一类改进的非凸二次规划有效集方法

一类改进的非凸二次规划有效集方法修乃华（河北师范学院数学系）ＡＣＬＡＳＳＯＦＩＭＰＲＯＶＥＤＡＣＴＩＶＥＳＥＴＭＥＴＨＯＤＳＦＯＲＮＯＮＣＯＮＶＥＸＱＵＡＤＲＡＴＩＣＰＲＯＧＲＡＭＭＩＮＧＰＲＯＢＬＥＭ￥ＸｉｕＮａｉ－ｈｕａ（Ｄｅｐｔ．ｏｆＭａｔｈ．...     

二元二次多项式可因式分解的充要条件及其分解公式

对于二元二次多项式ｆ（ｘ，ｙ）＝Ａｘ２＋Ｂｘｙ＋Ｃｙ２＋Ｄｘ＋Ｅｙ＋Ｆ（其中Ａ，Ｂ，Ｃ不全为零），设ｈ＝２ＣＤ－ＢＥＢ２－４ＡＣ，ｋ＝２ＡＥ－ＢＤＢ２－４ＡＣ，Ｆ１＝ｆ（ｈ、ｋ）＝１２Ｄｈ＋１２Ｅｋ＋Ｆ，△＝２ＡＢＤＢ２ＣＥＤＥ２Ｆ＝－２（Ｂ２－４Ａ...     

二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子

二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子沈伯骞，何平（辽宁师范大学数学系，大连１１６０２２）（辽宁警官专科学校，大连１１６０３３）ＥＸＡＭＰＬＥＳＯＦＯＮＥＤＯＵＢＬＥＬＩＭＩＴＣＹＣＬＥＯＲＴＷＯＳＩＮＧＬＥＬＩＭＩＴＣＹＣＬＥ...     

ALMOST PERIODIC SOLUTION OF TWO－SPECIES PATCHTYPE NONAUTONOMOUS DIFFUSIVE LOTKA－VOLTERRA COMPETITIVE MODELS

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＷＯ－ＳＰＥＣＩＥＳＰＡＴＣＨＴＹＰＥＮＯＮＡＵＴＯＮＯＭＯＵＳＤＩＦＦＵＳＩＶＥＬＯＴＫＡ－ＶＯＬＴＥＲＲＡＣＯＭＰＥＴＩＴＩＶＥ　ＭＯＤＥＬＳＬｕｏＧｕｉｌｉｅ（罗桂烈），ＬｉａｏＭｉｎｌｉ（廖民...     

SINGULARITY AND QUADRATURE REGULARITY OF（0，1，．．．，m－2，m）─INTERPOLATION ON THE ZEROS OF（1－x）P_（n－1）~（αβ）（x）

ＳＩＮＧＵＬＡＲＩＴＹＡＮＤＱＵＡＤＲＡＴＵＲＥＲＥＧＵＬＡＲＩＴＹＯＦ（０，１，．．．，ｍ－２，ｍ）─ＩＮＴＥＲＰＯＬＡＴＩＯＮＯＮＴＨＥＺＥＲＯＳＯＦ（１－ｘ）Ｐ_（ｎ－１）~（αβ）（ｘ）ＳｈｉＹｉｎｇｇｕａｎｇ（史应光）（ＣｏｍｐｕｔｉｎｇＣｅ...     

THE GENERAL SCHEME FOR HIGHER－ORDER DECOMPOSITIONS OF ZERO－CURVATURE EQUATIONS ASSOCIATED WITH■（2）

ＴＨＥＧＥＮＥＲＡＬＳＣＨＥＭＥＦＯＲＨＩＧＨＥＲ－ＯＲＤＥＲＤＥＣＯＭＰＯＳＩＴＩＯＮＳＯＦＺＥＲＯ－ＣＵＲＶＡＴＵＲＥＥＱＵＡＴＩＯＮＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨ■（２）￥ＺＥＮＧＹＵＮＢＯ（曾云波）（ＤｅｐｏｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａ...     

