University of Toronto SchoolsUniversity of Toronto Schools (UTS) is an independent secondary day school affiliated with the University of Toronto in Toronto, Ontario, Canada. The school follows a specialized academic curriculum, and admission is determined by competitive examination. UTS is associated with two Nobel Prize laureates. University of Toronto Schools was founded in 1910 as a "practice school", also known as a laboratory school, for the University of Toronto's Faculty of Education.
Preadditive categoryIn mathematics, specifically in , a preadditive category is another name for an Ab-category, i.e., a that is over the , Ab. That is, an Ab-category C is a such that every hom-set Hom(A,B) in C has the structure of an abelian group, and composition of morphisms is bilinear, in the sense that composition of morphisms distributes over the group operation. In formulas: and where + is the group operation. Some authors have used the term additive category for preadditive categories, but here we follow the current trend of reserving this term for certain special preadditive categories (see below).
Justin TrudeauJustin Pierre James Trudeau (ˈtruːdoʊ,_truːˈdoʊ , ʒystɛ̃ pjɛʁ dʒɛms tʁydo; born December 25, 1971) is a Canadian politician serving as the 23rd and current prime minister of Canada since 2015 and leader of the Liberal Party since 2013. Trudeau is the second-youngest prime minister in Canadian history after Joe Clark; he is also the first to be the child of a previous holder of the post, as the eldest son of Pierre Trudeau. Trudeau was born in Ottawa and attended Collège Jean-de-Brébeuf.
Knuth's up-arrow notationIn mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc.
Inverse functionIn mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by For a function , its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.
Inverse semigroupIn group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x = xyx and y = yxy, i.e. a regular semigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries. (The convention followed in this article will be that of writing a function on the right of its argument, e.g.
Political positions of John McCainU.S. Senator John McCain, a Republican Party politician from Arizona who was a member of the U.S. Congress from 1983 until his death in office in 2018, a two-time U.S. presidential candidate, and the nominee of the Republican Party in the 2008 U.S. Presidential election, took positions on many political issues through his public comments, his presidential campaign statements, and his senatorial voting record. Online, McCain used his Senate web site and his 2008 campaign web site to describe his political positions.
Rings of JupiterThe planet Jupiter has a system of faint planetary rings. The Jovian rings were the third ring system to be discovered in the Solar System, after those of Saturn and Uranus. The main ring was discovered in 1979 by the Voyager 1 space probe and the system was more thoroughly investigated in the 1990s by the Galileo orbiter. The main ring has also been observed by the Hubble Space Telescope and from Earth for several years. Ground-based observation of the rings requires the largest available telescopes.
Generalized inverseIn mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup.
Rings of SaturnThe rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entirely of water ice, with a trace component of rocky material. There is still no consensus as to their mechanism of formation. Although theoretical models indicated that the rings were likely to have formed early in the Solar System's history, newer data from Cassini suggested they formed relatively late.
Product of ringsIn mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the . Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings.
Battle of Sept-ÎlesThe Battle of Sept-Îles was a naval action fought on the night of 22/23 October 1943 during World War II as part of the Atlantic campaign. The battle took place off the Sept-Îles near the French coast in the English Channel between a light cruiser and six destroyers of the British Royal Navy hoping to intercept, a German blockade runner, which was accompanied by German torpedo-boat destroyers flotillas of the German Kriegsmarine.
