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In mathematics, a generalized map is a topological model which allows one to represent and to handle subdivided objects. This model was defined starting
Generalized_map
Combinatorial representation of a graph on an orientable surface
n-dimensional generalized maps". Computer-Aided Design. 23 (1): 59–82. doi:10.1016/0010-4485(91)90082-8. Lienhardt, P. (1994). "N-dimensional generalized combinatorial
Combinatorial_map
Form of abstraction
the map. In this way, every map has, to some extent, been generalized to match the criteria of display. This includes small cartographic scale maps, which
Generalization
Algebraic element satisfying some of the criteria of an inverse
}A=A.} A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse.
Generalized_inverse
Attractor Tutorial A new chaotic system and beyond: The generalized Lorenz-like system Gingerbreadman map Mira Fractals Half-inverted tearing Halvorsen: A tribute
List_of_chaotic_maps
Reduction of information complexity on maps
between the map's purpose and the precise detail of the subject being mapped. Well generalized maps are those that emphasize the most important map elements
Cartographic_generalization
Hao, Xiaoguang; Xue, Huaiping. "Generalized Equip-Difference Parallel Polyconical Projection Method for the Global Map" (PDF). Archived (PDF) from the
List_of_map_projections
Mathematical function that preserves angles
conformal mappings to a few types. The notion of conformality generalizes in a natural way to maps between Riemannian or semi-Riemannian manifolds. If U {\displaystyle
Conformal_map
Operation on mathematical functions
can be defined as gm. Under additional restrictions, this idea can be generalized so that the iteration count becomes a continuous parameter; in this case
Function_composition
Class of statistical models
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing
Generalized_linear_model
2009 video game
skip sections of the Wuhu Loop and Maka Wuhu maps, which Nintendo fixed a few months later. The Wuhu Town map was also included in Mario Kart 8 Deluxe. Wuhu
Wii_Sports_Resort
Vector satisfying some of the criteria of an eigenvector
linearly independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using generalized eigenvectors, a set
Generalized_eigenvector
Thematic map visualizing linear flow
between them (usually highly generalized), and the volume of flow. The most common example, dating back to Minard, is a map showing shipping between a set
Flow_map
Differential geometry topic
consistent with the definition above. Finally, the notion of Gauss map can be generalized to an oriented submanifold X of dimension k in an oriented ambient
Gauss_map
Tool in symplectic geometry
used to construct conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential
Momentum_map
Planar maps require at most four colors
can in fact be colored with three colors. This trick can be generalized: there are many maps where if the colors of some regions are selected beforehand
Four_color_theorem
Multilinear map that is 0 whenever arguments are linearly dependent
specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example
Alternating_multilinear_map
Gives a homomorphism from homotopy groups to homology groups
with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz, and generalizes earlier results of Henri
Hurewicz_theorem
Batholith in Idaho and Montana, United States
"Geologic and Structure Maps of the Wallace 1(degree) x 2 (degree) Quadrangle, Montana and Idaho". U.S. Geological Survey. Map I-1509-A: sheet 2 of 2.
Idaho_Batholith
Origins and events of data
Model". Robert Ikeda, Hyunjung Park and Jennifer Widom. Provenance for generalized map and reduce workflows. In Proc. of CIDR, January 2011. Y. Cui and J
Data_lineage
N-th root of the arithmetic mean of the given numbers raised to the power n
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include
Generalized_mean
In algebraic geometry a generalized Jacobian is a commutative algebraic group associated to a curve with a divisor, generalizing the Jacobian variety of
Generalized_Jacobian
Type of map projection
versions of the Dymaxion map can be generalized to other equilateral triangular faces, and even to certain quadrilaterals. Polyhedral map projections are useful
Polyhedral_map_projection
Doubling map on the unit interval
transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)
Dyadic_transformation
Function of two vectors linear in each argument
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each
Bilinear_map
Construction for adding objects to a Hilbert space
space theory. This was supplied by the apparatus of distributions, and a generalized eigenfunction theory was developed in the years after 1950. A rigged
Rigged_Hilbert_space
Generalization of open map in topology
of mathematics, a quasi-open map (also called quasi-interior map) is a function that generalizes the notion of open map. A function f : X → Y {\displaystyle
Quasi-open_map
1990 video game
