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In geometric graph theory, a convex embedding of a graph is an embedding of the graph into a Euclidean space, with its vertices represented as points
Convex_embedding
Graph that can be embedded in the plane
planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the
Planar_graph
Planar graph drawn by relaxing springs
theory, a Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free straight-line embedding with the properties
Tutte_embedding
Every Riemannian manifold can be isometrically embedded into some Euclidean space
Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into
Nash_embedding_theorems
Functional analysis theorem
In functional analysis, Rådström's embedding theorem is a result related to the set of compact and convex subsets of a normed vector space. It states that
Rådström's_embedding_theorem
isometric to a closed subset of a convex subset of some Banach space. (N.B. the image of this embedding is closed in the convex subset, not necessarily in the
Kuratowski_embedding
Planar graph with convex polygon faces
In graph drawing, a convex drawing of a planar graph is a drawing that represents the vertices of the graph as points in the Euclidean plane and the edges
Convex_drawing
Projection of data onto lower-dimensional manifolds
optimizes to find an embedding that aligns the tangent spaces. Maximum Variance Unfolding, Isomap and Locally Linear Embedding share a common intuition
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Mathematical set with an ordering
{\displaystyle \leq .} If an order-embedding between two posets S and T exists, one says that S can be embedded into T. If an order-embedding f : S → T {\displaystyle
Partially_ordered_set
Space with topology generated by convex sets
analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces
Locally convex topological vector space
Locally_convex_topological_vector_space
Embedding a graph in a topological space, often Euclidean
embedding, cellular embedding or map is an embedding in which every face is homeomorphic to an open disk. A closed 2-cell embedding is an embedding in
Graph_embedding
Swedish mathematician
can be isometrically embedded as a convex cone in a normed real vector-space. Under the embedding, the nonempty compact convex sets are mapped to points
Hans_Rådström
Flat-sided three-dimensional shape
reflecting. Convex polyhedra are a well-defined class of polyhedra with several equivalent standard definitions. Every convex polyhedron is the convex hull of
Polyhedron
result of Matthew Grayson showing that any embedded circle in the plane is deformed into a convex embedding, at which point Gage and Hamilton's result
Gauss_curvature_flow
Algebraic variety containing an algebraic torus
In algebraic geometry, a toric variety or torus embedding is a kind of algebraic variety that contains an algebraic torus whose group action extends to
Toric_variety
Type of mathematical functions
theorem, the Kodaira embedding theorem says that a compact Kähler manifold M, with a Hodge metric, there is a complex-analytic embedding of M into complex
Function of several complex variables
Function_of_several_complex_variables
Geometric model of the planar projection of the physical universe
relationship with out-of-plane points requires special consideration for their embedding in the ambient space R 3 {\displaystyle \mathbb {R} ^{3}} . In two dimensions
Euclidean_plane
tree has a greedy embedding. Unsolved problem in mathematics Does every polyhedral graph have a planar greedy embedding with convex faces? More unsolved
Greedy_embedding
Application of geometry in number theory
{\displaystyle r_{1}} real embeddings and r 2 {\displaystyle r_{2}} pairs of complex embeddings, then the Minkowski embedding realizes K ⊗ Q R ≅ R r 1 ×
Geometry_of_numbers
Well-quasi-ordering of finite trees
well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. A finitary application of the theorem gives the existence of a fast-growing
Kruskal's_tree_theorem
Non-orientable surface with one edge
equilateral-triangle version of the Möbius strip. This flat triangular embedding can lift to a smooth embedding in three dimensions, in which the strip lies flat in three
Möbius_strip
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
is an embedding of TVSs whose image is dense in the codomain; for any Banach space Y , {\displaystyle Y,} the canonical vector space embedding X ⊗ ^ π
Nuclear_space
Point in the convex hull of a set P in Rd, is the convex combination of d+1 points in P
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x {\displaystyle x} lies in the convex hull C o n v ( P ) {\displaystyle
