In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted co...In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.展开更多
This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays.The objective is to design a distribu...This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays.The objective is to design a distributed control strategy that ensures the output of each follower converges to the convex hull formed by the outputs of a group of leaders in mean square sense.A novel distributed observer is proposed by tackling both Markovian randomly switching topologies and unbounded delays.Then,a distributed state feedback controller and a distributed output feedback controller are developed based on the distributed observer,respectively.Finally,simulation results are provided to demonstrate the effectiveness of the proposed controllers.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 this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or...In this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or of order two with respect to the space variable.We prove some L^(2)(R)-norm decay estimates of solutions and their higher-order derivatives with respect to the space variable,where the decay rates depend on the number of the present frictional dampings,the regularity of the initial data,and some connections between the speeds of wave propagation of the two wave equations.Both our systems are considered under weaker conditions on the coefficients than the ones considered in the literature and they include the case where only one frictional damping is present,so they generate new difficulties and represent new situations that have not been studied earlier.展开更多
In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different posit...In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different positive constants, f （x） is locally Lipschitz continuous and bounded,？（x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions： the resonance case √1a＋ √1b ∈Q and the nonresonance case√1a ＋ √1b /∈Q.展开更多
Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbit...Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.展开更多
As the number of sensor network application scenarios continues to grow,the security problems inherent in this approach have become obstacles that hinder its wide application.However,it has attracted increasing attent...As the number of sensor network application scenarios continues to grow,the security problems inherent in this approach have become obstacles that hinder its wide application.However,it has attracted increasing attention from industry and academia.The blockchain is based on a distributed network and has the characteristics of non-tampering and traceability of block data.It is thus naturally able to solve the security problems of the sensor networks.Accordingly,this paper first analyzes the security risks associated with data storage in the sensor networks,then proposes using blockchain technology to ensure that data storage in the sensor networks is secure.In the traditional blockchain,the data layer uses a Merkle hash tree to store data;however,the Merkle hash tree cannot provide non-member proof,which makes it unable to resist the attacks of malicious nodes in networks.To solve this problem,this paper utilizes a cryptographic accumulator rather than a Merkle hash tree to provide both member proof and non-member proof.Moreover,the number of elements in the existing accumulator is limited and unable to meet the blockchain’s expansion requirements.This paper therefore proposes a new type of unbounded accumulator and provides its definition and security model.Finally,this paper constructs an unbounded accumulator scheme using bilinear pairs and analyzes its performance.展开更多
In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under d...In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.展开更多
In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state...In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.展开更多
In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In additio...In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.展开更多
In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results f...In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.展开更多
0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of sing...0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of singular integals of high order were investigated by many authors([1],[2],[3] etc. ) In 1987, the concepts of Hadamard principal value at one-side for singular integralsof high order and the rules of their differentiation are introduced [4]. In this paper we established the rulesof substitution of variable for one-sided Hadamard principal value of singular integrals of high order, andthen, we gave some applications in evaluation of real definite integrals.展开更多
By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, a...By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.展开更多
The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite n...The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.展开更多
In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, ...In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.展开更多
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti...The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.展开更多
In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Dis...In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.展开更多
In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of...In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation （SDDPE） is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.展开更多
Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a...Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
文摘In this study,the wave motion in elastodynamics for unbounded media is modeled using an unsplit-field perfectly matched layer(PML)formulation that is solved by employing an isogeometric analysis(IGA).In the adopted combination,the non-uniform rational B-spline(NURBS)functions are employed as basis functions.Moreover,the unbounded and artificial domains,defined in the PML method,are contained in a single patch domain.Based on the proposed scheme,the approximation of the geometry problem is set in a new scheme in which the PML’s absorbing and attenuation properties and the description of traveling waves can be represented.This includes a higher continuity and smoother approximation of the computed domain.As high-order NURBS basis functions are non-interpolatory,a penalty method is present to apply a time-dependent displacement load.The performance of the NURBS-based PML is analyzed through numerical examples for 1D and 2D domains,considering homogeneous and heterogeneous media.Further,we verify the long-time numerical stability of the present method.The developed method can be used to simulate hypothetical stratified domains commonly encountered in soil-structure interaction analyses.
