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
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
In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x....In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.展开更多
In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental ent...In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ（A）〈1/2.Suppose that k≥2 and f（k）＋A（z）f=0 has a solution f with λ（f）〈ρ（A）,and suppose that A1=A＋h,where h≡0 is an entire function with ρ（h）〈ρ（A）.Then g（k）＋A1（z）g=0 does not have a solution g with λ（g）〈∞.展开更多
In this paper, three robust zero-watermark algorithms named Direct Current coefficient RElationship (DC-RE), CUmulant combined Singular Value Decomposition (CU-SVD), and CUmulant combined Singular Value Decomposition ...In this paper, three robust zero-watermark algorithms named Direct Current coefficient RElationship (DC-RE), CUmulant combined Singular Value Decomposition (CU-SVD), and CUmulant combined Singular Value Decomposition RElationship (CU-SVD-RE) are proposed. The algorithm DC-RE gets the feature vector from the relationship of DC coefficients between adjacent blocks, CU-SVD gets the feature vector from the singular value of third-order cumulants, while CU-SVD-RE combines the essence of the first two algorithms. Specially, CU-SVD-RE gets the feature vector from the relationship between singular values of third-order cumulants. Being a cross-over studying field of watermarking and cryptography, the zero-watermark algorithms are robust without modifying the carrier. Numerical simulation obviously shows that, under geometric attacks, the performance of CU-SVD-RE and DC-RE algorithm are better and all three proposed algorithms are robust to various attacks, such as median filter, salt and pepper noise, and Gaussian low-pass filter attacks.展开更多
In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（...In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.展开更多
In this paper, the authors investigate the zeros and growth of solutions of second order linear differential equations with entire coefficients of [p, q]-order and obtain some results which improve and generalize some...In this paper, the authors investigate the zeros and growth of solutions of second order linear differential equations with entire coefficients of [p, q]-order and obtain some results which improve and generalize some previous results.展开更多
This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The...This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.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.
基金Foundation item： Supported by the National Natural Science Foundation of china（10571044）
文摘In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.
基金Supported by the National Natural Science Foundation of China (Grant No. 11171080)Foundation of Scienceand Technology Department of Guizhou Province (Grant No. [2010] 07)
文摘In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ（A）〈1/2.Suppose that k≥2 and f（k）＋A（z）f=0 has a solution f with λ（f）〈ρ（A）,and suppose that A1=A＋h,where h≡0 is an entire function with ρ（h）〈ρ（A）.Then g（k）＋A1（z）g=0 does not have a solution g with λ（g）〈∞.
基金Supported by the National Natural Science Foundation of China (No. 60672095, 60972165, and 61071111)the National High Technology Project of China (No. 2007AA-11Z210)+2 种基金the Doctoral Fund of Ministry of Education of China (No. 20100092120012 and 20070286004)the Foundation of High Technology Project in Jiangsu Provincethe Natural Science Foundation of Jiangsu Province (No.BK2010240)
文摘In this paper, three robust zero-watermark algorithms named Direct Current coefficient RElationship (DC-RE), CUmulant combined Singular Value Decomposition (CU-SVD), and CUmulant combined Singular Value Decomposition RElationship (CU-SVD-RE) are proposed. The algorithm DC-RE gets the feature vector from the relationship of DC coefficients between adjacent blocks, CU-SVD gets the feature vector from the singular value of third-order cumulants, while CU-SVD-RE combines the essence of the first two algorithms. Specially, CU-SVD-RE gets the feature vector from the relationship between singular values of third-order cumulants. Being a cross-over studying field of watermarking and cryptography, the zero-watermark algorithms are robust without modifying the carrier. Numerical simulation obviously shows that, under geometric attacks, the performance of CU-SVD-RE and DC-RE algorithm are better and all three proposed algorithms are robust to various attacks, such as median filter, salt and pepper noise, and Gaussian low-pass filter attacks.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123211171119)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.
基金Supported by the Natural Science Foundation of Jiangxi Province(Grant Nos.20132BAB21100220122BAB211005)+1 种基金the Youth Foundation of Education Bureau of Jiangxi Province(Grant Nos.GJJ14271GJJ14272)
文摘In this paper, the authors investigate the zeros and growth of solutions of second order linear differential equations with entire coefficients of [p, q]-order and obtain some results which improve and generalize some previous results.
文摘This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.
