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Table of Content
30 September 2008, Volume 23 Issue 3
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The Equivalence between Bergman Metric and Einstein-Kahler Metric on the Cartan-Hartogs Domain of the Fourth Type
2008, 23(3): 317-324.
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In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.
Some Hybrid Mean Values of a New Number Theoretic Function
REN Gang-lian
2008, 23(3): 325-329.
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Let p and q be two distinct primes, e
pq
(n) denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function e
pq
(n), and give some hybrid mean value formulas for e
pq
(n) and Dirichlet divisor function d(n).
A Class of Singularly Perturbed Nonlinear Shock Problems
OUYANG Cheng
2008, 23(3): 330-336.
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Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtained. And the known results are generalized.
Joint Invariants and Joint Differential Invariants of Some Transformation Groups
BAI Yong-qiang, LIU Zhen, PEI Ming
2008, 23(3): 337-343.
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The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.
An Existent Condition of Error Bounds for Abstract Linear Inequality System
ZHAI Zhi-chun
2008, 23(3): 344-348.
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We consider the abstract linear inequality system (A,C,b) and give a sufficient condition for the system (A,C,b) to have an error bound, which extends the previous result.
Fan-Browder Type Fixed Point Theorems and Its Applications on Generalized Convex Product Spaces
PIAO Yong-Jie
2008, 23(3): 349-355.
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Fan-Browder type fixed point theorems are obtained for non-selfmaps on non-compact generalized convex product spaces and new existence problems of(partially) maxi-mal element and equilibrium point are discussed as applications of above results.
Boundedness of Weighted Composition Operators on Bloch Type Spaces
GUO Ji-dong, LIU Pin, GAO Wen-hua, NUERDANBIEKE Baitakazi
2008, 23(3): 356-359.
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In this paper, we give a necessary and sufficient condition for weighted compo-sition operators C
u,φ
to be boundedness on Bloch type spaces B
α
. The theorem generalizes some previous results.
Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets
CHEN Qing-jiang, LIU Hong-yun
2008, 23(3): 360-367.
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The notion of vector-valued multiresolution analysis is introduced and the con-cept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and suffcient condition on the existence of orthogonal vector-valued wavelets is given by means of parauni-tary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L
2
(R,C
n
) from these wavelet packets.
A Kind of Generalization of the Curve Type Node Configuration in R
s
(s > 2)
ZHU Ping
2008, 23(3): 368-375.
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A kind of generalization of the Curve Type Node Configuration is given in this paper, and it is called the generalized node configuration CTNCB in R
s
(s > 2). The related multivariate polynomial interpolation problem is discussed. It is proved that the CTNCB is an appropriate node configuration for the polynomial space P
ns
(s > 2). And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.
The Factorization of Adjoint Polynomials of E
G(i)
-class Graphs and Chromatically Equivalence Analysis
ZHANG Bing-ru, YANG Ji-ming
2008, 23(3): 376-383.
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Let S
n
be the star with n vertices, and let G be any connected graph with p vertices. We denote by E
rp+(r-1)
the graph obtained from S
r
and rG by coinciding the i-th vertex of G with the vertex of degree r-1 of S
r
, while the i-th vertex of each component of (r-1)G be adjacented to r-1 vertices of degree 1 of S
r
, respectively. By applying the properties of adjoint polynomials. We prove that factorization theorem of adjoint polynomials of kinds of graphs Erp+(r-1) (r-1)K1 (1 ≤ i ≤ p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
Strong Converse Inequalities for Szász-Mirakjan Operators with Weights
LIU Guo-jun, XUE Yin-chuan , SUN Wei-bin
2008, 23(3): 384-389.
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In this paper, we give the strong converse inequalities of type B with the new K-functional K
λ
α(f,t
2
)
w
(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz
á
sz-Mirakjan operators, which extend the previous results.
Formal Concept Analysis Based on Set-valued Mapping
CHEN Li-ya , HUANG Tao, SONG Zhen-ming , PEI Zheng
2008, 23(3): 390-396.
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Formal concept analysis (FCA) is a discipline that studied the hierarchical struc-tures induced by a binary relation between a pair of sets, and applies in data analysis, infor-mation retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S : G → P(M), and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
Criteria Conditions for Generalized Diagonally Dominant Matrices
TIAN Su-xia
2008, 23(3): 397-402.
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In this paper, we provide some new criteria conditions for generalized strictly diagonally dominant matrices, such that the corresponding results in [1] are generalized and improved.
