Other well-known relations are the equivalence relation and the order relation. That way, sets of things can be ordered: Take the first element of a set, it is either equal to the element looked for, or there is an order relation that can be used to classify it. That way, the whole set can be classified (i.e., compared to some arbitrarily chosen element).
Relations can be transitive.One example of a transitive relation is the "smaller-than" relation. If X "is smaller than" Y,and Y is "smaller than" Z,then X "is smaller than" Z. In general, a transitive relation is a relation such that if relations (a,b) and (b,c) both belong to R, then (a,c) must also belongs to R.
Relations can be symmetric. One example of a symmetric relation is the relation "is equal to". If X "is equal to" Y, then Y "is equal to" X. In general, a symmetric relation is a relation such that if (a,b) belongs to R, then (b,a) must belong to R as well.
Relations can be asymmetric, such as the relation " is smaller than". In general, a relation is asymmetric if whether (a,b) belongs to R, (b,a) does not belong to R.
Relations can be reflexive. One example of a reflexive relation is the relation "is equal to" (e.g., for all X, X "is equal to" X). In general, a reflexive relation is a relation such that for all a in A, (a,a) belongs to R.
By definition, every subset of AxB is a relation from A to B.
In category theory, relations play an important role in the Cartesian closed categories, which transform morphisms from tuples to morphisms of single elements. That corresponds to Currying in the Lambda calculus.
In the relational database theory, a database is a set of relations.
To model a real world, the relations should be in a canonical form called normalized form in the data base argot.
That transformation ensure no loss of information, nor the insertion of spurious tuples with no corresponding meaning in the world represented in the database. The normalization process takes into account properties of relations like functional dependencies among their entries, keys and foreign keys, transitive and join dependencies.
María Isabel Carvajal
Maria Isabel Carvajal (January 1887 - May 13, 1949) was a Costa Rican writer and teacher. She was born in San Jose, Costa Rica. Carvajal wrote using the name Carmen Lyra.
Lyra studied at the school in her neighborhood in the Buenaventura Corrales. She studied pedagogy at the college and got the teacher’s certification. Lyra began teaching in the rural El Monte School in the province of Heredia. In 1906, she worked in the San Juan de Dios Hospital for a short time.
Lyra travelled to Europe. While there, she learned about new educational systems. When she returned, she worked with a teacher and founded the first pre-school in Costa Rica.
Lyra's first publication was the novel "En una silla de ruedas" (In a Wheelchair), in 1918. Her short stories were published in the "Pandemonium Magazine", "Ariel Magazine, and the "Repertorio Americano".
The stories of Carmen Lyra have been used in many schools. The most popular is "Cuentos de mi tía Panchita" (Story of my aunt Panchita). It was published in 1920. This story is well known by most Costa Rican.
Other works of Maria Isabel Carvajal are "Las fantasias de Juan Silvestre" (1918), "Obras Completas" (1975), "La cucarachita mandina" (1976) and "relatos escogidos" (1977).
Carmen Lyra was involved in Costa Rican politics. She was part of the communist party.
She helped organize women schoolteachers to burn down the building of the official newspaper and to overthrow the dictatorship of Costa Rica's Federico Tinoco Granados in 1919. She is credited with translating the Communist Manifesto into Spanish in 1920. She went on to take a leading role in the banana workers' strike of 1934. During this time, she wrote "Bananos y Hombres" (Bananas and Men).
In 1948, she was forced into leave Costa Rica after the Costa Rican Civil War because of her politics. She went to Mexico and died there in 1949.
How Pop Can You Get?
How Pop Can You Get? was the first and only album by American band The Bats.
All music and lyrics by The Bats (Jon Brion, Bill Murphy, Don Fertman)
San Pedro de Macorís Province
San Pedro de Macorís is a province of the Dominican Republic. It is in the southeastern part of the country. Its capital city is San Pedro de Macorís.
The province has the same name of the capital of the province. In English, San Pedro is "Saint Peter"; "Macorís" was the name of a group of native people that lived in the Hispaniola. That name "Macorís", or "Macorix", was given to the river where the city of San Pedro de Macorís was founded..
San Pedro de Macorís was created as a Maritime District (a special administrative category that has been abandoned) on 13 June 1882. The 1907 Dominican Constitution change its status to province. It was part of the old province of Santo Domingo and of the El Seibo province before being elevated to the category of province with the municipalities of Macorís (later, San Pedro de Macorís), Ramón Santana and San José de Los Llanos.
Consuelo was made a municipality in 1996, Quisqueya in 1998 and Guayacanes in 1992. In 2000, El Puerto became a municipal district and Gautier in 2002.
The San Pedro de Macorís province is bordered to the north by the Hato Mayor and El Seibo provinces, to the east by the La Romana province and to the west by the Monte Plata and Santo Domingo provinces.The Caribbean Sea is to the south of the province.
In (last national census), there were people living in the San Pedro de Macorís province, and 244,215 () living in towns and cities. The population density was persons/km².
Its population represents of the total population of the country and the province is ranked as the 7th (out of 31 plus the National District) more populated province.
, the total estimated propulation of the province is 299,933 inhabitants.
The largest city of the province is San Pedro de Macorís, its head municipality or capital, with an urban population (in ) of 185,255 inhabitants.
About 80% of the population is black, the rest of the 20% is mostly mulatto.
The San Pedro de Macorís province has a total area of . It has of the area of the Dominican Republic and it is ranked as the 18th (out of 31 plus the National District) largest province.
The altitude of the provincial capital, San Pedro de Macorís, is above sea level.
The San Pedro de Macorís province is in the "Llano Costero del Caribe" ("Caribbean Coastal Plain"), a large plain in southeastern Dominican Republic where there are many savannas with grasses. There are not high mountains in the province, only some low hills.
The rivers in this province are not very long but they have much water; their sources are in the mountains north of the province and flow south to the Caribbean Sea. The most important rivers are, from east to west:
The climate of the province is a tropical climate, hot most of the year.
There are 6 municipalities and 2 municipal districts (M.D.) in the province.
Because in the province there are many savannas with grasses, the main economic activity for centuries was cattle raising. It is still an important activity in the province.
In the last years of the 19th century, during the war of independence in Cuba, many Cuban and American companies came to the Dominican Republic to grow sugar cane and to produce sugar. San Pedro de Macorís is the Dominican province where there are more sugar cane factories and the port of San Pedro de Macorís became one of the most important port in the country.
In the city of San Pedro de Macorís, manufacturing is important, mainly cement, rum and in industries in the "Zona Franca" ("free zone" where the industries do not pay taxes and all the production is sent to other countries).
In the Guayacanes municipality, tourism is important and there are many hotels close to the beaches, mainly in the Juan Dolio beach.
Kurt Warner