National Natural Science Foundation of China(Grant No.11847061)。
文摘We suggest and develop a novel approach to determine edge/surface states in bounded systems based on the bulk Hamiltonian of their corresponding unbounded counterparts,where the k-space is extended to the complex k-one.This approach allows us to obtain simple conditions for the existence of edge/surface states in bounded systems.Our analysis also demonstrates that the emergence of such edge/surface states,which are intrinsically linked to the characteristics of system boundaries,cannot manifest without appropriate boundary conditions dictated by the necessity for wave function convergence.In order to demonstrate our method in action,we apply it to study some examples of non-topological and topological edge/surface states.We hope our discussion helps you gain a clearer and more intuitive understanding of the bulk–boundary correspondence.
基金Supported by the National Natural Science Foundation of China(11301419)the Research and innovation Team of China West Normal University(CXTD2020-5)。
文摘This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.
基金supported by the Natural Science Foundation of Zhejiang Province(No.LY19A010013)。
文摘In this paper,we utilize the theory of Kurzweil-Henstock integrals to investigate new criteria for boundedness in terms of two measures for generalized ordinary differential equations.As applications,we establish criteria for(h0,h)-uniform boundedness and(h0,h)-uniform ultimate boundedness in terms of two measures for impulsive differential equations.
基金Supported by Key Research Funds for the Universities of Henan Province(Grant No.19A110018)Foundation for Key Teacher of Henan Polytechnic University(Grant No.2022XQG-09).
文摘In this paper,In this paper,we first consider a specific discontinuous differential equation for a smooth and discontinuous(SD)oscillator x′′+2x(1-1√x^(2)+α^(2))=p(t),where p(t)is a given smooth 2π-periodic forcing function andαis a real parameter.Inspired by this special discontinuous oscillator,we study a more general discontinuous oscillator x′′+ω^(2)x+ϕ(x)=p(t),whereω∈R^(+)\N andϕ(x)has one discontinuous point.We show that every solution of this general discontinuous oscillator is bounded when some conditions are satisfied.
基金supported by the National Nature Science Foundation of China (61877028, 61773015).
文摘The adaptive H_(∞) finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system(NSHS)in this article.Under an appropriate adaptive state feedback,the NSHS can be equivalently transformed into a differential-algebraic system.Next,it is proved that the state feedback can be used as an adaptive H_(∞) finite-time boundedness controller of NSHS.Finally,the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.
基金The National Natural Science Foundation of China (No.10974093)the Scientific Research Foundation for Senior Personnel of Jiangsu University (No.07JDG014)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No.08KJD520015)
文摘In order to find the completeness threshold which offers a practical method of making bounded model checking complete, the over-approximation for the complete threshold is presented. First, a linear logic of knowledge is introduced into the past tense operator, and then a new temporal epistemic logic LTLKP is obtained, so that LTLKP can naturally and precisely describe the system＇s reliability. Secondly, a set of prior algorithms are designed to calculate the maximal reachable depth and the length of the longest of loop free paths in the structure based on the graph structure theory. Finally, some theorems are proposed to show how to approximate the complete threshold with the diameter and recurrence diameter. The proposed work resolves the completeness threshold problem so that the completeness of bounded model checking can be guaranteed.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(No.ZCLQN25A0103)。
文摘This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.
