关于凸子集和（绝对）收缩核

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核，以及在什么情况下为绝对收缩核。     

极大子因子

若N是一个Ⅱ1型因子,G是一个有限群且在N上有一个真外作用α,则当G的阶是素数对,N是Ⅱ1型因子M=N(?)αG的极大子因子．另一方面,假设 N(?) M是Ⅱ1型因子的一个包含,M(?)M1是N(?)M的基本构造,[M:N]= p∈N是素数,N’∩ M=CI,N’∩M1是交换的,N,(?)M深度为2,则N是M的极大子因子．     

Remarks on pseudo-valuation rings

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ε A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.     

U-标算子的结构分析

类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”．尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立．本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件．     

On JB-Rings

A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2.     

Formulation of the problem of the flutter of a shell of revolution and a shallow shell in a high-velocity supersonic gas flow

Aero-elastic vibration is investigated in the case of a shallow shell of revolution or a cylindrical panel, which respectively occupy a part of a thin cylindrical body or a thin profile, in a high-velocity supersonic gas flow at zero angle of attack. Particular attention is paid to finding the pressure interaction and this problem is solved within the framework of the law of plane sections in boundary-layer theory. An expression is obtained which refines and supplements the well-known formula of “piston” theory. A linearized formulation of the problem of the panel flutter of a shallow shell is presented. Using the example of a plate located on one of the sides of a wedge, it is shown that the formula of “piston” theory is complemented with a term which has the meaning of a compressive force in the plane of the plate. It is shown that, when account is taken of this term, there is a reduction in the critical flow velocity.     

Dimonoids

It is proved that a system of axioms for a dimonoid is independent and Cayley’s theorem for semigroups has an analog in the class of dimonoids. The least separative congruence is constructed on an arbitrary dimonoid endowed with a commutative operation. It is shown that an appropriate quotient dimonoid is a commutative separative semigroup. The least separative congruence on a free commutative dimonoid is characterized. It is stated that each dimonoid with a commutative operation is a semilattice of Archimedean subdimonoids, each dimonoid with a commutative periodic semigroup is a semilattice of unipotent subdimonoids, and each dimonoid with a commutative operation is a semilattice of a-connected subdimonoids. Various dimonoid constructions are presented.     

Generalising a characterisation of Hermitian curves

This article proves a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefèvre-Percsy. It is shown that if is a Buekenhout-Metz unital with respect to a line in such that a line of not through meets in a Baer subline, then is classical. An immediate corollary is that if is a unital in PG such that is Buekenhout-Metz with respect to two distinct lines, then is classical. Received 5 August 1999; revised 15 February 2000.     

最小填充问题的可分解性

起源于稀疏矩阵计算和其它应用领域的图G的最小填充问题是在图G中寻求一个内含边数最小的边集F使得G F是弦图.这里最小值|F|称为图G的填充数,表示为f(G).作为NP-困难问题,该问题的降维性质已被研究,其中包括它的可分解性.基本的可分解定理是:如果图G的一个点割集S是一个团,则G经由S是可分解的.作为推广,如果S是一个"近似"团(即只有极少数边丢失的团),则G经由S是可分解的.本文首先给出基本分解定理的另外一个推广:如果S是G的一个极小点割集且G-S含有至少|S|个分支,则G经由S是可分解的;其次,给出了这个新推广定理的一些应用.     

Jacobson-Chevalley稠密定理的一个推广

我们在[1]中证明了,一个半环(hemiring)关于它的Jacobson关系根的商同构于完全本原半环的亚直和。这使我们有兴趣对这个特殊的半环类——完全本原半环的结构作进一步的讨论。本文的主要结果是:一个半环是完全本原的当且仅当它是一个半模上的亚稠密自同态半环。这个定理给出了完全本原半环的结构,推广了Jacobson—Chevalley稠密定理。     

平坦的多项式剩余类环

本文证明了如果多项式的剩余类环 A=R[T]/fR[T]作为 R-模是平坦模,且R是约化环,则f是正规多项式.特别地,若R还是连通的,则f的首项系数是单位.也证明了弱整体有限的凝聚环是约化环,以及弱整体为有限的凝聚连通环是整环.     

