Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. Kazimierz Kuratowski was born in Warsaw, Vistula Land, on 2 February 1896, into an assimilated Jewish family, he was a son of Marek Kuratow, a barrister, Róża Karzewska. He completed a Warsaw secondary school, named after general Paweł Chrzanowski. In 1913, he enrolled in an engineering course at the University of Glasgow in Scotland, in part because he did not wish to study in Russian, he completed only one year of study when the outbreak of World War I precluded any further enrollment. In 1915, Russian forces withdrew from Warsaw and Warsaw University was reopened with Polish as the language of instruction. Kuratowski restarted his university education there the same year, this time in mathematics, he obtained his Ph. D. in 1921, in newly independent Poland. In autumn 1921 Kuratowski was awarded the Ph. D. degree for his groundbreaking work. His thesis statement consisted of two parts.
One was devoted to an axiomatic construction of topology via the closure axioms. This first part has been cited in hundreds of scientific articles; the second part of Kuratowski's thesis was devoted to continua irreducible between two points. This was the subject of a French doctoral thesis written by Zygmunt Janiszewski. Since Janiszewski was deceased, Kuratowski's supervisor was Stefan Mazurkiewicz. Kuratowski's thesis solved certain problems in set theory raised by a Belgian mathematician, Charles-Jean Étienne Gustave Nicolas, Baron de la Vallée Poussin. Two years in 1923, Kuratowski was appointed deputy professor of mathematics at Warsaw University, he was appointed a full professor of mathematics at Lwów Polytechnic in Lwów, in 1927. He was the head of the Mathematics department there until 1933. Kuratowski was dean of the department twice. In 1929, Kuratowski became a member of the Warsaw Scientific Society While Kuratowski associated with many of the scholars of the Lwów School of Mathematics, such as Stefan Banach and Stanislaw Ulam, the circle of mathematicians based around the Scottish Café he kept close connections with Warsaw.
Kuratowski left Lwów for Warsaw in 1934, before the famous Scottish Book was begun, hence did not contribute any problems to it. He did however, collaborate with Banach in solving important problems in measure theory. In 1934 he was appointed the professor at Warsaw University. A year Kuratowski was nominated as the head of Mathematics Department there. From 1936 to 1939 he was secretary of the Mathematics Committee in The Council of Science and Applied Sciences. During World War II, he gave lectures at the underground university in Warsaw, since higher education for Poles was forbidden under German occupation. In February 1945, Kuratowski started to lecture at the reopened Warsaw University. In 1945, he became a member of the Polish Academy of Learning, in 1946 he was appointed vice-president of the Mathematics department at Warsaw University, from 1949 he was chosen to be the vice-president of Warsaw Scientific Society. In 1952 he became a member of the Polish Academy of Sciences, of which he was the vice-president from 1957 to 1968.
After World War II, Kuratowski was involved in the rebuilding of scientific life in Poland. He helped to establish the State Mathematical Institute, incorporated into the Polish Academy of Sciences in 1952. From 1948 until 1967 Kuratowski was director of the Institute of Mathematics of the Polish Academy of Sciences, was a long-time chairman of the Polish and International Mathematics Societies, he served as vice-president of the International Mathematics Union as well as president of the Scientific Council of the State Institute of Mathematics. From 1948 to 1980 he was the head of the topology section. One of his students was Andrzej Mostowski. Kazimierz Kuratowski was one of a celebrated group of Polish mathematicians who would meet at Lwów's Scottish Café, he was a member of the Warsaw Scientific Society. What is more, he was chief editor in "Fundamenta Mathematicae", a series of publications in "Polish Mathematical Society Annals". Furthermore, Kuratowski worked as an editor in the Polish Academy of Sciences Bulletin.
He was one of the writers of the Mathematical monographs, which were created in cooperation with the Institute of Mathematics of the Polish Academy of Sciences. High quality research monographs of the representatives of Warsaw's and Lwów’s School of Mathematics, which concerned all areas of pure and applied mathematics, were published in these volumes. Kazimierz Kuratowski was an active member of many scientific societies and foreign scientific academies, including the Royal Society of Edinburgh, Germany, Hungary and the Union of Soviet Socialist Republics. In 1981, IMPAN, the Polish Mathematical Society, Kuratowski's daughter Zofia Kuratowska established a prize in his name for achievements in mathematics to people under the age of 30 years; the prize is considered the most prestigious of awards for young Polish mathematicians. Kuratowski’s research focused on abstract topological and metric structures, he implemented the closure axioms. This was fundamental for the development of topological space theory and irreducible continuum theor
Leonardsville Township is a township in Traverse County, United States. The population was 150 at the 2000 census. Leonardsville Township was organized in 1881, named for Patrick Leonard, an early settler. According to the United States Census Bureau, the township has a total area of 38.5 square miles, all of it land. As of the census of 2000, there were 150 people, 48 households, 39 families residing in the township; the population density was 3.9 people per square mile. There were 54 housing units at an average density of 1.4/sq mi. The racial makeup of the township was 99.33% White, 0.67% from two or more races. Hispanic or Latino of any race were 1.33% of the population. There were 48 households out of which 43.8% had children under the age of 18 living with them, 72.9% were married couples living together, 18.8% were non-families. 16.7% of all households were made up of individuals and 6.3% had someone living alone, 65 years of age or older. The average household size was 3.13 and the average family size was 3.49.
