Ehrenfeucht–Fraïssé games on ordinals

Two structures A and B are n-equivalent if player II has a winning strategy in the n-move Ehrenfeucht–Fraïssé game on A and B. Ordinals and m-coloured ordinals are studied up to n-equivalence for various values of m and n.     

An analysis of Chinese Super League partial results

Some of the history of soccer/world football in China is presented. Then consideration turns to the 2008 Chinese Super League. It has 16 teams. The results from the first half of the season, i.e. 15 rounds, are studied. The response of interest for a specific game is whether the home team won, tied or lost, who the home team was, and who the opponent was. The response is ordinal-valued. A generalized linear model is fit and then, given the remaining fixtures, used to predict the final standings of the season. Other explanatories, such as round number, are considered for inclusion in the model. Simulation is employed to estimate probabilities of interest. This work was supported by US National Science Foundation (Grant No. DMS-0707157)     

Primitive recursive analogues of regular cardinals based on ordinal representation systems for KPi and KPM

In this paper, we develop primitive recursive analogues of regular cardinals by using ordinal representation systems for KPi and KPM. We also define primitive recursive analogues of inaccessible and hyperinaccessible cardinals. Moreover, we characterize the primitive recursive analogue of the least (uncountable) regular cardinal.     

卤代烷第一电离能的自相关拓扑研究

基于有机物系统命名法的原子序数(gi)及其染色序数(gi′)对分子中非氢原子具有优异的选择性,并能反映其所处的化学环境.1阶原子序数自相关拓扑指数(1G)及其染色指数(1G′)定义为:1G=∑(gi·gi)-1、 1G′=∑(gi′·gi′)-1.它们不仅计算简单, 而且对烷烃、卤代烃的同分异构体的区分能力优于著名的Kier指数(1Xv).27种卤代烷第一电离能(Ip)的递变规律可表征为: Ip=7.4545-0.79341G′-0.70671G +1.5514Xp, 其复相关系数为0.9982, 优于文献的0.9976.估算结果较好.     

基于序数偏差融合度的动态匹配决策方法

针对具有不确定偏好序信息的动态匹配决策问题,提出了一种决策方法。首先,给出了序数偏差的相关描述;然后,把在同一时刻的不同方案间或同一方案在不同时刻间的序数偏差关系作为证据,并通过证据组合求出双边序数偏差融合度;在此基础上,构建了优化模型,获得双边匹配方案。最后,通过一个算例说明了该方法的可行性和有效性。     

不确定偏好序信息下考虑主体心理行为的双边匹配决策方法

针对基于不确定偏好序信息的双边匹配问题,本文提出了一种决策方法。给出了双边匹配和不确定偏好序的相关概念,同时给出了不确定偏好序信息下考虑主体心理行为的双边匹配问题描述;以每个主体给出的临界值作为其参照点,计算了每个主体给出的不确定偏好序相对于参照点的收益或损失;考虑到主体损失规避的心理行为特征,依据TODIM思想计算每个主体对另一方主体的益损值的感知价值;在此基础上,构建了求解该双边匹配问题的双目标优化模型,使用线性加权法将双目标优化模型转化为单目标优化模型,通过求解该单目标优化模型获得匹配结果;最后,通过IT服务外包中的供给方与需求方的双边匹配实例分析说明了所提方法的有效性。     

Complexity of Elements in Rings

If R is a ring with subset S then the rational closure Div _R (S) of S in R is the smallest subring D of R containing S such that U(D)=DU(R) where U(D), resp. U(R), denotes the group of units of D resp. R. In this paper a new approach to the so-called complexity is given in order to describe how the elements of Div _R (S) are built from elements of S.     

The Derived Mappings and the Order of a Set-Valued Mapping Between Topological Spaces

Previous investigations of, in particular, continuous selections have led to the definition of the derived mappings and, here, the order of a set-valued mapping between topological spaces. The relation between the topological spaces and the possible orders of set-valued mappings between them is considered and examples are constructed to show that each ordinal number is the order of some set-valued mapping.     

How to develop Proof-Theoretic Ordinal Functions on the basis of admissible ordinals

In ordinal analysis of impredicative theories so-called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on admissible sets also renders a new and perspicuous approach to well-ordering proofs possible. MSC: 03F15, 03F35.