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Canonical Form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and which allows it to be identified in a unique way. The distinction between "canonical" and "normal" forms varies from subfield to subfield. In most fields, a canonical form specifies a ''unique'' representation for every object, while a normal form simply specifies its form, without the requirement of uniqueness. The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero. More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: *Jordan normal form is a canonical form for matrix similarity. *The row echelon form is a canonical form, when one considers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anagram Canonical Svg
An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. For example, the word ''anagram'' itself can be rearranged into ''nag a ram'', also the word ''binary'' into ''brainy'' and the word ''adobe'' into ''abode''. The original word or phrase is known as the ''subject'' of the anagram. Any word or phrase that exactly reproduces the letters in another order is an anagram. Someone who creates anagrams may be called an "anagrammatist", and the goal of a serious or skilled anagrammatist is to produce anagrams that reflect or comment on their subject. Examples Anagrams may be created as a commentary on the subject. They may be a parody, a criticism or satire. For example: * "New York Times" = " monkeys write" * "Church of Scientology" = "rich-chosen goofy cult" * "McDonald's restaurants" = " Uncle Sam's standard rot" * "coronavirus" = "carnivorous" * "She Sells Sanctuary" = "Santa; shy, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idempotence
Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property of referential transparency). The term was introduced by American mathematician Benjamin Peirce in 1870 in the context of elements of algebras that remain invariant when raised to a positive integer power, and literally means "(the quality of having) the same power", from + '' potence'' (same + power). Definition An element x of a set S equipped with a binary operator \cdot is said to be ''idempotent'' under \cdot if : . The ''binary operation'' \cdot is said to be ''idempotent'' if : . Examples * In the monoid (\mathbb, \times) of the natural numbers with multiplication, on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Julius Richelot
Friedrich Julius Richelot (6 November 1808 – 31 March 1875) was a German mathematician, born in Königsberg. He was a student of Carl Gustav Jacob Jacobi. He was promoted in 1831 at the Philosophical Faculty of the University of Königsberg with a dissertation on the division of the circle into 257 equal parts (see references) and was a professor there. Richelot authored numerous publications in German, French and Latin, among them — with his 1832 dissertation — the first known guide to the Euclidean construction of the regular 257-gon with compass and straightedge. In 1825 he joined the Corps Masovia.Kösener Korps-Listen 1910, 141, 8 He died in Königsberg in 1875. See also *Timeline of abelian varieties This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves. Early history * c. 1000 Al-Karaji writes on congruent numbers Seventeenth century * Fermat studies descent for elliptic curves * 1643 Ferm ... References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gotthold Eisenstein
Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician. He specialized in number theory and mathematical analysis, analysis, and proved several results that eluded even Carl Friedrich Gauss, Gauss. Like Évariste Galois, Galois and Niels Henrik Abel, Abel before him, Eisenstein died before the age of 30. He was born and died in Berlin, Kingdom of Prussia, Prussia. Early life His parents, Johann Konstantin Eisenstein and Helene Pollack, were of Jewish descent and converted to Protestantism prior to his birth. From an early age, he demonstrated talent in mathematics and music. As a young child he learned to play piano, and he continued to play and compose for piano throughout his life. He suffered various health problems throughout his life, including meningitis as an infant, a disease that took the lives of all five of his brothers and sisters. In 1837, at the age of 14, he enrolled at Friedrich Wilhelm Gymnasium (school), Gymnasium, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Logan (statesman)
James Logan (October 20, 1674October 31, 1751) was a Scots-Irish colonial American statesman, administrator, and scholar who served as the fourteenth mayor of Philadelphia and held a number of other public offices. Logan was born in the town of Lurgan in County Armagh, Ireland to Ulster Scots Quakers. He served as colonial secretary to William Penn. He was a founding trustee of the College of Philadelphia, the predecessor of the University of Pennsylvania. Life James Logan was born at Lurgan, County Armagh, on October 20, 1674. His parents were Patrick Logan (1640–1700) and Isabella, Lady Hume (1647–1722), who married in early 1671, in Midlothian, Scotland. His father had a Master of Arts degree from the University of Edinburgh, and originally was an Anglican clergyman before converting to Quakerism, or the Society of Friends. Although apprenticed to a Dublin linen draper, he appears to have received a good classical and mathematical education, and to have acquired a k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archetypal
