Controlled stereochemistry of polyamides derived from cis/trans‐1,4‐cyclohexanedicarboxylic acid

A series of copolyamides 12.y was synthesized either with y = 6, or 1,4‐cyclohexanedicarboxylic acid (1,4‐CHDA) residue, or a mixture of both. The influence of the synthetic route of 1,4‐CHDA containing polyamides on the obtained cis–trans ratio of the incorporated 1,4‐CHDA was investigated. The use of acid chlorides provided a synthetic route with full control of the cis–trans ratio of the 1,4‐CHDA residue during synthesis, whereas synthesis at elevated pressure and temperature caused isomerization. The content and cis–trans ratio of 1,4‐CHDA in the copolyamides were determined by solution ¹³C NMR spectroscopy. Increasing the degree of partial substitution of the adipic acid by 1,4‐CHDA resulted in an increase in T_m, even for low molar precentages of 1,4‐CHDA. This phenomenon points to isomorphous crystallization of both the 12.6 and 12.CHDA repeating units. The mps of the synthesized polyamides were independent of the initial cis–trans ratio of 1,4‐CHDA, provided that the samples were annealed at 300 °C before DSC analysis. The polyamides exhibited a different melting pattern depending on the 1,4‐CHDA content. At a low a 1,4‐CHDA content a net exothermic recrystallization occurred during melting, whereas at higher contents of 1,4‐CHDA this recrystallization occurs to a lesser extent, and two separate melting areas are observed. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 833–840, 2001     

Positron annihilation in BaF2 crystals

Positron lifetime measurements in BaF₂ were performed in the temperature range 10 to 292 K. Three lifetime components were resolved, the third component having a very low intensity. The intensity of the second component increases between 12 and 80 K. For further increase of the temperature, up to 290 K, the intensity of this component falls from about 63% to 37%. An increased positronium formation probability is suggested for explaining this observation. Some alternative explanations are discussed, as well.     

High‐Silica Zeolite SSZ‐61 with Dumbbell‐Shaped Extra‐Large‐Pore Channels

The synthesis of the high‐silica zeolite SSZ‐61 using a particularly bulky polycyclic structure‐directing agent and the subsequent elucidation of its unusual framework structure with extra‐large dumbbell‐shaped pore openings are described. By using information derived from a variety of X‐ray powder diffraction and electron microscopy techniques, the complex framework structure, with 20 Si atoms in the asymmetric unit, could be determined and the full structure refined. The Si atoms at the waist of the dumbbell are only three‐connected and are bonded to terminal O atoms pointing into the channel. Unlike the six previously reported extra‐large‐pore zeolites, SSZ‐61 contains no heteroatoms in the framework and can be calcined easily. This, coupled with the possibility of inserting a catalytically active center in the channel between the terminal O atoms in place of H⁺, afford SSZ‐61 intriguing potential for catalytic applications.     

The core and related solution concepts for infinite assignment games

Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the utopia payoff for games with an infinite value. In this solution each player receives the maximal amount he can think of with respect to the underlying assignment problem. This solution is contained in the core of the game. Second, we study two solutions for assignment games with a finite value. Our main result is the existence of core-elements of these games, although they are hard to calculate. Therefore another solution, the f-strong ε-core is studied. This particular solution takes into account that due to organisational limitations it seems reasonable that only finite groups of agents will eventually protest against unfair proposals of profit distributions. The f-strong ε-core is shown to be nonempty. These authors’ research is partially supported by the Generalitat Valenciana (Grant number GV-CTIDIA-2002-32) and by the Government of Spain (through a joint research grant Universidad Miguel Hernández — Università degli Studi di Genova HI2002-0032).     

Strong equilibria in claim games corresponding to convex games

This paper deals with a specific aspect of the problem of coalition formation in a situation described by a TU-game. First, we define a very simple normal form game which models the process of coalition formation. To define the payoff functions of the players we use an allocation rule for TU-games. The main objective of this paper is ascertain what conditions of the allocation rule lead to the grand coalition being a strong equilibrium of the normal form game, when the original TU-game is convex. Received January 1996/Revised version December 1996/Final version May 1997     

On consistent solutions for strategic games

Nash equilibria for strategic games were characterized by Peleg and Tijs (1996) as those solutions satisfying the properties of consistency, converse consistency and one-person rationality.  There are other solutions, like the ɛ-Nash equilibria, which enjoy nice properties and appear to be interesting substitutes for Nash equilibria when their existence cannot be guaranteed. They can be characterized using an appropriate substitute of one-person rationality. More generally, we introduce the class of “personalized” Nash equilibria and we prove that it contains all of the solutions characterized by consistency and converse consistency. Received January 1996/Final version December 1996     

Drop out monotonic rules for sequencing situations

This note introduces a new monotonicity property for sequencing situations. A sequencing rule is called drop out monotonic if no player will be worse off whenever one of the players decides to drop out of the queue before processing starts. This intuitively appealing property turns out to be very strong: we show that there is at most one rule satisfying both stability and drop out monotonicity. For the standard model of linear cost functions, the existence of this rule is established.     

Various characterizations of convex fuzzy games

This note enlarges the literature on convex fuzzy games with new characterizing properties of such games besides the increasing average marginal return property, namely: the monotonicity of the first partial derivatives, the directional convexity and forC ²-functions the non-negativity of the second order partial derivatives.