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non_inertial_reference_frame	Non Inertial Reference Frame	A non-inertial reference frame (also known as an accelerated reference frame) is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, they vary in non-inertial frames, with apparent motion depending on the acceleration.	https://en.wikipedia.org/wiki/Non-inertial_reference_frame	Non Inertial Reference Frame: A non-inertial reference frame (also known as an accelerated reference frame) is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, they vary in non-inertial frames, with apparent motion depending on the acceleration.
non_measurable_set	Non Measurable Set	In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume". The existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory. In Zermelo–Fraenkel set theory, the axiom of choice entails that non-measurable subsets of R {\displaystyle \mathbb {R} } exist.	https://en.wikipedia.org/wiki/Non-measurable_set	Non Measurable Set: In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume". The existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory. In Zermelo–Fraenkel set theory, the axiom of choice entails that non-measurable subsets of R {\displaystyle \mathbb {R} } exist.
non_integer_base_of_numeration	Non Integer Base Of Numeration	A non-integer representation uses non-integer numbers as the radix, or base, of a positional numeral system. For a non-integer radix β > 1, the value of	https://en.wikipedia.org/wiki/Non-integer_base_of_numeration	Non Integer Base Of Numeration: A non-integer representation uses non-integer numbers as the radix, or base, of a positional numeral system. For a non-integer radix β > 1, the value of
non_positive_curvature	Non Positive Curvature	In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero. The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces.	https://en.wikipedia.org/wiki/Non-positive_curvature	Non Positive Curvature: In mathematics, spaces of non-positive curvature occur in many contexts and form a generalization of hyperbolic geometry. In the category of Riemannian manifolds, one can consider the sectional curvature of the manifold and require that this curvature be everywhere less than or equal to zero. The notion of curvature extends to the category of geodesic metric spaces, where one can use comparison triangles to quantify the curvature of a space; in this context, non-positively curved spaces are known as (locally) CAT(0) spaces.
nonagon	Nonagon	In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon.	https://en.wikipedia.org/wiki/Nonagon	Nonagon: In geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon.
non_uniform_random_numbers	Non Uniform Random Numbers	Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator. Computational algorithms are then used to manipulate a single random variate, X, or often several such variates, into a new random variate Y such that these values have the required distribution. The first methods were developed for Monte-Carlo simulations in the Manhattan Project,[citation needed] published by John von Neumann in the early 1950s.	https://en.wikipedia.org/wiki/Non-uniform_random_variate_generation	Non Uniform Random Numbers: Non-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator. Computational algorithms are then used to manipulate a single random variate, X, or often several such variates, into a new random variate Y such that these values have the required distribution. The first methods were developed for Monte-Carlo simulations in the Manhattan Project,[citation needed] published by John von Neumann in the early 1950s.
noncommutative_geometry	Noncommutative Geometry	Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which x y {\displaystyle xy} does not always equal y x {\displaystyle yx} ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.	https://en.wikipedia.org/wiki/Noncommutative_geometry	Noncommutative Geometry: Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which x y {\displaystyle xy} does not always equal y x {\displaystyle yx} ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.
noncommutative_algebraic_geometry	Noncommutative Algebraic Geometry	Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients).	https://en.wikipedia.org/wiki/Noncommutative_algebraic_geometry	Noncommutative Algebraic Geometry: Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients).
noncommutative_logic	Noncommutative Logic	Noncommutative logic is an extension of linear logic that combines the commutative connectives of linear logic with the noncommutative multiplicative connectives of the Lambek calculus. Its sequent calculus relies on the structure of order varieties (a family of cyclic orders that may be viewed as a species of structure), and the correctness criterion for its proof nets is given in terms of partial permutations. It also has a denotational semantics in which formulas are interpreted by modules over some specific Hopf algebras.	https://en.wikipedia.org/wiki/Noncommutative_logic	Noncommutative Logic: Noncommutative logic is an extension of linear logic that combines the commutative connectives of linear logic with the noncommutative multiplicative connectives of the Lambek calculus. Its sequent calculus relies on the structure of order varieties (a family of cyclic orders that may be viewed as a species of structure), and the correctness criterion for its proof nets is given in terms of partial permutations. It also has a denotational semantics in which formulas are interpreted by modules over some specific Hopf algebras.
noncommutative_ring	Noncommutative Ring	In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring.	https://en.wikipedia.org/wiki/Noncommutative_ring	Noncommutative Ring: In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring.
