title: Akbar Hashemi Rafsanjani

text: Hashemi refers to the point that the Islamic Republican Party established in the early years of revolution in Iran. Ruhollah Khomeini, at first step, was disagree with establishment of Party because he known the establishment of party as something gradually. But After consultation of Hashemi with Khomeini, the opinion of Khomeini has changed. There were many negotiations and consultations on the instructions of Party. People like Yadollah Sahabi and Habibollah Peyman were to communicate but after a while there were no communication with them. Although Mortaza Motahhari had not any disagreement to establishing party but at the same time he hadn't any communication with party. In fact, the idea of establishment of republic party was necessary in order to give the Mullahs an organization and political collection. The party has established formally on 17 February 1979, namely two weeks after the victory of Islamic Revolution. The members of the party even determined their members in Kanoon Touhid in early days. The financial expenses of party originated from the voluntary aids of people. At first, religious scholars or clerics took part in the party. In early days there were no financial problem but after a while the problem appeared. Khomeini tried to give financial aid to the party with giving money. The members primarily chose from revolutionary individuals and believed persons.


title: Akbar Hashemi Rafsanjani

text: From his marriage to Effat Marashi in 1958, Rafsanjani had three sons: Mohsen, Mehdi, and Yasser, as well as two daughters, Fatemeh and Faezeh. Only Faezeh Hashemi chose a political life, which led to her becoming a Majlis representative and then the publisher of the weekly newspaper "Zan" (meaning "Woman" in English), which was closed in February 1999. In 2016, his daughter, Faezeh Hashemi, sparked a debate on religious persecution in Iran by visiting the female leader of the persecuted Baháʼí religious minority. The two women had met in prison, when Faezeh was serving a six-month sentence for "spreading propaganda against the system". Rafsanjani's daughter, Fatemeh is President of Charity Foundation for Special Diseases and Mohsen was chairman of Tehran Metro Organization and now is vice president of Azad University. His wife, Effat is the granddaughter of Mohammed Kazem Yazdi.


title: Akbar Hashemi Rafsanjani

text: The Rafsanjani family took their name from his great grandfather, whose last name was Hashem. When Akbar Hashemi was born, his father was a rich businessman with a valuable pistachio business.


title: Akbar Hashemi Rafsanjani

text: Only months after the revolution, Rafsanjani was shot once in the stomach by gunmen from one of the groups vying for power amid the political turmoil. He was not seriously wounded, and neither was his wife who jumped in front to shield him from the attack. "Great men of history do not die", Khomeini said in announcing that Rafsanjani had survived.


title: Akbar Hashemi Rafsanjani

text: In addition, the full text of his Friday Prayer sermons and his congress keynote speeches are also published separately. Based on his diary, viewpoints, speeches and interviews, several independent books have been published so far.


title: Akbar Hashemi Rafsanjani

text: The book in fact considered as a key to the subjects and concepts of Quran. The book has been written by Hashemi and several other scholars.


title: Akbar Hashemi Rafsanjani

text: Although he was a close follower of Ayatollah Khomeini and considered as a central elite during Islamic revolution, at the same time he was fan of reconstruction of shattered country after war and according to this fact, he selected his cabinets from western-educated technocrats and social reformers. His cabinet largely was a reformist one. Rafsanjani acquired both the support of Imam Khomeini in one hand and Majlis in other hand. In fact, he tried to transfer the economy towards the free-market system. There was a gap among Rafsanjani and Khatami and reform agenda because of his partnership with those who were conservative. The first face of reformist movements began by Rafsanjani.


title: Casey Siemaszko

text: Siemaszko was born in Chicago and grew up on the city's northwest side. He attended Saint Ignatius College Preparatory School and graduated from the Goodman School of Drama at DePaul University in 1983. His father, Konstanty (1918–1999), was a Polish Roman Catholic and a former member of the Polish Navy. He joined the Polish Underground and was a survivor of the Sachsenhausen concentration camp. He emigrated to Chicago in 1959 and became a well-known local choreographer and a fixture in the Polish community. His mother, Collette McAllister (1931–2008), was English. His sister Nina is an actress and his brother, Corky, is a writer for "Daily News" and a reporter for "NBC News."


title: Henry Tandey

text: Private Henry James Tandey VC, DCM, MM (born Tandy, 30 August 1891 – 20 December 1977) was a British recipient of the Victoria Cross, the highest award for gallantry in the face of the enemy that can be awarded to British and Commonwealth forces. He was the second most highly decorated British private of the First World War and is most commonly remembered as the soldier who allegedly spared Adolf Hitler's life during the war. Born with the family name of Tandy, he later changed his surname to Tandey after problems with his father, because of this, some military records have a different spelling of his name.


title: Henry Tandey

text: Henry James Tandey was born at the Angel Hotel, Regent Street, Leamington, Warwickshire, the son of a former soldier whose wife had died early in their child's life. He attended St. Peters' primary school in Augusta Place, Leamington. He also spent part of his childhood in an orphanage before becoming a boiler attendant at a hotel.


title: Henry Tandey

text: Tandey enlisted into the Green Howards Regiment on 12 August 1907. After basic training he was posted to their 2nd Battalion on 23 January 1908, serving with them in Guernsey and South Africa prior to the outbreak of World War I. He took part in the Battle of Ypres in October 1914, and was wounded on 24 October 1916, at the Battle of the Somme. On discharge from hospital he was posted to the 3rd Battalion on 5 May 1917, before moving to the 9th Battalion on 11 June 1917. He was wounded a second time on 27 November 1917, during the Battle of Passchendaele. After his 2nd period of hospital treatment he returned to the 3rd Battalion, on 23 January 1918, before being posted to the 12th Battalion on 15 March 1918, where he remained until 26 July 1918. On 26 July 1918 Tandey transferred from the Green Howards to The Duke of Wellington's (West Riding Regiment). He was posted to their 5th Battalion on 27 July 1918.


title: Henry Tandey

text: On 28 August 1918, during the 2nd Battle of Cambrai, the 5th Battalion was in action to the west of the Canal du Nord. Tandey was in charge of one of several bombing parties on the German trenches. As the forward parties were being held up Tandey took two men and dashed across open ground (No man's land) under fire and bombed a trench. He returned with twenty prisoners. This action led to the capture of the German positions and Tandey was awarded the Distinguished Conduct Medal (DCM) on 5 December 1918, the citation read:


title: Henry Tandey

text: On 12 September, the 5th Battalion was involved in an attack at Havrincourt, where Tandey again distinguished himself. Having rescued several wounded men under fire the previous day, Tandey again led a bombing party into the German trenches, returning with more prisoners. For this action Tandey was awarded the Military Medal (MM) on 13 March 1919.


title: Henry Tandey

text: Tandey was 27 years old and a private in the 5th Battalion Duke of Wellington's (West Riding) Regiment when he performed the actions which earned him the Victoria Cross (VC).


title: Henry Tandey

text: On 28 September 1918, during a counter-attack at the canal, following the capture of Marcoing, France, his platoon was stopped by machine-gun fire. Tandey crawled forward, located the gun position and with a Lewis gun team, silenced it. Reaching the canal crossing, he restored the plank bridge under heavy fire. In the evening, he and eight comrades were surrounded by an overwhelming number of the enemy. Tandey led a bayonet charge, fighting so fiercely that 37 of the enemy were driven into the hands of the remainder of his company. Although twice wounded, Tandey refused to leave until the fight was won, eventually going into hospital for the third time on 4 October 1918.


title: Henry Tandey

text: Although disputed, Adolf Hitler and Tandey allegedly encountered each other at the French village of Marcoing. The story is set on 28 September 1918, while Tandey was serving with the 5th Duke of Wellington's Regiment, and relates that a weary German soldier wandered into Tandey's line of fire. The enemy was wounded and did not appear to have a weapon. Tandey chose not to shoot. The German soldier saw him lower his rifle and nodded his thanks before wandering off. That soldier is purported to have been Adolf Hitler. The author David Johnson, who wrote a book on Henry Tandey, believes this story was an urban legend.


title: Henry Tandey

text: Hitler apparently saw a newspaper report about Tandey being awarded the VC (in October 1918, whilst serving with the 5th Battalion Duke of Wellington's (West Riding) Regiment), recognised him, and clipped the article.


title: Henry Tandey

text: In 1937, Hitler was made aware of a particular Fortunino Matania painting by Dr Otto Schwend, a member of his staff. Schwend had been a medical officer during the First Battle of Ypres in 1914. He had been sent a copy of the painting by a Lieutenant Colonel Earle in 1936. Earle had been treated by Schwend in a medical post at the Menin Crossroads and they remained in touch after the war.


title: Henry Tandey

text: The painting was commissioned by the Green Howards Regiment from the Italian artist in 1923, showing a soldier purported to be Tandey carrying a wounded man at the Kruiseke Crossroads in 1914, northwest of Menin. The painting was made from a sketch, provided to Matania, by the regiment, based on an actual event at that crossroads. A building shown behind Tandey in the painting belonged to the Van Den Broucke family, who were presented with a copy of the painting by the Green Howard's Regiment.


title: Henry Tandey

text: Schwend obtained a large photo of the painting to gift it to Hitler. Captain Weidemann, Hitler's adjutant, wrote the following response:


title: Henry Tandey

text: Apparently Hitler identified the soldier carrying the wounded man as Tandey from the photo of him in the newspaper clipping he had obtained in 1918.


title: Henry Tandey

text: In 1938, when Neville Chamberlain visited Hitler at his alpine retreat, the Berghof, for the discussions that led to the Munich Agreement, he noticed the painting and asked about it. Hitler replied: That man came so near to killing me that I thought I should never see Germany again; Providence saved me from such devilishly accurate fire as those English boys were aiming at us.


title: Henry Tandey

text: According to the story, Hitler asked Chamberlain to convey his best wishes and gratitude to Tandey. Chamberlain promised to phone Tandey in person on his return, which apparently he did. The Cadbury Research Centre, which holds copies of Chamberlain's papers and diaries, has no references relating to Tandey from the records of the 1938 meeting. The story further states that the phone was answered by a nine-year-old child called William Whateley. William was related to Tandey's wife Edith. However, Tandey at that time lived at 22 Cope Street, Coventry, and worked for the Triumph Motor Company. According to the company records, they only had three phone lines, none of which was at Tandey's address. British Telecommunications archive records also have no telephones registered to that address in 1938.


