Niagara in summer and winter.

The dates for each issue have been estimated.

John Burtniak Postcard Collection

326 images (b&w and col.) mounted on 54 poster boards ; 64 x 36 cm or smaller. 4 compact disc

ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

Community Newspapers on Microfilm

Reel 1. E.J. Palmer's Grimsby illustrated; Merritton advance; The Evening review; Niagara Falls evening review; The academy; St. Catharines constitutional; St. Catharines daily news; St. Catharines daily standard; St. Catharines daily times; St. Catharines evening journal; St. Catharines evening star. -- Reel 2. St. Catharines evening star. -- Reel 3. St. Catharines evening star. -- Reel 4. St. Catharines evening star; St. Catharines gazette; St. Catharines journal; St. Catharines semi-weekly post; St. Catharines star journal; St. Catharines weekly news; St. Catharines weekly star; St. Catharines women's patriotic journal; St. Catharines women's standard; Welland Canadian farmer supplement; Welland Canadian farmer and grange record; Welland Canal works; Welland telegraph extra; Welland telegraph; Welland tribune and telegraph. -- Reel 5. Beamsville express; Vineland Jordan post; Grimsby independent; Haldimand advocate; Haldimand tribune; Niagara onghiara; Smithville pioneer; The Irish Canadian. -- Reel 7. St. Catharines daily times. -- Reel 8. St. Catharines daily times. -- Reel 9. St. Catharines daily times. -- Reel 10. The Monck reform press; Herald (Fonthill); Independent (Grimsby); Beamsville express; Post express (Lincoln); Jordan post (Vineland); The gleaner and Niagara newspaper; Niagara advance; Pelham herald; Port Colborne news; Farmers' journal and Welland Canal intelligencer; Welland tribune; Welland Tribune; Welland tribune and telegraph; Evening tribune (Welland Ship Canal, centenary issue).

Second Welland Canal - Book 2, Survey Map 16 - Deep Cut in Thorold

Survey map of the Second Welland Canal created by the Welland Canal Company showing the canal in the Thorold Township between Allanburg and Port Robinson. Identified structures and features associated with the Canal include the Deep Cut and the towing path. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are also identified and include streets and roads (ex. Road to Port Allanburg), and the Spoil Bank. Properties and property owners of note are: Lots 185, 186, and 187, J. J. Church and H. Vanderburgh. Four properties adjacent to the canal are outlined in blue and labeled J through M, with L and K belonging to John Beatty, M belonging to John Coulter, and J belonging to G. Jordan (formerly belonging to John Coleman Jordan).

Second Welland Canal - Book 2, Survey Map 17 - Deep Cut and Port Robinson

Survey map of the Second Welland Canal created by the Welland Canal Company showing the canal at Port Robinson. Identified structures and features associated with the Canal include the Deep Cut, Old Channel of Canal, and the towing path. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are also identified and include streets and roads (ex. Road to Port Allanburg), the Spoil Bank, an island, several bridges, and a church. Several unidentified structures are present but not labeled. Properties and property owners of note are: Lots 202, 203, and 204. Lot 203 is divided into several properties labeled A - J. Owners of these properties include James McCoppen, John Coulter, James Griffith, John C. Jordan, W. Hendershot, John Greer, Charles Richards, C. Stuart, and S. D. Woodruff. Other property owners include D. McFarland.

Second Welland Canal - Book 3, Survey Map 1 - Canal to Chippewa Creek with Port Robinson

Survey map of the Second Welland Canal created by the Welland Canal Company showing Port Robinson and the canal to Chippewa Creek. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are also identified and include streets and roads (ex. Front Street, Bridge Street, and Cross Street), the Welland railroad, Dry Dock leased to D. McFarland and Abbey, G. Jordan Tavern, D. McFarland and Co. Burnt Saw Mill, I. Pew Shop, Old Locks, New Lock, Canal to Chippewa Creek, Chippewa Creek, covered drain from dry dock, a barn and several bridges. Properties and property owners of note are: Lots 202, Broken Front lots 202 and 203, D. McFarland, and G. Jordan.

Second Welland Canal - Book 3, Survey Map 2 - Canal to Chippewa Creek with Port Robinson

Survey map of the Second Welland Canal created by the Welland Canal Company showing the canal as it passes through Port Robinson. Identified structures associated with the Canal include the Guard Lock, Collector Toll Office, towing path, and the New Cut of the canal. The surveyors' measurements and notes can be seen in red and black ink and pencil. Local area landmarks are also identified and include streets and roads (ex. Island Street, Bridge Street, John Street, and Cross Street), bridges (Swing Bridge, and several unnamed bridges), Welland Railroad, Canal to Chippewa Creek (and two old locks and one new lock associated with the canal), Chippewa Creek, Back Water, an unnamed Island, Dry Dock leased to McFarland and Abbey, Abbey's Office, D. McFarland and Co. Saw Mill (Burnt), G. Jordan Tavern, Robert Elliot Store House and Wharf, Isaac Pew's Shop, Colemans Hotel, R. Band and Co. Girst Mill, Donaldson and Co. Grist Mill, H. Marlatt Dwelling House and barn, Henry W. Timms Hotel, Methodist Church, Post Office, Blacksmith Shop, a church, a structure labeled B. Patch, and a number of other structures that are not named. Properties and property owners of note are: Lots 202 and 203, S. Hill, D. McFarland, Church Society, G. Jordan, D. Coleman, John Brown, Rob Coulter, Robert Elliot, Isaac Pew, James McCoppen, William Bell, Charles Stuart, Andrew Elliot, Robert Band, Ed. Feney, John Betty, F. Sharp, William B. Hendershot, A. Brownson, H. Marlatt, J. S. Powell, and the School Trustees. Two reserved properties are labeled in red.The current spelling of Chippewa Creek is Chippawa. Although it not possible to make out the entire name of the H. W. Timms hotel located at Front and Bridge Street on the map itself, it was discovered to belong to Henry W. Timms after consulting the 1851-52 Canada Directory.

