The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration o...The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way.展开更多
Prediction of channel dredging volume is critical for project cost estimation. However, many proposed approximate methods are not accurate. This paper presents a novel numerical method to accurately calculate the dred...Prediction of channel dredging volume is critical for project cost estimation. However, many proposed approximate methods are not accurate. This paper presents a novel numerical method to accurately calculate the dredg- ing volume using a 3D stratum model (DSM) and a channel surface model. First, the 3D DSM is constructed rapidly yet accurately from non-uniform rational B-splines (NURBS) surfaces through Boolean operation between a physical terrain model and a stratum surfaces model. Then, a parametric channel surface model is built from cross-section data and a channel center line using code implemented in the VC++ programming language. Finally, the volumes of different types of physical stratums can be calculated automatically and hierarchically to determine the dredging volume. Practical application shows that the DSM method is more precise and faster compared to the section method, and that the implementation of the developed software provides an interactive graphical user interface and visual presentation.展开更多
In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a s...In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.展开更多
A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compac...A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in FC- spaces.As applications,some new fixed point theorems are obtained in FC-spaces.These theorems improve and generalize many known results in recent literature.展开更多
This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.展开更多
文摘The enumeration of elements of c.e. sets in the theory of computability and computational complexity has already been investigated. However, the order of this enumeration has received less attention. The enumeration orders of elements of c.e. sets by means of Turing machines on natural numbers are investigated. In this paper, we consider the enumeration orders of elements of c.e. sets on rational numbers. We present enumeration order reducibility and enumeration order equivalence on rational numbers and propose some lemmas and theorems on these concepts. Also, we show that the theories here hold for Rc and we could repeat the same theories in this domain, in a same way.
基金Supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51021004)National Natural Science Foundation of China(No. 50879056)National Key Technologies R&D Program in the 12th Five-Year Plan of China(No. 2011BAB10B06)
文摘Prediction of channel dredging volume is critical for project cost estimation. However, many proposed approximate methods are not accurate. This paper presents a novel numerical method to accurately calculate the dredg- ing volume using a 3D stratum model (DSM) and a channel surface model. First, the 3D DSM is constructed rapidly yet accurately from non-uniform rational B-splines (NURBS) surfaces through Boolean operation between a physical terrain model and a stratum surfaces model. Then, a parametric channel surface model is built from cross-section data and a channel center line using code implemented in the VC++ programming language. Finally, the volumes of different types of physical stratums can be calculated automatically and hierarchically to determine the dredging volume. Practical application shows that the DSM method is more precise and faster compared to the section method, and that the implementation of the developed software provides an interactive graphical user interface and visual presentation.
基金the National Natural Science Foundation of China （No. 60473114） the Natural Science Foundation of Auhui Province （No. 070416227）+2 种基金 the Natural Science Research Scheme of Education Department of Anhui Province （No. KJ2008B246） Colleges and Universities in Anhui Province Young Teachers Subsidy Scheme （No. 2008jq1110） the Science Research Foundation of Chaohu College （No. XLY-200705）.
文摘In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.
基金Foundation item： the Natural Science Foundation of Sichuan Provincial Education Department of China （No. 2003A081 SZD0406）.
文摘A class of finitely continuous topological spaces(in short,FC-spaces)is introduced. Some new KKM type theorems and coincidence theorems involving admissible set-valued map- pings and the set-valued mapping with compactly local intersection property are proved in FC- spaces.As applications,some new fixed point theorems are obtained in FC-spaces.These theorems improve and generalize many known results in recent literature.
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.
