The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

An Interactive Theorem Prover for First-Order Dynamic Logic

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs. The method of proving correctness of properties of a computer program using the well-known Hoare Logic can be implemented by utilizing the robustness of dynamic logic. For a very broad range of languages and applications in program veri cation, a theorem prover named KIV (Karlsruhe Interactive Veri er) Theorem Prover has already been developed. But a high degree of automation and its complexity make it di cult to use it for educational purposes. My research work is motivated towards the design and implementation of a similar interactive theorem prover with educational use as its main design criteria. As the key purpose of this system is to serve as an educational tool, it is a self-explanatory system that explains every step of creating a derivation, i.e., proving a theorem. This deductive system is implemented in the platform-independent programming language Java. In addition, a very popular combination of a lexical analyzer generator, JFlex, and the parser generator BYacc/J for parsing formulas and programs has been used.

John N. Jackson papers, 1960-1989, n.d.

John N. Jackson was born in Nottingham, England in 1926. He developed a passion for landforms and geography from his father, a high school math and science teacher who had studied geology. During the Second World War, he served in the British Navy. He received his BA from the University of Birmingham, and a PhD from the University of Manchester. After spending a year as a visiting professor at the University of British Columbia, he was hired in 1965 as the founding head of the Geography Department at Brock University. He taught at Brock for more than 25 years, immersing himself in the geography and history of the Niagara area. He became particularly interested in the history of the Welland Canals. He authored 20 books on various topics, including land use in Niagara, the history of St. Catharines, the Welland Canal, and railways in the Niagara Peninsula. He died in 2010, at the age of 84.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.

Indenture of Land Sold by John Robertson to John Jackson

Indenture regarding land sold by John Robertson of Niagara to John Jackson of Niagara. This transaction is for part of Lot no. 93 in Niagara Township. This document was registered in the Lincoln and Haldimand Registry on September 10, 1823 in Book J folio 322 - instrument no. 6357. Date of transaction was May 5, 1823.

Indenture between David Secord and John Jackson

Indenture between David Secord of Niagara Township and John Jackson of Niagara Township regarding the sale of part of Lot no. 90 situated in St. Davids, June 10, 1825.

Indenture between Stroughton Moore and George Jackson

Indenture of bargain and sale between Stroughton Moore of St. Davids and George Jackson of St. Davids for part of Lot no. 90 in the Township of Niagara - instrument no. 10.818, July 27, 1835.

Indenture between George Jackson and William Woodruff

Indenture of bargain and sale between George Jackson of Saint Davids and William Woodruff of St. Davids regarding the sale of part of Lot no. 90 in the Township of Niagara - instrument no. 12.482, March 21, 1839.

Indenture between Joseph Jackson and William Woodruff (B)

Indenture of bargain and sale between Joseph Jackson of Buffalo, New York and William Woodruff of St. Davids regarding Lot no. 90 in Niagara Township. This was registered in the County of Lincoln on April 30, 1842 in Book B, folio 299. The instrument no. is 732. It was written 17 March 1842.

Indenture between Joseph Jackson and William Woodruff (A)

Indenture of bargain and sale between Joseph Jackson of Buffalo, New York and William Woodruff of St. Davids regarding Lot no. 90 in St. Davids. This was registered in the County of Lincoln on April 30, 1842 in book B, folio 300. The instrument no. is 733. It was written 17 march 1842.

Notice to appear for Jury Duty in the Dispute between Stephen Jackson and Caleb Garion (Plaintiffs) and William Woodruff (Defendent)

Notice to appear for jury duty in the dispute between Stephen Jackson and Caleb Garion (plaintiffs) and William Woodruff (defendant) regarding the mill of the late John Jackson and the title deeds of the said property and the family bible of the late John Jackson containing the registry and births of his family. This is a 1 page printed document, Sept. 6, 1848.

Letter addressed to Jeremiah Jackson of Wall Street, New York from his brother A. Jackson, Austin, Texas

Letter addressed to Jeremiah Jackson of Wall Street, New York from his brother A. Jackson, Austin, Texas. This letter introduces his brother A, Jackson to Mr. Collier. Mr. Collier delivered the letter on his way home to St. Catharines, April 14, 1845.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Candidate Stability and Nonbinary Social Choice

A desirable property of a voting procedure is that it be immune to the strategic withdrawal of a candidate for election. Dutta, Jackson, and Le Breton (Econometrica, 2001) have established a number of theorems that demonstrate that this condition is incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of these impossibility theorems.