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Property of a differential manifold that includes complex structures
generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure.
Generalized_complex_structure
Smooth manifold
is closed under the Lie bracket. A generalized almost complex structure integrates to a generalized complex structure if the subspace is closed under the
Almost_complex_manifold
Topics referred to by the same term
A complex structure may refer to: Almost complex manifold Complex manifold Linear complex structure Generalized complex structure Complex structure deformation
Complex_structure
Concept in differential geometry
bracket. This bracket is used to describe the integrability of generalized complex structures. A more general example arises from a Lie algebroid A {\displaystyle
Courant_algebroid
Type of topological space
different dimensions in specific ways. The notion generalizes both manifolds and simplicial complexes and has particular significance for algebraic topology
CW_complex
British mathematician
his article on generalized Calabi–Yau manifolds, he introduced the notion of generalized complex manifolds, providing a single structure that incorporates
Nigel_Hitchin
Class of spinors constructed using Clifford algebras
in 10D, superstrings, generalized complex structures and parametrizing solutions of integrable hierarchies. Consider a complex vector space V {\displaystyle
Pure_spinor
Algebraic structure
Hodge structures have been generalized for all complex varieties (even if they are singular and non-complete) in the form of mixed Hodge structures, defined
Hodge_structure
British professor of theoretical physics (born 1957)
Hull is known for his work on string theory, M-theory, and generalized complex structures. Edward Witten drew partially from Hull's work for his development
Chris_Hull
It is a generalization of the Lie bracket from an operation on the tangent bundle
the Courant bracket is the integrability condition of a generalized almost complex structure. Let X {\displaystyle X} and Y {\displaystyle Y} be vector
Courant_bracket
Nonspecific long-lasting anxiety
Generalized anxiety disorder (GAD) is an anxiety disorder characterized by excessive, uncontrollable, and often irrational worry about events or activities
Generalized_anxiety_disorder
Concept in mathematical physics
articles of the Hitchin functional. As with Hitchin's introduction of generalized complex manifolds, this is an example of a mathematical tool found useful
Hitchin_functional
Academic concept
complexities that artists draw from. The term structure of feeling seeks to describe a complex experience, since structures of feeling capture something formative
Structure_of_feeling
Theory in theoretical physics
Topological string is closely related to Hitchin's ideas on generalized complex structure, Hitchin system, and ADHM construction etc.. The 2-dimensional
Topological_string_theory
Type of mathematical space
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. Flag varieties
Generalized_flag_variety
Objects extending the notion of functions
In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers. There is more than one recognized theory
Generalized_function
Vector satisfying some of the criteria of an eigenvector
eigenvectors to have complex values. The set spanned by all generalized eigenvectors for a given λ {\displaystyle \lambda } forms the generalized eigenspace for
Generalized_eigenvector
Classifications of epileptic seizures
focal seizures, generalized-onset seizures became generalized seizures, and unknown-onset seizures became unknown whether focal or generalized. Other changes
Seizure_types
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
Differentiable manifold
differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an
CR_manifold
Swedish-American sociologist (1937–2025)
generalized game theory is especially open to the use of concepts such as incomplete information and bounded rationality. Proponents of generalized game
Tom_R._Burns
Mathematical structure in differential geometry
ISSN 1945-001X. Bailey, Michael (2013-08-01). "Local classification of generalize complex structures". Journal of Differential Geometry. 95 (1). arXiv:1201.4887
Poisson_manifold
Unsolved problem in geometry
description of de Rham cohomology to include extra structure that is present in the case of complex algebraic varieties. It received little attention before
Hodge_conjecture
Monster and modular connection
Ryba's conjecture should generalize to Tate cohomology of composite order elements, and the nature of any connections to generalized moonshine and other moonshine
Monstrous_moonshine
Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
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
Mathematical structure in abstract algebra
generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers
*-algebra
Mathematical structure
after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes
Building_(mathematics)
Image edge detection algorithm
ISSN 1687-9309. Scharr, Hanno (2007). "Optimal Filters for Extended Optical Flow". Complex Motion. Lecture Notes in Computer Science. Vol. 3417. Berlin, Heidelberg:
Sobel_operator
Data structure
In computing, GiST or Generalized Search Tree, is a data structure and API that can be used to build a variety of disk-based search trees. GiST is a generalization
GiST