small area. Both space and planetary exploration employ relatively generalized maps to simplify the program and eliminate minor details. Space combat uses
MegaTraveller 1: The Zhodani Conspiracy
MegaTraveller_1:_The_Zhodani_Conspiracy
Mathematical concept
functionals, covectors). Slack variables are dual to generalized barycentric coordinates, and, dually to generalized barycentric coordinates (which are not unique
Slack_variable
Musical keyboards with regular arrangements of keys
A generalized keyboard is a musical keyboard, a type of isomorphic keyboard, with regular, tile-like arrangements usually with rectangular or hexagonal
Generalized_keyboard
Concept in topology
the degree of a map plays an important role in topology and geometry. In physics, the degree of a continuous map (for instance a map from space to some
Degree of a continuous mapping
Degree_of_a_continuous_mapping
quasisymmetric homeomorphism between metric spaces is a map that generalizes bi-Lipschitz maps. While bi-Lipschitz maps shrink or expand the diameter of a set by no
Quasisymmetric_map
Quantum analog of Bayes' theorem
Petz map has been generalized in various ways in the field of quantum information theory. A crucial property of the Petz recovery map is its ability to
Petz_recovery_map
Wreath product of cyclic group m and symmetrical group n
In mathematics, the generalized symmetric group is the wreath product S ( m , n ) := C m ≀ S n {\displaystyle S(m,n):=C_{m}\wr S_{n}} of the cyclic group
Generalized_symmetric_group
Mapping equal to its square under mapping composition
through P. See Affine space § Projection for an accurate definition, generalized to any dimension.[citation needed] The concept of projection in mathematics
Projection_(mathematics)
Algebraic structure used in topology
this gives the notion of a generalized homology theory or a generalized cohomology theory, defined below. There are generalized cohomology theories such
Cohomology
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which
Linear_map
Field of mathematics and science based on non-linear systems and initial conditions
The findings of attractor coexistence, obtained from classical and generalized Lorenz models, suggested a revised view that "the entirety of weather
Chaos_theory
Property of a differential manifold that includes complex structures
powers of the cotangent bundle. Generalized geometry unites these two fields by treating sections of the generalized tangent bundle, which is the direct
Generalized_complex_structure
Computational quantum mechanical modelling method to investigate electronic structure
states in the absence of a magnetic field, although they have since been generalized to encompass these. The first HK theorem demonstrates that the ground-state
Density_functional_theory
Software tool for 3D geologic modelling
and geometric characterization of fault networks using 3-dimensional generalized maps. Mathematical Geology, 28, 625–656. (Best paper award in Mathematical
GeoModeller
Markup language
The Standard Generalized Markup Language (SGML; ISO 8879:1986) is a standard for defining generalized markup languages for documents. ISO 8879 Annex A
Standard Generalized Markup Language
Standard_Generalized_Markup_Language
Theorem in topology
by Johansson (1938) proved it using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem. Papakyriakopoulos
Dehn's_lemma
Theorem
result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced
Schwartz_kernel_theorem
Order-preserving mathematical function
the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus, a function
Monotonic_function
Bakken Formation. Outline of the Western Canadian Sedimentary Basin Generalized map showing the location of the Montney Formation. Duvernay depositional
Fracking_in_Canada
Press. ISBN 978-0-521-58519-4. Media related to Generalized suffix tree at Wikimedia Commons A C implementation of Generalized Suffix Tree for two strings
Generalized_suffix_tree
Structure-preserving map between two algebraic structures of the same type
of those can be defined in a way that may be generalized to any class of morphisms. A homomorphism is a map between two algebraic structures of the same
Homomorphism
Most widely known generalized inverse of a matrix
= A + {\textstyle A^{+}AA^{+}=A^{+}} , it is called a generalized reflexive inverse. Generalized inverses always exist but are not in general unique. Uniqueness
Moore–Penrose_inverse
Topological space that locally resembles Euclidean space
charts is obtained which covers the entire sphere. This can be easily generalized to higher-dimensional spheres. A manifold can be constructed by gluing
Manifold
Matrix of partial derivatives of a vector-valued function
the function that maps y to f(x) + Jf(x) ⋅ (y – x) is the best linear approximation of f(y) for all points y close to x. The linear map h → Jf(x) ⋅ h is
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Physical quantity of hot and cold
temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space
Temperature
