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Roger C. Lyndon
Roger Conant Lyndon (December 18, 1917 – June 8, 1988) was an American mathematician, for many years a professor at the University of Michigan.. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. Biography Lyndon was born on December 18, 1917, in Calais, Maine, the son of a Unitarian minister. His mother died when he was two years old, after which he and his father moved several times to towns in Massachusetts and New York. He did his undergraduate studies at Harvard University, originally intending to study literature but eventually settling on mathematics, and graduated in 1939. He took a job as a banker, but soon afterwards returned to graduate school at Harvard, earning a master's degree in 1941. After a brief teaching stint at the Georgia Institute of Technology, he returned to Harvard for the third time in 1942 and while there taught navigation as part of the V-12 Navy Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyndon
{{disambig, geo ...
Lyndon may refer to: Places * Lyndon, Alberta, Canada * Lyndon, Rutland, East Midlands, England * Lyndon, Solihull, West Midlands, England United States * Lyndon, Illinois * Lyndon, Kansas * Lyndon, Kentucky * Lyndon, New York * Lyndon, Ohio * Lyndon, Pennsylvania * Lyndon, Vermont * Lyndon, Sheboygan County, Wisconsin, a town * Lyndon, Juneau County, Wisconsin, a town Other uses * Lyndon State College, a public college located in Lyndonville, Vermont People * Lyndon (name), given name and surname See also * Lyndon School (other) * Lyndon Township (other) * * Lydon (other) * Lynden (other) * Lindon (other) * Linden (other) Linden may refer to: Trees * ''Tilia'' (also known as lime and basswood Basswood), a genus ** American linden, a common name for ''Tilia americana'' ** Large-leaved linden, a common name for ''Tilia platyphyllos'' ** Little-leaf linden, a common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald G
Donald is a masculine given name derived from the Gaelic name ''Dòmhnall''.. This comes from the Proto-Celtic *''Dumno-ualos'' ("world-ruler" or "world-wielder"). The final -''d'' in ''Donald'' is partly derived from a misinterpretation of the Gaelic pronunciation by English speakers, and partly associated with the spelling of similar-sounding Germanic names, such as ''Ronald''. A short form of ''Donald'' is ''Don''. Pet forms of ''Donald'' include ''Donnie'' and ''Donny''. The feminine given name ''Donella'' is derived from ''Donald''. ''Donald'' has cognates in other Celtic languages: Modern Irish ''Dónal'' (anglicised as ''Donal'' and ''Donall'');. Scottish Gaelic ''Dòmhnall'', ''Domhnull'' and ''Dòmhnull''; Welsh '' Dyfnwal'' and Cumbric ''Dumnagual''. Although the feminine given name ''Donna'' is sometimes used as a feminine form of ''Donald'', the names are not etymologically related. Variations Kings and noblemen Domnall or Domhnall is the name of many ancie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivariant Map
In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group. That is, applying a symmetry transformation and then computing the function produces the same result as computing the function and then applying the transformation. Equivariant maps generalize the concept of invariants, functions whose value is unchanged by a symmetry transformation of their argument. The value of an equivariant map is often (imprecisely) called an invariant. In statistical inference, equivariance under statistical transformations of data is an important property of various estimation methods; see invariant estimator for details. In pure mathematics, equivariance is a central object of study in equivariant topology and its subtopics equivariant cohomology and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of '' states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that determines the new state of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav A
Gustav, Gustaf or Gustave may refer to: *Gustav (name), a male given name of Old Swedish origin Art, entertainment, and media * ''Primeval'' (film), a 2007 American horror film * ''Gustav'' (film series), a Hungarian series of animated short cartoons * Gustav (''Zoids''), a transportation mecha in the ''Zoids'' fictional universe *Gustav, a character in ''Sesamstraße'' *Monsieur Gustav H., a leading character in ''The Grand Budapest Hotel'' Weapons *Carl Gustav recoilless rifle, dubbed "the Gustav" by US soldiers *Schwerer Gustav, 800-mm German siege cannon used during World War II Other uses *Gustav (pigeon), a pigeon of the RAF pigeon service in WWII *Gustave (crocodile), a large male Nile crocodile in Burundi *Gustave, South Dakota *Hurricane Gustav (other), a name used for several tropical cyclones and storms *Gustav, a streetwear clothing brand See also *Gustav of Sweden (other) *Gustav Adolf (other) *Gustave Eiffel (other) * * *Gustavo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Group
In mathematics, the free group ''F''''S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''−1''t'', but ''s'' ≠ ''t''−1 for ''s'',''t'',''u'' ∈ ''S''). The members of ''S'' are called generators of ''F''''S'', and the number of generators is the rank of the free group. An arbitrary group ''G'' is called free if it is isomorphic to ''F''''S'' for some subset ''S'' of ''G'', that is, if there is a subset ''S'' of ''G'' such that every element of ''G'' can be written in exactly one way as a product of finitely many elements of ''S'' and their inverses (disregarding trivial variations such as ''st'' = ''suu''−1''t''). A related but different notion is a free abelian group; both notions are particular instances of a free object from universal algebra. As such, free groups are defined by their universal property. History Free ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicographic Order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied. A generalization defines an order on a Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. Motivation and definition The words in a lexicon (the set of words used in some language) have a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotient Group
A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo ''n'' can be obtained from the group of integers under addition by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class (known as a congruence class) as a single entity. It is part of the mathematical field known as group theory. For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written G\,/\,N, where G is the original group and N is the normal subgroup. (This is pronounced G\bmod N, where \mbox is short for modulo.) Much of the importance o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