A BRANCH－AND－BOUND ALGORITHM IN THE TOURING－PATH PROBLEM AND ITS COMPUTER IMPLEMENTATION

ＡＢＲＡＮＣＨ－ＡＮＤ－ＢＯＵＮＤＡＬＧＯＲＩＴＨＭＩＮＴＨＥＴＯＵＲＩＮＧ－ＰＡＴＨＰＲＯＢＬＥＭＡＮＤＩＴＳＣＯＭＰＵＴＥＲＩＭＰＬＥＭＥＮＴＡＴＩＯＮＸｕＸｕｓｏｎｇ（徐绪松）（ＳｃｈｏｏｌｏｆＭａｎａｇｅｍｅｎｔ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔ...     

单机总误时排序问题的序扩张

单机总误时排序问题的序扩张林诒勋（郑州大学数字系，郑州４５００５２）ＯＲＤＥＲＥＸＴＥＮＳＩＯＮＳＦＯＲＴＨＥＳＩＮＧＬＥＭＡＣＨＩＮＥＴＯＴＡＬＴＡＲＤＩＮＥＳＳＰＲＯＢＬＥＭ￥ＬＩＮＹＩＸＵＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｚｈ...     

THE MATCHED QUEUEING SYSTEM GI。PH/PH/1

ＴＨＥＭＡＴＣＨＥＤＱＵＥＵＥＩＮＧＳＹＳＴＥＭＧＩ。ＰＨ／ＰＨ／１ＸＵＧＵＡＮＣＨＵＩ（ＧＵＡＮＧ－ＨＵＩＨＳＶ）（徐光煇）；ＨＥＱＩＭＩＮＧ（何启明）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙ...     

ON BAHADUR－TYPE ASYMPTOTIC EFFICIENCY OF POINT ESTIMATORS UNDER IRREGULAR TRUNCATED DISTRIBUTION FAM

ＯＮＢＡＨＡＤＵＲ－ＴＹＰＥＡＳＹＭＰＴＯＴＩＣＥＦＦＩＣＩＥＮＣＹＯＦＰＯＩＮＴＥＳＴＩＭＡＴＯＲＳＵＮＤＥＲＩＲＲＥＧＵＬＡＲＴＲＵＮＣＡＴＥＤＤＩＳＴＲＩＢＵＴＩＯＮＦＡＭＩＬＹ￥ＣｈｅｎＧｕｉｊｉｎｇ（陈桂景）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔ...     

乘积的平方性

本文证明了乘积 (f(x)=ax²+bx+c∈Z[x]是二次不可约多项式)在n充分大时不是平方数.       

乘积∏_(k=1)~n(ak~2+bk+c)的平方性

本文证明了乘积∏_(k=1)~n(ak~2+6k+c)(f(x)=ax~2+bx+c∈Z[x]是二次不可约多项式)在n充分大时不是平方数.     

Derivations and extensions of lie color algebra

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.     

弱Galois扩张与反Smash积

本文对（H,K）-余模代数A，讨论了弱Galois扩张A／C，证明了k的每个自由二次扩张是弱Galois扩张．并利用反Smash积＃op（K，A）与K－余不变子代数C之间的Morita联系讨论A的投射性、Galois扩张及其传递性．     

Structure of Degenerate Block Algebras

Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {e_x | x A/{0}} and Lie product [e_x,e_y] = (x,y)e_x+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H²(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL²( , F) and HL²(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.     

一个矩阵分解算法的推广及应用

对样本相关系数矩阵等行和分解算法作了简化和推广,使算法不仅可以应用在基于正态总体非独立样本的假设检验问题,也可以有效地运用在最优化算法中牛顿法等与二次函数极小化有关的问题上.     

Rigid extensions of ℓ-groups of continuous functions

Let C(X, ℤ), C(X, ℂ) and C(X) denote the ℓ-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X, respectively. Characterizations are given for the extensions C(X, ℤ) ⩽ C(X, ℚ) ⩽ C(X) to be rigid, major, and dense.     

On a Generalization of Nikolskij's Extension Theorem in the Case of Two Variables

A modification of the Nikolskij extension theorem for functions from Sobolev spaces H ^k() is presented. This modification requires the boundary to be only Lipschitz continuous for an arbitrary k however, it is restricted to the case of two-dimensional bounded domains.     

Student problems with a modelling exercise

In this paper an attempt is made to outline some of the problems facing the student who undertakes a course in mathematical modelling. A case study, considered by several cohorts of students, is used as a medium for introducing the various types of obstacles the students encounter. This approach also results in a demonstration of some of the errors that can be made in operating a modelling course and the paper concludes by offering suggestions on how to overcome certain difficulties that are exposed.