title: Henry Tandey

text: Historical research throws serious doubts on whether the incident actually ever occurred. Hitler took his second leave from military service on 10 September 1918 for 18 days. This means that he was in Germany on the presumed date of the facts.


title: Henry Tandey

text: On 13 March 1919 a supplement to the "London Gazette" announced that Tandey had been awarded the Military Medal (MM). The following day he was discharged from service and only one day later he re-enlisted into the Duke of Wellington's 3rd Battalion on a 'Short Service Engagement'. Three days later (18 March 1919) he was promoted to acting lance corporal. He remained with the 3rd Battalion on 'Home Service' until 4 February 1921, when he transferred to the 2nd Battalion. Four days later on 8 February 1921 he requested to revert to the rank of private.


title: Henry Tandey

text: Tandey served with the 2nd Battalion in Gibraltar from 11 April 1922 to 18 February 1923, in Turkey from 19 February – 23 August 1923 and finally in Egypt from 24 August 1923 until 29 September 1925. He was finally discharged from the army on 5 January 1926.


title: Henry Tandey

text: In addition to his major awards Tandey had also been Mentioned in Despatches on five occasions. He was personally decorated by King George V at Buckingham Palace on 17 December 1919.


title: Henry Tandey

text: Tandey returned to Leamington Spa and married. In 1940, during the Coventry Blitz, his home was bombed by the Luftwaffe. A journalist approached him outside his bombed Coventry home, asking him about his alleged encounter with Hitler. "If only I had known what he would turn out to be," Tandey is quoted as saying. "When I saw all the people and women and children he had killed and wounded I was sorry to God I let him go." However, there is no evidence, not even anecdotal, he was either hounded or avoided after the claims.


title: Henry Tandey

text: Tandey became a commissionaire at the Standard Triumph Works, Fletchamstead a position he held for 38 years.


title: Henry Tandey

text: Tandey died in 1977, childless, at the age of 86. At his request, he was cremated and his ashes buried in the Masnieres British Cemetery at Marcoing, France, on 23 May 1978, by his undertaker Pargetter and Son. Due to French laws it was not permissible for his ashes to be scattered, or any form of ceremony or commemoration made to him.


title: Henry Tandey

text: Henry Tandey Court, on Union Road, in Leamington Spa, is named after him. It was originally a workshop and builders yard of Mr. G.F.Smith, who built St. Marks Church and Vicarage.


title: Henry Tandey

text: A blue plaque was installed outside the Angel Hotel where Henry Tandey was born and at St Peter's School.


title: Henry Tandey

text: Tandey donated his medals to the Duke of Wellington's Regiment Museum in Halifax, West Yorkshire. On special occasions and parades he would sign them out to wear. During the last period that he had signed them out, he died. Unaware that the medals should have been returned to the museum, the medals were auctioned at Sotheby's in London by his wife and a private collector subsequently purchased them. They were presented to the Green Howards Regimental Museum (the regiment in which he had earlier served), by Sir Ernest Harrison OBE, at a ceremony in the Tower of London on 11 November 1997, twenty years after Tandey died.


title: Henry Tandey

text: A copy of Tandey's Victoria Cross is now displayed at the Green Howards Regimental Museum in Richmond, North Yorkshire. Along with others, the original VC is kept in a local bank vault.


title: Henry Tandey

text: On 6 June 2006 The Green Howards and the Duke of Wellington's (West Riding) Regiment amalgamated with the Prince of Wales's Own Regiment of Yorkshire to form the Yorkshire Regiment.


title: Kanabō

text: The (literally "metal stick" or "metal club") is a spiked or studded two-handed war club used in feudal Japan by samurai. Other related weapons of this type are the nyoibo, konsaibo, , and ararebo. Related solid iron weapons with no spikes or studs are the (or kanamuchi) and the (also known as a gojo or kirikobo).


title: Kanabō

text: "Kanabō" and other related club-like weapons were constructed out of heavy wood or made entirely from iron, with iron spikes or studs on one end. For wooden "kanabō", one or both ends could be covered with iron caps. "Kanabō"-type weapons came in all manner of shapes and sizes, with the largest ones being two-handed and as tall as a man, while smaller ones were primarily one-handed and the length of a forearm.


title: Kanabō

text: Their shape could be similar to that of a baseball bat, with a thicker outer end tapering towards a slender handle with a pommel, or they could be straight all the way from the handle to the end. The shaft cross-section could be round (as in a baseball bat) or polygonal; that is, multi-faceted with flat surfaces arrayed around the central axis.


title: Kanabō

text: The "kanabō" was also a mythical weapon, often used in tales by "oni", who reputedly possessed superhuman strength. This is alluded to by the Japanese saying "like giving a "kanabō" to an "oni"—meaning to give an extra advantage to someone who already has the advantage (i.e. the strong made stronger).


title: Relational algebra

text: In database theory, relational algebra is a theory that uses algebraic structures with a well-founded semantics for modeling data, and defining queries on it. The theory was introduced by Edgar F. Codd.


title: Relational algebra

text: The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. Relational databases store tabular data represented as relations. Queries over relational databases often likewise return tabular data represented as relations.


title: Relational algebra

text: The main purpose of the relational algebra is to define operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express potentially complex queries that transform potentially many input relations (whose data are stored in the database) into a single output relation (the query results).


title: Relational algebra

text: Unary operators accept as input a single relation; examples include operators to filter certain attributes (columns) or tuples (rows) from an input relation.


title: Relational algebra

text: Binary operators accept as input two relations; such operators combine the two input relations into a single output relation by, for example, taking all tuples found in either relation, removing tuples from the first relation found in the second relation, extending the tuples of the first relation with tuples in the second relation matching certain conditions, and so forth.


title: Relational algebra

text: Other more advanced operators can also be included, where the inclusion or exclusion of certain operators gives rise to a family of algebras.


title: Relational algebra

text: Relational algebra received little attention outside of pure mathematics until the publication of E.F. Codd's relational model of data in 1970. Codd proposed such an algebra as a basis for database query languages. (See section Implementations.)


title: Relational algebra

text: Five primitive operators of Codd's algebra are the "selection", the "projection", the "Cartesian product" (also called the "cross product" or "cross join"), the "set union", and the "set difference".


title: Relational algebra

text: The relational algebra uses set union, set difference, and Cartesian product from set theory, but adds additional constraints to these operators.


title: Relational algebra

text: For set union and set difference, the two relations involved must be "union-compatible"—that is, the two relations must have the same set of attributes. Because set intersection is defined in terms of set union and set difference, the two relations involved in set intersection must also be union-compatible.


title: Relational algebra

text: For the Cartesian product to be defined, the two relations involved must have disjoint headers—that is, they must not have a common attribute name.


title: Relational algebra

text: In addition, the Cartesian product is defined differently from the one in set theory in the sense that tuples are considered to be "shallow" for the purposes of the operation. That is, the Cartesian product of a set of "n"-tuples with a set of "m"-tuples yields a set of "flattened" -tuples (whereas basic set theory would have prescribed a set of 2-tuples, each containing an "n"-tuple and an "m"-tuple). More formally, "R" × "S" is defined as follows:


title: Relational algebra

text: The cardinality of the Cartesian product is the product of the cardinalities of its factors, that is, |"R" × "S"| = |"R"| × |"S"|.


title: Relational algebra

text: A projection is a unary operation written as formula_2 where formula_3 is a set of attribute names. The result of such projection is defined as the set that is obtained when all tuples in "R" are restricted to the set formula_4.


title: Relational algebra

text: Note: when implemented in SQL standard the "default projection" returns a multiset instead of a set, and the projection to eliminate duplicate data is obtained by the addition of the codice_1 keyword.


title: Relational algebra

text: A generalized selection is a unary operation written as formula_5 where is a propositional formula that consists of atoms as allowed in the normal selection and the logical operators (and), (or) and (negation). This selection selects all those tuples in "R" for which holds.


title: Relational algebra

text: To obtain a listing of all friends or business associates in an address book, the selection might be written as formula_6. The result would be a relation containing every attribute of every unique record where is true or where is true.


title: Relational algebra

text: A rename is a unary operation written as formula_7 where the result is identical to "R" except that the "b" attribute in all tuples is renamed to an "a" attribute. This is simply used to rename the attribute of a relation or the relation itself.


title: Relational algebra

text: There is also the formula_9 notation, where "R" is renamed to "x" and the attributes formula_4 are renamed to formula_11.


title: Relational algebra

text: Natural join (⋈) is a binary operator that is written as ("R" ⋈ "S") where "R" and "S" are relations. The result of the natural join is the set of all combinations of tuples in "R" and "S" that are equal on their common attribute names. For an example consider the tables "Employee" and "Dept" and their natural join:


title: Relational algebra

text: This can also be used to define composition of relations. For example, the composition of "Employee" and "Dept" is their join as shown above, projected on all but the common attribute "DeptName". In category theory, the join is precisely the fiber product.


title: Relational algebra

text: The natural join is arguably one of the most important operators since it is the relational counterpart of the logical AND operator. Note that if the same variable appears in each of two predicates that are connected by AND, then that variable stands for the same thing and both appearances must always be substituted by the same value (this is a consequence of the idempotence of the logical AND). In particular, natural join allows the combination of relations that are associated by a foreign key. For example, in the above example a foreign key probably holds from "Employee"."DeptName" to "Dept"."DeptName" and then the natural join of "Employee" and "Dept" combines all employees with their departments. This works because the foreign key holds between attributes with the same name. If this is not the case such as in the foreign key from "Dept"."Manager" to "Employee"."Name" then these columns must be renamed before taking the natural join. Such a join is sometimes also referred to as an equijoin (see "θ"-join).


title: Relational algebra

text: where "Fun(t)" is a predicate that is true for a relation "t" (in the mathematical sense) iff "t" is a function (that is, "t" does not map any attribute to multiple values). It is usually required that "R" and "S" must have at least one common attribute, but if this constraint is omitted, and "R" and "S" have no common attributes, then the natural join becomes exactly the Cartesian product.