A Chart for Evaluating Product Research and Development Projects

A method of evaluating research and development projects is described. The method is based on the use of an evaluation chart. The main purpose of the chart is to calculate a project score which is a measure of a selected evaluation criterion. A method of constructing a chart is illustrated using a project index as the evaluation criterion. The chart contains a list of twelve questions, the answers to which are assumed to be the main determinants of the variables in the formula of the index. Each question is followed by a set of answers from which a choice is to be made, and underneath each answer is a numerical score. The numerical scores are logarithmic functions of the answers to which they relate, and when added together give a project score which is a logarithmic function of the index. Various methods of using the chart, and a suggested evaluation procedure, are also described.     

Almost Alternating Diagrams and Fibered Links in S3

Let R be a Seifert surface obtained by applying Seifert's algorithmto a connected diagram D for a link L. In this paper, lettingD be almost alternating, we give a practical algorithm to determinewhether L is a fibered link and R is a fiber surface. We furthershow that L is a fibered link and R is a fiber surface for Lif and only if R is a Hopf plumbing, that is, a successive plumbingof a finite number of Hopf bands. It has been known for sometime that this is true if D is alternating, and we show thatit is not always true if D is 2-almost alternating. In the appendix,we partially answer C. Adams's open question concerning almostalternating diagrams. 2000 Mathematical Subject Classification:57M25.     

Does contraction preserve triangular meshes?

A triangular graph is a planar graph in which each face is a 3-cycle, except possibly for the exterior face, and without articulation nodes. The embedding of a triangular graph in the plane is called a triangular mesh. More generally, a triangular graph with multiple contours is a planar graph without articulation nodes in which each face is a 3-cycle, except possibly for a fixed number of them. A contraction along an edge in a graph is the result of identifying the two endpoints of the edge. In this paper a necessary and sufficient condition is shown for which triangularity (possibly with multiple contours) is preserved after contraction. Moreover, when a licit contraction is performed, the question to answer is whether or not it is possible to derive the embedding of the contracted triangular graph from the original triangular mesh by redrawing only around the contraction zone.Part of this work was done when the author was in his sabbatical year at the University of California at Los Angeles.     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

正则带的拟强半格分解

本文研究了正则带的结构问题.利用拟强半格分解方法,获得了带为正则带当且仅当它为矩形带的拟强半格,推广了Yamada和Kimura关于正规带是矩形带的强半格的结果.     

Optimal pricing and quantity of products with two offerings

This paper analyzes the decision of a firm offering two versions of a product, a deluxe and a regular. While both products satisfy the same market, the deluxe version is sold at a high price relative to its cost and is aimed at the high end of the demand curve. The regular version is sold at a low price relative to its cost and is targeted to customers at the low end of the demand curve. This two-offering strategy is especially popular with book publishers where a paperback book is introduced some time after the hardbound version is introduced. The time between the introduction of the two versions of the product is accompanied by a downward shift in the demand curve due to customers losing interest in the product or satisfying their demand from a secondary used market. We solve a profit maximization model for a firm using a two-offering strategy. The model is solved for linear and exponential deterioration in demand, which is assumed to be deterministic. Also, a model with linear deterioration in demand, which is assumed to be stochastic, is solved. The results indicate that substantial improvements in profit can be obtained by using the two-offering strategy. Numerical sensitivity analysis and examples are used to illustrate the results.     

Coorbits of Quantum Homogeneous Spaces

The notion of coorbits for spaces with quantum group actions is introduced. A space with a quantum group action is given by a pair of algebras: an associative algebra which is the analog of a classical topological space, and a Hopf algebra which is the analog of a classical topological group. The Hopf algebra acts on the associative algebra via a comodule structure mapping which is also an algebra homomorphism. For a space with a quantum group action, a coorbit is a pair of spaces given by the image and the kernel of an algebra homomorphism from the associative algebra to the Hopf algebra. The coorbits of several types of quantum homogeneous spaces are discussed. In the case when the associative algebra is the group algebra of a group and the Hopf algebra is a quotient of the group algebra, the connection between the set of coorbits and the character group is established.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

点是Gδ-集的∑*-空间的构成定理

在林寿与我最近合作的一篇文章中指出了∑*-空间的构成定理需重新考虑.本文就是要证明在空间X的每个点是Gδ-集的条件下该构成定理是成立的,所得的结论是:X是T1且每个点是Gδ-集的∑*-空间,如果f:X→Y是闭的满连续映射,则在Y中有一σ-闭离散子空间Z,使得对每个y∈Y\Z,f-1(y)是X的w1-紧子空间.为得到该主要结果,本文证明了若空间X是每个点是Gδ-集的次亚紧空间.则X中的每个闭离散子集是X中的Gδ-集.