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.

Chelated fluoroboron cations : synthesis and multinuclear nmr studies

The preparation of chelated difluoroboron cations (DD)BF2+, where DD is a saturated polydentate tertiary-amine or polydentate aromatic ligand, has been systematically studied by using multinuclear solution and solid state nuclear magnetic resonance spectroscopy and fast atom bombardment mass spectrometry. Three new methods of synthesis of (DD)BF2+ cations are reported, and compared with the previous method of reacting a chelating donor with Et20.BF3. The methods most effective for aromatic donors such as 1,1O-phenanthroline are ineffective for saturated polydentate tertiary-amines like N,N,N' ,Nil ,Nil-pentamethyldiethylenetriamine. Polydentate tertiary-amine donors that form 5-membered rings upon bidentate chelation were found to chelate effectively when the BF2 source contained two leaving groups (a heavy halide and a Lewis base such as pyridine =pyr or isoxazole =ISOX), i.e., pyr.BF2X (X = CI or Br), ISOX.BF2X and (pyr)2BF2+. Those that would form 6membered rings upon chelation do not chelate by any of the four methods. Polydentate aromatic ligands chelate effectively when the BF2 source contained a weak Lewis base, e.g., ISOX.BF3, ISOX.BF2X and Et20.BF3. Bidentate chelation by polydentate tertiaryamine and aromatic donors leads to nmr parameters that are significantly different then their (D)2BF2+ relatives (D =monod~ntate t-amines or pyridines). The chelated haloboron cations (DD)BFCI+, and (DD)BFBr+ were generated from D.BFX2 adducts for all ligands that form BF2+ cations above. In addition, the (DD)BCI2+ and (DD)BBr2+ cations were formed from D.BX3 adducts by the chelating aromatic ligands, except for the aromatic ligand 1,8-bis(dimethylamino)naphthalene, which formed only the (DD)BF2+ cation, apparently due to its extreme steric hindrance. Chelation by a donor is a two-step reaction. For polydentate tertiary-amine ligands, the two rates appear to be very dependent on the two possible leaving groups on the central boron atom. The order of increasing ease of displacement for the donors was: pyr < Cl < Br < ISOX. The rate of chelation by polydentate aromatic ligands appears to be dependent on the displacement of the first ligand from the boron. The order of increasing ease of displacement for the donors was: pyr < CI < ISOX ~ Br < Et20.

The influence of familial smoking behaviours on adolescent smoking behaviours

The ability to identify adolescents who are at risk for becoming smokers may prove useful in developing effective smoking prevention programs. The purpose of this stUdy was to assess the importance of familial smoking behaviours on adolescent smoking patterns. The results were based on responses to The Grade 7 Lincoln County Smoking Survey designed by Chudzik and Partington (1994), and are a part of the "Peer Assisted Learning Program· (PAL) presented by the Niagara Regional Health Services Department, with the cooperation of a local Board of Education (Region of Niagara). The results indicate that 12% of the total group of 450 Grade 7 student respondents were current smokers at the time the data were collected (13% males and 11% females), while more than 37% of individuals indicated that they had tried smoking previously. Of the individuals who were classified as smokers, 11% reported that they smoked because their parents smoked, but only 6% reported that they smoked because their siblings smoked. More concerning, however, is the finding that 4% of smokers reported that they felt pressured to smoke by their relatives. In a society that is becoming increasingly concerned about health, it is also alarming to observe that only 50% of the respondents within this sample reported that there were no smokers (parents/siblings) in their homes. The results also indicate that 33% percent of respondents had grandparents who continued to smoke, and 53% of respondents indentified other relatives who continued to smoke.

British Methodist Episcopal Church Tithing Ticket, 1875

This is a quarterly tithing ticket from the British Methodist Episcopal Church, signed by R. Miller, Minister, and dated November 28, 1875. It was in the possession of the Rick Bell Family of St. Catharines, Ontario. Relatives of the Bell family include former Black slaves from the United States who settled in Canada.

British Methodist Episcopal Church Tithing Ticket, 1879

A first quarterly tithing ticket from the British Methodist Episcopal Church, signed by W. Grayson, Minister, and dated August 1, 1879. This ticket was in the possession of the Rick Bell Family of St. Catharines, Ontario. Relatives of the Bell family include former Black slaves from the United States who settled in Canada.

British Methodist Episcopal Church Tithing Ticket, 1884

A third quarterly tithing ticket from the British Methodist Episcopal Church, signed by the Minister, and dated February 17, 1884. This ticket was in the possession of the Rick Bell family of St. Catharines, Ontario. Relatives of the Bell family include former Black slaves from the United States who settled in Canada.

William Still's Boarding House advertisement [n.d.]

Original advertisement for William Still's Boarding House, No. 832 South Street, below 9th, south side Philad'a [sic]. Not dated. The advertisement includes handwritten marginalia, possibly by William Still, on the left-hand side referring to St. Catharines. There is a small embossed stamp on the upper left-hand corner of the advertisement. This item was in the possession of the Rick Bell Family of St. Catharines.Handwritten marginalia (original spelling and punctuation): "Do remember me very kindly to all my enquiring friends _ I but seldom hear of late from St. Catherines" The street number printed in the original advertisement (374) has been crossed out in black ink and a handwritten "832" has been inserted. William Still was an African-American abolitionist from Philadelphia and clerk of the Anti-Slavery Society who by his own account assisted 649 slaves receive freedom. He kept records on fugitive slaves so their relatives could find them later. In 1872, he published his records in a book entitled, The Underground Railroad. Source: William Still Underground Railroad Foundation: http://www.undergroundrr.com/foundation/about.htm

W.W. Tyrrill receipt, June 1888

A receipt from W.W. Tyrrill, of St. Catharines, Ontario dated June 2, 1888, for a ladies Swiss watch priced at $11.00. The receipt is a rental agreement which specifies the terms of a fee payment schedule. Information on the receipt indicates Mr. Tyrrill sold watches, jewelry, silver plated goods, albums and Bibles. He is also listed as an agent for pianos, organs and Singer sewing machines. This receipt was in the possession of Iris Sloman Bell, of St. Catharines. Relatives of the Sloman Bell families include former Black slaves from the United States who settled in southern Ontario.There are various spellings of the Tyrrill name within the Bell family archive. Other forms of the name include Tyrell, Tyrrell, and Terrell.