title: Relational algebra

text: The natural join can be simulated with Codd's primitives as follows. Assume that "c"...,"c" are the attribute names common to "R" and "S", "r"...,"r" are the


title: Relational algebra

text: attribute names unique to "S". Furthermore, assume that the attribute names "x"...,"x" are neither in "R" nor in "S". In a first step the common attribute names in "S" can be renamed:


title: Relational algebra

text: Consider tables "Car" and "Boat" which list models of cars and boats and their respective prices. Suppose a customer wants to buy a car and a boat, but she does not want to spend more money for the boat than for the car. The "θ"-join (⋈) on the predicate "CarPrice" ≥ "BoatPrice" produces the flattened pairs of rows which satisfy the predicate. When using a condition where the attributes are equal, for example Price, then the condition may be specified as "Price"="Price"


title: Relational algebra

text: In order to combine tuples from two relations where the combination condition is not simply the equality of shared attributes it is convenient to have a more general form of join operator, which is the "θ"-join (or theta-join). The "θ"-join is a binary operator that is written as formula_12 or formula_13 where "a" and "b" are attribute names, "θ" is a binary relational operator in the set {<, ≤, =, ≠, >, ≥}, "υ" is a value constant, and "R" and "S" are relations. The result of this operation consists of all combinations of tuples in "R" and "S" that satisfy "θ". The result of the "θ"-join is defined only if the headers of "S" and "R" are disjoint, that is, do not contain a common attribute.


title: Relational algebra

text: Note, however, that a computer language that supports the natural join and selection operators does not need "θ"-join as well, as this can be achieved by selection from the result of a natural join (which degenerates to Cartesian product when there are no shared attributes).


title: Relational algebra

text: In SQL implementations, joining on a predicate is usually called an "inner join", and the "on" keyword allows one to specify the predicate used to filter the rows. It is important to note: forming the flattened Cartesian product then filtering the rows is conceptually correct, but an implementation would use more sophisticated data structures to speed up the join query.


title: Relational algebra

text: The left semijoin is a joining similar to the natural join and written as formula_14 where formula_15 and formula_16 are relations. The result is the set of all tuples in formula_15 for which there is a tuple in formula_16 that is equal on their common attribute names. The difference from a natural join is that other columns of formula_16 do not appear. For example, consider the tables "Employee" and "Dept" and their semijoin:


title: Relational algebra

text: The semijoin can be simulated using the natural join as follows. If formula_22 are the attribute names of formula_15, then


title: Relational algebra

text: Since we can simulate the natural join with the basic operators it follows that this also holds for the semijoin.


title: Relational algebra

text: The antijoin, written as "R" ▷ "S" where "R" and "S" are relations, is similar to the semijoin, but the result of an antijoin is only those tuples in "R" for which there is "no" tuple in "S" that is equal on their common attribute names.


title: Relational algebra

text: Given this, the antijoin is sometimes called the anti-semijoin, and the antijoin operator is sometimes written as semijoin symbol with a bar above it, instead of ▷.


title: Relational algebra

text: The division is a binary operation that is written as "R" ÷ "S". Division is not implemented directly in SQL. The result consists of the restrictions of tuples in "R" to the attribute names unique to "R", i.e., in the header of "R" but not in the header of "S", for which it holds that all their combinations with tuples in "S" are present in "R". For an example see the tables "Completed", "DBProject" and their division:


title: Relational algebra

text: If "DBProject" contains all the tasks of the Database project, then the result of the division above contains exactly the students who have completed both of the tasks in the Database project.


title: Relational algebra

text: More formally the semantics of the division is defined as follows:where {"a"...,"a"} is the set of attribute names unique to "R" and "t"["a"...,"a"] is the restriction of "t" to this set. It is usually required that the attribute names in the header of "S" are a subset of those of "R" because otherwise the result of the operation will always be empty.


title: Relational algebra

text: The simulation of the division with the basic operations is as follows. We assume that "a"...,"a" are the attribute names unique to "R" and "b"...,"b" are the attribute names of "S". In the first step we project "R" on its unique attribute names and construct all combinations with tuples in "S":


title: Relational algebra

text: In the prior example, T would represent a table such that every Student (because Student is the unique key / attribute of the Completed table) is combined with every given Task. So Eugene, for instance, would have two rows, Eugene → Database1 and Eugene → Database2 in T.


title: Relational algebra

text: In practice the classical relational algebra described above is extended with various operations such as outer joins, aggregate functions and even transitive closure.


title: Relational algebra

text: Whereas the result of a join (or inner join) consists of tuples formed by combining matching tuples in the two operands, an outer join contains those tuples and additionally some tuples formed by extending an unmatched tuple in one of the operands by "fill" values for each of the attributes of the other operand. Outer joins are not considered part of the classical relational algebra discussed so far.


title: Relational algebra

text: The operators defined in this section assume the existence of a "null" value, "ω", which we do not define, to be used for the fill values; in practice this corresponds to the NULL in SQL. In order to make subsequent selection operations on the resulting table meaningful, a semantic meaning needs to be assigned to nulls; in Codd's approach the propositional logic used by the selection is extended to a three-valued logic, although we elide those details in this article.


title: Relational algebra

text: Three outer join operators are defined: left outer join, right outer join, and full outer join. (The word "outer" is sometimes omitted.)


title: Relational algebra

text: The left outer join is written as "R" ⟕ "S" where "R" and "S" are relations. The result of the left outer join is the set of all combinations of tuples in "R" and "S" that are equal on their common attribute names, in addition (loosely speaking) to tuples in "R" that have no matching tuples in "S".


title: Relational algebra

text: In the resulting relation, tuples in "S" which have no common values in common attribute names with tuples in "R" take a "null" value, "ω".


title: Relational algebra

text: Since there are no tuples in "Dept" with a "DeptName" of "Finance" or "Executive", "ω"s occur in the resulting relation where tuples in "Employee" have a "DeptName" of "Finance" or "Executive".


title: Relational algebra

text: Let "r", "r", ..., "r" be the attributes of the relation "R" and let {("ω", ..., "ω")} be the singleton


title: Relational algebra

text: relation on the attributes that are "unique" to the relation "S" (those that are not attributes of "R"). Then the left outer join can be described in terms of the natural join (and hence using basic operators) as follows:


title: Relational algebra

text: The right outer join behaves almost identically to the left outer join, but the roles of the tables are switched.


title: Relational algebra

text: The right outer join of relations "R" and "S" is written as "R" ⟖ "S". The result of the right outer join is the set of all combinations of tuples in "R" and "S" that are equal on their common attribute names, in addition to tuples in "S" that have no matching tuples in "R".


title: Relational algebra

text: In the resulting relation, tuples in "R" which have no common values in common attribute names with tuples in "S" take a "null" value, "ω".


title: Relational algebra

text: Since there are no tuples in "Employee" with a "DeptName" of "Production", "ω"s occur in the Name and EmpId attributes of the resulting relation where tuples in "Dept" had "DeptName" of "Production".


title: Relational algebra

text: Let "s", "s", ..., "s" be the attributes of the relation "S" and let {("ω", ..., "ω")} be the singleton


title: Relational algebra

text: relation on the attributes that are "unique" to the relation "R" (those that are not attributes of "S"). Then, as with the left outer join, the right outer join can be simulated using the natural join as follows:


title: Relational algebra

text: The full outer join is written as "R" ⟗ "S" where "R" and "S" are relations. The result of the full outer join is the set of all combinations of tuples in "R" and "S" that are equal on their common attribute names, in addition to tuples in "S" that have no matching tuples in "R" and tuples in "R" that have no matching tuples in "S" in their common attribute names.


title: Relational algebra

text: In the resulting relation, tuples in "R" which have no common values in common attribute names with tuples in "S" take a "null" value, "ω". Tuples in "S" which have no common values in common attribute names with tuples in "R" also take a "null" value, "ω".


title: Relational algebra

text: The full outer join can be simulated using the left and right outer joins (and hence the natural join and set union) as follows:


title: Relational algebra

text: There is nothing in relational algebra introduced so far that would allow computations on the data domains (other than evaluation of propositional expressions involving equality). For example, it is not possible using only the algebra introduced so far to write an expression that would multiply the numbers from two columns, e.g. a unit price with a quantity to obtain a total price. Practical query languages have such facilities, e.g. the SQL SELECT allows arithmetic operations to define new columns in the result SELECT unit_price * quantity AS total_price FROM t, and a similar facility is provided more explicitly by Tutorial D's codice_2 keyword. In database theory, this is called extended projection.


title: Relational algebra

text: Furthermore, computing various functions on a column, like the summing up of its elements, is also not possible using the relational algebra introduced so far. There are five aggregate functions that are included with most relational database systems. These operations are Sum, Count, Average, Maximum and Minimum. In relational algebra the aggregation operation over a schema ("A", "A", ... "A") is written as follows:


title: Relational algebra

text: The attributes preceding the "g" are grouping attributes, which function like a "group by" clause in SQL. Then there are an arbitrary number of aggregation functions applied to individual attributes. The operation is applied to an arbitrary relation "r". The grouping attributes are optional, and if they are not supplied, the aggregation functions are applied across the entire relation to which the operation is applied.


title: Relational algebra

text: Let's assume that we have a table named with three columns, namely and . We wish to find the maximum balance of each branch. This is accomplished by "G"(). To find the highest balance of all accounts regardless of branch, we could simply write "G"().


title: Relational algebra

text: Although relational algebra seems powerful enough for most practical purposes, there are some simple and natural operators on relations that cannot be expressed by relational algebra. One of them is the transitive closure of a binary relation. Given a domain "D", let binary relation "R" be a subset of "D"×"D". The transitive closure "R" of "R" is the smallest subset of "D"×"D" that contains "R" and satisfies the following condition:


title: Relational algebra

text: It can be proved using the fact that there is no relational algebra expression "E"("R") taking "R" as a variable argument that produces "R".


title: Relational algebra

text: SQL however officially supports such fixpoint queries since 1999, and it had vendor-specific extensions in this direction well before that.


title: Relational algebra

text: The primary goal is to transform expression trees into equivalent expression trees, where the average size of the relations yielded by subexpressions in the tree is smaller than it was before the optimization. The secondary goal is to try to form common subexpressions within a single query, or if there is more than one query being evaluated at the same time, in all of those queries. The rationale behind the second goal is that it is enough to compute common subexpressions once, and the results can be used in all queries that contain that subexpression.


