半群的代数K-理论方法(Ⅰ)——半群的Grothendieck群

本文及其续试将代数K-理论方法引入半群理论的研究。 设S是一个半群(有单位元和零元),P(S)是有限生成投射(单式、中心左)S-系范畴。本文定义半群S的Grothendieck群K_0S是K_0P(S),并证明了,K_0S是个自由Abel群,它的秩等于S的非零正则?-类的集合的基数。由此,定义了一般半群(未必有单位元和零元)的秩,考察了半群的秩与它们的代数结构之间的关系。接着讨论了K_0的函子性质。最后,对于交换半群S,刻划了K_0S的环结构。     

半群的代数K-理论方法(Ⅰ)——半群的Grothendieck群

本文及其续试将代数K-理论方法引入半群理论的研究。 设S是一个半群(有单位元和零元),P(S)是有限生成投射(单式、中心左)S-系范畴。本文定义半群S的Grothendieck群K_0S是K_0P(S),并证明了,K_0S是个自由Abel群,它的秩等于S的非零正则?-类的集合的基数。由此,定义了一般半群(未必有单位元和零元)的秩,考察了半群的秩与它们的代数结构之间的关系。接着讨论了K_0的函子性质。最后,对于交换半群S,刻划了K_0S的环结构。     

弱Hopf代数与正则幺半群

本文定义了弱Ｈｏｐｆ代数并研究了弱Ｈｏｐｆ代数的弱对极与类群元幺半群的关系．首先,本文给出弱Ｈｏｐｆ代数的一些基本性质;然后,对类群元幺半群是逆半群或纯正半群的某些弱Ｈｏｐｆ代数,描述了其弱对极的一些性质;最后,给出一类其类群元幺半群为正则半群的弱Ｈｏｐｆ代数．     

基半群为0-J-严格单半群的零直并的代数

设Ａ是代数闭域ｋ上的一个具乘基Ｂ的有限维含幺结合代数，称半群Ｂ∪｛０｝为Ａ的基半群．本文给出了０ Ｊ 严格单半群的定义．对于基半群为０ Ｊ 严格单半群的零直并的代数，完全研究了它的代数表示型     

基半群为O—J—严格单半群的零直并的代数

设Ａ是代数闭域Ｋ上的一个具乘基Ｂ的有限维含幺结合代数，称半群Ｂ∪（０）为Ａ的基半群。本文给出了０－Ｊ－严格单半群的定义，对于基半群为Ｏ－Ｊ－严格单半群的零直并的代数，完全研究了它的代数表示型。     

P-正则半群的结构

本文定义了一类称之为PR-系的代数,证明了每个PR-系是一个P-正则半群, 而且每个P-正则半群可用这种方式来进行构造.     

直觉模糊变换半群的积与覆盖关系

提出了直觉模糊变换半群的(全)直积,圈积,直觉模糊变换半群的覆盖的定义,利用代数的手段讨论了直觉模糊变换半群的积的结合性质,研究了直觉模糊变换半群的积的覆盖关系.     

紧拓扑半群上概率测度卷积序列的极限性质

本文讨论紧拓扑半群上概率测度卷积序列的若干重要极限性质．在第１节中，我们讨论测度集的代数结构与其支撑集代数结构的关系．第２节的定理１，通过支撑集的代数结构给出组合收敛测度序列的一个极限定理．在定理２中我们讨论独立同分布时的情形，建立了一类紧半群上的Ｋａｗａｄａ－Ｉｔ型结果．这些定理推广了紧群、紧交换半群、紧Ｌ－Ｘ半群上一些相应的结论．     

关于半群的直觉模糊拟理想

给出了半群中直觉模糊拟理想的等价定义,研究了半群中直觉模糊拟理想的若干性质和刻画,并用直觉模糊拟理想刻画群,完全正则半群和群半格．     

可换幺半群的结构

关于“群”有各种各样的定义 ,本文给出了有限幺半群成为群的一个条件 .并对有限可换幺半群进行了讨论 ,通过对它的商集的研究 ,建立了有限可换幺半群与有限可换幺群之间的联系 ,从而揭示了有限可换幺半群的结构     

