主要介绍了一种证明弱解存在性的一种方法——变分法,变分法的基本内容是确定泛函的极值点和临界点,在一定条件下微分方程边值问题常常可以转化为变分问题来研究。首先通过给定的泛函求极值元,极值点处的方程在分部积分的意义下满足弱...主要介绍了一种证明弱解存在性的一种方法——变分法,变分法的基本内容是确定泛函的极值点和临界点,在一定条件下微分方程边值问题常常可以转化为变分问题来研究。首先通过给定的泛函求极值元,极值点处的方程在分部积分的意义下满足弱解定义,其次构造极小元泛函,将所求问题转化为求解相应泛函的极值元,即得方程弱解的存在性,接下来证明泛函极值元的存在性和弱解的唯一性,从而由变分方法确定该四阶定态p-Laplace方程弱解的存在性问题。This paper introduces a method to prove the existence of weak solutions—variational method. The basic content of variational method is to determine the extreme point and critical point of the functional. Under certain conditions, the boundary value problem of differential equations can often be studied by converting the variational problem. This paper first uses the given functional to find the extreme value element, and the equation at the extreme point satisfies the definition of weak solution in the sense of distribution integral. Secondly, we construct the minimal element functionals, and transform the problem into the corresponding universal extreme element, and we obtain the existence of weak solutions, and next, we prove the uniqueness of weak solutions and the existence of functional extremum elements. we finally give the existence of weak solutions for the weak solutions of the fourth-order stationary p-Laplace equation through the variational method.展开更多
A new three-dimensional laterolog array sonde（3D-LS） is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferentia...A new three-dimensional laterolog array sonde（3D-LS） is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferential detection abilities. Six investigation modes are designed using the 3D finite-element method and different investigation depths are simulated based on the pseudo-geometrical factor of the six modes. The invasion profile is described using multi-array radial logs. From the analysis of the pseudo-geometrical factor, the investigation depth of the 3D-LS is about 1.5 m for conductive invasion, which is close to that of the dual laterolog tool but greater than that of the highly integrated azimuthal laterolog sonde. The vertical and azimuthal resolution is also analyzed with the same method. The 3DLS can detect low-resistivity anomalies of 0.5 m thickness and 15？ around the borehole for infinitely thick formations. This study lays the foundation for more work on 3D laterolog array sonde for evaluating low-resistivity anomalies.展开更多
A novel neuMOS source follower circuit is presented.The cell can complete the s ource follower function even if the input voltage is lower than the threshold of the source follower,thus high-precision operation of th...A novel neuMOS source follower circuit is presented.The cell can complete the s ource follower function even if the input voltage is lower than the threshold of the source follower,thus high-precision operation of the circuit is achieved. The simulation and the measurement results show that its precision is higher tha n that of other neuMOS source follower circuits.展开更多
In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field...In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.展开更多
This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are i...This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.展开更多
文摘主要介绍了一种证明弱解存在性的一种方法——变分法,变分法的基本内容是确定泛函的极值点和临界点,在一定条件下微分方程边值问题常常可以转化为变分问题来研究。首先通过给定的泛函求极值元,极值点处的方程在分部积分的意义下满足弱解定义,其次构造极小元泛函,将所求问题转化为求解相应泛函的极值元,即得方程弱解的存在性,接下来证明泛函极值元的存在性和弱解的唯一性,从而由变分方法确定该四阶定态p-Laplace方程弱解的存在性问题。This paper introduces a method to prove the existence of weak solutions—variational method. The basic content of variational method is to determine the extreme point and critical point of the functional. Under certain conditions, the boundary value problem of differential equations can often be studied by converting the variational problem. This paper first uses the given functional to find the extreme value element, and the equation at the extreme point satisfies the definition of weak solution in the sense of distribution integral. Secondly, we construct the minimal element functionals, and transform the problem into the corresponding universal extreme element, and we obtain the existence of weak solutions, and next, we prove the uniqueness of weak solutions and the existence of functional extremum elements. we finally give the existence of weak solutions for the weak solutions of the fourth-order stationary p-Laplace equation through the variational method.
基金sponsored by the National Oil and Gas Major Projects(No.2011ZX05020-009)
文摘A new three-dimensional laterolog array sonde（3D-LS） is presented. The 3DLS is based on existing high-resolution laterolog array and azimuthal resistivity imaging sondes with radial, longitudinal, and circumferential detection abilities. Six investigation modes are designed using the 3D finite-element method and different investigation depths are simulated based on the pseudo-geometrical factor of the six modes. The invasion profile is described using multi-array radial logs. From the analysis of the pseudo-geometrical factor, the investigation depth of the 3D-LS is about 1.5 m for conductive invasion, which is close to that of the dual laterolog tool but greater than that of the highly integrated azimuthal laterolog sonde. The vertical and azimuthal resolution is also analyzed with the same method. The 3DLS can detect low-resistivity anomalies of 0.5 m thickness and 15？ around the borehole for infinitely thick formations. This study lays the foundation for more work on 3D laterolog array sonde for evaluating low-resistivity anomalies.
文摘A novel neuMOS source follower circuit is presented.The cell can complete the s ource follower function even if the input voltage is lower than the threshold of the source follower,thus high-precision operation of the circuit is achieved. The simulation and the measurement results show that its precision is higher tha n that of other neuMOS source follower circuits.
基金supported by the National Natural Science Foundation of China under Grant No.11161034the Science Foundation of the Education Department of Jiangxi Province under Grant No.Gjj12012
文摘In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.
基金supported by the National Natural Science Foundation of China under Grant Nos.61473189,61374176,61203142 and 61203073a Doctoral Program of High Education of China under Grant No.20110073120027partly by the Excellent Young Technology Innovation Foundation of Hebei University of Technology under Grant No.2012005
文摘This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.