title: Relational algebra

text: Rules about selection operators play the most important role in query optimization. Selection is an operator that very effectively decreases the number of rows in its operand, so if the selections in an expression tree are moved towards the leaves, the internal relations (yielded by subexpressions) will likely shrink.


title: Relational algebra

text: Selection is idempotent (multiple applications of the same selection have no additional effect beyond the first one), and commutative (the order selections are applied in has no effect on the eventual result).


title: Relational algebra

text: A selection whose condition is a conjunction of simpler conditions is equivalent to a sequence of selections with those same individual conditions, and selection whose condition is a disjunction is equivalent to a union of selections. These identities can be used to merge selections so that fewer selections need to be evaluated, or to split them so that the component selections may be moved or optimized separately.


title: Relational algebra

text: Cross product is the costliest operator to evaluate. If the input relations have "N" and "M" rows, the result will contain formula_33 rows. Therefore, it is important to decrease the size of both operands before applying the cross product operator.


title: Relational algebra

text: This can be effectively done if the cross product is followed by a selection operator, e.g. formula_34. Considering the definition of join, this is the most likely case. If the cross product is not followed by a selection operator, we can try to push down a selection from higher levels of the expression tree using the other selection rules.


title: Relational algebra

text: In the above case the condition "A" is broken up in to conditions "B", "C" and "D" using the split rules about complex selection conditions, so that formula_35 and "B" contains attributes only from "R", "C" contains attributes only from "P", and "D" contains the part of "A" that contains attributes from both "R" and "P". Note, that "B", "C" or "D" are possibly empty. Then the following holds:


title: Relational algebra

text: Selection is distributive over the set difference, intersection, and union operators. The following three rules are used to push selection below set operations in the expression tree. For the set difference and the intersection operators, it is possible to apply the selection operator to just one of the operands following the transformation. This can be beneficial where one of the operands is small, and the overhead of evaluating the selection operator outweighs the benefits of using a smaller relation as an operand.


title: Relational algebra

text: Selection commutes with projection if and only if the fields referenced in the selection condition are a subset of the fields in the projection. Performing selection before projection may be useful if the operand is a cross product or join. In other cases, if the selection condition is relatively expensive to compute, moving selection outside the projection may reduce the number of tuples which must be tested (since projection may produce fewer tuples due to the elimination of duplicates resulting from omitted fields).


title: Relational algebra

text: Projection is idempotent, so that a series of (valid) projections is equivalent to the outermost projection.


title: Relational algebra

text: Successive renames of a variable can be collapsed into a single rename. Rename operations which have no variables in common can be arbitrarily reordered with respect to one another, which can be exploited to make successive renames adjacent so that they can be collapsed.


title: Relational algebra

text: The first query language to be based on Codd's algebra was Alpha, developed by Dr. Codd himself. Subsequently, ISBL was created, and this pioneering work has been acclaimed by many authorities as having shown the way to make Codd's idea into a useful language. Business System 12 was a short-lived industry-strength relational DBMS that followed the ISBL example.


title: Relational algebra

text: In 1998 Chris Date and Hugh Darwen proposed a language called Tutorial D intended for use in teaching relational database theory, and its query language also draws on ISBL's ideas. Rel is an implementation of Tutorial D.


title: Relational algebra

text: Even the query language of SQL is loosely based on a relational algebra, though the operands in SQL (tables) are not exactly relations and several useful theorems about the relational algebra do not hold in the SQL counterpart (arguably to the detriment of optimisers and/or users). The SQL table model is a bag (multiset), rather than a set. For example, the expression formula_53 is a theorem for relational algebra on sets, but not for relational algebra on bags; for a treatment of relational algebra on bags see chapter 5 of the "Complete" textbook by Garcia-Molina, Ullman and Widom.


title: Relational algebra

text: Practically any academic textbook on databases has a detailed treatment of the classic relational algebra.


title: Vulcan Centaur

text: Vulcan Centaur is a two-stage-to-orbit, heavy-lift launch vehicle that is under development by the United Launch Alliance (ULA) since 2014 with an initial flight expected in early 2023. It is principally designed to meet launch demands for the U.S. government's National Security Space Launch (NSSL) program for use by the United States Space Force and U.S. intelligence agencies for national security satellite launches.


title: Vulcan Centaur

text: The maiden flight is slated to launch Astrobotic Technology's "Peregrine" lunar lander for NASA's Commercial Lunar Payload Services (CLPS) program and Kuiper Systems' Kuipersat-1 and Kuipersat-2, no earlier than 2023, after multiple delays from the initially planned first flight in 2019.


title: Vulcan Centaur

text: Vulcan is ULA's first new launch vehicle design; it adapts and evolves technologies that were developed for the Atlas V and Delta IV rockets of the USAF's EELV program. The first-stage propellant tanks have the same diameter as the Delta IV Common Booster Core but will contain liquid methane and liquid oxygen propellants rather than the Delta IV's liquid hydrogen and liquid oxygen.


title: Vulcan Centaur

text: Vulcan's upper stage is the Centaur V, an upgraded variant of the Centaur III, the world’s first high energy upper stage. The Centaur III variant is currently used on the Atlas V. A version of the RL-10 engine with a nozzle extension, the RL-10CX, will be used on the Vulcan Centaur Heavy. Previous plans called for the Centaur V to be eventually upgraded with Integrated Vehicle Fluids technology to become the Advanced Cryogenic Evolved Stage (ACES), but this was subsequently cancelled. Vulcan is intended to undergo the human-rating certification process to allow the launch of crewed craft, such as the Boeing CST-100 Starliner or a future version of the Sierra Nevada Dream Chaser spaceplane.


title: Vulcan Centaur

text: The Vulcan booster has a outer diameter to support the Blue Origin BE-4 engines' liquid methane fuel. In September 2018, after a competition with the Aerojet Rocketdyne AR1, the BE-4 was selected to power Vulcan's first stage.


title: Vulcan Centaur

text: Up to six GEM-63XL solid rocket boosters (SRB)s can be attached to the first stage in pairs, providing additional thrust during the first part of the flight and allowing the six-SRB Vulcan Centaur Heavy to launch a higher mass payload than the most capable Atlas V 551.


title: Vulcan Centaur

text: The Vulcan Centaur will have a four-character designation for each configuration, in which the first character represents the first stage of the vehicle; Vulcan is designated with the letter "V". The second character shows the upper stage; Centaur is designated "C". The third character represents the number of SRBs attached to the Vulcan; "0", "2", "4" or "6". The final character represents the payload-fairing length configuration, which is indicated by "S" (Standard; ) or "L" (Long; ). For example, "VC6L" would represent a Vulcan first stage, a Centaur upper stage, six SRBs and a long-configuration fairing. The single-core Vulcan Centaur Heavy will have a Vulcan first stage, a Centaur upper stage with RL10CX engines with a nozzle extension and six SRBs.


title: Vulcan Centaur

text: Payload to low-Earth orbit (LEO) is for a 200km (120mi) circular orbit at a 28.7° inclination; payload to the International Space Station is for a 407km (253mi) circular orbit at 51.6° inclination; payload to polar LEO is for a 200km (120mi) circular orbit at 90° inclination. These capabilities are driven by the need to meet NSSL requirements, with room for future growth.


title: Vulcan Centaur

text: A single-core Vulcan Centaur with six solid-rocket boosters can put 27,200 kilograms into low-Earth orbit. This is almost as much as the three-core Delta IV Heavy.


title: Vulcan Centaur

text: ULA had considered a number of launch vehicle concepts in the decade since the company was formed in 2006. Various concepts for derivative vehicles based on the Atlas and Delta lines of launch vehicles they inherited from their predecessor companies were presented to the US government for funding. None were funded beyond the concept stage.


title: Vulcan Centaur

text: In early 2014, geopolitical and US political considerations led to an effort by ULA to consider the possible replacement of the Russian-supplied RD-180 engine used on the first stage booster of the Atlas V. Events such as the Annexation of Crimea by the Russian Federation in February 2014 brought into focus that relying on foreign hardware to launch critical national security spacecraft could be undesirable. Formal study contracts were issued by ULA in June 2014 to a number of US rocket engine suppliers. ULA was also facing competition from SpaceX—then seen to affect its core national security market of US military launches—and by July 2014, the US Congress was debating whether to legislatively ban future use of the RD-180 engine.


title: Vulcan Centaur

text: In September 2014, ULA announced that it had entered into a partnership with Blue Origin to develop the BE-4 liquid oxygen (LOX) and liquid methane (CH) engine to replace the RD-180 on a new first stage booster. The engine was already in its third year of development by Blue Origin, and ULA said it expected the new stage and engine to start flying no earlier than 2019. Two of the -thrust BE-4 engines were to be used on a new launch vehicle booster.


title: Vulcan Centaur

text: In October 2014, ULA announced a major restructuring of company processes and workforce in order to halve launch costs. One of the reasons given for the restructuring and new cost reduction goals was new competition in the launch market from SpaceX.


title: Vulcan Centaur

text: ULA stated it planned to have preliminary design ideas in place for a blending of its existing Atlas V and Delta IV technologies by the end of 2014, in order to build a successor to the Atlas V that would allow them to cut Atlas V launch costs in half.


title: Vulcan Centaur

text: At the time of the 2015 announcement, ULA proposed an incremental approach to rolling out the new launch vehicle and its technologies. Vulcan deployment was expected to begin with a new first stage that was based on the Delta IV's fuselage diameter and production process, and initially expected to use two BE-4 engines or the AR1 as an alternative. The initial second stage was planned to be the Atlas V's Common Centaur and Centaur III with its existing RL10 engine. A later upgrade, the Advanced Cryogenic Evolved Stage (ACES), was conceptually planned for full development in the late 2010s and to be introduced a few years after Vulcan's first flight. ULA also announced a design concept for reuse of the Vulcan booster engines, thrust structure and first stage avionics, which could be detached as a module from the propellant tanks after booster engine cutoff; the module would re-enter the atmosphere behind an inflatable heat shield. Neither the ACES second stage nor the SMART reuse for the first stage became funded development projects by ULA , even though ULA stated the "first stage propulsion module accounts for around 65% of Vulcan Centaur's costs."


title: Vulcan Centaur

text: Through the first several years, the ULA board of directors made quarterly funding commitments to Vulcan Centaur development. , the U.S. government had committed approximately US$1.2 billion in a public–private partnership to Vulcan Centaur development and future funding was dependent on ULA securing an NSSL contract.