noncrossing_partition	Noncrossing Partition	In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free probability. The number of noncrossing partitions of a set of n elements is the nth Catalan number. The number of noncrossing partitions of an n-element set with k blocks is found in the Narayana number triangle.	https://en.wikipedia.org/wiki/Noncrossing_partition	Noncrossing Partition: In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free probability. The number of noncrossing partitions of a set of n elements is the nth Catalan number. The number of noncrossing partitions of an n-element set with k blocks is found in the Narayana number triangle.
nonelementary_integral	Nonelementary Integral	In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives.	https://en.wikipedia.org/wiki/Nonelementary_integral	Nonelementary Integral: In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives.
nondeterministic_finite_automaton	Nondeterministic Finite Automaton	In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if	https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton	Nondeterministic Finite Automaton: In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if
nonequilibrium_partition_identity	Nonequilibrium Partition Identity	The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the fluctuation theorem previously known as the Kawasaki identity:	https://en.wikipedia.org/wiki/Nonequilibrium_partition_identity	Nonequilibrium Partition Identity: The nonequilibrium partition identity (NPI) is a remarkably simple and elegant consequence of the fluctuation theorem previously known as the Kawasaki identity:
nonlinear_functional_analysis	Nonlinear Functional Analysis	Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.	https://en.wikipedia.org/wiki/Nonlinear_functional_analysis	Nonlinear Functional Analysis: Nonlinear functional analysis is a branch of mathematical analysis that deals with nonlinear mappings.
nonlinear_partial_differential_equation	Nonlinear Partial Differential Equation	In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.	https://en.wikipedia.org/wiki/Partial_differential_equation	Nonlinear Partial Differential Equation: In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
nonnegative_matrix	Nonnegative Matrix	is a matrix in which all the elements are equal to or greater than zero, that is,	https://en.wikipedia.org/wiki/Nonnegative_matrix	Nonnegative Matrix: is a matrix in which all the elements are equal to or greater than zero, that is,
nonlinear_programming	Nonlinear Programming	In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.	https://en.wikipedia.org/wiki/Nonlinear_programming	Nonlinear Programming: In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
nonobtuse_mesh	Nonobtuse Mesh	In computer graphics, a nonobtuse triangle mesh is a polygon mesh composed of a set of triangles in which no angle is obtuse, i.e. greater than 90°. If each (triangle) face angle is strictly less than 90°, then the triangle mesh is said to be acute. Every polygon with n {\displaystyle n} sides has a nonobtuse triangulation with O ( n ) {\displaystyle O(n)} triangles (expressed in big O notation), allowing some triangle vertices to be added to the sides and interior of the polygon. These nonobtuse triangulations can be further refined to produce acute triangulations with O ( n ) {\displaystyle O(n)} triangles.	https://en.wikipedia.org/wiki/Nonobtuse_mesh	Nonobtuse Mesh: In computer graphics, a nonobtuse triangle mesh is a polygon mesh composed of a set of triangles in which no angle is obtuse, i.e. greater than 90°. If each (triangle) face angle is strictly less than 90°, then the triangle mesh is said to be acute. Every polygon with n {\displaystyle n} sides has a nonobtuse triangulation with O ( n ) {\displaystyle O(n)} triangles (expressed in big O notation), allowing some triangle vertices to be added to the sides and interior of the polygon. These nonobtuse triangulations can be further refined to produce acute triangulations with O ( n ) {\displaystyle O(n)} triangles.
nonstandard_analysis	Nonstandard Analysis	The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers.	https://en.wikipedia.org/wiki/Nonstandard_analysis	Nonstandard Analysis: The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using limits rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers.
normal_coordinates	Normal Coordinates	In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p. In a normal coordinate system, the Christoffel symbols of the connection vanish at the point p, thus often simplifying local calculations. In normal coordinates associated to the Levi-Civita connection of a Riemannian manifold, one can additionally arrange that the metric tensor is the Kronecker delta at the point p, and that the first partial derivatives of the metric at p vanish.	https://en.wikipedia.org/wiki/Normal_coordinates	Normal Coordinates: In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p. In a normal coordinate system, the Christoffel symbols of the connection vanish at the point p, thus often simplifying local calculations. In normal coordinates associated to the Levi-Civita connection of a Riemannian manifold, one can additionally arrange that the metric tensor is the Kronecker delta at the point p, and that the first partial derivatives of the metric at p vanish.
norm_mathematics	Norm Mathematics	In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and zero is only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself.	https://en.wikipedia.org/wiki/Norm_(mathematics)	Norm Mathematics: In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and zero is only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm, or, sometimes, the magnitude or length of the vector. This norm can be defined as the square root of the inner product of a vector with itself.