In the township the population was spread out with 34.7% under the age of 18, 9.3% from 18 to 24, 22.7% from 25 to 44, 19.3% from 45 to 64, 14.0% who were 65 years of age or older. The median age was 34 years. For every 100 females, there were 108.3 males. For every 100 females age 18 and over, there were 108.5 males. The median income for a household in the township was $26,875, the median income for a family was $27,500. Males had a median income of $14,250 versus $21,250 for females; the per capita income for the township was $10,125. There were 19.4% of families and 17.2% of the population living below the poverty line, including 10.0% of under eighteens and 11.4% of those over 64
A mental model captures ideas in a problem domain, while a conceptual model represents'concepts' and relationships between them. A conceptual model in the field of computer science is a special case of a general conceptual model. To distinguish from other types of models, it is known as a domain model. Conceptual modeling should not be confused with other modeling disciplines such as data modelling, logical modelling and physical modelling; the conceptual model is explicitly chosen to be independent of design or implementation concerns, for example, concurrency or data storage. The aim of a conceptual model is to express the meaning of terms and concepts used by domain experts to discuss the problem, to find the correct relationships between different concepts; the conceptual model attempts to clarify the meaning of various ambiguous terms, ensure that problems with different interpretations of the terms and concepts cannot occur. Such differing interpretations could cause confusion amongst stakeholders those responsible for designing and implementing a solution, where the conceptual model provides a key artifact of business understanding and clarity.
Once the domain concepts have been modeled, the model becomes a stable basis for subsequent development of applications in the domain. The concepts of the conceptual model can be mapped into physical design or implementation constructs using either manual or automated code generation approaches; the realization of conceptual models of many domains can be combined to a coherent platform. A conceptual model can be described using various notations, such as UML, ORM or OMT for object modelling, ITE, or IDEF1X for Entity Relationship Modelling. In UML notation, the conceptual model is described with a class diagram in which classes represent concepts, associations represent relationships between concepts and role types of an association represent role types taken by instances of the modelled concepts in various situations. In ER notation, the conceptual model is described with an ER Diagram in which entities represent concepts and optionality represent relationships between concepts. Regardless of the notation used, it is important not to compromise the richness and clarity of the business meaning depicted in the conceptual model by expressing it directly in a form influenced by design or implementation concerns.
This is used for defining different processes in a particular company or institute. Halpin T, Morgan T: Information Modeling and Relational Databases, Morgan Kaufmann, 2008. ISBN 978-0-12-373568-3. Fowler, Martin: Analysis Patterns, Reusable object models, Addison-Wesley Longman, 1997. ISBN 0-201-89542-0. Stewart Robinson, Roger Brooks, Kathy Kotiadis, Durk-Jouke Van Der Zee: Conceptual Modeling for Discrete-Event Simulation, 2010. ISBN 978-1-4398-1037-8 David W. Embley, Bernhard Thalheim: Handbook of Conceptual Modeling, 2011. ISBN 978-3-642-15864-3
Bromfield was a railway station which served Bromfield, a small settlement in Cumbria on the English side of the Solway Firth. The station opened in 1873 by the Caledonian Railway on a line constructed from the Caledonian Railway Main Line at Kirtlebridge across the Glasgow South Western Line forming the Solway Junction Railway over the Solway Viaduct to Brayton; the line opened in 1869 and freight has run from it since 13 September 1869. Bromfield station was opened by the Solway Junction Railway part of the Caledonian Railway. At first the station was a request stop, however on 1 January 1873 a crossing keeper was appointed and the level crossing signalled. At the south end of the station was a siding leading to the goods yard, worked by a frame, controlled by the train tablet for the section Abbey Junction and Brayton; the station siding was 1 3/4 from Brayton Junction. The station today is a private house; the passenger service was never well patronised. In 1910 only three trains in each direction served the station, with an Brayton to Abbey Junction working once a week.
It was further reduced to being just one carriage at the front of an occasional goods train and in September 1917 this was suspended, but was reinstated in 1920. Passenger services were withdrawn in 1921 and the line south of Annan over the Solway Viaduct was closed completely; the station had one platform with two simple station buildings, one stone and the other constructed of wood. The closure of the station was directly linked to the closure of the Solway viaduct; the line remained open to through traffic until 14 February 1933. Until October 1895 the station name was shown as Broomfield in timetables; the track was removed from Bromfield in 1937. Notes SourcesEdgar, Stuart & Sinton, John M.. The Solway Junction Railway. Oxford: Oakwood Press. ISBN 978-0853613954. Mullay, A. J.. Rails across the border: the story of Anglo-Scottish Railways. Wellingborough: Patrick Stephens Limited. ISBN 1-85260-186-8. Quick, Michael. Railway passenger stations in Great Britain: a chronology. Oxford: Railway and Canal Historical Society.