title: Vulcan Centaur

text: By March 2016, the United States Air Force (USAF) had committed up to US$202 million of funding for Vulcan development. ULA had not yet estimated the total cost of development but CEO Tory Bruno noted "new rockets typically cost US$2 billion, including US$1 billion for the main engine". In April 2016, ULA Board of Directors member and President of Boeing's Network and Space Systems (N&SS) division Craig Cooning expressed confidence in the possibility of further USAF funding of Vulcan development.


title: Vulcan Centaur

text: In March 2018, Tory Bruno said the Vulcan-Centaur had been "75% privately funded" up to that point. In October 2018, following a request for proposals and technical evaluation, ULA was awarded US$967 million to develop a prototype Vulcan launch system as part of the National Security Space Launch program. Other providers Blue Origin and Northrop Grumman Innovation Systems were awarded US$500 million and US$792 million in development funding, with detailed proposals and a competitive selection process to follow in 2019. The USAF's goal with the next generation of Launch Service Agreements was to desist from "buying rockets" and move to acquire services from launch service providers but U.S. government funding of launch vehicle development continued.


title: Vulcan Centaur

text: In September 2015, it was announced BE-4 rocket engine production would be expanded to increase production capacity for testing. The following January, ULA was designing two versions of the Vulcan first stage; the BE-4 version has a diameter to support the use of less-dense methane fuel. In late 2017, the upper stage was changed to the larger and heavier Centaur V, and the launch vehicle was renamed Vulcan Centaur. The single-core Vulcan Centaur will be capable of lifting "30% more" than a Delta IV Heavy, meeting the NSSL requirements.


title: Vulcan Centaur

text: In May 2018, ULA announced the selection of Aerojet Rocketdyne's RL10 engine for the Vulcan Centaur upper stage. That September 2018, ULA announced the selection of the Blue Origin BE-4 engine for Vulcan's booster. That October 2018, the USAF released an NSSL launch service agreement with new requirements, delaying Vulcan's initial launch to April 2021, after an earlier postponement to 2020.


title: Vulcan Centaur

text: On 8 July 2019, CEO Tory Bruno released images of two Vulcan qualification test articles — the liquefied natural gas tank and thrust structure — on Twitter. The following day, Peter Guggenbach, the CEO of RUAG Space, released an image of a Vulcan payload attachment fitting. On 31 July the same year, two images of the mated LNG tank and thrust structure were similarly released. On 2 August 2019, Blue Origin released on Twitter an image of a BE-4 engine at full power on a test stand. On 6 August 2019, the first two parts of Vulcan's mobile launcher platform (MLP) were transported to the Spaceflight Processing Operations Center (SPOC) near SLC-40 and SLC-41, Cape Canaveral, Florida. The MLP was fabricated in eight sections and will move at on existing rail dollies and stand tall. On 12 August 2019, ULA submitted Vulcan Centaur for phase 2 of the USAF's launch services competition. As of February 2020, the tankage for the second operational rocket was under construction in the ULA factory in Decatur, Alabama.


title: Vulcan Centaur

text: In October 2019, the first launch of Vulcan was planned for July 2021, carrying Astrobotic Technology's "Peregrine" lunar lander. In June 2020, ULA said it could be earlier and announced a target launch date of early 2021. On 7 August 2020, the United States Space Force awarded ULA 60% of all National Security Space Launch payloads from 2022 to 2027. That December 2020, ULA said BE-4 engine delivery was expected in mid-2021, and that the Vulcan's first launch would not happen before the end of 2021. In June 2021, Astrobotic reported that due to the COVID-19 pandemic, they needed more time to prepare "Peregrine", delaying the first flight of Vulcan to 2022 and later to 2023. The Government Accountability Office (GAO) also stated that the first-stage engine was experiencing technical difficulties, and may not be qualified in time to support a Vulcan launch in 2021.


title: Vulcan Centaur

text: In February 2021, ULA shipped the first completed Vulcan core booster to Florida for pathfinder tests ahead of the Vulcan's debut launch.


title: Vulcan Centaur

text: The Pathfinder Tanking Test core booster was transferred to SLC-41 for first stage cryogenic tanking tests in April 2021.


title: Vulcan Centaur

text: It was loaded with just LOX in August 2021, and with just CH in September 2021, and was rolled out to SLC-41 on Oct 4 for a combined LOX & CH tanking and pressurisation test on Oct 5.


title: Vulcan Centaur

text: On 14 August 2019, ULA won a commercial competition when it was announced the second Vulcan certification flight would be SNC Demo-1, the first of six Dream Chaser CRS-2 flights awarded to ULA. Launches are planned to begin in 2023. They will use the four-SRB Vulcan configuration. On 19 August 2019, it was announced Astrobotic Technology selected ULA to launch their Peregrine lander on the first Vulcan certification flight. Peregrine is scheduled to be launched in early 2023 from SLC-41 at Cape Canaveral Space Force Station (CCSFS) on a mission to the lunar surface.


title: Vulcan Centaur

text: The Space Force's USSF-51 launch in late 2022 had been intended to be the first national security classified mission, but in May 2021 the spacecraft was reassigned to an Atlas V to "mitigate schedule risk associated with Vulcan Centaur non-recurring design validation".


title: Vulcan Centaur

text: In early 2021, NASA added the Vulcan Centaur to the Launch Services II contract (NLS II). This makes the Vulcan Centaur part of the Launch Services Program and subjects it to the "on-ramp" provisions in NLS II. The on-ramp provisions allow existing launch providers to introduce new vehicles that NASA has not yet provided for.


title: Vulcan Centaur

text: Since the formal announcement in 2015, ULA has spoken of several technologies that would extend the Vulcan launch vehicle's capabilities. These include enhancements to the first stage to make the most expensive components potentially reusable and enhancements to the second stage to increase its long-term mission duration to operate for months in Earth orbit cislunar space.


title: Vulcan Centaur

text: The ACES upper stage—fueled with liquid oxygen (LOX) and liquid hydrogen (LH) and powered by up to four rocket engines with the engine type yet to be selected—was a conceptual upgrade to Vulcan's upper stage at the time of the announcement in 2015. This stage could subsequently be upgraded to include the Integrated Vehicle Fluids technology that would allow the upper stage a much longer in-orbit life of weeks rather than hours. The ACES upper stage was eventually cancelled when in September 2020, ULA made public that the ACES development would not be continued and the Vulcan second stage would now be the Centaur V upper stage. The Centaur V is based on the upper stage used by the Atlas V but larger and more powerful. A senior executive at ULA said the Centaur V design was also heavily influenced by ACES.


title: Vulcan Centaur

text: However, ULA said in 2021 that it is working to add more value to upper stages by having them perform tasks such as operating as space tugs. CEO Tory Bruno says ULA is working on upper stages with hundreds of times the endurance of those currently in use.


title: Vulcan Centaur

text: The Sensible Modular Autonomous Return Technology (SMART) reuse concept was also announced during the initial April 2015 unveiling of Vulcan. The booster engines, avionics, and thrust structure would be detached as a module from the propellant tanks after booster engine cutoff. The module would descend through the atmosphere behind an inflatable heat shield. After parachute deployment, a helicopter would capture the module in mid-air. ULA estimated this technology would reduce the cost of the first stage propulsion by 90%, and 65% of the total first-stage cost. By 2020, ULA had not announced firm plans to fund, build and test this engine-reuse concept, though in late 2019 they stated they were "still planning to eventually reuse Vulcan's first-stage engines".


title: Vulcan Centaur

text: In April 2021 CEO Tory Bruno said that the additional launches purchased by Amazon for the Kuiper satellite constellation would require a higher launch cadence and that this provided support for the business case to go forward with the SMART concept.


title: Vulcan Centaur

text: In July 2022, ULA pivoted and changed the high-level design objective of the engine reuse recovery concept. Rather than recover the descending booster engines with a helicopter, ULA is now planning to attempt recovery of the engines following atmospheric reentry, descent, and splashdown floating in the ocean on the inflatable aeroshell.


title: Vulcan Centaur

text: As of late 2020, ULA said it is studying a possible three-core variant of the Vulcan Centaur. This rocket was tentatively dubbed the Vulcan Heavy, not to be confused with the planned single-core Vulcan Centaur Heavy with six SRBs.


title: Moscow, third Rome

text: Moscow, third Rome (; ) is a theological and political concept asserting Moscow as the successor to ancient Rome, with the Russian world carrying forward the legacy of the Roman Empire. The term "third Rome" refers to a historical topic of debate in European culture: the question of the successor city to the "first Rome" (Rome, within the Western Roman Empire) and the "second Rome" (Constantinople, within the Eastern Roman Empire).


title: Moscow, third Rome

text: "Moscow, Third Rome" is a theological and a political concept which was formulated in the 15th–16th centuries in the Tsardom of Rus.


title: Moscow, third Rome

text: After the fall of Tǎrnovo to the Ottoman Turks in 1393, a number of Bulgarian clergymen sought shelter in the Russian lands and transferred the idea of the Third Rome there, which eventually resurfaced in Tver, during the reign of Boris of Tver, when the monk Foma (Thomas) of Tver had written "The Eulogy of the Pious Grand Prince Boris Alexandrovich" in 1453.


title: Moscow, third Rome

text: Within decades after the capture of Constantinople by Mehmed II of the Ottoman Empire on 29 May 1453, some Eastern Orthodox people were nominating Moscow as the "Third Rome", or the "New Rome".


title: Moscow, third Rome

text: The Turks captured Constantinople in 1453 and the fortress of Mangup – the last fragment of the Empire of Trebizond and thus the Byzantine Empire – fell at the end of 1475. Even before the fall of Constantinople, the Eastern Orthodox Slavic states in the Balkans had fallen under Turkish rule. The fall of Constantinople caused tremendous fears, many considered the fall of Constantinople as a sign the End time was near (in 1492 it was 7000 Anno Mundi); others believed that the emperor of the Holy Roman Empire (although he was a Roman Catholic) now took the place of the emperors of Constantinople. There were also hopes that Constantinople would be liberated soon. Moreover, the Eastern Orthodox Church was left without its Eastern Orthodox "Basileus". Therefore, the question arose of who would become the new "basileus". At the end of the various "Tales" about the fall of Constantinople, which gained great popularity in Moscow Russia, it was directly stated that the Rus' people would defeat the Ishmaelites (Muslims) and their king would become the "basileus" in the City of Seven Hills (Constantinople). The Grand Prince of Moscow remained the strongest of the Eastern Orthodox rulers; Ivan III married Sophia Paleologue, broke his formal subordination to the Golden Horde (already divided into several Tatar kingdoms) and became an independent ruler. All of this strengthened Moscow's claims to primacy in the Eastern Orthodox world. However, the liberation of Constantinople was still far away — the Moscow State had no opportunity to fight the Ottoman Empire.


