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.

Message from the President of the United States, in relation to the claim of Virginia, an account of interest paid by that State, on moneys borrowed for the payment of the militia thereof, for services rendered the United States

April 13, 1824. Printed by order of the Senate of the United States. At head of title: 18th congress, 1st session. [64]. Printed by Cales and Seaton

A report of the Secretary of State, in relation to individuals selected from American prisoners of war, and sent to Great Britain for trial, and also in relation to any orders for retaliation

Printed by Roger C. Weightman

Thoughts upon the conduct of our administration in relation both to Great Britain and France, more especially in reference to the late negotiation, concerning the attack on the Chesapeake

Printed at the Repertory Office

An Examination of Youth Perceptions and Understandings of their Experiences with Extrajudicial Sanctions in Relation to Key Principles of the YCJA

It is unclear how the principles of meaningful consequences, fair and proportionate accountability, and rehabilitation and reintegration under the Youth Criminal Justice Act (2003) are understood and experienced by youth participating in diversion from youth court. Interviews with 20 youth revealed that, from their understanding, extrajudicial sanctions were viewed as accomplishing the goals of meaningful consequences and fair and proportionate accountability relatively well, but less emphasis was placed on rehabilitation and reintegration. The findings suggest that there may be a need an examination of the spectrum of responses available to youth under the umbrella of Extrajudicial Sanctions and their ability to achieve the key principles of the legislation. Implications for both youth and policy are addressed.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

The Dynamic Interplay of Attachment and Temperament in Relation to Dimensions of Aggression

The current study examined whether overt and relational forms of reactive and proactive aggression were differentially related to adolescents’ temperament and attachment security. Measures of adolescents’ temperament, attachment security, and aggression were completed by 211 adolescents, ages 10–14, and their caregivers. Attachment security was consistently associated with all four dimensions of aggression, whereas proneness to frustration was found to be uniquely associated with reactive-overt aggression. Additionally, it was found that at lower levels of effortful control more secure attachment was related to lower levels of reactive-relational aggression. Results also indicated that, for girls, the relation between attachment and proactive-overt and proactive-relational aggression was only significant when effortful control was low. Conversely, for boys, the relation between attachment and proactive-overt aggression and proactive-relational aggression was significant when effortful control was high. Implications of these findings and limitations to the current study are discussed.

The Reluctance of Cattle to Change a Learned Choice May Confound Preference Tests

The conclusion of the article states "it appears that previously learned choices may affect future choices in Y-mazes for cattle. Another area that needs to be researched is the effects of a mildly aversive treatment versus a severely aversive treatment on the tendency of a bovine to resist changing a learned choice".

Certificate for Ten Shares of Accumulative Preference Capital Stock in Lincoln Manufacturing Company Limited

Certificate for 10 shares of accumulative preference capital stock in Lincoln Manufacturing Company Limited to Hamilton K. Woodruff, April 10, 1923.

Certificate for Twenty Shares of Accumulative Preference Capital Stock in Lincoln Manufacturing Company Limited

Certificate for 20 shares of accumulative preference capital stock in Lincoln Manufacturing Company Limited to Hamilton K. Woodruff, April 14, 1923.

Certificate for Ten Shares of Accumulative Preference Shares of Capital Stock in Lincoln Manufacturing Company Limited

Certificate for 10 shares of accumulative preference shares of capital stock in Lincoln Manufacturing Company Limited to Hamilton K. Woodruff, July 4, 1923.

Certificate for Five Shares of Preference Shares in English Inns Limited

Certificate for 5 shares of preference shares in English Inns Limited to Hamilton K. Woodruff, Aug. 29, 1929.

Certificate for One Hundred Preference Shares in the Tait Storage Battery Company, Limited

Certificate for 100 preference shares in The Tait Storage Battery Company, Limited to the estate of Hamilton K. Woodruff, March 2, 1934.