Statistical modeling method
regression model. Multivariate analogues of ordinary least squares (OLS) and generalized least squares (GLS) have been developed. "General linear models" are
Linear_regression
Matrices named after Élie Cartan
the Killing form is due to Cartan.[citation needed] A (symmetrizable) generalized Cartan matrix is a square matrix A = ( a i j ) {\displaystyle A=(a_{ij})}
Cartan_matrix
Regularization technique for ill-posed problems
of the regularized problem. For the generalized case, a similar representation can be derived using a generalized singular-value decomposition. Finally
Ridge_regression
Branch of mathematics
structure maps called a spectrum. In other words, to give a generalized cohomology theory is to give a spectrum. A K-theory is an example of a generalized cohomology
Homotopy_theory
Study of spatial information
information. By placing data in a spatial context, even though it is generalized, cartographic generalization creates additional information by revealing
Technical_geography
Maps whose domain and codomain are acted on by the same group, and the map commutes
{\displaystyle z} and returns g ⋅ z {\displaystyle g\cdot z} . Equivariant maps can be generalized to arbitrary categories in a straightforward manner. Every group
Equivariant_map
Curve along which a 3-D surface is at equal elevation
available. Meteorological contour maps may present collected data such as actual air pressure at a given time, or generalized data such as average pressure
Contour_line
Township in Minnesota, United States
a compilation of Sioux and Ojibwe (Chippewa) Indian Treaties and a generalized map of ceded territories by year, see For a guide to cultural, governmental
Badger Township, Polk County, Minnesota
Badger_Township,_Polk_County,_Minnesota
Operation in calculus
infinitesimally thin vertical slabs. In the early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue
Integral
Statistical estimation technique
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there
Generalized_least_squares
Major climatic change and biotic turnover during the Triassic
would die out in the early Norian. By cutting rhynchosaurs off from more generalized niches, the CPE would have reduced their versatility and increased their
Carnian_pluvial_episode
Mathematics award
VII, France "Developed the theory of distributions, a new notion of generalized function motivated by the Dirac delta-function of theoretical physics
Fields_Medal
subsystems. The decomposition theorem generalizes this fact to the case of a proper, but not necessarily smooth map f : X → Y {\displaystyle f:X\to Y} between
Decomposition theorem of Beilinson, Bernstein and Deligne
Decomposition_theorem_of_Beilinson,_Bernstein_and_Deligne
homotopy groups are trivial. Homotopical connectivity is defined for maps, too. A map is n-connected if it is an isomorphism "up to dimension n, in homotopy"
Homotopical_connectivity
Mathematical map between topological spaces
possible to generalize the notion of proper maps of topological spaces to locales and topoi, see (Johnstone 2002). Almost open map – Map that satisfies
Proper_map
Technique for wavelet analysis
Wavelet Domain for Generalized Lifting Image Compression" (PDF). ICASSP 2009 (submitted). Rolon, J. C.; Mendonça, E.; Salembier, P. Generalized Lifting With
Lifting_scheme
Data structure holding key/value pairs
implementation-defined. A multimap generalizes an associative array by allowing multiple values to be associated with a single key. A bidirectional map is a related abstract
Associative_array
Map that displays roads and transport links
Official Automobile Blue Book". The book was the first collection of generalized road maps spanning Boston, New York, Baltimore, Washington and Philadelphia
Road_map
A generalized probabilistic theory (GPT) is a general framework to describe the operational features of arbitrary physical theories. A GPT must specify
Generalized probabilistic theory
Generalized_probabilistic_theory
Matrix approximation problem in linear algebra
JHU Press. p. 327. ISBN 978-1421407944. Schönemann, P.H. (1966), "A generalized solution of the orthogonal Procrustes problem" (PDF), Psychometrika,
Orthogonal_Procrustes_problem
Process of generalization
in other related area. Patterns from one mathematical object can be generalized to other similar objects in the same class. The main disadvantage of
Abstraction
Formulation of classical mechanics using momenta
mechanics replaces (generalized) velocities q ˙ i {\displaystyle {\dot {q}}^{i}} used in Lagrangian mechanics with (generalized) momenta. Both theories
Hamiltonian_mechanics
Convex polytope, the n-dimensional analogue of a square and a cube
generates a 4-dimensional unit hypercube (a unit tesseract). This can be generalized to any number of dimensions. This process of sweeping out volumes can
Hypercube
On the structure of complete Riemannian manifolds of non-positive sectional curvature
generalized the theorem to Riemannian manifolds in 1928 (Helgason 1978; do Carmo 1992; Kobayashi & Nomizu 1969). The theorem was further generalized to
