Divisible designs from twisted dual numbers

The generalized chain geometry over the local ring $K(\varepsilon ; \sigma)The generalized chain geometry over the local ring of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated. Dedicated to Helmut M?urer on the occasion of his 70th birthday     

Extended dual affine planes

We study a class of diagram geometries, achieve a characterization of extended dual affine planes, and embed extended dual affine planes in extended projective planes. The geometries studied are rank 3 diagram geometries such that the residue of a point is a dual net, and the residue of a plane is linear; the dual of such a geometry has partitions on lines and planes which are reminiscent of parallelism of lines and planes of an affine 3-space. Examples of these geometries (some in dual form) include extended dual affine planes, Laguerre planes, 3-nets, and orthogonal arrays of strength 3. Theorem: Any such finite geometry satisfying Buekenhout's intersection property, and such that any two points are coplanar, is an extended dual affine plane (and has order 2, 4, or 10). Theorem: This geometry may be embedded in an extended projective plane of the same order.This research was partially supported by NSF Grant MCS-8102361.     

协方差结构分析中拟似然估计的对偶几何方法

本文应用几何方法研究了协方差结构分析中的拟似然估计.对于该模型引进了对偶几何,在此基础上得到了拟似然估计的二阶渐近性质.通过对偶曲率给出了拟似然估计的偏差、方差和信息损失,并且给出了反映拟观察信息和拟期望信息之间关系的一个极限定理.     

平移积分几何中的对偶运动公式

本文利用对偶混合体积建立平移积分几何中的对偶运动公式.这些公式是将关于均质积分的基本运动公式推广到对偶均质积分和对偶混合体积情形.     

Graphical analysis of duality and the Kuhn-Tucker conditions in linear programming

Careful inspection of the geometry of the primal linear programming problem reveals the Kuhn-Tucker conditions as well as the dual. Many of the well-known special cases in duality are also seen from the geometry, as well as the complementary slackness conditions and shadow prices. The latter at demonstrated to differ from the dual variables in situations involving primal degeneracy. Virtually all the special relationships between linear programming and duality theory can be seen from the geometry of the primal and an elementary application of vector analysis.     

Strongly uniform extensions of dual 2-designs

A strongly α-uniform partial line space of order (s, t) is called an α-partial geometry. If α = t+1, then the geometry is a dual 2-design. Locally triangular and locally Grassman graphs correspond to triangular extensions of certain dual 2-designs, and the class of strongly uniform quasi-biplanes coincides with the class of strongly uniform extensions of dual 2-designs. We study strongly uniform extensions of dual 2-designs.     

多目标规划的对偶二阶条件

本文针对多目标规划 ( VP)的 Lagrange对偶规划 ( VD) ,从几何直观的角度出发 ,给出对偶规划( VD)的二阶最优性条件 ,即对偶二阶条件 ,并证明了相应的最优性定理 .     

THE PLACE OF EXPERIMENTAL TASKS IN GEOMETRY TEACHING: LEARNING FROM THE TEXTBOOK DESIGNS OF THE EARLY 20th CENTURY

The dual nature of geometry, in that it is a theoretical domain and an area of practical experience, presents mathematics teachers with opportunities and dilemmas. Opportunities exist to link theory with the everyday knowledge of pupils but the dilemmas are that learners very often find the dual nature of geometry a chasm that is very difficult to bridge. With research continuing to focus on understanding the nature of this problem, with a view to developing better pedagogical techniques, this paper examines the place of experimental tasks in the process of learning geometry. In particular, the paper provides some results from an analysis of innovative geometry textbooks designed in the early part of the 20^th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis suggests that experimental tasks have a vital role to play and that a potent tool for informing the design of such tasks, so that they build effectively on pupils' geometrical intuition, is the notion of the geometrical eye, a term coined by Charles Godfrey in 1910 as "the power of seeing geometrical properties detach themselves from a figure".     

An axiomatic foundation of Cayley-Klein geometries

We present a common axiomatic characterization of Cayley-Klein geometries over fields of characteristic \({\neq 2}\). To this end the axiom system of Bachmann (Aufbau der Geometrie aus dem Spiegelungsbegriff, 2nd edn. Springer, Heidelberg1973) for plane absolute geometry, which allows a common axiomatization of Euclidean, hyperbolic and elliptic geometry, is generalized. The notion of plane absolute geometry is broadened in several aspects. The most important one is that the principle of duality holds: the dual of a Cayley-Klein geometry is also a Cayley-Klein geometry. The various Cayley-Klein geometries are singled out by additional axioms like the Euclidean or hyperbolic parallel axiom or their dual statements.     

