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Elementary Special Functions
Elementary may refer to: Arts, entertainment, and media Music * ''Elementary'' (Cindy Morgan album), 2001 * ''Elementary'' (The End album), 2007 * ''Elementary'', a Melvin "Wah-Wah Watson" Ragin album, 1977 Other uses in arts, entertainment, and media * ''Elementary'' (TV series), a 2012 American drama television series * "Elementary, my dear Watson", a catchphrase of Sherlock Holmes Education * Elementary and Secondary Education Act, US * Elementary education, or primary education, the first years of formal, structured education * Elementary Education Act 1870, England and Wales * Elementary school, a school providing elementary or primary education Science and technology * ELEMENTARY, a class of objects in computational complexity theory * Elementary, a widget set based on the Enlightenment Foundation Libraries * Elementary abelian group, an abelian group in which every nontrivial element is of prime order * Elementary algebra * Elementary arithmetic * Elementary c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary (Cindy Morgan Album)
''Elementary'' is the seventh album from contemporary Christian music singer Cindy Morgan (singer), Cindy Morgan. Track listing All songs written by Cindy Morgan, except where noted. # "The World Needs Your Love" – 3:23 # "Good Thing" (Alex Alzamora, Morgan) – 2:51 # "Elementary" – 2:48 # "Love Can" – 4:22 # "New World" (Morgan, Drew and Shannon, Andrew Ramsey) – 3:31 # "Believe" (Brent Bourgeois, Morgan) – 3:25 # "End of the World" (Morgan, Pat McDonald (musician), Pat McDonald, Tony Nicholas) – 3:12 # "Walk in the Rain" (Bobby Bluebell, Morgan) – 2:36 # "Grape Soda" (spoken intro) – 0:19 # "Sunshine" – 3:43 # "Happy" (Brian Lenthall, Morgan) – 3:06 # "Love is Waiting" – 4:04 # "In These Rooms" – 5:55 # "I Love You" – 3:43 *Track information and credits taken from the album's liner notes. Personnel * Cindy Morgan – lead vocals, backing vocals, acoustic piano, electric piano * Brent Bourgeois – keyboards, acoustic piano, backing vocals * Jeff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Abelian Group
In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same order. This common order must be a prime number, and the elementary abelian groups in which the common order is ''p'' are a particular kind of ''p''-group. A group for which ''p'' = 2 (that is, an elementary abelian 2-group) is sometimes called a Boolean group. Every elementary abelian ''p''-group is a vector space over the prime field with ''p'' elements, and conversely every such vector space is an elementary abelian group. By the classification of finitely generated abelian groups, or by the fact that every vector space has a basis, every finite elementary abelian group must be of the form (Z/''p''Z)''n'' for ''n'' a non-negative integer (sometimes called the group's ''rank''). Here, Z/''p''Z denotes the cyclic group of order ''p'' (or equivalently the integers mod ''p''), and the superscript notation means the ''n''-f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Function
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or ''x''1/''n''). All elementary functions are continuous on their domains. Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s. Many textbooks and dictionaries do not give a precise definition of the elementary functions, and mathematicians differ on it. Examples Basic examples Elementary functions of a single variable include: * Constant functions: 2,\ \pi,\ e, etc. * Rational powers of : x,\ x^2,\ \sqrt\ (x^\frac),\ x^\frac, etc. * Exponential functions: e^x, \ a^x * Logarithm In mathematics, the logarithm o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Proof
In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime number theorem, could only be proved by invoking "higher" mathematical theorems or techniques. However, as time progresses, many of these results have also been subsequently reproven using only elementary techniques. While there is generally no consensus as to what counts as elementary, the term is nevertheless a common part of the mathematical jargon. An elementary proof is not necessarily simple, in the sense of being easy to understand or trivial. In fact, some elementary proofs can be quite complicated — and this is especially true when a statement of notable importance is involved.. Prime number theorem The distinction between elementary and non-elementary proofs has been considered especially important ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number: electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles. Ordinary matter is composed of atoms, themselves once thought to be indivisible elementary particles. The name ''atom'' comes from the Ancient Greek word ''ἄτομος'' ( atomos) which means ''indivisible'' or ''uncuttable''. Despite the theories about atoms that had existed for thousands of years, the factual existence of ato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary OS
Elementary OS (stylized as elementary OS) is a Linux distribution based on Ubuntu LTS. It promotes itself as a "thoughtful, capable, and ethical" replacement to macOS and Microsoft Windows, Windows and has a pay what you want, pay-what-you-want model. The operating system, the desktop environment (called #Pantheon desktop environment, Pantheon), and accompanying applications are developed and maintained by elementary, Inc. Design philosophy The human interface guidelines of the elementary OS project focus on immediate usability with a gentle learning curve, rather than full-fledged customization. The three core rules the developers set for themselves were "concision", "accessible configuration" and "minimal documentation". Since its inception, elementary OS has received praise and criticism for its design. ''Wired'' claimed that it closely resembled macOS, visually and in user experience. The elementary developers say that while it may look like macOS at first, they have a lot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Definition
In mathematical logic, an elementary definition is a definition that can be made using only finitary first-order logic, and in particular without reference to set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ... or using extensions such as plural quantification. Elementary definitions are of particular interest because they admit a complete proof apparatus while still being expressive enough to support most everyday mathematics (via the addition of elementarily-expressible axioms such as Zermelo–Fraenkel set theory (ZFC)). Saying that a definition is elementary is a weaker condition than saying it is algebraic. Related * Elementary theory References * Mac Lane and Moerdijk, ''Sheaves in Geometry and Logic: A First Introduction to Topos Theory,'' page 4. {{mathlogic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Charge
The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . In SI units, the coulomb is defined such that the value of the elementary charge is exactly or 160.2176634 zeptocoulombs (zC). Since the 2019 revision of the SI, the seven SI base units are defined in terms of seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from blackb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Arithmetic
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and Division (mathematics), division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools. Numeral systems In numeral system, numeral systems, Numerical digit, digits are characters used to represent the value of numbers. An example of a numeral system is the predominantly used Hindu–Arabic numeral system, Indo-Arabic numeral system (0 to 9), which uses a Base 10, decimal positional notation. Other numeral systems include the Kaktovik numerals, Kaktovik system (often used in the Eskimo-Aleut languages of Alaska, Canada, and Greenland), and is a vigesimal positional notation system. Regardless of the numeral system used, the results of arithmetic operations are unaffected. Successor function and ordering In elementary arithmetic, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Algebra
Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variable (mathematics), variables (quantities without fixed values). This use of variables entails use of algebraic notation and an understanding of the general rules of the Operation (mathematics), operations introduced in arithmetic: addition, subtraction, multiplication, division, etc. Unlike abstract algebra, elementary algebra is not concerned with algebraic structures outside the realm of real number, real and complex numbers. It is typically taught to secondary school students and at introductory college level in the United States, and builds on their understanding of arithmetic. The use of variables to denote quantities allows general relationships between quantities to be formally and concisely expressed, and thus enables solving a broader scope of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