Algebraic structure used in topology
generalized homology theory or a generalized cohomology theory, defined below. There are generalized cohomology theories such as K-theory or complex cobordism
Cohomology
Period of symptoms due to excessive or synchronous neuronal brain activity
between generalized and focal seizures is the age at onset, which is significantly lower in patients with generalized seizures. Generalized tonic–clonic
Seizure
Number with a real and an imaginary part
alternative complex structure on R 2 . {\displaystyle \mathbb {R} ^{2}.} This is generalized by the notion of a linear complex structure. Hypercomplex
Complex_number
Method of detecting shapes within images
was invented by Richard Duda and Peter Hart in 1972, who called it a "generalized Hough transform" after the related 1962 patent of Paul Hough. The transform
Hough_transform
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real
Complex_polytope
Interrelated entities that form a whole
work by pushing on it). In 1850, the German physicist Rudolf Clausius generalized this picture to include the concept of the surroundings and began to
System
In statistics, hierarchical generalized linear models extend generalized linear models by relaxing the assumption that error components are independent
Hierarchical generalized linear model
Hierarchical_generalized_linear_model
Manifold with Riemannian, complex and symplectic structure
manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by
Kähler_manifold
Class of algorithms
following algorithms are described for a binary tree, but they may be generalized to other trees as well. 0 Traversal method: 1 Previous node Restart Start
Tree_traversal
Fractal named after mathematician Benoit Mandelbrot
is well-known, even outside mathematics, for how it exhibits complex fractal structures when visualized and magnified, despite having a relatively simple
Mandelbrot_set
summation is one way to compute a divergent series. Clarke generalized derivative Clarke generalized derivative. cluster 1. A cluster point of a net x α {\displaystyle
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Study of triangles in other spaces than the Euclidean plane
orthoschemes - right simplexes (right triangles generalized to n dimensions) - studied by Schoute who called the generalized trigonometry of n Euclidean dimensions
Generalized_trigonometry
ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra
List_of_cohomology_theories
Branch of mathematics studying (smooth) functions of manifolds
admit a differentiable structure, and if so, how many? Notably, the smooth case of dimension 4 is the last open case of the generalized Poincaré conjecture;
Geometric_topology
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
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
Research field in deep learning
complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes
Topological_deep_learning
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
Tensor related to gradients
detection Edge detection Lucas-Kanade method Affine shape adaptation Generalized structure tensor J. Bigun and G. Granlund (1986), Optimal Orientation Detection
Structure_tensor
Feature detection algorithm in computer vision
the Hessian, or more generally considering a more general family of generalized scale-space interest points. Recently, a slight variation of the descriptor
Scale-invariant feature transform
Scale-invariant_feature_transform
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
Positive integer of the form (2^(2^n))+1
primes today are generalized Fermat primes. Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number
Fermat_number
Type of social exchange
exchange resources with each other, generalized exchange naturally involves more than two parties. Examples of generalized exchange include; matrilateral cross-cousin
Generalized_exchange
In image analysis, the generalized structure tensor (GST) is an extension of the Cartesian structure tensor to curvilinear coordinates. It is mainly used
Generalized_structure_tensor
Software library for numerical linear algebra
QR, Cholesky and Schur decomposition. The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying
LAPACK
Protein complex
The membrane attack complex (MAC) or terminal complement complex (TCC) is a complex of proteins typically formed on the surface of pathogen cell membranes
Complement membrane attack complex
Complement_membrane_attack_complex
Basic unit of life forms
September 2025. "Prokaryote structure". khanacademy. Retrieved 2025-08-16. Knoll, Andrew H. (2011). "The Multiple Origins of Complex Multicellularity". Annual
Cell_(biology)
abelian group A {\displaystyle A} pg 134. Note, this construction can be generalized to commutative rings R {\displaystyle R} as well from its underlying
Eilenberg–MacLane_spectrum
Mechanical and acoustical property
more complex systems, including multi-degree-of-freedom systems and elastic continua such as beams and plates, the concept has been generalized to describe
Transmissibility_(vibration)
Expression denoting a set of sets in formal semantics
we can define the model of a generalized quantifier as follows. Given a first-order language augmented with generalized quantifiers Q 1 , Q 2 , … {\displaystyle
Generalized_quantifier
Practice of publicly funded construction projects as propaganda