Carathéodory's theorem (convex hull)
Carathéodory's_theorem_(convex_hull)
Geometrical object in four-dimensional space
smooth) isometric embedding into R3, but by the Nash–Kuiper theorem it does admit C1 isometric embeddings into R3 (constructed via convex integration). The
Clifford_torus
Planar graphs have straight drawings
straight-line combinatorially isomorphic re-embedding of G in which triangle abc is the outer face of the embedding. (Combinatorially isomorphic means that
Fáry's_theorem
definition is reminiscent of the Klain embedding, but more involved. Details can be found in. The Goodey-Weil embedding is a linear injection of Val i {\displaystyle
Valuation_(geometry)
Graph representing faces of another graph
graph: it is not planar but can be embedded in a torus, with each face of the embedding being a triangle. This embedding has the Heawood graph as its dual
Dual_graph
Vector space with a notion of nearness
induced by Y . {\displaystyle Y.} A topological vector space embedding (abbreviated TVS embedding), also called a topological monomorphism, is an injective
Topological_vector_space
American mathematician (1943–2024)
that if the initial immersion is an embedding, then all future immersions in the mean curvature flow are embeddings as well. Furthermore, convexity of
Richard_S._Hamilton
infranilmanifold is finitely covered by a nilmanifold. Isometric embedding is an embedding preserving the Riemannian metric. Isometry is a surjective map
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Type of monotone function
must be an order embedding. However, not every order embedding is a coretraction. As a trivial example, the unique order embedding f : ∅ → { 1 } {\displaystyle
Order_embedding
Spatial tiling of convex uniform polyhedra
geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral
Convex_uniform_honeycomb
Cycles in a graph that cover each edge twice
an embedding on a manifold: the cell complex formed by the cycles of the cover may have non-manifold topology at its vertices. The circular embedding conjecture
Cycle_double_cover
American mathematician and Nobel Laureate (1928–2015)
of the embedding to be very small, with the effect that in many cases it is logically impossible that a highly-differentiable isometric embedding exists
John_Forbes_Nash_Jr.
Graph-theoretic description of polyhedra
method of W. T. Tutte, the Tutte embedding. Tutte's method begins by fixing one face of a polyhedral graph into convex position in the plane. This face
Steinitz's_theorem
{\displaystyle Y} . By Rådström's embedding theorem, K {\displaystyle {\mathcal {K}}} can be isometrically embedded as a convex cone C {\displaystyle C} in
Integral_of_a_correspondence
Graph data structure
known as half-edge data structure, is a data structure to represent an embedding of a planar graph in the plane, and polytopes in 3D. This data structure
Doubly_connected_edge_list
Partial differential equation technique
Nash embedding theorem, specifically the Nash–Kuiper theorem, which says that any short smooth ( C ∞ {\displaystyle C^{\infty }} ) embedding or immersion
Homotopy_principle
Graph orientation with one source and sink
an st-edge-numbering and st-edge-orientation of a graph are known. Convex embedding, a higher-dimensional generalization of bipolar orientations Rosenstiehl
Bipolar_orientation
1967 mathematics textbook
Convex Polytopes is a graduate-level mathematics textbook about convex polytopes, higher-dimensional generalizations of three-dimensional convex polyhedra
Convex_Polytopes
Complete manifolds of non-negative sectional curvature largely reduce to the compact case
nonnegative sectional curvature, then there exists a closed totally convex, totally geodesic embedded submanifold whose normal bundle is diffeomorphic to M. Such
Soul_theorem
Parabolic partial differential equation
is any smooth embedding, then the mean curvature flow with initial data f {\displaystyle f} eventually consists exclusively of embeddings with strictly
Mean_curvature_flow
Hong Kong mathematician
manifolds.[CY77b] Any strictly convex closed hypersurface in the Euclidean space ℝn + 1 can be naturally considered as an embedding of the n-dimensional sphere
Shiu-Yuen_Cheng
Mathematical concept
{A} \mathbf {x} +\mathbf {s} =\mathbf {b} } . Slack variables give an embedding of a polytope P ↪ ( R ≥ 0 ) f {\displaystyle P\hookrightarrow (\mathbf
Slack_variable
Physical simulation to visualize graphs
in the plane with all faces convex by fixing the vertices of the outer face of a planar embedding of the graph into convex position, placing a spring-like
Force-directed_graph_drawing
