This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
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
To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is...To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is constructed for the system.The new variable introduced can be separated from the difference scheme to obtain another difference scheme containing only the original variable.The energy method is applied to the theoretical analysis of the difference scheme.Results show that the difference scheme is uniquely solvable and satisfies the energy conservation law corresponding to the original problem.Moreover,the difference scheme converges when the step ratio satisfies a constraint condition,and the temporal and spatial convergence orders are both two.Numerical examples verify the convergence order and the invariant of the difference scheme.Furthermore,the step ratio constraint is unnecessary for the convergence of the difference scheme.Compared with a known two-level nonlinear difference scheme,the proposed difference scheme has more advantages in numerical calculation.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform c...We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.展开更多
Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic sol...Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.展开更多
The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simu...The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.展开更多
A linearized and conservative finite difference scheme is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov （KGZ） equation. The new scheme is also decoupled in computation, which means th...A linearized and conservative finite difference scheme is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov （KGZ） equation. The new scheme is also decoupled in computation, which means that no iteration is needed and parallel computation can be used, so it is expected to be more efficient in imple- mentation. The existence of the difference solution is proved by Browder fixed point theorem. Besides the standard energy method, in order to overcome the difficulty in obtaining a priori estimate, an induction argument is used to prove that the new scheme is uniquely solvable and second order convergent for U in the discrete L∞- norm, and for N in the discrete L2-norm, respectively, where U and N are the numeri- cal solutions of the KGZ equation. Numerical results verify the theoretical analysis.展开更多
The aim of this paper is to study the order of meromorphic solutions of linear difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0,where the coefficients Aj(z)(j=0,...,n)are entire functions.We obtain some resu...The aim of this paper is to study the order of meromorphic solutions of linear difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0,where the coefficients Aj(z)(j=0,...,n)are entire functions.We obtain some results by giving some restrictions on coefficients of above equation with no dominating coefficient and partially answer a question of I.Laine and C.C.Yang.展开更多
In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable...In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.展开更多
Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. T...Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. The sunken defects proposed in this paper is a w idth abnormity defect on the FPC trace,w hich w ould cause the latent open circuit defect and affect the electrical function of circuit. The problem of flexible deformation and w idth difference make the FPC trace detection harder. Therefore,this paper proposed a detection scheme combined w ith linear masks and circle distribution characteristic. Firstly,this scheme preprocessed the acquired FPC image,divided the trace into several sub-regions and obtained the line w idth values of each trace transverse section. Then the line w idth sequences w ere searched w ith the linear difference template of gray scale. Thus,the sunken defects alternative positions w ere located. Lastly,the circle distribution characteristic is defined to identify the real defect areas from the alternative regions acquired from the previous step. Thus,the detection of sunken defects on the FPC trace w as accomplished.The algorithm w as tested in the self-built image database,w hich show s the better detection performance than the other typical algorithms.展开更多
After more than 30 years of rapid urbanization, the overall urbanization rate of China reached 56.1% in 2015.However, despite China's rapid increase in its overall rate of urbanization, clear regional differences ...After more than 30 years of rapid urbanization, the overall urbanization rate of China reached 56.1% in 2015.However, despite China's rapid increase in its overall rate of urbanization, clear regional differences can be observed. Furthermore, inadequate research has been devoted to in-depth exploration of the regional differences in China's urbanization from a national perspective, as well as the internal factors that drive these differences. Using prefecture-level administrative units in China as the main research subject, this study illustrates the regional differences in urbanization by categorizing the divisions into four types based on their urbanization ratio and speed(high level: low speed; high level: high speed; low level: high speed; and low level: low speed). Next, we selected seven economic and geographic indicators and applied an ordered logit model to explore the driving factors of the regional differences in urbanization. A multiple linear regression model was then adopted to analyze the different impacts of these driving factors on regions with different urbanization types. The results showed that the regional differences in urbanization were significantly correlated to per capita GDP, industry location quotients, urban-rural income ratio,and time distance to major centers. In addition, with each type of urbanization, these factors were found to have a different driving effect. Specifically, the driving effect of per capita GDP and industry location quotients presented a marginally decreasing trend, while main road density appeared to have a more significant impact on cities with lower urbanization rates.展开更多
The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general...The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.展开更多
基金supported by the NNSF of China(Grant No.41405083)Hunan Provincial Natural Science Foundation of China(Grant No.2015JJ3098)
文摘This paper establishes several new Lyapunov-type inequalities for the system of nonlinear difference equations■,which extend/supplement and improve some related existing ones.
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The National Natural Science Foundation of China(No.11671081).