title: Moscow, third Rome

text: At the end of the 15th century, the emergence of the idea that Moscow is truly a new Rome can be found; the whole idea of Moscow as third Rome could be traced as early as 1492, when Metropolitan of Moscow Zosimus expressed it. Metropolitan Zosima, in a foreword to his work of 1492 "Presentation of the Paschalion" (), quite clearly expressed it, calling Ivan III "the new Tsar Constantine of the new city of Constantine — Moscow." This idea is best known in the presentation of the monk Philotheus of the early 16th century:


title: Moscow, third Rome

text: The Moscow scholars explained the fall of Constantinople as the divine punishment for the sin of the Union with the Catholic Church, but they did not want to obey the Patriarch of Constantinople, although there were no unionist patriarchs since the Turkish conquest in 1453 and the first Patriarch since then, Gennadius Scholarius, was the leader of the anti-unionists. At the next synod, held in Constantinople in 1484, the Union was finally declared invalid. Having lost its Christian "basileus" after the Turkish conquest, Constantinople as a center of power lost a significant part of its authority. On the contrary, the Moscow rulers soon began to consider themselves real "Tsars" (this title was already used by Ivan III), and therefore according to them the center of the Eastern Orthodox Church should have been located in Moscow, and thus the bishop of Moscow should become the head of the Orthodoxy. The text of the bishop's oath in Muscovy, edited in 1505–1511, condemned the ordination of metropolitans in Constantinople, calling it "the ordination in the area of godless Turks, by the pagan "tsar"."


title: Moscow, third Rome

text: Stirrings of this sentiment began during the reign of Ivan III of Russia, who styled himself Czar (cf. Caesar), who had married Sophia Paleologue. Sophia was a niece of Constantine XI, the last Byzantine emperor. By the rules and laws of inheritance followed by most European monarchies of the time, Ivan could claim that he and his offspring were heirs of the fallen Empire, but the Roman traditions of the empire had never recognized automatic inheritance of the Imperial office.


title: Moscow, third Rome

text: It was also Sophia's brother, Andreas Palaiologos, who held the rights of succession to the Byzantine throne. Andreas died in 1502, having sold his titles and royal and imperial rights to Ferdinand II of Aragon and Isabella I of Castile. A stronger claim was based on religious symbolism. The Orthodox faith was central to Byzantine notions of their identity and what distinguished them from "barbarians". Vladimir the Great had converted Kievan Rus' to Orthodoxy in 988, in return for which he became the first barbarian to ever get an Imperial princess as a wife.


title: Moscow, third Rome

text: "The liturgical privileges that the Byzantine emperor enjoyed carried over to the Muscovite tsar. In 1547, for instance, when Ivan IV was crowned tsar, not only was he anointed as the Byzantine emperor had been after the late twelfth century, but he was also allowed to communicate in the sanctuary with the clergy."


title: Moscow, third Rome

text: During Ecumenical Patriarch Jeremias II's visit to Moscow in 1588-9 "to collect funds to assist the [Eastern] Orthodox communities living in the Ottoman Empire", Jeremias recognized in 1589 the Metropolitan of Moscow as patriarch. This recognition was "a victory for those who saw Moscow as the Third Rome."


title: Moscow, third Rome

text: Shortly before Joseph II inherited the States of the House of Austria, he traveled to Russia in 1780. In her conversations with him Catherine II made it clear that she would renew the Byzantine empire and to use her one-year-old grandson Konstantin as Emperor of Constantinople. The guest tried to suggest to the host that he could be held harmless in the Papal States.


title: Moscow, third Rome

text: The "Russian world" is ecclesiastical in its form, but geopolitical in its essence; it is a concept that was put forward in a keynote speech on November 3, 2009, by Patriarch Kirill (Gundyayev) of Moscow which he described as a "common civilisational space" of countries sharing Eastern Orthodoxy, Russian culture and language, and a common historical memory. The "Russian world" under the Patriarch Kirill focused only on the Eastern Slavic countries of Eastern Europe; that is, on Ukraine and Belarus, while leading the Russian Orthodox Church to isolate itself.


title: Moscow, third Rome

text: The ideas of the Russian world are used as a justification for the revival of the Russian Empire. It has been suggested that Vladimir Putin envisions a recreation of Russia's "mission", at least in terms of the Slavic people, although it has also been noted that this viewpoint may be highly exaggerated.


title: Hot Chip

text: Hot Chip are an English synthpop band formed in London in 1995. The group consists of multi-instrumentalists Alexis Taylor, Joe Goddard, Al Doyle, Owen Clarke, and Felix Martin. They are occasionally joined by former member Rob Smoughton for live performances and studio recordings. The group primarily produces music in the synth-pop and alternative dance genres, drawing influences from house and disco.


title: Hot Chip

text: Hot Chip began as a bedroom recording project for Taylor and Goddard, who met while students at Elliott School, Putney; their earliest lineup included Smoughton as their drummer. After completing two EPs, "Mexico" (2001) and "San Frandisco" (2002), the group released their debut album, "Coming on Strong" (2004) and added Doyle, Clarke, and Martin to their lineup. The band's second album, "The Warning" (2006), was nominated for the Mercury Prize. Their follow-up, "Made in the Dark" (2008), included the single "Ready for the Floor", which was nominated for the Grammy Award for Best Dance Recording. The band have subsequently released the albums "One Life Stand" (2010), "In Our Heads" (2012), "Why Make Sense?" (2015), "A Bath Full of Ecstasy" (2019), and "Freakout/Release" (2022).


title: Hot Chip

text: Outside of Hot Chip, the band members, individually and in partnership with each other, are active in other musical acts and occasionally perform DJ sets.


title: Hot Chip

text: Hot Chip formed as a duo around 1995 consisting of Alexis Taylor and Joe Goddard, who met as students at Elliott School, Putney. With a shared love of R&B and house music, they started collaborating on music around 1998. Early formative releases included 2001's "Mexico EP" on Victory Garden Records (VG14), and the self-released "San Frandisco" EP in 2002. After years of self-releasing records, they signed with Moshi Moshi in 2003 and released their debut LP "Coming on Strong" in 2004. During this period, they were joined by Owen Clarke, Felix Martin and Al Doyle. They started working on their second album and signed a UK and US record deal with DFA Records and EMI. DFA and Astralwerks released their debut album for the first time in the United States in late 2005.


title: Hot Chip

text: "The Guardian" names Roxy Music, Prince, Arthur Russell and Madonna as influences on Hot Chip; the band have also paid "tribute and... homage" to Orchestral Manoeuvres in the Dark (OMD).


title: Hot Chip

text: In 2006, Hot Chip released their second album, "The Warning". Now signed to EMI in the United Kingdom, the band gained more mainstream appeal as well as the attention of critics. The album was shortlisted for the 2006 Nationwide Mercury Prize and was Mixmag's Album of the Year 2006. This album spawned also two UK top 40 singles: "Over and Over" in March 2006 and "Boy from School" in May 2006. "Over and Over" received attention for its music video, which was directed by Nima Nourizadeh, and was also named as the best single of 2006 by British music magazine "NME".


title: Hot Chip

text: The band released their third studio album, "Made in the Dark", on 4 February 2008. The first song to be released from it was "Shake a Fist", which was released as a limited one-sided 12-inch vinyl in August 2007. The second release was "Ready for the Floor" in January 2008, which peaked at number six on the UK Singles Chart. In order to promote "Ready for the Floor", the band appeared on "Friday Night with Jonathan Ross" in January 2008, and Joe Goddard appeared on "Never Mind the Buzzcocks" on 31 January. In February 2008, the band performed on the American talk shows Jimmy Kimmel and Carson Daly. At the end of 2008, "Ready for the Floor" received a Grammy Award for Best Dance Recording nomination, but the song later lost out to "Harder, Better, Faster, Stronger (Alive 2007)" by Daft Punk. On 7 May 2008, the group performed their third single, "One Pure Thought", on Radio 1's Live Lounge. The hypnotic clip for "One Pure Thought" was selected as one of the best music videos of 2008 by AllMusic.


title: Hot Chip

text: Having completed a world tour in February 2009, Hot Chip returned to London and began writing and recording their fourth album, "One Life Stand".


title: Hot Chip

text: In early 2009, Alexis Taylor told "NME" that the band recorded new songs including "Alley Cats", which the band played regularly while touring in 2008/2009. Initially, Taylor hinted that the album was going to be "a bit calmer this time" in comparison to "Made in the Dark" with songs that are "more mid-tempo and disco influenced", although the two tracks released prior to the album, "Take It In" and "One Life Stand", suggest that it will be more upbeat than first suggested, and may be more influenced by early house music. Alongside the regular band members, Hot Chip collaborated on several of the album tracks with the drummer Charles Hayward from This Heat and Camberwell Now, Leo Taylor, drummer from the London-based band The Invisible and the Trinidadian steel pan player Fimber Bravo.


title: Hot Chip

text: About the album, Taylor stated, "I think "In Our Heads" was a bit speedier, and made with less pressure, but more fun – partly due to people in the band not having too many hang ups about how good the material was – we seemed to be happy with the songs we were writing and they came quickly – and partly due to the fact that we had been enjoying ourselves elsewhere, whether at home, or on tour, or recording with our other projects, or DJing. I think that is right about [having a] subtler confidence, but it may also be that we are a bit more accepted these days as we keep doing what we want, and gradually people stop saying 'why' to everything and each decision. The songwriting developed quickly from songs that were dreamt ('Now There is Nothing'); songs that were written via email file sending (fully fleshed out instrumentals from Joe developing into songs with added percussion/chord changes and singing by me; e.g. 'Flutes'); songs that we bashed out in collaborative writing sessions between Joe and myself ('Don't Deny Your Heart', 'How Do You Do?'); songs that one or the other of us wrote largely separately 'These Chains'– Joe/'Look at Where We Are'- Alexis); songs that a few of us in the room wrote more of: 'Dark and Stormy', or to some extent "Let Me Be Him" (at least in chorus terms); or finally songs that were written after we completed the last album and which were still in our minds: 'Always Been Your Love', 'Doctor'." "Dark and Stormy" has been since released as a non-album single.