Quasi-Stationarity of Discrete-Time Markov Chains with Drift to Infinity

We consider a discrete-time Markov chain on the non-negative integers with drift to infinity and study the limiting behavior of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state probabilities of the original chain conditioned on not having left state 0 for the last time are equal to the state probabilities of its dual conditioned on non-absorption. This allows us to establish the simultaneous existence, and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasi-stationary distribution in the usual sense, a similar statement is not possible for the original chain.     

On the existence of dual solutions for Lorentzian cost functions

The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal transport is timelike on a set of full measure. In the second part the persistence of absolute continuity along an optimal transportation under obvious assumptions is proven and a solution to the relativistic Monge problem is provided.     

Finite geometries which contain dual affine planes

Finite geometries in which each plane is projective or dual affine over the field of two elements, or affine over the field of three elements, are studied. It is shown that no connected geometry can mix all three species of planes, and the geometries in which projective and dual affine planes occur are classified.     

The dual geometry of Hermitian two-point codes

In this paper, we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.     

Geometrical formulation of Hamiltonian boundary value problems

A geometrical formulation of nonlinear Hamiltonian boundary value problems is presented. It involves a distance geometry which is a generalization of hypercircle geometry for linear boundary value problems. The connection with dual extremum principles is also exhibited.     

碳限额及交易下零售商低碳宣传的双渠道供应链决策与协调

在碳限额及交易下,考虑制造商碳减排技术投入和零售商低碳宣传,分别构建了无低碳宣传成本分摊、低碳宣传成本分摊的分散决策和集中式决策博弈模型通过对模型的分析,指出通过碳减排成本和低碳宣传成本分摊能够实现双渠道供应链协调.研究结果表明:在碳限额及交易机制下,碳减排率与碳排放交易价格成正向变化关系,低碳宣传水平、双渠道供应链利润与碳排放交易价格成U变化关系;碳减排率、低碳宣传水平、双渠道供应链利润与消费者低碳偏好系数、低碳宣传对消费者的影响系数都成正向变化关系;碳减排率、低碳宣传水平、双渠道供应链利润都与低碳宣传成本、碳减排成本系数成反向变化关系.     

The Fundamental Group as the Structure of a Dually Affine Space

This paper dualizes the setting of affine spaces as originally introduced by Diers for application to algebraic geometry and expanded upon by various authors, to show that the fundamental groups of pointed topological spaces appear as the structures of dually affine spaces. The dual of the Zariski closure operator is introduced, and the 1-sphere and its copowers together with their fundamental groups are shown to be examples of complete objects with respect to the Zariski dual closure operator.     

外包策略下的三级供应链系统协调问题研究

由于存在着激烈的商业竞争,供需匹配成为供应链追求高绩效的关键.本文在制造商采取产能外包的策略下,引入二次采购契约研究制造商和销售商之间的契约订货问题.研究表明:1)供应链上存在一个核心企业来主导供应链契约的制定;2)本文设计的二次采购契约机制对分散式供应链的协调是有效的;3)制造商通过产能外包解决由于销售商的二次采购造成的缺货,可以使其更好地满足销售商的产品需求,进而提高供应链整体收益.最后,通过算例对研究结果作进一步说明.     

A (c. L*-Geometry for the Sporadic Group J2

We prove the existence of a rank three geometry admitting the Hall–Janko group J2 as flag-transitive automorphism group and Aut(J2) as full automorphism group. This geometry belongs to the diagram (c·L*) and its nontrivial residues are complete graphs of size 10 and dual Hermitian unitals of order 3.     

ON MAXIMA OF DUAL FUNCTION OF THE CDT SUBPROBLEM

1. IntroductionConsider the following the CDT problem Pwhere g e n", B E n"'", A E n"'", c E urn, a > 0, (2 0, B is a symmetric matrix notnecessajry positive semi--definde, and throughout this paperg the norm 11' 11 denotes the Euclideannorm. For the conveniellt of our following discussion, let F be the feasible region of the CDTsubproblem,andProblem (1.1)--(1.3) arises in some trust region algorithms for equality constrained optillilzation aiming to conquer the inconsistency between the…