In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between t...In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.展开更多
In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon t...In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously.By virtue of a priori estimates and some limit analyses,the weak limit of the nonlinear principal term is identified via the Young measures method.展开更多
In this paper, we study the Cauchy problem of the Camassa-Holm equation with a zero order dissipation. We establish local well-posedness and investigate the blow-up phenomena for the equation.
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational...The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.展开更多
In this research, we have improved a relaxation method for triangular meshes intended for finite element fluid simulations which contain discrete element particles. The triangle edges are treated as springs which rela...In this research, we have improved a relaxation method for triangular meshes intended for finite element fluid simulations which contain discrete element particles. The triangle edges are treated as springs which relax their lengths towards a “better” force equilibrium where the triangles are closer to equilateral shape. The actual kernel is an improved zero order integrator which is able to follow reconfigurations of the particles faster than earlier methods. The improved relaxation allows larger timesteps in the flow simulation and leads to more stable, faster mesh reconfigurations for fast moving particles in the flow. Additionally, this demonstrates how integrators of the same order zero can nevertheless have different convergence speeds towards展开更多
In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization...In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.展开更多
The first purpose of this paper is to study the properties on some q-shift difference differential polynomials of meromorphic functions,some theorems about the zeros of some q-shift difference-differential polynomials...The first purpose of this paper is to study the properties on some q-shift difference differential polynomials of meromorphic functions,some theorems about the zeros of some q-shift difference-differential polynomials with more general forms are obtained.The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for q-shift difference differential monomials of meromorphic functions,we obtain some relations amongδ(∞,f),δ(∞,f′),δ(∞,f(z)^(n)f(qz+c)^(m)f′(z)),δ(∞,f(qz+c);f′(z))andδ(∞,f(z)^(n)f(qz+c)^(m)).展开更多
针对工业机器人末端作业时轴向低频隔振难的问题,设计一种由等边六边形拉簧装置和正刚度弹簧组构成的轴向准零刚度(Quasi Zero Stiffness,QZS)隔振器。首先,通过静力学分析初始高度对等边六边形拉簧装置负刚度性能和隔振器刚度特性的影...针对工业机器人末端作业时轴向低频隔振难的问题,设计一种由等边六边形拉簧装置和正刚度弹簧组构成的轴向准零刚度(Quasi Zero Stiffness,QZS)隔振器。首先,通过静力学分析初始高度对等边六边形拉簧装置负刚度性能和隔振器刚度特性的影响;其次,建立非线性动力学方程,应用谐波平衡法推导力传递率,通过数值仿真分析振动幅值、阻尼比、初始高度和负载对力传递率的影响。最后,在不同外部激励下对轴向QZS隔振器和线性隔振器进行实验研究,并将实验结果与四阶龙格库塔法求解的加速度响应进行对比。结果表明:轴向QZS隔振器在载荷为20~80 N时能隔离3.2~20 Hz的振动;相较于其对应的线性隔振器,该隔振器的固有频率降低到1.8 Hz,起始隔振频率降低76.6%,隔振频带增宽166.7%。展开更多
In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the o...In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.展开更多
文摘In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)the University-Level Research Fund Project in Guizhou University of Finance and Economics(Grant No.2022KYYB01)。
文摘In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously.By virtue of a priori estimates and some limit analyses,the weak limit of the nonlinear principal term is identified via the Young measures method.
文摘In this paper, we study the Cauchy problem of the Camassa-Holm equation with a zero order dissipation. We establish local well-posedness and investigate the blow-up phenomena for the equation.
文摘The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.
文摘In this research, we have improved a relaxation method for triangular meshes intended for finite element fluid simulations which contain discrete element particles. The triangle edges are treated as springs which relax their lengths towards a “better” force equilibrium where the triangles are closer to equilateral shape. The actual kernel is an improved zero order integrator which is able to follow reconfigurations of the particles faster than earlier methods. The improved relaxation allows larger timesteps in the flow simulation and leads to more stable, faster mesh reconfigurations for fast moving particles in the flow. Additionally, this demonstrates how integrators of the same order zero can nevertheless have different convergence speeds towards
基金Program for New Century Excellent Talents in University of China (NCET-05-0607)National Natural Science Fou-ndation of China (No.60774010)Project for Fundamental Research of Natural Sciences in Universities of Jingsu Province (No.07KJB510114)
文摘In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11761035,12161074)the Natural Science Foundation of Jiangxi Province(Grant No.20181BAB201001)the Foundation of Education Department of Jiangxi Province(Grant Nos.GJJ190876,GJJ202303,GJJ201813,GJJ191042)。
文摘The first purpose of this paper is to study the properties on some q-shift difference differential polynomials of meromorphic functions,some theorems about the zeros of some q-shift difference-differential polynomials with more general forms are obtained.The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for q-shift difference differential monomials of meromorphic functions,we obtain some relations amongδ(∞,f),δ(∞,f′),δ(∞,f(z)^(n)f(qz+c)^(m)f′(z)),δ(∞,f(qz+c);f′(z))andδ(∞,f(z)^(n)f(qz+c)^(m)).
基金supported by the National Natural Science Foundation of China (11171119 and 10871076)
文摘In this article, we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations, and obtain some relations of the exponent of convergence of zeros and the order of growth of entire solutions to complex linear difference equations.
