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In mathematics, a generalized mean, also known as power mean or Hölder mean ( named after Otto Hölder ), is an abstraction of the Pythagorean means including arithmetic, geometric, and harmonic means.
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mathematics and generalized
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y ( x ) of Bessel's differential equation:
The concept of prime number is so important that it has been generalized in different ways in various branches of mathematics.
The mathematics related to this generalized problem becomes even more interesting when one considers the average number of moves in a shortest sequence of moves between two initial and final disk configurations that are chosen at random.
In mathematics, a pseudometric space is a generalized metric space in which the distance between two distinct points can be zero.
He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis ( GRH ).
In mathematics, a generalized permutation matrix ( or monomial matrix ) is a matrix with the same nonzero pattern as a permutation matrix, i. e. there is exactly one nonzero entry in each row and each column.
Since then, the concept has been generalized, and the connections with quadratic number fields, the modular group, and other areas of mathematics have been further elucidated.
In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using Lebesgue integration and absolute continuity.
However, the concept of coherent states has been considerably generalized, to the extent that it has become a major topic in mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing ( see Coherent states in mathematical physics ).
Noncommutative geometry ( NCG ) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces which are locally presented by noncommutative algebras of functions ( possibly in some generalized sense ).
One of the most important aspects of functions of bounded variation is that they form an algebra of discontinuous functions whose first derivative exists almost everywhere: due to this fact, they can and frequently are used to define generalized solutions of nonlinear problems involving functionals, ordinary and partial differential equations in mathematics, physics and engineering.
In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.
In mathematics, the concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre ; for example, taking the centre as origin, they are points with related vectors v and − v.
In mathematics, a generalized flag variety ( or simply flag variety ) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold.
In mathematics, the generalized Gauss – Bonnet theorem ( also called Chern – Gauss – Bonnet theorem ) presents the Euler characteristic of a closed even-dimensional Riemannian manifold as an integral of a certain polynomial derived from its curvature.
However, in mathematics Newton's laws of motion can be generalized to multidimensional and curved spaces.
In mathematics, the generalized taxicab number Taxicab ( k, j, n ) is the smallest number which can be expressed as the sum of j kth positive powers in n different ways.
In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.
* Brown – Peterson cohomology, a generalized cohomology theory in mathematics
In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds.
In algebraic topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory.
* Partition function ( mathematics ), a generalized review of canonical ensemble concepts.
mathematics and mean
But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.
In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.
The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.
In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.
In mathematics, the arithmetic – geometric mean ( AGM ) of two positive real numbers and is defined as follows:
The geometric mean, in mathematics, is a type of mean or average, which indicates the central tendency or typical value of a set of numbers.
In mathematics, the harmonic mean ( sometimes called the subcontrary mean ) is one of several kinds of average.
* Lambda can mean the empty set in mathematics, though other symbols are more commonly used, such as.
( The Greek letter delta " Δ ", is commonly used in mathematics to mean " difference " or " change ".
The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.
Thus, formalism need not mean that mathematics is nothing more than a meaningless symbolic game.
In mathematics, the root mean square ( abbreviated RMS or rms ), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity.
This approach departs from the classical logic used in conventional mathematics by denying the general applicability of the law of excluded middle — i. e., not ( a ≠ b ) does not have to mean a = b. A nilsquare or nilpotent infinitesimal can then be defined.
The term theory is used informally within mathematics to mean a self-consistent body of definitions, axioms, theorems, examples, and so on.
* Deviation ( statistics ), the difference between the value of an observation and the mean of the population in mathematics and statistics
In mathematics, the term primitive element can mean:
In mathematics, by sigma function one can mean one of the following:
mathematics and also
Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.
The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.
Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.
It is also commonly used in mathematics in algebraic solutions representing quantities such as angles.
The term may be also used loosely or metaphorically to denote highly skilled people in any non -" art " activities, as well — law, medicine, mechanics, or mathematics, for example.
He also applied mathematics in generalizing physical laws from these experimental results.
Despite being quite religious, he was also interested in mathematics and science, and sometimes is claimed to have contradicted the teachings of the Church in favour of scientific theories.
He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.
His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.
He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.
In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.
It can also be used in topics as diverse as mathematics, gastronomy, fashion and website design.
In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
He won a scholarship to the University and majored in mathematics, and also studied astronomy, physics and chemistry.
His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".
In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.
Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.
It can also be used to denote abstract vectors and linear functionals in mathematics.
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
The term can also be applied to some degree to functions in mathematics, referring to the anatomy of curves.
Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics.
It has also given rise to a new theory of the philosophy of mathematics, and many theories of artificial intelligence, persuasion and coercion.
Most undergraduate programs emphasize mathematics and physics as well as chemistry, partly because chemistry is also known as " the central science ", thus chemists ought to have a well-rounded knowledge about science.
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.
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