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.

Conscription Letter Envelope

An envelope from the Army and Navy Department "The International Committee of Young Men's Christian Associations (in the Field) General Office". The handwritten note on the front reads: "Capsule that decided someone's fate for conscription".

Envelope Addressed to Miss Julia Woodruff

Envelope addressed to Miss Julia Woodruff of St. Davids. Postmarks include: Suspension Bridge, N.Y., May 20, 1857; Clifton, May 20, 1857 and St. Davids, May 21, 1857.

Envelope Addressed to Noah Phelps, Lincoln Paper Mill Co.

Envelope addressed to Noah Phelps, Lincoln Paper Mill Co. with no postmarks, Merritton [In about 1877 Noah Phelps, Samuel Woodruff, Partrick Joseph Larkin and John Conlon were involved in the founding of a paper mill with Sylvester Neelon], n.d.

Envelope sent to Mr. Welland D. Woodruff at Thomas Cooks and Sons, Columbo, Indiana

Envelope postmarked Indo-Ceylon, special flight X’mas 1936, Bombay, Jan. 1937 and Thomas Cook and Son, Jan. 2, 1937. The letter is addressed to Mr. Welland D. Woodruff at Thomas Cook and Son, Columbo, India. This is crossed out and sent on to Royal Trust Co. 3 St. James St., London, England. This is crossed out and finally sent to the Mayfair Hotel, London, England, 1936-1937.

Letter and envelope addressed to Mr. Samuel D. Woodruff of St. Catharines

Letter and envelope addressed to Mr. Samuel D. Woodruff of St. Catharines. The envelope is postmarked St. Catharines, Dec. 31, 1887, Port Robinson, Dec. 31, 1887 and Welland, Dec. 31, 1887. The letter to S.D. Woodruff from Calvin Cudney and it says that he has enclosed $35 in interest, Dec. 29, 1887.

Application for Loan, Mortgage Loan Envelope, and Abstract of Title

Atkins, Sarah A. and Carlisle A. Gardner includes: Application for Loan, July 26, 1884; Mortgage Loan Envelope no. 255 for July 1, 1884 – July 1, 1889 and Abstract of Title, August 28, 1884.

Cogswell, Maria, includes: Application for loan on Real Estate, Insurance Policy, Mortgage Loan Envelope

Cogswell, Maria, includes: Application for loan on Real Estate, Feb. 20, 1882; Insurance Policy no. 2199780 from the Royal Insurance Company of Liverpool, March 17, 1887 and Mortgage Loan Envelope for mortgage no. 1535 from March 1, 1882 – March 1, 1887.

Crew, Isaac M., includes: Application for Loan, Mortgage Loan Envelope, and Abstract of Title

Crew, Isaac M., includes: Application for Loan, March 10, 1885; Mortgage Loan Envelope no. 679 for Jan. 1, 1885 – Jan. 1, 1890 and Abstract of Title, April 13, 1885.

Crick, Henry A., includes Application for Loan, and Mortgage Loan Envelope

Crick, Henry A., includes Application for Loan, Jan. 8, 1885 and Mortgage Loan Envelope no. 637 for Jan. 1, 1885 – Jan. 1, 1890.

Mank, Isaac, Mortgage Loan Envelope no. 640

Mank, Isaac, Mortgage Loan Envelope no. 640 for Jan. 1, 1885 – Jan. 1, 1890

Sampson, Albert, includes Application for a Loan on Real Estate, and an envelope with Mr. Sampson’s name crossed out

Sampson, Albert, includes Application for a Loan on Real Estate, April 19, 1882 and an envelope with Mr. Sampson’s name crossed out and postmarked Sept. 1882.

Schmidt, John, includes: Application for Loan, and Mortgage Loan Envelope, and Abstract of Title

Schmidt, John, includes: Application for Loan, Aug. 8, 1884 and Mortgage Loan Envelope no. 302 for July 1, 1884 – July 1, 1889 and Abstract of Title, Sept. 6, 1884.

Port Dalhousie and the Thorold Railway pay roll for the months of June, July and August, 1855, signed by S.D. Woodruff. There is an envelope included with this document, Aug. 21, 1855

Port Dalhousie and the Thorold Railway pay roll for services of engineering and contingencies furnished for the months of June, July and August, 1855, signed by S.D. Woodruff. There is an envelope included with this document, Aug. 21, 1855.