title: Hot Chip

text: On 10 February 2015, the band announced their sixth studio album, "Why Make Sense?" and released the first single, "Huarache Lights". The album was released on 18 May 2015.


title: Hot Chip

text: On 4 April 2019, the band announced that their seventh studio album, "A Bath Full of Ecstasy", would be released on 21 June 2019. The first single from the album, "Hungry Child", was released on the same day. They released the second single, "Melody of Love", on 29 May 2019.


title: Hot Chip

text: It was announced on 19 April 2022 that Hot Chip would release their eighth studio album "Freakout/Release" on 19 August 2022, with the lead single "Down" preceding the release. The announcement coincided with Hot Chip's US, UK and European tour, which began in San Francisco on 19 April 2022.<ref name="F/R"></ref> They released a second single, "Eleanor", on 7 July 2022, which is about Samuel Beckett driving André the Giant to school.


title: Hot Chip

text: During live performances, Hot Chip reinvent their studio compositions to form what has been described by "Glide magazine" as "heavy beat-driven improvisation[s]" that create "an atmosphere of excitement, energy and the unexpected." Festival appearances include V Festival, Dour Festival, Glastonbury, Treasure Island Festival, Roskilde festival, Sónar, Benicassim, Electric Picnic, Bestival, Lovebox Festival, Bonnaroo, the Reading and Leeds Festivals, the Big Day Out, Melt! Festival, T in the Park, Summer Sundae, Splendour in the Grass, Lollapalooza and Lollapalooza Chile, the Brazilian TIM Festival, Oxegen, Coachella, Way Out West Festival, Austin City Limits, Ultra Music Festival, and the Osheaga Festival.


title: Hot Chip

text: The band is also known for its DJ talent; they have released several mix CDs and mixes for national and international radio stations and they all DJ regularly worldwide.


title: Hot Chip

text: Al Doyle played guitar with LCD Soundsystem on tour and was present during their concert at Madison Square Garden in 2011.


title: Hot Chip

text: In April 2012 "Boy from School" featured in "The Simpsons" episode "A Totally Fun Thing That Bart Will Never Do Again".


title: Hot Chip

text: Hot Chip released a album in 2007, and the mix album "A Bugged Out Mix by Hot Chip" in 2009 on the Bugged Out label.


title: Hot Chip

text: In 2008, the band released an EP which included collaborations with Robert Wyatt. Wyatt sang and reworked versions of three tracks from "Made in the Dark", and the "Hot Chip with Robert Wyatt and Geese" EP also included a remix by Geese, a string quartet based in London who have regularly contributed to Hot Chip's recordings.


title: Hot Chip

text: Alexis Taylor released a solo album in 2008, "Rubbed Out", which saw him focusing more on the fundamental sounds used by Hot Chip. This led to a more downtempo and bluesy album than his works with Hot Chip.


title: Hot Chip

text: Joe Goddard has also released solo productions including "Bassline '12" and "Gabriel", the latter of which was featured in the 2013 video game "Grand Theft Auto V". He has also remixed songs from other artists including Disclosure, Breach, Dirty Projectors, Nneka, and Kanye West.


title: Hot Chip

text: The band covered the William Onyeabor song "Atomic Bomb" for the Luaka Bop compilation "What?!" in 2014.


title: Hot Chip

text: Hot Chip were parodied in an episode of pre-school children's TV show Hey Duggee, as an a capella band Hot Cheep, made up of four birds.


title: Hot Chip

text: Featured in a series 7 episode of Peep Show with Mark playing the Name Game and incorrectly guessing their name as Hot Potatoe.


title: Hot Chip

text: Their song "Flutes" from their 2012 album "In Our Heads" was featured in the re-release of "Grand Theft Auto V" on the fictional radio station Radio Mirror Park.


title: Hot Chip

text: Their song "Straight To The Morning" featuring "Jarvis Cocker" featured in the game "Forza Horizon 5" on the radio station Horizon Pulse.


title: Bill Williams (actor)

text: William Herman Katt (born Herman August Wilhelm Katt; May 15, 1915 – September 21, 1992), known as Bill Williams, was an American television and film actor. He is best known for his starring role in the early television series "The Adventures of Kit Carson", which aired in syndication from 1951 to 1955.


title: Bill Williams (actor)

text: Williams was born in Brooklyn, New York to German immigrant parents. He attended the Pratt Institute, and became a professional swimmer, performing in underwater shows. He landed a walk-on role as a theater usher in "King Kong" (1933). He enlisted in the United States Army during World War II, but was discharged before the end and became an actor. His credited debut was in "Murder in the Blue Room" in 1944, using the professional name Bill Williams. His first starring role was opposite Susan Hayward in "Deadline at Dawn" (1946).


title: Bill Williams (actor)

text: Williams appeared in ten films before he landed the lead role in television's "The Adventures of Kit Carson," which ran for 105 episodes. When the series ended, Williams' star power faded. It was revived in 1957 when he co-starred with Betty White on television in "Date with the Angels". Williams portrayed Federal agent Martin Flaherty in "The Scarface Mob" (1959), the pilot for ABC's "The Untouchables". However, when the series was accepted, the role went to Jerry Paris. Williams turned down the lead in "Sea Hunt" in 1958, believing that an underwater show would not work on television. Lloyd Bridges accepted the part and turned it into a hit. Williams did star as a former Navy frogman in "", which ran for just one season. He played a variety of roles on "Perry Mason", in which his wife Barbara Hale co-starred as Raymond Burr's secretary Della Street. In a 1962 episode, "The Case of the Crippled Cougar," he played defendant Mike Preston. In 1963, he was murder victim Floyd Grant in "The Case of the Bluffing Blast." In 1965 Williams played murderer Charles Shaw in "The Case of the Murderous Mermaid," and was murderer Burt Payne in "The Case of the 12th Wildcat". Williams appeared with his son in a final season episode of "Ironside", bringing him together again with Raymond Burr. He also made numerous guest appearances on television and worked in low-budget science fiction films until his retirement.


title: Bill Williams (actor)

text: Williams married actress Barbara Hale on June 22, 1946. They met during the filming of "West of the Pecos" and had two daughters, Jodi and Juanita, and a son, actor William Katt.


title: Bill Williams (actor)

text: Bill Williams died of a brain tumor at age 77 in 1992 and is buried at Forest Lawn Memorial Park (Hollywood Hills).


title: Bill Williams (actor)

text: For his contributions to television, Bill Williams has a star on the Hollywood Walk of Fame. It is at 6161 Hollywood Blvd.


title: Solenoid valve

text: Solenoid valves differ in the characteristics of the electric current they use, the strength of the magnetic field they generate, the mechanism they use to regulate the fluid, and the type and characteristics of fluid they control. The mechanism varies from linear action, plunger-type actuators to pivoted-armature actuators and rocker actuators. The valve can use a two-port design to regulate a flow or use a three or more port design to switch flows between ports. Multiple solenoid valves can be placed together on a manifold.


title: Solenoid valve

text: Solenoid valves are the most frequently used control elements in fluidics. Their tasks are to shut off, release, dose, distribute or mix fluids. They are found in many application areas. Solenoids offer fast and safe switching, high-reliability, long service life, good medium compatibility of the materials used, low control power and compact design.


title: Solenoid valve

text: There are many valve design variations. Ordinary valves can have many ports and fluid paths. A 2-way valve, for example, has 2 ports; if the valve is open, then the two ports are connected and fluid may flow between the ports; if the valve is closed, then ports are isolated. If the valve is open when the solenoid is not energized, then the valve is termed normally open (N.O.). Similarly, if the valve is closed when the solenoid is not energized, then the valve is termed normally closed (N.C.). There are also 3-way and more complicated designs. A 3-way valve has 3 ports; it connects one port to either of the two other ports (typically a supply port and an exhaust port).


title: Solenoid valve

text: Solenoid valves are also characterized by how they operate. A small solenoid can generate a limited force. An approximate relationship between the required solenoid force "F", the fluid pressure "P", and the orifice area "A" for a direct acting solenoid valve is:


title: Solenoid valve

text: Where "d" is the orifice diameter. A typical solenoid force might be . An application might be a low pressure (e.g., ) gas with a small orifice diameter (e.g., for an orifice area of and approximate force of ).


title: Solenoid valve

text: If the force required is low enough, the solenoid is able to directly actuate the main valve. These are simply called Direct-Acting solenoid valves. When electricity is supplied, electrical energy is converted to mechanical energy, physically moving a barrier to either obstruct flow (if it is N.O.) or allow flow (if it is N.C.). A spring is often used to return the valve to its resting position once power is shut off. Direct-acting valves are useful for their simplicity, although they do require a large amount of power relative to other types of solenoid valves.


title: Solenoid valve

text: If fluid pressures are high and orifice diameter is large, a solenoid may not generate enough force on its own to actuate the valve. To solve this, a Pilot-Operated solenoid valve design can be used. Such a design uses the pressurized fluid itself to apply the forces required to actuate the valve, with the solenoid as a "pilot" directing the fluid (see subsection below). These valves are used in dishwashers, irrigation systems, and other applications where large pressures and/or volumes are desired. Pilot-operated solenoids tend to consume less energy than direct-action, although they will not work at all without sufficient fluid pressure and are more susceptible to getting clogged if the fluid has solid impurities.


title: Solenoid valve

text: A direct-acting solenoid valve typically operates in 5 to 10 milliseconds. Pilot-operated valves are slightly slower; depending on their size, typical values range from 15 to 150 milliseconds.


title: Solenoid valve

text: Power consumption and supply requirements of the solenoid vary with application, being primarily determined by fluid pressure and orifice diameter. For example, a popular -inch 150 psi sprinkler valve, intended for 24 VAC (50–60 Hz) residential systems, has a momentary inrush of 7.2 VA, and a holding power requirement of 4.6 VA. Comparatively, an industrial -inch 10,000 psi valve, intended for 12, 24, or 120 VAC systems in high-pressure fluid and cryogenic applications, has an inrush of 300 VA and a holding power of 22 VA. Neither valve lists a minimum pressure required to remain closed in the unpowered state.