normal_extension	Normal Extension	In abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over L. This is one of the conditions for an algebraic extension to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. For finite extensions, a normal extension is identical to a splitting field.	https://en.wikipedia.org/wiki/Normal_extension	Normal Extension: In abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K that has a root in L splits into linear factors over L. This is one of the conditions for an algebraic extension to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. For finite extensions, a normal extension is identical to a splitting field.
normal_family	Normal Family	A Normal Family (Korean: 보통의 가족) is a 2023 South Korean drama film directed by Hur Jin-ho and written by Park Eun-kyo and Park Joon-seok, based on the 2009 novel The Dinner by Herman Koch. It is the fourth film adaptation of the novel, following the 2013 Dutch film Het Diner, the 2014 Italian film I nostri ragazzi, and the 2017 American film The Dinner. The film stars Sul Kyung-gu, Jang Dong-gun, Kim Hee-ae, and Claudia Kim. It centres on two wealthy families who meet for dinner to discuss and decide how to handle a violent crime committed by their children.	https://en.wikipedia.org/wiki/A_Normal_Family	Normal Family: A Normal Family (Korean: 보통의 가족) is a 2023 South Korean drama film directed by Hur Jin-ho and written by Park Eun-kyo and Park Joon-seok, based on the 2009 novel The Dinner by Herman Koch. It is the fourth film adaptation of the novel, following the 2013 Dutch film Het Diner, the 2014 Italian film I nostri ragazzi, and the 2017 American film The Dinner. The film stars Sul Kyung-gu, Jang Dong-gun, Kim Hee-ae, and Claudia Kim. It centres on two wealthy families who meet for dinner to discuss and decide how to handle a violent crime committed by their children.
normal_geometry	Normal Geometry	In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point.	https://en.wikipedia.org/wiki/Normal_(geometry)	Normal Geometry: In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point.
normal_matrix	Normal Matrix	In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*:	https://en.wikipedia.org/wiki/Normal_matrix	Normal Matrix: In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*:
normal_distribution	Normal Distribution	I ( μ , σ ) = ( 1 / σ 2 0 0 2 / σ 2 ) {\displaystyle {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}	https://en.wikipedia.org/wiki/Normal_distribution	Normal Distribution: I ( μ , σ ) = ( 1 / σ 2 0 0 2 / σ 2 ) {\displaystyle {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}
normal_mode	Normal Mode	A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.	https://en.wikipedia.org/wiki/Normal_mode	Normal Mode: A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.
normal_number	Normal Number	In mathematics, a real number is said to be simply normal in an integer base b[Note 1] if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b−n.	https://en.wikipedia.org/wiki/Normal_number	Normal Number: In mathematics, a real number is said to be simply normal in an integer base b[Note 1] if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b−n.
normal_operator	Normal Operator	In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon H\rightarrow H} that commutes with its Hermitian adjoint N ∗ {\displaystyle N^{\ast }} , that is: N ∗ N = N N ∗ {\displaystyle N^{\ast }N=NN^{\ast }} .	https://en.wikipedia.org/wiki/Normal_operator	Normal Operator: In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon H\rightarrow H} that commutes with its Hermitian adjoint N ∗ {\displaystyle N^{\ast }} , that is: N ∗ N = N N ∗ {\displaystyle N^{\ast }N=NN^{\ast }} .
normal_p_complement	Normal P Complement	In group theory, a branch of mathematics, a normal p-complement of a finite group for a prime p is a normal subgroup of order coprime to p and index a power of p. In other words the group is a semidirect product of the normal p-complement and any Sylow p-subgroup. A group is called p-nilpotent if it has a normal p-complement.	https://en.wikipedia.org/wiki/Normal_p-complement	Normal P Complement: In group theory, a branch of mathematics, a normal p-complement of a finite group for a prime p is a normal subgroup of order coprime to p and index a power of p. In other words the group is a semidirect product of the normal p-complement and any Sylow p-subgroup. A group is called p-nilpotent if it has a normal p-complement.
normal_plane_geometry	Normal Plane Geometry	In geometry, a normal plane is any plane containing the normal vector of a surface at a particular point.	https://en.wikipedia.org/wiki/Normal_plane_(geometry)	Normal Plane Geometry: In geometry, a normal plane is any plane containing the normal vector of a surface at a particular point.
