Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Categorical abstract algebraic logic: The categorical Suszko operator

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so‐called, protoalgebraic π‐institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko operator to the π‐institution framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Highly efficient Meinwald rearrangement reactions of epoxides catalyzed by copper tetrafluoroborate

Epoxides undergo a highly efficient and selective rearrangement in the presence of catalytic quantities of copper tetrafluoroborate to give carbonyl compounds in excellent yields. The low toxicity and ease of handling of this reagent make it an attractive alternative to the more corrosive Lewis acids frequently employed.     

Equilibria for networks with malicious users

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. An extended abstract of this work appeared in the Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC) 2003. G. Karakostas’ research was supported by an NSERC Discovery research grant and MITACS. Part of this research was done when Viglas was a postdoctoral fellow at the University of Toronto, Canada.     

Amidrazones. 14. The formation of 1,1-disubstituted hydrazines from the base-promoted hydrolysis of 1,l-disubstituted-3-amino-4,5-dihydro-1H-pyrazolium halides: Mechanistic considerations

Three mechanistic pathways are considered for the hydroxide-promoted conversion of 1,1-disubstituted-3-amino-4,5-dihydro-1H-pyrazolium halides 1 to 1,1-disubstituted hydrazines, ammonia and sodium 3-hydroxypropanoate. Evidence presented in this paper supports a hydrolysis mechanism c that is initiated by hydroxide ion addition to the 3-position of 1 to form a tetrahedral intermediate 7 .     

Global stability of a two-species piecewise linear volterra ecosystem

This paper extends the results of Goh [1], and Takeuchi and Adachi [2,3] concerning the generalized linear Volterra model. We introduce a piecewise linear Volterra model for a two- species system. The solution of the steady-state problem is then shown to be equivalent to finding the solution to the Generalized Linear Complementarity Problem. We show when this nonnegative equilibrium is unique and globally asymptotically stable in the sense of Goh [1].