Bell Family Bible, Family Record, 1853-1897

The Family Record page from the Bell Family Bible providing information on the births of Bell ancestors. Relatives of the Bell family include former American slaves who later settled in Canada. This Bible was in the possession of the Rick Bell Family of St. Catharines, Ontario.

Bell Family Bible, Deaths, Tyrrell, 1886-1908

The Deaths page from the Bell Family Bible listing the deaths of Jane Tyrrell in 1886, William C. Tyrrell in 1898, and Lewis Tyrrell in 1908. This Bible was in the possession of the Rick Bell family of St. Catharines, Ontario. Relatives of the Bell family were former Black slaves from the United States who settled in Canada.The handwritten entry appears to read as follows: "Jane Tyrrell, died March 1st 1886 age 64 yrs. William C. Tyrrell died January 15th 1898 by accident in Albany N.Y. age 33 yrs 3 months Lewis Tyrrell died September 25th 1908 at his late residence Vine and Welland Ave. St. Catharines age 81 yrs 5 months." There are various spellings of the Tyrrell name within the Bell family archive. Other forms of the name include Tyrell, Tyrrill, and Terrell.

Cabinet Card by C. Arthur, Photographer, St. Catharines [n.d.]

An unidentified young woman is featured in this black and white cabinet card by photographer C. Arthur, of St. Catharines, Ontario. The address of Mr. Arthur's studio is printed along the bottom of the photograph. This photograph was among the family memorabilia owned by Iris Sloman Bell of St. Catharines. The Sloman - Bell families include relatives who were former African American slaves who settled in Canada.Charles A. Arthur is listed as a photographer in St. Catharines from 1880 - 1883 and Charles P. Arthur (possibly a son?) was a photographer in the same city in 1898. Source: Phillips, Glen C. The Ontario photographers list (1851-1900). Sarnia: Iron Gate Publishing Co., 1990.

Photograph of Unidentified Woman by C. Arthur, Photographer, St. Catharines [n.d.]

An unidentified young woman is featured in this undated black and white studio photograph by C. Arthur, Photographer, of St. Catharines, Ontario. This small cabinet card photograph was in the possession of the Iris Sloman Bell family of St. Catharines. Relatives of the Sloman - Bell families include former African American slaves who settled in Canada.Two photographers by the name of Arthur are listed as working in St. Catharines, Ontario in the second half of the 19th century. Charles A. Arthur was a photographer from 1880 - 1883, while Charles P. Arthur (possibly a son?) is listed as a photographer in 1898. Source: Phillips, Glen C. The Ontario photographers list (1851-1900). Sarnia: Iron Gate Publishing Co., 1990.

Photograph of Young Woman by R. F. Uren, Photographer, St. Catharines [n.d.]

Undated black and white cabinet card portrait of an unidentified young woman. This photograph was taken by R. F. Uren whose studio was located at 79 St. Paul St., St. Catharines, Ontario. This item was among the memorabilia in the possession of the Rick Bell family of St. Catharines. Relatives of the Bell family are descended from former Black slaves from the United States.Richard Frank (R.F.) Uren was a photographer in St. Catharines from 1886-1895. Source: Phillips, Glen C. The Ontario photographers list (1851-1900). Sarnia: Iron Gate Publishing Co., 1990.

Photograph of Bell Family Relative [n.d.]

Small black and white photograph mounted on black card of an unidentified Bell family relative, possibly a sibling of Irene Bell, whose photo is similarly featured. This undated photograph was in the possession of the Rick Bell family, whose relatives include former Black slaves from the United States.According to the 1911 Census of Canada, Irene Bell had the following siblings: Ernest Bell, born 1889 Archie Bell, born 1895 Allen Bell, born 1901 Kenneth Bell, born 1910

Photograph of Mary Bell by F. Pfaff, Photographer, Erie, Pa. [n.d.]

A cabinet card believed to be of Mary Bell, photographed by F. Pfaff, Artistic Photographer, of Erie, Pennsylvania. A handwritten entry on the reverse of the photo lists the address "231 Duke St.", however, the company's logo identifies its address as 1011 State St., Ground Floor Gallery. This photograph was in the possession of Iris Sloman Bell, of St. Catharines, Ontario. The Sloman - Bell family includes relatives who are former Black slaves from the United States."Cabinet card photographs were first introduced in 1866. They were initially employed for landscapes rather than portraitures. Cabinet cards replaced Carte de visite photographs as the popular mode of photography. Cabinet cards became the standard for photographic portraits in 1870. Cabinet cards experienced their peak in popularity in the 1880's. Cabinet cards were still being produced in the United States until the early 1900's and continued to be produced in Europe even longer. The best way to describe a cabinet card is that it is a thin photograph that is mounted on a card that measures 4 1/4″ by 6 1/2″. Cabinet cards frequently have artistic logos and information on the bottom or the reverse of the card which advertised the photographer or the photography studio's services. " Source: http://cabinetcardgallery.wordpress.com/category/cabinet-card-history/