From Sergeants and Soldiers to Chiral Conflict Effects in Helical Polymers by Acting on the Conformational Composition of the Comonomers

Different communication mechanisms can be switched within a copolymer by acting on the conformational composition of the components and their chirality. Thus, a sergeant and soldiers effect is produced in two diastereomeric copolymer series, poly[(S)- 1 _r-co-(S)- 2 _(1−r)] and poly[(R)- 1 _r-co-(S)- 2 _(1−r)], owing to the presence in chloroform of a preferred conformation in (S)- 2 , and a conformational equilibrium in 1 , where a P helix is induced independently of the absolute configuration of the soldier. In THF, the presence of a conformational equilibrium at the pendants of the two components produces a reciprocal chiral enhancement effect by copolymerization of the two monomers, while in DMF, a third chiral to chiral communication switch is produced due to the presence of a single conformer at the pendant group of the two components. In such a case, a chiral conflict or chiral accord effect is produced depending if the two components induce the same or the opposite helical sense.     

Algebraic coalitions

The idea of an algebra in is introduced. Within congruence modular varieties such algebras are shown to be the abelian algebras with a one-element subalgebra. This leads on to the notion of algebraic coalition, which is characterized for congruence modular varieties and for varieties of Jónsson–Tarski algebras. This characterization displays an intimate relationship between algebraic coalitions, Gumm difference terms, and the centre of an algebra. Received July 16, 1996; accepted in final form May 2, 1997.     

基于Choquet积分形式的模糊联盟核心

在具有联盟结构的合作对策中,针对局中人以某种程度参与到合作中的情况,研究了模糊联盟结构的合作对策的收益分配问题。首先,定义了具有模糊联盟结构的合作对策及相关概念。其次,定义了Choquet积分形式的模糊联盟核心,提出了该核心与联盟核心之间的关系,对于强凸联盟对策,证明Choquet积分形式的模糊Owen值属于其所对应的模糊联盟核心。最后通过算例,对该分配模型的可行性进行分析。     

Protectionism and blocking power indices

We study here the protectionist role of blocking coalitions in a voting game. More precisely, we first present necessary properties that a family of coalitions must satisfy in order to be the blocking family of some game and show that they are sufficient conditions too. Furthermore, a procedure to determine all games having a given blocking family is provided. With regard to uniqueness and multiplicity, (a) the blocking families that univocally determine the game are characterized by means of a separation condition, and (b) it is shown that in the nonseparating case at least three games share each nonempty blocking family, and an upper bound is given for the number of such games. Some numerical examples illustrate our results. Finally, power indices related to the blocking structure are discussed. Research partially supported by Grant SGR 2005–00651 of the Catalonia Government and Grant MTM 2006–06064 of the Education and Science Spanish Ministry and the European Regional Development Fund.     

Schmidt's game, badly approximable matrices and fractals

We prove that for every M,N∈N, if τ is a Borel, finite, absolutely friendly measure supported on a compact subset K of RMN, then K∩BA(M,N) is a winning set in Schmidt's game sense played on K, where BA(M,N) is the set of badly approximable M×N matrices. As an immediate consequence we have the following application. If K is the attractor of an irreducible finite family of contracting similarity maps of RMN satisfying the open set condition (the Cantor's ternary set, Koch's curve and Sierpinski's gasket to name a few known examples), then

dimK=dimK∩BA(M,N).     

A cops and robber game in multidimensional grids

We theoretically analyze the ‘cops and robber’ game for the first time in a multidimensional grid. It is shown that in an n-dimensional grid, at least n cops are necessary if one wants to catch the robber for all possible initial configurations. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, we revisit the game in a two-dimensional grid and provide an independent proof of the fact that the robber can be caught even by a single cop under certain conditions.     

基于联盟结构的模糊合作博弈的收益分配方案

研究了具有联盟结构的企业联盟模糊情况下各局中人的收益分配问题.首先拓展了Owen联盟值在经典意义下满足的5个公理,利用Choquet积分给出了基于联盟结构的模糊合作博弈的Owen联盟值,即模糊Owen联盟值的具体形式,并证明该联盟值满足新定义的5个公理.最后用实例验证了模糊Owen联盟值方法,并对计算结果进行分析。     

On the design of voting games

By focusing on the protectionist tendency found in the design of voting games, a thorough analysis is provided for the role of blocking coalitions in a simple game. We characterize those blocking families that univocally determine the game, and show that otherwise at least three games share a given nonempty blocking family, also giving an upper bound for the number of such games. Some examples illustrate the application of these ideas to political science.     

公平性与数学化（Ⅱ）权力指数

对一个加权选举系统引入权力指数概念,并用具体例子计算一些政府组织的有关指数。     

一类具有限制联盟结构的合作对策的两阶段Shapley值

讨论一类具有限制联盟结构的合作对策,其中局中人通过优先联盟整体参与大联盟的合作,同时优先联盟内部有合取权限结构限制,利用两阶段Shapley值的分配思想并考虑到权限结构对优先联盟内合作的限制,给出了此类合作对策的解。 该解可看做具有联盟结构的合作对策的两阶段Shapley值的推广。 证明了该解满足的公理化条件,并验证了这些条件的独立性。