(combinatorics, order theory) Four functions theorem (combinatorics) Hahn embedding theorem (ordered groups) Hausdorff maximality theorem (set theory) Kleene
List_of_theorems
Graph made from vertices and edges of a convex polyhedron
representation of it as a subdivision of a convex polygon into smaller convex polygons may be found using the Tutte embedding. Tait conjectured that every cubic
Polyhedral_graph
Graph drawing with vertices on a line
drawn using semicircles or other convex curves above or below the line. These drawings are also called linear embeddings or circuit diagrams. Applications
Arc_diagram
Solving an optimization problem with a quadratic objective function
positive definite, the problem is a special case of the more general field of convex optimization. Quadratic programming is particularly simple when Q is positive
Quadratic_programming
approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids. A new
Dvoretzky's_theorem
Topological vector space
locally convex inductive limits do occur in natural questions of analysis. If each of the bonding maps f i j {\displaystyle f_{i}^{j}} is an embedding of TVSs
LF-space
Optimization problem
geometric programs (GGPs). CVXPY is a Python-embedded modeling language for specifying and solving convex optimization problems, including GPs, GGPs, and
Geometric_programming
All numbers between two given numbers
embeddable into the product [ 0 , 1 ] κ {\displaystyle [0,1]^{\kappa }} of κ {\displaystyle \kappa } copies of the intervals. The concepts of convex sets
Interval_(mathematics)
Machine learning technique
we can start with a simple encoder without self-attention, such as an "embedding layer", which simply converts each input word into a vector by a fixed
Attention_(machine_learning)
Locally convex topological vector space
a Hausdorff locally convex space then the canonical injection from X {\displaystyle X} into its bidual is a topological embedding if and only if X {\displaystyle
Reflexive_space
projective-plane embeddings of graphs with planar covers The strong Papadimitriou–Ratajczak conjecture: every polyhedral graph has a convex greedy embedding Turán's
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Painting by George Washington Lambert
The Convex Mirror is a c 1916 oil with pencil on wood panel painting by Australian artist George Washington Lambert. The work depicts the interior of Belwethers
The_Convex_Mirror
Area of discrete mathematics
embedding (or imbedding) of a graph in surface and linkless embedding, graph minors, crossing number, map coloring, and voltage graph. The embedding of
Graph_theory
Convex polytope whose vertices all have integer Cartesian coordinates
polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex hull of its integer
Integral_polytope
Order-preserving mathematical function
(Tu-Tv,u-v)\geq 0\quad \forall u,v\in X.} Kachurovskii's theorem shows that convex functions on Banach spaces have monotonic operators as their derivatives
Monotonic_function
Swedish mathematician and concert pianist
{\displaystyle D<{\sqrt {m}}} . Consequently, the optimal embedding is the natural embedding, which realizes { 0 , 1 } m {\displaystyle \{0,1\}^{m}} as
Per_Enflo
3D shape made of polyhedra sharing a common center
connected to form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull.[citation needed] Another convex polyhedron is formed
Polytope_compound
manifolds, a symplectic embedding φ : ( M , η ) → ( N , ν ) {\displaystyle \varphi :(M,\eta )\to (N,\nu )} is a smooth embedding φ : M → N {\displaystyle
Non-squeezing_theorem
Combinatorial theory of mechanics and discrete geometry
flexing, and consequent deterioration of the structure. A rigid graph is an embedding of a graph in a Euclidean space which is structurally rigid. That is,
Structural_rigidity
Branch of mathematics
the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied intrinsically
Geometry
Undirected unit-distance graph requiring four colors
that the unbounded face is the convex hull of the embedding and every bounded face is a pseudotriangle with only three convex vertices. The complement graph
Moser_spindle
Existence of geodesic circles on surfaces
closed geodesics (i.e. three embedded geodesic circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Mathematical tree with cycle through leaves
cross (this is called a planar embedding), and the cycle connects the leaves in their clockwise ordering in this embedding. Thus, the cycle forms the outer
Halin_graph
Partition of a toroidal surface into polygons
by Stewart, are the quasi-convex toroidal polyhedra. These are Stewart toroids that include all of the edges of their convex hulls. For such a polyhedron
Toroidal_polyhedron