Improving the Stability Problemof the Finite Difference Scheme for Reaction-diffusion Equation
on XU Chen-mei
2008, 23(3): 403-408.
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This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equa-tion (2.1) is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite dif-ference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
The Derivation Algebra of the Cartan-type Lie Superalgebra H
CHEN Yu-zhen, WANG Ying , MA Bao-lin
2008, 23(3): 409-414.
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In this paper, the derivation algebra of Lie superalgebra H of Cartan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following: Der
F
H = ad
H
(H + Fh) ⊕ {(adD
i
)
pt
| i = 1,2,··· ,m, t = 1,2,··· ,t
i
-1} .
Multi-component KN Hierarchy and Associated two Integrable Couplings as Well as Their Hamiltonian Structure
JIANG Xiao-wu, LI Zhu
2008, 23(3): 415-422.
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Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.
Finite Simple Lattice Implication Algebras
ZHU Yi-quan
2008, 23(3): 423-429.
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In this paper, some necessary and suffcient conditions that a finite lattice impli-cation algebra is simple are established. Specially, it is proved that a finite lattice implication algebra L is simple if and only if (L,≤) is a chain, if and only if there exists the unique dual atom in L. Also, it is given that a finite lattice implication algebra with order of a prime number is simple.
The Direct Product of Graded Finite Posets
LIU Wei , CHEN Shu-wei , JIANG Bao-qing
2008, 23(3): 430-436.
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A new concept Graded Finite Poset is proposed in this paper. Through discussing some basic properties of it, we come to that the direct product of graded finite posets is connected if and only if every graded finite poset is connected. The graded function of a graded finite poset is unique if and only if the graded finite poset is connected.
On the Solutions of an Equation Involving the Smarandache Power Function SP(n)
PAN Xiao-wei
2008, 23(3): 437-441.
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For any positive integer n, the famous Smarandache power function SP(n) is defined as the smallest positive integer m such that n|mm, where m and n have the same prime divisors. The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP(n) and obtain some interesting results. At the same time, we give an open problem about the related equation.
On the Fractional Extensions in Commutative Ordered Semigroups
LUO Cong-wen
2008, 23(3): 442-445.
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In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a frac-tional ordered semigroup and a homomorphism φs : R → S
-1
R. Secondly, we characterize the commutative ordered semigroup so constructed by a universal mapping property.
A High-order Accuracy Explicit Difference Scheme with Branching Stability for Solving Higher-dimensional Heat-conduction Equation
MA Ming-shu, MA Ju-yi , GU Shu-min, ZHU Lin-lin
2008, 23(3): 446-452.
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A high-order accuracy explicit difference scheme for solving 4-dimensional heat-conduction equation is constructed. The stability condition is r = △t/△x
2
=△t/△y
2
= △t/△z△ = △t/△w
2
< 3/8, and the truncation error is O(△t
2
+△x
4
).
Decomposition of Soliton Hierarchy Associated with a Schroinger Type Spectral Problem
XING Xiu-zhi , WU Jing-zhu, GENG Xian-guo
2008, 23(3): 453-457.
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The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.
Improved Cotes Formula and Error Analysis
DU Yue-peng, XIAO Ze-chang
2008, 23(3): 458-461.
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The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.
Mixed Traffic Flow Capacity of More Major Lanes Unsignalized Intersection
TIAN Xin-xian
2008, 23(3): 462-469.
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Highway capacity is defined as maximum volume of traffic flow through the par-ticular highway section under given traffic conditions, road conditions and so on. Highway construction and management is judged by capacity standard. The reasonable scale and time of highway construction, rational network structure and optimal management mode of highway network can be determined by analyzing the fitness between capacity and traffic vol-ume. All over the world, highway capacity is studied to different extent in different country. Based on the gap acceptance theory, the mixed traffic flow composed of two representative vehicle types heavy and light vehicles is analyzed with probability theory. Capacity model of the minor mixed traffic flows crossing m major lanes, on which the traffic flows fix in with M3 distributed headway, on the unsignalized intersection is set up, and it is an extension of minor lane capacity theory for one vehicle-type and one major-lane traffic flow.
The Existence of Solutions of (k, n −k) Conjugate Boundary Value Problems in Banach Spaces
YANG Hui, WANG Feng
2008, 23(3): 470-474.
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In this paper, by use of the Schauder fixed-point theorem, the existence of solution of (k,n-k) Conjugate boundary value problems in Banach spaces is investigated.