ISBN 978-0-901461-57-5. OCLC 612226077. Further readingJowett, Alan. Jowett's Railway Atlas of Great Britain and Ireland: From Pre-Grouping to the Present Day. Sparkford: Patrick Stephens Ltd. ISBN 978-1-85260-086-0. OCLC 22311137. Jowett, Alan. Jowett's Nationalised Railway Atlas. Penryn, Cornwall: Atlantic Transport Publishers. ISBN 978-0-906899-99-1. OCLC 228266687. RAILSCOT on Solway Junction Railway Railways of the Solway Plain Bromfield Station
The Williams College Investment Office is the subsidiary office of Williams College responsible for managing the College's endowment of over US $2 billion. The Office is located in Massachusetts, its Chief Investment Officer is Collette Chilton. In 2006, Williams College established the Investment Office to manage the endowment. In the early 2000s, the endowment had exceeded US $1 billion and the College decided more complex investment management was required to continue to grow the fund; the College hired Collette Chilton as Chief Investment Officer and set up an office in Boston, Massachusetts. The Investment Office has a staff of nine people who directly oversee the management of the College's portfolio. Advising the staff are three Advisory Committees, made up of Williams alumni or parents with financial expertise. Overseeing all is the Investment Committee, consisting of eight members, responsible for the Investment Pool. On the staff level, the Chief Investment Officer remains Collette Chilton.
The Co-Chairs of the Marketable Assets Advisory Committee are Ole Andreas Halvorsen and Elizabeth Robinson. The Co-Chairs of the Non-Marketable Assets Advisory Committee are Timothy Barrows and Jonathan Sokoloff; the Co-Chairs of the Real Assets Advisory Committee are Robert Pinkard. The Chair of the Investment Committee is Jonathan Kraft; the Investment Office does not directly invest in any stocks. Rather, the staff hires managers to invest the different assets in the portfolio. There are ten asset classes: global long equity, global long/short equity, absolute return, venture capital, real assets, real estate, investment grade fixed income, non-investment grade fixed income, cash; the Office has a long-term return objective of 5% plus inflation. Overall, the Investment Office had a rate of return of -1.5% in the 2016 fiscal year, an overall annual return of 7.3% for the ten years since the office was established
Rod Gerald was a quarterback for the Ohio State Buckeyes from 1975–1977 and became a wide receiver in 1978. Gerald attended South Oak Cliff High School in Dallas, Texas where he was named as an all-Texas quarterback, he was recruited by several schools in the Southern Conferences and considered signing with Tennessee. Following a trip to Columbus, Ohio for the annual Michigan-Ohio State Rivalry, he was recruited by Woody Hayes to sign with the Ohio State Buckeyes; as a freshman, Gerald was behind Cornelius Greene in the depth chart. While he did see some on-field action, his production was limited to 16 rushing attempts and two passing attempts, he did manage to rush for three touchdowns in his debut season. In his sophomore season, Gerald became the starting quarterback for the Buckeyes, he ranked in the top ten in the nation. During the first quarter in the game against Purdue, Gerald was carted off the field after he injured his back; the diagnosis was that he had fractured three transverse processes in his spine, which sidelined him for the next four games.
He returned as the starter for the 1977 Orange Bowl where the No. 11 Buckeyes defeated No. 12 Colorado 27–10. In Gerald's junior season, he once again took over the starting role, he finished the season 9–3 with losses coming to No. 3 Oklahoma, No. 5 Michigan and in the 1978 Sugar Bowl to No. 3 Alabama. The Buckeyes were co-Big Ten Champions with a conference record of 7–1, he was named to the all-Big Ten team for his accomplishments. The 1978 season saw Freshman phenom Art Schlichter join the team, it was with the addition of Schlichter. In order to maintain a starting spot, Gerald transitioned to wide receiver for his final year; that year ended with Ohio State losing to No. 7 Clemson in the 1978 Gator Bowl. It was in this game where Woody Hayes punched an opposing player and was Hayes' last game as Ohio State's coach. Gerald had struggled with drug use during his time at Ohio State, he left the university and went back to Texas following his college career and didn't graduate with a degree. Following his return to Texas, Gerald had two children, a daughter and a son.
In the late 1980s he decided to return to Central Ohio where he would return to Ohio State and graduate with a degree in 1989. Following his graduation, he became a housing inspector for the City of Columbus. In 1994, Gerald relapsed on drugs following the death of his brother; when his father died in 1998, he fell further into his addiction. Gerald moved back to Dallas where he became homeless and spent 11 months in jail for burglary. After he was released from jail, Gerald began to turn his life around and reconciled with his children and started to speak publicly about his journey. Gerald now lives in Dallas, Texas