RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

Federal-provincial relations and the environment : attaining sustainable development through cooperation /

A study of intergovernmental relations in the area of the environment will determine whether the current Canadian federal structure represents a dangerous impediment to the promotion of sustainable development. This paper examines the interjurisdictional quagmire that has developed from the fact that authority over the environment is a functionally concurrent field for the two orders of government. A history of federal-provincial relations in the area of environmental protection is followed by an analysis of the advantages and disadvantages associated with competitive and cooperative federalism. For the purpose of this paper, cooperative federalism is characterized by the presence of a formal institutional system to facilitate interaction between politicians and bureaucrats from both orders of government. Competitive federalism is defined as a system that lacks a formal institutional structure to promote discussion and coordination between federal and provincial officials in a specific field of interest. Last, I examine thirty sustainable development issues following the structure established in Agenda 21 to determine the impact of the present federal system on the development of these objectives. This study concludes that Canadian federalism is not a dangerous impediment to the promotion of sustainable development. Cooperative federalism in a form that does not eliminate the ability of governments to revert to competition promotes the emergence of an institutional system that facilitates information-sharing and discussion between the two orders of government, thus leading to coordinated efforts in the field of the environment. Respect for the current division of powers in this area is also essential to the cohesiveness of Canadian society. Policy-makers and advocates for a sustainable society should focus on working within the present system.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

New Building Blocks for Dual-Property Molecule-Based Magnets

Two classes of compounds have been prepared and characterized as building blocks for chiral magnets and ferromagnetic conductors. In the fIrst project, the organic framework of a pentadentate, (N302) macro cycle has been synthetically modifIed to introduce phenyl substituents into its organic framework and the synthesis of four new [Fe(In(N302)(CN)2] complexes (I) - (IV) is presented. [Molecular diagram availble in pdf] This work represents the fIrst structural and magnetic studies of a family of spin crossover macrocycles that comprise of both structural and stereo-isomers. Magnetic susceptibility and Mossbauer data for the R,R-complex (I) is consistent with both a thermal and a light induced spin crossover transition. The X-ray data supports a change in geometry accompanying the thermal spin transition, from a high spin (HS) 7 -coordinate complex at room temperature to a low spin (LS) 5-coordinate complex at 100 K. The crystal structure ofthe racemic complex (III) reveals a HS, 7-coordinate complex at 200 K that undergoes no signifIcant structural changes on cooling. In contrast, the magnetic - susceptibility and Mossbauer data collected on a powder sample of the racemic complex are consistent with a LS complex. Finally, the meso complex (IV) was prepared and its structure and magnetic properties are consistent with a 5-coordinate LS complex that remains low spin, but undergoes conformational changes on cooling in solution. The chiral [Fe(H)(N302)(CN)2] macro cycle (I), together with its Mn(H) and Fe(H) derivatives have also been exploited as building blocks for the self-assembly of chiral magnets. In the second project, a synthetic route for the preparation of tetrathiafulvalene (TTF) donors covalently attached to a diisopropyl verdazyl radical via a cross conjugated pyridyl linker IS presented. Following this strategy, four new TTF-py- (diisopropyl)verdazyl radicals have been prepared and characterized (V) - (VIII) . [Molecular diagram available in pdf] The first (2:1) charge transfer complex ofa TTF-py-(diisopropyl)verdazyl radical donor and a TCNQ acceptor has been prepared and structurally characterized. The crystal packing shows that the donor and acceptor molecules are organized in a mixed stacking arrangement consistent with its insulating behaviour. EPR and magnetic susceptibility data support intramolecular ferromagnetic interactions between the TTF and the verdazyl radicals and antiferromagnetic interactions between TTF donors within a stack. In an attempt to increase the intramolecular exchange interaction between the two radicals, a TTF-x-(diisopropyl)verdazyl radical (IX) was prepared, where the two radicals are connected ia a conjugated divinylene linker. The neutral radical donors stack in a more favourable head-to-head arrangement but the bulky isopropyl groups prevent the donor radicals from stacking close enough together to facilitate good orbital overlap. [Molecular diagram available in pdf].