normal_space	Normal Space	In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A normal Hausdorff space is called a T4 space. Strengthenings of these concepts are detailed in the article below and include completely normal spaces and perfectly normal spaces, and their Hausdorff variants: T5 spaces and T6 spaces. All these conditions are examples of separation axioms.	https://en.wikipedia.org/wiki/Normal_space	Normal Space: In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A normal Hausdorff space is called a T4 space. Strengthenings of these concepts are detailed in the article below and include completely normal spaces and perfectly normal spaces, and their Hausdorff variants: T5 spaces and T6 spaces. All these conditions are examples of separation axioms.
normal_surface	Normal Surface	In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron in several components called normal disks. Each normal disk is either a triangle which cuts off a vertex of the tetrahedron, or a quadrilateral which separates pairs of vertices. In a given tetrahedron there cannot be two quadrilaterals separating different pairs of vertices, since such quadrilaterals would intersect in a line, causing the surface to be self-intersecting.	https://en.wikipedia.org/wiki/Normal_surface	Normal Surface: In mathematics, a normal surface is a surface inside a triangulated 3-manifold that intersects each tetrahedron in several components called normal disks. Each normal disk is either a triangle which cuts off a vertex of the tetrahedron, or a quadrilateral which separates pairs of vertices. In a given tetrahedron there cannot be two quadrilaterals separating different pairs of vertices, since such quadrilaterals would intersect in a line, causing the surface to be self-intersecting.
normal_subgroup	Normal Subgroup	In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and only if g n g − 1 ∈ N {\displaystyle gng^{-1}\in N} for all g ∈ G {\displaystyle g\in G} and n ∈ N . {\displaystyle n\in N.} The usual notation for this relation is N ◃ G . {\displaystyle N\triangleleft G.}	https://en.wikipedia.org/wiki/Normal_subgroup	Normal Subgroup: In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and only if g n g − 1 ∈ N {\displaystyle gng^{-1}\in N} for all g ∈ G {\displaystyle g\in G} and n ∈ N . {\displaystyle n\in N.} The usual notation for this relation is N ◃ G . {\displaystyle N\triangleleft G.}
normalization_statistics	Normalization Statistics	In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment.	https://en.wikipedia.org/wiki/Normalization_(statistics)	Normalization Statistics: In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment.
normed_algebra	Normed Algebra	In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm:	https://en.wikipedia.org/wiki/Normed_algebra	Normed Algebra: In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm:
notation_for_differentiation	Notation For Differentiation	In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent variable have been proposed by various mathematicians, including Leibniz, Newton, Lagrange, and Arbogast. The usefulness of each notation depends on the context in which it is used, and it is sometimes advantageous to use more than one notation in a given context. For more specialized settings—such as partial derivatives in multivariable calculus, tensor analysis, or vector calculus—other notations, such as subscript notation or the ∇ operator are common. The most common notations for differentiation (and its opposite operation, antidifferentiation or indefinite integration) are listed below.	https://en.wikipedia.org/wiki/Notation_for_differentiation	Notation For Differentiation: In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent variable have been proposed by various mathematicians, including Leibniz, Newton, Lagrange, and Arbogast. The usefulness of each notation depends on the context in which it is used, and it is sometimes advantageous to use more than one notation in a given context. For more specialized settings—such as partial derivatives in multivariable calculus, tensor analysis, or vector calculus—other notations, such as subscript notation or the ∇ operator are common. The most common notations for differentiation (and its opposite operation, antidifferentiation or indefinite integration) are listed below.
normed_vector_space	Normed Vector Space	In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V {\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R {\displaystyle \mathbb {R} } or to C {\displaystyle \mathbb {C} } , then a norm on V {\displaystyle V} is a map V → R {\displaystyle V\to \mathbb {R} } , typically denoted by ‖ ⋅ ‖ {\displaystyle \lVert \cdot \rVert } , satisfying the following four axioms:	https://en.wikipedia.org/wiki/Normed_vector_space	Normed Vector Space: In mathematics, a normed vector space or normed space is a vector space, typically over the real or complex numbers, on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If V {\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R {\displaystyle \mathbb {R} } or to C {\displaystyle \mathbb {C} } , then a norm on V {\displaystyle V} is a map V → R {\displaystyle V\to \mathbb {R} } , typically denoted by ‖ ⋅ ‖ {\displaystyle \lVert \cdot \rVert } , satisfying the following four axioms:
nowhere_dense_set	Nowhere Dense Set	In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. For example, the integers are nowhere dense among the reals, whereas the interval (0, 1) is not nowhere dense.	https://en.wikipedia.org/wiki/Nowhere_dense_set	Nowhere Dense Set: In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. For example, the integers are nowhere dense among the reals, whereas the interval (0, 1) is not nowhere dense.