also been generalized outside of the context of Imelda and Ferdinand Marcos and the Philippines. The term is a play on the "Oedipus complex" of psychoanalytic
Edifice_complex
Polygons which have an accompanying imaginary dimension for each real dimension
dimensions to be visualized. A complex polygon is generalized as a complex polytope in C n {\displaystyle \mathbb {C} ^{n}} . A complex polygon may be understood
Regular_complex_polygon
Mental illness with multiple personality states
to severe symptoms is a result of different etiologies and biological structures. Other terms used in the literature, including personality, personality
Dissociative identity disorder
Dissociative_identity_disorder
Relation between genus, degree, and dimension of function spaces over surfaces
work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond. A Riemann
Riemann–Roch_theorem
Field of mathematics which studies incidence structures
ordinary n-gon that contains them both. Generalized 3-gons are projective planes. Generalized 4-gons are called generalized quadrangles. By the Feit-Higman theorem
Incidence_geometry
Chaos 2D Strange Attractor Tutorial A new chaotic system and beyond: The generalized Lorenz-like system Gingerbreadman map Mira Fractals Half-inverted tearing
List_of_chaotic_maps
One of two foundational theories of quantum chemistry
structure resembles a Lewis structure, but when a molecule cannot be fully represented by a single Lewis structure, multiple valence bond structures are
Valence_bond_theory
Mathematics award
original on 31 August 2006. Retrieved 24 August 2006. UNESCO (2015). A Complex Formula: Girls and Women in Science, Technology, Engineering and Mathematics
Fields_Medal
Feature descriptor used in computer vision
C-HOG descriptor blocks against generalized Haar wavelets, PCA-SIFT descriptors, and shape context descriptors. Generalized Haar wavelets are oriented Haar
Histogram of oriented gradients
Histogram_of_oriented_gradients
Numerical method for solving boundary value problems
The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential
Proper generalized decomposition
Proper_generalized_decomposition
System responsible for combining morphemes into complex structures
paradigm are: Arc pair grammar Generalized phrase structure grammar (GPSG) Generative semantics Head-driven phrase structure grammar (HPSG) Lexical functional
Syntax
Structure-preserving map between two algebraic structures of the same type
algebra. The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set
Homomorphism
Phylum of invertebrate animals
systems are mainly open. The "generalized" mollusc's feeding system consists of a rasping "tongue", the radula, and a complex digestive system in which exuded
Mollusca
Analytical method for social structure
regular or generalized. Using blockmodeling, a network can be analyzed using newly created blockmodels, which transforms large and complex network into
Blockmodeling
Branch of geometry that studies combinatorial properties and constructive methods
also generalize the higher-dimensional analogs and the finite structures are sometimes called finite geometries. Formally, an incidence structure is a
Discrete_geometry
Reals with an extra square root of +1 adjoined
55(4):296. Anthony A. Harkin & Joseph B. Harkin (2004) Geometry of Generalized Complex Numbers, Mathematics Magazine 77(2):118–29. F. Reese Harvey. Spinors
Split-complex_number
Human-readable data serialization language
(XML) but has a minimal syntax that intentionally differs from Standard Generalized Markup Language (SGML). It uses Python-style indentation to indicate
YAML
Image processing method
horizontal strokes (being the one-dimensional cells of an abstract cell complex corresponding to the image) mostly compose a connected sequence representing
Edge_detection
Genetic condition causing non-cancerous tumours
Tuberous sclerosis complex (TSC) is a rare, multi-system genetic disorder that causes the growth of benign tumors in various organs, including the brain
Tuberous_sclerosis
Type of vector space in math
square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions. Geometric intuition
Hilbert_space
Open subset of the real–number line
_{\mathcal {L}}} is a generalized fractal string which cannot be realized as an ordinary fractal string. A concrete example of such a generalized fractal string
Fractal_string
structures defined on them. It differs from other branches of topology as the topological spaces do not have to be similar to manifolds. Generalized trigonometry
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Riemannian manifold with SU(n) holonomy
the special unitary group, in a manner that is compatible with the complex structure. M {\displaystyle M} has a Kähler metric with global holonomy contained
Calabi–Yau_manifold
Overview of mechanics based on the least action principle
in the context as generalized coordinates. The kinetic and potential energies of the system are expressed using these generalized coordinates or momenta
Analytical_mechanics
over X {\displaystyle X} with a complex linear structure on the stable normal bundle. Complex bordism is a generalized homology theory, corresponding to
Complex_cobordism
Two-dimensional Turing machine with emergent behavior
runs on a square lattice of black and white cells. The idea has been generalized in several different ways, such as turmites which add more colors and
Langton's_ant
Type of mathematical functions