An algorithm for constructing star-shaped drawings of plane graphs

A straight-line planar drawing of a plane graph is called a convex drawing if every facial cycle is drawn as a convex polygon. Convex drawings of graphs is a well-established aesthetic in graph drawing, however not all planar graphs admit a convex drawing. Tutte [W.T. Tutte, Convex representations of graphs, Proc. of London Math. Soc. 10 (3) (1960) 304–320] showed that every triconnected plane graph admits a convex drawing for any given boundary drawn as a convex polygon. Thomassen [C. Thomassen, Plane representations of graphs, in: Progress in Graph Theory, Academic Press, 1984, pp. 43–69] gave a necessary and sufficient condition for a biconnected plane graph with a prescribed convex boundary to have a convex drawing.In this paper, we initiate a new notion of star-shaped drawing of a plane graph as a straight-line planar drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. A star-shaped drawing is a natural extension of a convex drawing, and a new aesthetic criteria for drawing planar graphs in a convex way as much as possible. We give a sufficient condition for a given set A of corners of a plane graph to admit a star-shaped drawing whose concave corners are given by the corners in A, and present a linear time algorithm for constructing such a star-shaped drawing.     

Box-Rectangular Drawings of Plane Graphs

In this paper we introduce a new drawing style of a plane graph G called a box-rectangular drawing. It is defined to be a drawing of G on an integer grid such that every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. We establish a necessary and sufficient condition for the existence of a box-rectangular drawing of G. We also give a linear-time algorithm to find a box-rectangular drawing of G if it exists.     

On farthest points of sets

For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set.     

The KdV soliton crosses a dissipative and dispersive border

We demonstrate the behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or dispersion; beyond the layer dispersion is constant (but not necessarily of the same value) and dissipation is null. The transmitted wave either retains the form of a soliton (though of different parameters) or scatters a into a number of them. And a reflection wave may be negligible or absent. This models a situation similar to a light passing from a humid air to a dry one through the vapor saturation/condensation area. Some rough estimations for a prediction of an output are given using the relative decay (or accumulation) of the KdV conserved quantities in a dissipative area; in particular for a restriction for a number of solitons in the transmitted signal.     

Staircase Parameterization in Dynamical Selection

This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed.     

Enumerating bases of self-dual matroids

We define involutively self-dual matroids and prove that an enumerator for their bases is the square of a related enumerator for their self-dual bases. This leads to a new proof of Tutte's theorem that the number of spanning trees of a central reflex is a perfect square, and it solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted version of the latter result.We give an algebraic analogue relating to the critical group of a graph, a finite abelian group whose order is the number of spanning trees of the graph. We prove that the critical group of a central reflex is a direct sum of two copies of an abelian group, and conclude with an analogous result in Kalai's setting.     

Mean-variance portfolio selection for a non-life insurance company

We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise. We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process. In order to find optimal strategies we apply techniques from the stochastic control theory.     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

Palm calculus for a process with a stationary random measure and its applications to fluid queues

We consider a process associated with a stationary random measure, which may have infinitely many jumps in a finite interval. Such a process is a generalization of a process with a stationary embedded point process, and is applicable to fluid queues. Here, fluid queue means that customers are modeled as a continuous flow. Such models naturally arise in the study of high speed digital communication networks. We first derive the rate conservation law (RCL) for them, and then introduce a process indexed by the level of the accumulated input. This indexed process can be viewed as a continuous version of a customer characteristic of an ordinary queue, e.g., of the sojourn time. It is shown that the indexed process is stationary under a certain kind of Palm probability measure, called detailed Palm. By using this result, we consider the sojourn time processes in fluid queues. We derive the continuous version of Little's formula in our framework. We give a distributional relationship between the buffer content and the sojourn time in a fluid queue with a constant release rate.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.