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.

Letter to William Collver or John Roberts, 1849

A letter to “my dear Mr. Collver and co.” The writer mentions the “circuit” that she has traveled, and a conference which she attended. In regard to the circuit, she talks about her interest in the Welland Canal. The references all seem to be religious in nature. She asks Mr. Collver how he likes the new preacher and says that in a letter that the preacher published in the newspaper he refers to the “breaking of Jordan Chapel”. She says that a society of teetotalers has been established in her town and they are known as “Sons of Temperance”. She also mentions “my man Brown” who was there but has left, leaving her to have the circuit by herself. She signs off with “I am yours affectionately [Eleanor Corman]. The second part of the letter is addressed to “my dear Mr. Roberts”. She asks him for some music that she would like, but cannot find in Kingston. She would like him to “come down and teach singing” this winter. She also asks him to give her regards to Mr. P. Beamer and family. She ends this part of the letter with “Nothing further yours affectionately [Eleanor Corman]”. There are 4 red postmarks on the outside of the letter and they are: Picton, July 31, 1849 Cobourg, August 2, 1849 St. Catharines, August 4, 1849 There is one other postmark which is too faded to be legible.

The 19th Century Tombstone Database Project Records, 1790-1890 (non-inclusive)

The 19th Century Tombstone Database project was funded by the program Federal Summer Youth Employment scheme in the summer of 1982 and led by Dr. David W. Rupp, a Professor at the Classics Department, Brock University. The main goal of the project was to collect information related to various cemeteries in Niagara region and burials that took place from 1790-1890. Data was collected and presented in the form of data summary forms of persons, tombstone sketches, photographs of tombstones, maps, and computer printouts. The materials created as a result of a research completed for the 19th Century Tombstone Database project are important as a number of the tombstones have been damaged or gone missing since the research was finished. Before Dr. Rupp retired from Brock University, he donated project materials to the Brock University Special Collections and Archives.

Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

Clendenan-Thompson family fonds

Daniel Clendenan (1793-1866) was the son of Abraham Clendenan, a private in Butler’s Rangers. He was married to Susan[na] [Albrecht ] Albright, daughter of Amos Albright. Daniel and Susan[na] had twelve children and belonged to the Disciple Church. In 1826 Daniel Clendenan purchased Part lot 14, Concession 6, Louth Township from Robert Roberts Loring. On this property he built a home and conducted the business of blacksmithing and along with William Jones operated a lumber mill. Volume 1 and the first part of Volume 2 are Daniel Clendenan’s account books. Daniel and his wife Susan are buried in the Vineland Mennonite cemetery. Daniel and Susan[na]’s youngest daughter, Sarah, married widower Andrew Thompson (1825-1901), son of Charles and grandson of Solomon. Andrew Thompson had settled in the Wainfleet area in 1854 and had owned a mill in Wellandport. Daniel Clendenan, in ill health, passed ownership of Lot 14, Concession 6, Louth Township to his son-in-law Andrew Thompson. Robert Roberts Loring, the original owner of lot 14, concession 6 in Louth was born in September of 1789 in England. He joined the 49th Regiment of Foot as an ensign in December of 1804 and arrived in Quebec the following July. He served with Isaac Brock and Roger Sheaffe. In 1806 he was promoted to lieutenant. Loring was hired by Lieutenant General Gordon Drummond and accompanied him to Ireland in 1811, but the outbreak of war in the States in 1812 drew Loring back to Canada. On June 26, 1812 Loring became a captain in the 104th Regiment of Foot. On October 29 of the same year, he was appointed aide-de-camp to Sheaffe who was the administrator of Upper Canada. During the American attack on York in April 1813, Loring suffered an injury to his right arm from which he never recovered. In December of 1813, Drummond assumed command of the forces in Upper Canada and he appointed Loring as his aide-de-camp, later civil secretary and eventually his personal secretary. Loring was with Drummond in 1813 at the capture of Fort Niagara (near Youngstown), N.Y. He was also with Drummond in the attacks on Fort Niagara, settlements along the American side of the Niagara River, and then York and Kingston. In July of 1814 he was promoted to brevet major, however he was captured at the Battle of Lundy’s Lane and he spent the remainder of the conflict in Cheshire, Massachusetts. One of his fellow captives was William Hamilton Merritt. Loring remained in the army and had numerous military posts in Canada and England. He retired in 1839 and lived the last of his years in Toronto. He died on April 1, 1848. Sources: http://www.biographi.ca/en/bio/loring_robert_roberts_7E.html and “Loring, Robert Roberts” by Robert Malcomson in The Encyclopedia Of the War Of 1812 edited by Spencer Tucker, James R. Arnold, Roberta Wiener, Paul G. Pierpaoli, John C. Fredriksen

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.