Cartan–Hadamard_theorem
Long exact sequence
is generalized by the Serre spectral sequence. Consider a fiber-oriented sphere bundle with total space E, base space M, fiber Sk and projection map π
Gysin_homomorphism
Type of mathematical space
In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space
Generalized_flag_variety
Modification using the principle of template matching
The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template
Generalised_Hough_transform
Data structure for approximate set membership
The information content of the array relative to its size is low. The generalized Bloom filter (k greater than 1) allows many more bits to be set while
Bloom_filter
expand trade benefits to the countries in the Caribbean Basin, renew the generalized system of preferences, and reauthorize the trade adjustment assistance
List of acts of the 106th United States Congress
List_of_acts_of_the_106th_United_States_Congress
Conjecture on zeros of the zeta function
would also work for the generalized Riemann hypothesis for Dirichlet L-functions. Several results first proved using the generalized Riemann hypothesis were
Riemann_hypothesis
Instantaneous rate of change (mathematics)
velocity, and the second derivative is its acceleration. Derivatives can be generalized to functions of several real variables. In this case, the derivative
Derivative
Tool in linear algebra and matrix analysis
that A or D is singular, substituting a generalized inverse for the inverses on M/A and M/D yields the generalized Schur complement. The Schur complement
Schur_complement
Excessive sweating
specific, narrowly defined, clinical disorder. Hyperhidrosis can either be generalized, or localized to specific parts of the body. Hands, feet, armpits, groin
Hyperhidrosis
Largest natural deposit of asphalt in the world, located in Trinidad and Tobago
Generalized geological map of Trinidad. The Los Bajos wrench fault cuts across the southwest portion of the island.
Pitch_Lake
Study of how people perceive dialects
exist. Computerized methods of interpretation can also be used to draw generalized maps to be generated from the responses. Degree of Difference: In this method
Perceptual_dialectology
operator is a linear map from (level 1) Siegel modular forms of degree d to Siegel modular forms of degree d − 1, generalizing taking the constant term
Siegel_operator
Topics referred to by the same term
GMM may refer to: Garuda Mataram Motor, company of Indonesia Generalized method of moments, an econometric method GMM Grammy, a Thai entertainment company
GMM
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
{\displaystyle 1/p!} in § Properties of the generalized Kronecker delta below disappearing. In terms of the indices, the generalized Kronecker delta is defined as:
Kronecker_delta
Calculus for deriving computer programs
{\displaystyle *} , f l a t t e n {\displaystyle \mathrm {flatten} } , and a generalized version of / {\displaystyle /} above, respectively, while i n i t s {\displaystyle
Bird–Meertens_formalism
Mathematical model of the time dependence of a point in space
{\displaystyle y_{t+1}=ax_{t}+b} More generally this can be generalized into a generic discrete map from a n-dimensional manifold to itself: y t + 1 i = f
Dynamical_system
Concept in geometry including line and circle
line is a Euclidean isometry (distance-preserving transformation) which maps lines to lines and circles to circles; but an inversion in a circle is not
Generalised_circle
Progressive neurodegenerative disease
www.alzforum.org. "Alzheimer's Disease Brain Cell Atlas- brain-map.org". portal.brain-map.org. "What's the deal with Alzheimer's disease and amyloid?".
Alzheimer's_disease
Association of one output to each input
give precise definitions for these weakly specified functions. These generalized functions may be critical in the development of a formalization of the
Function_(mathematics)
Algebraic structure
generalized topology in the Boolean algebra. Given an interior algebra its open elements form a generalized topology. Conversely given a generalized topological
Interior_algebra
Matrix factorisation in mathematics
T are upper triangular. The generalized Schur decomposition is also sometimes called the QZ decomposition. The generalized eigenvalues λ {\displaystyle
Schur_decomposition
Neurological movement disorder
changes or damage to the nervous system and inheritance. Types include generalized dystonia, focal dystonia, psychogenic dystonia, acute dystonic reaction
Dystonia
Purported ancient tribal confederation of the Late Bronze Age
between the intellectual and ideological dimensions of archaeology. To generalize beyond specific, highly localized data, archaeologists must utilize familiar
Sea_Peoples
Number
empty product. The role of 0 as the smallest counting number can be generalized or extended in various ways. In set theory, 0 is the cardinality of the
0
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