文摘To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is constructed for the system.The new variable introduced can be separated from the difference scheme to obtain another difference scheme containing only the original variable.The energy method is applied to the theoretical analysis of the difference scheme.Results show that the difference scheme is uniquely solvable and satisfies the energy conservation law corresponding to the original problem.Moreover,the difference scheme converges when the step ratio satisfies a constraint condition,and the temporal and spatial convergence orders are both two.Numerical examples verify the convergence order and the invariant of the difference scheme.Furthermore,the step ratio constraint is unnecessary for the convergence of the difference scheme.Compared with a known two-level nonlinear difference scheme,the proposed difference scheme has more advantages in numerical calculation.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
文摘We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.
基金supported by National Natural Science Foundation of China (Grant No. 10871076)
文摘Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.
基金supported by the Iraqi ministry of higher education and scientific research
文摘The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.
文摘A linearized and conservative finite difference scheme is presented for the initial-boundary value problem of the Klein-Gordon-Zakharov （KGZ） equation. The new scheme is also decoupled in computation, which means that no iteration is needed and parallel computation can be used, so it is expected to be more efficient in imple- mentation. The existence of the difference solution is proved by Browder fixed point theorem. Besides the standard energy method, in order to overcome the difficulty in obtaining a priori estimate, an induction argument is used to prove that the new scheme is uniquely solvable and second order convergent for U in the discrete L∞- norm, and for N in the discrete L2-norm, respectively, where U and N are the numeri- cal solutions of the KGZ equation. Numerical results verify the theoretical analysis.
基金Supported by the National Natural Science Foundation of China(Grant No.11661043)the Foundation of Education Department of Jiangxi Province(Grant No.GJJ2200320)。
文摘The aim of this paper is to study the order of meromorphic solutions of linear difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0,where the coefficients Aj(z)(j=0,...,n)are entire functions.We obtain some results by giving some restrictions on coefficients of above equation with no dominating coefficient and partially answer a question of I.Laine and C.C.Yang.
文摘In this paper, a linearized three level difference scheme is derived for two-dimensional model of an alloy solidification problem called Sivashinsky equation. Further, it is proved that the scheme is uniquely solvable and convergent with convergence rate of order two in a discrete L<sup>∞</sup>-norm. At last, numerical experiments are carried out to support the theoretical claims.
文摘Trace is the important composition structure of printed circuit board,w hich connects the devices,it is also the module that taking up the highest proportion,thus,it is the major testing target of quality assurance. The sunken defects proposed in this paper is a w idth abnormity defect on the FPC trace,w hich w ould cause the latent open circuit defect and affect the electrical function of circuit. The problem of flexible deformation and w idth difference make the FPC trace detection harder. Therefore,this paper proposed a detection scheme combined w ith linear masks and circle distribution characteristic. Firstly,this scheme preprocessed the acquired FPC image,divided the trace into several sub-regions and obtained the line w idth values of each trace transverse section. Then the line w idth sequences w ere searched w ith the linear difference template of gray scale. Thus,the sunken defects alternative positions w ere located. Lastly,the circle distribution characteristic is defined to identify the real defect areas from the alternative regions acquired from the previous step. Thus,the detection of sunken defects on the FPC trace w as accomplished.The algorithm w as tested in the self-built image database,w hich show s the better detection performance than the other typical algorithms.
基金supported by the National Science and Technology Support Program(Grant No.2014BAL04B01)the National Natural Science Foundation of China(Grant No.4159084)the National Social Science Fund of China(Grant No.14BGL149)
文摘After more than 30 years of rapid urbanization, the overall urbanization rate of China reached 56.1% in 2015.However, despite China's rapid increase in its overall rate of urbanization, clear regional differences can be observed. Furthermore, inadequate research has been devoted to in-depth exploration of the regional differences in China's urbanization from a national perspective, as well as the internal factors that drive these differences. Using prefecture-level administrative units in China as the main research subject, this study illustrates the regional differences in urbanization by categorizing the divisions into four types based on their urbanization ratio and speed(high level: low speed; high level: high speed; low level: high speed; and low level: low speed). Next, we selected seven economic and geographic indicators and applied an ordered logit model to explore the driving factors of the regional differences in urbanization. A multiple linear regression model was then adopted to analyze the different impacts of these driving factors on regions with different urbanization types. The results showed that the regional differences in urbanization were significantly correlated to per capita GDP, industry location quotients, urban-rural income ratio,and time distance to major centers. In addition, with each type of urbanization, these factors were found to have a different driving effect. Specifically, the driving effect of per capita GDP and industry location quotients presented a marginally decreasing trend, while main road density appeared to have a more significant impact on cities with lower urbanization rates.
基金supported by the National Natural Science Foundation of China under Grant No.11171366"the Fundamental Research Funds for the Central Universities"South-Central University for Nationalities under Grant No.CZY12014
文摘The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.