文摘This paper addresses the problem of containment control for heterogeneous multi-agent systems subject to Markovian randomly switching topologies and unbounded communication delays.The objective is to design a distributed control strategy that ensures the output of each follower converges to the convex hull formed by the outputs of a group of leaders in mean square sense.A novel distributed observer is proposed by tackling both Markovian randomly switching topologies and unbounded delays.Then,a distributed state feedback controller and a distributed output feedback controller are developed based on the distributed observer,respectively.Finally,simulation results are provided to demonstrate the effectiveness of the proposed controllers.
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.
文摘In this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or of order two with respect to the space variable.We prove some L^(2)(R)-norm decay estimates of solutions and their higher-order derivatives with respect to the space variable,where the decay rates depend on the number of the present frictional dampings,the regularity of the initial data,and some connections between the speeds of wave propagation of the two wave equations.Both our systems are considered under weaker conditions on the coefficients than the ones considered in the literature and they include the case where only one frictional damping is present,so they generate new difficulties and represent new situations that have not been studied earlier.
基金Supported by the Tianyuan Special Foundation（11526148） Supported by the National Natural Science Foundation of China（l1571187, 11461056）
文摘In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different positive constants, f （x） is locally Lipschitz continuous and bounded,？（x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions： the resonance case √1a＋ √1b ∈Q and the nonresonance case√1a ＋ √1b /∈Q.
文摘Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.
基金supported by the NSFC(61772454)the Researchers Supporting Project No.RSP-2020/102 King Saud University,Riyadh,Saudi Arabiafunded by National Key Research and Development Program of China(2019YFC1511000).
文摘As the number of sensor network application scenarios continues to grow,the security problems inherent in this approach have become obstacles that hinder its wide application.However,it has attracted increasing attention from industry and academia.The blockchain is based on a distributed network and has the characteristics of non-tampering and traceability of block data.It is thus naturally able to solve the security problems of the sensor networks.Accordingly,this paper first analyzes the security risks associated with data storage in the sensor networks,then proposes using blockchain technology to ensure that data storage in the sensor networks is secure.In the traditional blockchain,the data layer uses a Merkle hash tree to store data;however,the Merkle hash tree cannot provide non-member proof,which makes it unable to resist the attacks of malicious nodes in networks.To solve this problem,this paper utilizes a cryptographic accumulator rather than a Merkle hash tree to provide both member proof and non-member proof.Moreover,the number of elements in the existing accumulator is limited and unable to meet the blockchain’s expansion requirements.This paper therefore proposes a new type of unbounded accumulator and provides its definition and security model.Finally,this paper constructs an unbounded accumulator scheme using bilinear pairs and analyzes its performance.
基金Supported by the NNSF of China(60464001) Guangxi Science Foundation(0575092).
文摘In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.
文摘In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.
基金Supported by the National Natural Science Foundation of China(Grant No.11271092)the Natural Science Foundation of Guangdong Province(Grant No.S2011010005367)
文摘In this paper, we construct a function φ in L^2（C^n,dVα） which is unbounded on any neighborhood of each point in C^n such that Tφ is a trace class operator on the Segal- Bargmann space H^2（Cn, dVα）. In addition, we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H^2 （C^n, dVα）.
基金The NNSF (10071031) of China China Postdoctoral Science Foundation.
文摘In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.
文摘0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of singular integals of high order were investigated by many authors([1],[2],[3] etc. ) In 1987, the concepts of Hadamard principal value at one-side for singular integralsof high order and the rules of their differentiation are introduced [4]. In this paper we established the rulesof substitution of variable for one-sided Hadamard principal value of singular integrals of high order, andthen, we gave some applications in evaluation of real definite integrals.
文摘By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.
基金This work was supported by the China State Major Key Project for Basic Researches Science Fund of the Ministry of Education
文摘The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.
基金NSFC!( 1 9671 0 1 7) and NSF!( A970 1 2 ) of Fujian.
文摘In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.
文摘The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.
文摘In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.
文摘In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation （SDDPE） is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.
文摘Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
