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
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
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
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,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
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers...This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.展开更多
This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system ...This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.展开更多
In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f...In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.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
In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utili...In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine.展开更多
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.展开更多
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 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.
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(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 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.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金supported by the Graduate Education Innovation Funds(2022CXZZ088)at Central China Normal University in Chinasupported by the NSFC(12225106,11931012)the Fundamental Research Funds(CCNU22LJ002)for the Central Universities in China。
文摘This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.
基金Project jointly supported by the National Natural Science Foundation of China(Grant No.12372013)Program for Science and Technology Innovation Talents in Universities of Henan Province,China(Grant No.24HASTIT034)+3 种基金the Natural Science Foundation of Henan Province,China(Grant No.232300420122)the Humanities and Society Science Foundation from the Ministry of Education of China(Grant No.19YJCZH265)China Postdoctoral Science Foundation(Grant No.2019M651633)First Class Discipline of Zhejiang-A(Zhejiang University of Finance and Economics Statistics),the Collaborative Innovation Center for Data Science and Big Data Analysis(Zhejiang University of Finance and Economics-Statistics).
文摘This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.
基金supported by the Key Research Funds for the Universities of Henan Province(No.19A110018)the Foundation for Key Teachers of Henan Polytechnic University(No.2022XQG-09)。
文摘In this paper we study the boundedness and unboundedness of the solutions of the smooth and discontinuous(SD)oscillatorbegin{equation*}x''+f(x)x'+x-frac{x}{sqrt{x^{2}+alpha^{2}}}=p(t).end{equation*}Since f(x)≠0,the system is non-Hamiltonian,so we have to introduce some reversibility assumptions to apply a suitable twist theorem,for reversible maps with small twist.Moreover,when the nonnegative parameterαdecreases to 0,the system becomes discontinuous.In this case,we need to introduce some suitable transformations to overcome the lack of regularity.We will prove that for any nonnegative parameterα,when p(t)is an odd periodic function satisfying∣∣∫2π0p(t)sintdift∣∣<4,all the solutions are bounded;when p(t)satisfies∣∣∫2π0p(t)sintdift∣∣>4,the SD oscillator has unbounded solutions,and when p(t)satisfies∣∣∫_(0)^(2π)p(t)sintdift∣∣≥4+|F|_(∞),all the solutions are unbounded.
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 in part by the National Natural Science Foundation of China(12171124,61933007)the Natural Science Foundation of Heilongjiang Province of China(ZD2022F003)+2 种基金the National High-End Foreign Experts Recruitment Plan of China(G2023012004L)the Royal Society of UKthe Alexander von Humboldt Foundation of Germany
文摘In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.
