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中文
Table of Content
30 March 2006, Volume 21 Issue 1
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On Smarandache Multiplicative Sequence and Its Generation
XU Zhe-feng
2006, 21(1): 1-3.
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The main purpose of this paper is to introduce the general Smarandache multiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequences.
Inverse Theorem of Approximation in L
p
for the Stancu Integral-type Operators on a Simplex
ZHANG Chun-gou
2006, 21(1): 4-9.
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In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in L
p
(1≤p<+∞)has been obtained.
Factorization of Width-two CSL Algebras and Nest Algebras
YANG You-long, WU Yan
2006, 21(1): 10-14.
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In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T=US, where U is unitary and 5 belongs to width-two CSL algebra alg when nest M or N is a countable nest, or S belongs to alg when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T=US where S∈D
-1
N
and U is unitary as N be a countable nest.
Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Multiply Type-ⅡCensoring
WANG Rong-hua, FEI He-liang
2006, 21(1): 15-27.
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n present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.
Strong Convergence of Empirical Distribution for a Class of Random Matrices
LIANG Qing-wen, MIAO Bai-qi, WANG Da-peng
2006, 21(1): 28-32.
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Let {v
ij
}, i, j = 1, 2,…, be i.i.d. random variables with E
v11=
0, E
2
v11
=1 and a
i
= (a
i1
,…,a
iM
) be random vectors with {a
ij
} being i.i.d. random variables. Define X
N
=(x
1
,…, X
K)
and ... The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
An Existence Result of the Elliptic Equation Δu+K（x）e
2u
=0
WU San-xing
2006, 21(1): 33-37.
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This paper considers the existence problem of an elliptic equation, which is equivalent to solving the so called prescribing conformal Gaussian curvature problem on the hyperbolic disc H
2
. An existence result is proved. In particular, K(x) is allowed to be unbounded above.
Extremal Cut-width Problem for Graphs
HAO Jian-xiu, YANG Ai-feng
2006, 21(1): 38-43.
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The problem studied in this paper is to determine e(p, C), the minimum size of a connected graph G with given vertex number p and cut-width C.
A Geometric Proof of the Convexity Preserving Property of NURBS Curves
LIU Chao-yang
2006, 21(1): 44-48.
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NURBS curves are convexity preserving, i.e. once the control polygon is convex, the associated NURBS curve will also be convex. In this paper this property is proved geometrically.
Existence for Semilinear Wave Equations with Low Regularity
YANG Ning, YANG Han
2006, 21(1): 49-56.
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In this paper,we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations
….
We proved that the range of s is ,respectively,with if n=2, and δ>0 if n=3, and δ≥0 if n≥4. Which is consistent with Lindblad's
counterexamples [3] for n=3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.
A Note on the Product Borel Probability Measure
MA Dong-kui, XU Zhi-ting
2006, 21(1): 57-61.
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In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.
A Note on Strongly Regular Self-complementary Graphs
TIAN Fang
2006, 21(1): 62-65.
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Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k+1, where 4k+1=x2+y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k+1 orders.
The General and Centro(Kewsy) Symmetric Solutions to a System of Matrix Equations over an Arbitrary Skew Field
QIN Jian-guo, SONG Guang-ai
2006, 21(1): 66-70.
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Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.
Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models
KONG Fan-chao, WANG Jin-liang
2006, 21(1): 71-79.
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This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.
The Problem of Stabilization for Dynamical Systems
ZHANG Zhi-ping, WANG Jian-ping
2006, 21(1): 80-84.
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In this paper, we are concerned with the problem of stabilization for autonomous dynamical systems. We use theories in Liapunov stability and Lasalle stability theory and show that system (H) is stabilizable.
2π-periodic Solution for a Kind High Order Delay Duffing Equation
LIN Wen-xian
2006, 21(1): 85-89.
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In this paper, the high order delay Duffing equation ax
(2n)
+bx+g(x(t-τ)) =p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained.
Quasilinear Robin Problem with Boundary Perturbation
CHEN Xue-dong
2006, 21(1): 90-95.
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A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.
On an Extension of Hibert's Inequality and Applications
YANG Bi-cheng
2006, 21(1): 96-102.
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This paper gives a new generalization of Hilbert’s inequality with a best constant factor involving theβfunction. An applications, we consider the equivalent form and some particular results.
Single Machine Scheduling Problem with Release Dates and Two Hierarchical Criteria to Minimize Makespan and Stocking Cost
Single Machine Scheduling Problem with Release Dates and Two Hierarchical Criteria to Minimize Makespan and Stocking CostLI Wen-hua
2006, 21(1): 103-109.
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In this paper, the single machine scheduling problem with release dates and two hierarchical criteria is discussed. The first criterion is to minimize makespan, and the second criterion is to minimize stocking cost. We show that this problem is strongly NP-hard. We also give an O(n2) time algorithm for the special case that all stocking costs of jobs in unit time are 1.
The Existence and Local Behavior of the Bivariate Quadratic Function Approximation
ZHENG Cheng-de
2006, 21(1): 110-114.
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This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Pade form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.
Function Theory of a Class of Bounded Reinhardt Domains
LI Xian
2006, 21(1): 115-123.
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In this paper, we consider a class of bounded Reinhardt domains D
α
(m, n
1
,…,n
m
). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that D
α
is a quasiconvex domain and D
α
is a stronger quasiconvex domain if and only if D
α
is a hypersphere.
Analysis of Optimal Portfolio with Different Utility Function
YAO Yuan, SHI Ben-shan
2006, 21(1): 124-128.
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The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.
On the Maximum Spectral Radius of (m,n)-trees with Given Diameter
CHENG Wei, TAN Shang-wang
2006, 21(1): 129-137.
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Let (V, U) be the vertex-partition of tree T as a bipartite graph. T is called an (m,n)-tree if |V|=m and |U| = n. For given positive integers m,n and d, the maximum spectral radius of all (m,n)-trees on diameter d are obtained, and all extreme graphs are determined.
On Growth and Covering Theorem for Strongly Spirallike Mapping of Type β with Order α
LIU Jie-ming, WAN Zhi-jun
2006, 21(1): 138-142.
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In this paper, we deduce growth and covering theorem for f(x) by the other means,where f(x) is strongly spirallike mapping of type β with orderαdefined on Unit Ball B of complex Banach space. and still give growth upper bound and distortion upper bound for subordinate mapping.
k-Factors and Spanning Subgraph in Graphs
WANG Zhi-guo, ZHANG Yi
2006, 21(1): 143-147.
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In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.
Single-period Two-product Inventory Model with Reorder and Substitution
LI Xiao-shen, GAO Ke-quan
2006, 21(1): 148-158.
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In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer’s substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi’s, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.