title: Solenoid valve

text: While there are multiple design variants, the following is a detailed breakdown of a typical pilot-operated solenoid valve. They may use metal seals or rubber seals, and may also have electrical interfaces to allow for easy control.


title: Solenoid valve

text: The diagram to the right shows the design of a basic valve, controlling the flow of water in this example. The top half shows the valve in its closed state. An inlet stream of pressurized water enters at A. B is an elastic diaphragm and above it is a spring pushing it down. The diaphragm has a pinhole through its center which allows a very small amount of water to flow through. This water fills cavity C so that pressure is roughly equal on both sides of the diaphragm. However, the pressurized water in cavity C acts across a much greater area of the diaphragm than the water in inlet A. From the equation formula_2, the force from cavity C pushing downward is greater than the force from inlet A pushing upward, and the diaphragm remains closed.


title: Solenoid valve

text: Diaphragm B will stay closed as long as small drain passage D remains blocked by a pin, which is controlled by solenoid E. In a normally closed valve, supplying an electric current to the solenoid will raise the pin via magnetic force, and the water in cavity C drains out through passage D faster than the pinhole can refill it. Less water in cavity C means the pressure on that side of the diaphragm drops, proportionately dropping the force too. With the downward force of cavity C now less than the upward force of inlet A, the diaphragm is pushed upward, thus opening the valve. Water now flows freely from A to F. When the solenoid is deactivated and passage D is closed, water once again accumulates in cavity C, closing the diaphragm once the downward force exerted is great enough.


title: Solenoid valve

text: This process is the opposite for a normally open pilot-operated valve. In that case, the pin is naturally held open by a spring, passage D is open, and cavity C is never able to fill up enough, pushing open diaphragm B and allowing unobstructed flow. Supplying an electric current to the solenoid pushes the pin into a closed position, blocking passage D, allowing water to accumulate in cavity C, and ultimately closing diaphragm B.


title: Solenoid valve

text: In this way, a pilot-operated solenoid valve can be conceptualized as two valves working together: a direct-acting solenoid valve which functions as the "brain" to direct the "muscle" of a much more powerful main valve which gets actuated pneumatically or hydraulically. This is why pilot-operated valves will not work without a sufficient pressure differential between input and output, the "muscle" needs to be strong enough to push back against the diaphragm and open it. Should the pressure at the output rise above that of the input, the valve would open regardless of the state of the solenoid and pilot valve.


title: Solenoid valve

text: The core or plunger is the magnetic component that moves when the solenoid is energized. The core is coaxial with the solenoid. The core's movement will make or break the seals that control the movement of the fluid. When the coil is not energized, springs will hold the core in its normal position.


title: Solenoid valve

text: The core tube contains and guides the core. It also retains the plugnut and may seal the fluid. To optimize the movement of the core, the core tube needs to be nonmagnetic. If the core tube were magnetic, then it would offer a shunt path for the field lines. In some designs, the core tube is an enclosed metal shell produced by deep drawing. Such a design simplifies the sealing problems because the fluid cannot escape from the enclosure, but the design also increases the magnetic path resistance because the magnetic path must traverse the thickness of the core tube twice: once near the plugnut and once near the core. In some other designs, the core tube is not closed but rather an open tube that slips over one end of the plugnut. To retain the plugnut, the tube might be crimped to the plugnut. An O-ring seal between the tube and the plugnut will prevent the fluid from escaping.


title: Solenoid valve

text: The solenoid coil consists of many turns of copper wire that surround the core tube and induce the movement of the core. The coil is often encapsulated in epoxy. The coil also has an iron frame that provides a low magnetic path resistance.


title: Solenoid valve

text: The valve body must be compatible with the fluid; common materials are brass, stainless steel, aluminum, and plastic.


title: Solenoid valve

text: To simplify the sealing issues, the plugnut, core, springs, shading ring, and other components are often exposed to the fluid, so they must be compatible as well. The requirements present some special problems. The core tube needs to be non-magnetic to pass the solenoid's field through to the plugnut and the core. The plugnut and core need a material with good magnetic properties such as iron, but iron is prone to corrosion. Stainless steels can be used because they come in both magnetic and non-magnetic varieties. For example, a solenoid valve might use 304 stainless steel for the body, 305 stainless steel for the core tube, 302 stainless steel for the springs, and 430 F stainless steel (a magnetic stainless steel) for the core and plugnut.


title: Solenoid valve

text: Solenoid valves are used in fluid power pneumatic and hydraulic systems, to control cylinders, fluid power motors or larger industrial valves. Automatic irrigation sprinkler systems also use solenoid valves with an automatic controller. Domestic washing machines and dishwashers use solenoid valves to control water entry into the machine. They are also often used in paintball gun triggers to actuate the hammer valve. Solenoid valves are usually referred to simply as "solenoids."


title: Solenoid valve

text: Solenoid valves can be used for a wide array of industrial applications, including general on-off control, calibration and test stands, pilot plant control loops, process control systems, and various original equipment manufacturer applications.


title: Independent and identically distributed random variables

text: In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing.


text: In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent, identically distributed (IID) random variables”.


text: In other words, the terms "random sample" and "IID" are basically one and the same. In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.”


text: Independent and identically distributed random variables are often used as an assumption, which tends to simplify the underlying mathematics. In practical applications of statistical modeling, however, the assumption may or may not be realistic.


text: The i.i.d. assumption is also used in central limit theorem, which states that the probability distribution of the sum (or average) of i.i.d. variables with finite variance approaches a normal distribution.


text: Often the i.i.d. assumption arises in the context of sequences of random variables. Then "independent and identically distributed" implies that an element in the sequence is independent of the random variables that came before it. In this way, an i.i.d. sequence is different from a Markov sequence, where the probability distribution for the "n"th random variable is a function of the previous random variable in the sequence (for a first order Markov sequence). An i.i.d. sequence does not imply the probabilities for all elements of the sample space or event space must be the same. For example, repeated throws of loaded dice will produce a sequence that is i.i.d., despite the outcomes being biased.


text: Suppose that the random variables formula_1 and formula_2 are defined to assume values in formula_3. Let formula_4 and formula_5 be the cumulative distribution functions of formula_1 and formula_2, respectively, and denote their joint cumulative distribution function by formula_8.


text: Two random variables formula_1 and formula_2 are independent if and only if formula_14. (See further .)


text: Two random variables formula_1 and formula_2 are i.i.d. if they are independent "and" identically distributed, i.e. if and only if


text: The definition extends naturally to more than two random variables. We say that formula_17 random variables formula_18 are i.i.d. if they are independent (see further ) "and" identically distributed, i.e. if and only if


text: In probability theory, two events A, B are called independent if and only if P(A and B) = P(A)P(B). In the following P(AB) is short for P(A and B).


text: Suppose there are the two events of the experiment A, B if P(A) > 0, there is possibility P(B|A). Generally, the occurrence of A has an effect on the probability of B, which is called conditional probability, and only when the occurrence of A has no effect on the occurrence of B, there is P(B|A) = P(B).


text: Note: If P(A) > 0, P(B) > 0 then A, B are mutually independent which cannot be established with mutually incompatible at the same time, that is, independence must be compatible and mutual exclusion must be related.


text: Suppose A, B, C are three events. If P(AB) = P(A)P(B), P(BC) = P(B)P(C), P(AC) = P(A)P(C), P(ABC) = P(A)P(B)P(C) are satisfied, then the events A, B, C are independent of each other.


text: A more general definition is there are n events, A, A...,A. If the probabilities of the product events for any 2, 3, ..., n events are equal to the product of the probabilities of each event, then the events A, A, ..., A are independent of each other.


text: A sequence of outcomes of spins of a fair or unfair roulette wheel is i.i.d. One implication of this is that if the roulette ball lands on "red", for example, 20 times in a row, the next spin is no more or less likely to be "black" than on any other spin (see the Gambler's fallacy).


text: In signal processing and image processing the notion of transformation to i.i.d. implies two specifications, the "i.d."part and the "i." part:


text: (i.) the signal spectrum must be flattened, i.e. transformed by filtering (such as deconvolution) to a white noise signal (i.e. a signal where all frequencies are equally present).


text: Choose a card from a standard deck of cards containing 52 cards, then place the card back in the deck. Repeat it for 52 times. Record the number of King appears


text: Many results that were first proven under the assumption that the random variables are i.i.d. have been shown to be true even under a weaker distributional assumption.


text: The most general notion which shares the main properties of i.i.d. variables are exchangeable random variables, introduced by Bruno de Finetti. Exchangeability means that while variables may not be independent, future ones behave like past ones – formally, any value of a finite sequence is as likely as any permutation of those values – the joint probability distribution is invariant under the symmetric group.


text: This provides a useful generalization – for example, sampling without replacement is not independent, but is exchangeable.


text: In stochastic calculus, i.i.d. variables are thought of as a discrete time Lévy process: each variable gives how much one changes from one time to another.


text: One may generalize this to include continuous time Lévy processes, and many Lévy processes can be seen as limits of i.i.d. variables—for instance, the Wiener process is the limit of the Bernoulli process.


text: Machine learning uses currently acquired massive quantities of data to deliver faster, more accurate results. Therefore, we need to use historical data with overall representativeness. If the data obtained is not representative of the overall situation, then the rules will be summarized badly or wrongly.


text: Through i.i.d. hypothesis, the number of individual cases in the training sample can be greatly reduced.


text: This assumption makes maximization very easy to calculate mathematically. Observing the assumption of independent and identical distribution in mathematics simplifies the calculation of the likelihood function in optimization problems. Because of the assumption of independence, the likelihood function can be written like this


text: In order to maximize the probability of the observed event, take the log function and maximize the parameter θ. That is to say, to compute:


text: The computer is very efficient to calculate multiple additions, but it is not efficient to calculate the multiplication. This simplification is the core reason for the increase in computational efficiency. And this Log transformation is also in the process of maximizing, turning many exponential functions into linear functions.


title: Love Island (2015 TV series, series 8)

text: The eighth series of "Love Island" was broadcast from 6 June 2022 to 1 August 2022 on ITV2 with Laura Whitmore presenting the series and Iain Stirling narrating.