a Stein manifold, and more generalized Stein space. C n {\displaystyle \mathbb {C} ^{n}} is also considered to be a complex projective variety, a Kähler
Function of several complex variables
Function_of_several_complex_variables
Topological space that locally resembles Euclidean space
locally ringed space, whose structure sheaf is locally isomorphic to the sheaf of continuous (or differentiable, or complex-analytic, etc.) functions on
Manifold
Image edge detection algorithm
threshold values to filter out the false edges. However, as the image gets complex, different local areas will need very different threshold values to accurately
Canny_edge_detector
Quantum-mechanical framework for simulating molecules and solids
causal structure. An approach which does not suffer from this issue was later introduced through an action based on the Keldysh formalism of complex-time
Time-dependent density functional theory
Time-dependent_density_functional_theory
Type of Riemannian manifold
, g ) {\displaystyle (M,g)} endowed with three integrable almost complex structures I , J , K {\displaystyle I,J,K} that are Kähler with respect to the
Hyperkähler_manifold
Boundary set in the complex plane
= sin z Generalized Newton fractal for p(z) = z3 − 1, a = −1/2. The color was chosen based on the argument after 40 iterations. Generalized Newton fractal
Newton_fractal
Statistical distribution of complex random variables
distribution (a complex normal distribution is a bivariate normal distribution) Generalized chi-squared distribution Wishart distribution Complex random variable
Complex_normal_distribution
Mathematical transform that expresses a function of time as a function of frequency
transform can be generalized to the fractional Fourier transform, which involves rotations by other angles. This can be further generalized to linear canonical
Fourier_transform
Mathematical object
topology, a branch of mathematics, a spectrum is an object representing a generalized cohomology theory. Every such cohomology theory is representable, as
Spectrum_(topology)
Topological manifold with a piecewise linear structure on it
manifolds): it is categorically "better behaved" than DIFF — for example, the Generalized Poincaré conjecture is true in PL (with the possible exception of dimension
Piecewise_linear_manifold
Branch of mathematics
was extended in the 1950s, when Samuel Eilenberg and Norman Steenrod generalized this approach. They defined homology and cohomology as functors equipped
Algebraic_topology
Combinatorial representation of a graph on an orientable surface
Boundary representation Generalized maps Doubly connected edge list Quad-edge data structure Rotation system Simplicial complex Winged edge Bollobás, Béla;
Combinatorial_map
Method for describing the electronic structure of molecules using quantum mechanics
orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th
Molecular_orbital_theory
Commutative group where every element is the sum of elements from one finite subset
ways, generalizing the two forms of the fundamental theorem of finite abelian groups. The theorem, in both forms, in turn generalizes to the structure theorem
Finitely generated abelian group
Finitely_generated_abelian_group
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Tamil
Complete
Boy/Male
Indian
Complete
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Boy/Male
Indian
Complete
Girl/Female
Hindu, Indian
Complex
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Girl/Female
Tamil
Complete
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Girl/Female
Bengali, Indian
Good Complex
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Tamil
Complete
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
Surname or Lastname
Spanish (Lestón)
Spanish (Lestón) : habitational name from any of four places called Lestó in A Coruña province, Galacia.English : unexplained; perhaps a habitational name from Leiston in Suffolk, so named from Old English lēg ‘beacon fire’ + tūn ‘farmstead’, ‘settlement’.
Boy/Male
Arabic, Australian, Indian, Iranian, Muslim, Parsi
Liberal; Garden
Girl/Female
Christian & English(British/American/Australian)
Dutiful
Boy/Male
Bengali, Hindu, Indian, Kannada, Sanskrit, Tamil, Telugu
A Flower
Girl/Female
Biblical
The Lord liveth.
Boy/Male
Hindu, Indian
Lord Krishna
Boy/Male
Muslim
The holy, The divine, The pure, The purifier
Boy/Male
Hindu, Indian, Malayalam, Marathi, Sanskrit, Tamil
Praise; Salutation
Male
Egyptian
, a name probably referring to Aroeris.
Boy/Male
Indian, Tamil
Snaker
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
GENERALIZED COMPLEX-STRUCTURE
n.
One who compiles; esp., one who makes books by compilation.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
n.
A complex; an aggregate of parts; a complication.
v. t.
To make universal; to generalize.
a.
Repeatedly compound; made up of complex constituents.
imp. & p. p.
of Generalize
n.
A generalized concept of magnitude.
imp. & p. p.
of Compile
imp. & p. p.
of Couple
a.
Intricate; entangled; complicated; complex.
a.
Complex, complicated.
imp. & p. p.
of Comply
adv.
In a complex manner; not simply.
p. pr. & vb. n.
of Generalize
a.
Not complex; uncompounded; simple.
a.
Comprising structural characters which are separated in more specialized forms; synthetic; as, a generalized type.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
a.
See Couple-close.