The concept of an archetype (; ) appears in areas relating to behavior, historical psychology, and literary analysis. An archetype can be any of the following: # a statement, pattern of behavior, prototype, "first" form, or a main model that other statements, patterns of behavior, and objects copy, emulate, or "merge" into. Informal synonyms frequently used for this definition include "standard example", "basic example", and the longer-form "archetypal example"; mathematical archetypes often appear as "canonical examples". # the Platonic concept of ''pure form'', believed to embody the fundamental characteristics of a thing. # a collectively-inherited unconscious idea, a pattern of thought, image, etc., that is universally present, in individual psyches, as in Jungian psychology # a constantly-recurring symbol or motif in literature, painting, or mythology. This definition refers to the recurrence of characters or ideas sharing similar traits throughout various, seemingly un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard
Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object that bears a defined relationship to a unit of measure used for calibration of measuring devices * Standard (timber unit), an obsolete measure of timber used in trade * Breed standard (also called bench standard), in animal fancy and animal husbandry * BioCompute Standard, a standard for next generation sequencing * ''De facto'' standard, product or system with market dominance * Gold standard, a monetary system based on gold; also used metaphorically for the best of several options, against which the others are measured * Internet Standard, a specification ratified as an open standard by the Internet Engineering Task Force * Learning standards, standards applied to education content * Standard displacement, a naval term describing the wei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norm
Naturally occurring radioactive materials (NORM) and technologically enhanced naturally occurring radioactive materials (TENORM) consist of materials, usually industrial wastes or by-products enriched with radioactive elements found in the environment, such as uranium, thorium and potassium and any of their decay products, such as radium and radon. Produced water discharges and spills are a good example of entering NORMs into the surrounding environment. Natural radioactive elements are present in very low concentrations in Earth's crust, and are brought to the surface through human activities such as oil and gas exploration or mining, and through natural processes like leakage of radon gas to the atmosphere or through dissolution in ground water. Another example of TENORM is coal ash produced from coal burning in power plants. If radioactivity is much higher than background level, handling TENORM may cause problems in many industries and transportation. NORM in oil and gas exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic period (), and the Classical period (). Ancient Greek was the language of Homer and of fifth-century Athenian historians, playwrights, and philosophers. It has contributed many words to English vocabulary and has been a standard subject of study in educational institutions of the Western world since the Renaissance. This article primarily contains information about the Epic and Classical periods of the language. From the Hellenistic period (), Ancient Greek was followed by Koine Greek, which is regarded as a separate historical stage, although its earliest form closely resembles Attic Greek and its latest form approaches Medieval Greek. There were several regional dialects of Ancient Greek, of which Attic Greek developed into Koine. Dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canonical
The adjective canonical is applied in many contexts to mean "according to the canon" the standard, rule or primary source that is accepted as authoritative for the body of knowledge or literature in that context. In mathematics, "canonical example" is often used to mean "archetype". Science and technology * Canonical form, a natural unique representation of an object, or a preferred notation for some object Mathematics * * Canonical coordinates, sets of coordinates that can be used to describe a physical system at any given point in time * Canonical map, a morphism that is uniquely defined by its main property * Canonical polyhedron, a polyhedron whose edges are all tangent to a common sphere, whose center is the average of its vertices * Canonical ring, a graded ring associated to an algebraic variety * Canonical injection, in set theory * Canonical representative, in set theory a standard member of each element of a set partition Differential geometry * Canonical one-form, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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