Differentiable manifold
embedded manifold in some C n {\displaystyle \mathbb {C} ^{n}} . Thus not only are we embedding the manifold, but we also demand for global embedding
CR_manifold
Term in mathematics
it can be defined as a complex manifold admitting a proper holomorphic embedding into C n {\displaystyle \mathbb {C} ^{n}} for some n {\displaystyle n}
Stein_manifold
functional analysis, a locally convex vector lattice (LCVL) is a topological vector lattice that is also a locally convex space. LCVLs are important in
Locally_convex_vector_lattice
Length in a vector space
1\right\}.} Conversely: Any locally convex topological vector space has a local basis consisting of absolutely convex sets. A common method to construct
Norm_(mathematics)
Shape with three sides
3n-3} bitangent lines. The convex hull of any pseudotriangle is a triangle. A non-planar triangle is a triangle not embedded in a Euclidean space, roughly
Triangle
Theorem in geometry about convex sets
theorem on convex sets, published by Johann Radon in 1921, states that: Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect
Radon's_theorem
American mathematician
Rockafellar developed a general duality theory based on convex conjugate functions that centers on embedding a problem within a family of problems obtained by
R._Tyrrell_Rockafellar
Goldberg polyhedron with 42 faces
In geometry, the chamfered dodecahedron is a convex polyhedron with 80 vertices, 120 edges, and 42 faces: 30 hexagons and 12 pentagons. It is constructed
Chamfered_dodecahedron
a Hausdorff locally convex space then the canonical injection from X {\displaystyle X} into its bidual is a topological embedding if and only if X {\displaystyle
Infrabarrelled_space
Visualisation method for hierchical data
been proposed that use regions that are general convex polygons, not necessarily rectangular. Convex treemaps were developed in several steps, each step
Treemapping
Product of the principal curvatures of a surface
surface is embedded into R3 and endowed with the Riemannian metric given by the first fundamental form. Suppose that the image of the embedding is a surface
Gaussian_curvature
Type of polytope in mathematics
In mathematics, specifically in combinatorial commutative algebra, a convex lattice polytope P is called normal if it has the following property: given
Normal_polytope
Visual depiction of a partially ordered set
ISBN 978-3-540-58950-1 Jünger, Michael; Leipert, Sebastian (1999), "Level planar embedding in linear time", Graph Drawing (Proc. GD '99), Lecture Notes in Computer
Hasse_diagram
Finitelt generated commutative monoid
follows that ι {\displaystyle \iota } is an embedding. In other words, every affine monoid can be embedded into a group. If M {\displaystyle M} is a submonoid
Affine_monoid
In mathematics, an invariant convex cone is a closed convex cone in a Lie algebra of a connected Lie group that is invariant under inner automorphisms
Invariant_convex_cone
Generalized Euclidean space in mathematics
projective Hilbert spaces is not a projective space. The Segre mapping is an embedding of the Cartesian product of two projective spaces into the projective
Projective_Hilbert_space
Generalised alphabetical order
Locally convex Normed Related Antichain Cofinal Cofinality Comparability Graph Duality Filter Hasse diagram Ideal Net Subnet Order morphism Embedding Isomorphism
Lexicographic_order
Belgian mathematician (1954–2018)
convex geometry. In 1985, he proved Bourgain's embedding theorem in metric dimension reduction, which states that every metric space can be embedded into
Jean_Bourgain
Continuous deformation between two continuous functions
t = 0 giving the K1 embedding, ending at t = 1 giving the K2 embedding, with all intermediate values corresponding to embeddings. However, this definition
Homotopy
Technique in numerical linear algebra
time. One of the important ideas been used is called Oblivious Subspace Embedding (OSE), it is first proposed by Sarlos. For p = 1 {\displaystyle p=1}
Low-rank_approximation
Embedding a topological space into a compact space as a dense subset
line. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. It is often useful to embed topological
Compactification (mathematics)
Compactification_(mathematics)
On chains and antichains in partial orders
; Saks, Michael E. (1988), "Combinatorial representation and convex dimension of convex geometries", Order, 5 (1): 23–32, doi:10.1007/BF00143895, S2CID 119826035
Dilworth's_theorem
Graph drawn with all edges intersecting
A thrackle is an embedding of a graph in the plane in which each edge is a Jordan arc and every pair of edges meet exactly once. Edges may either meet
Thrackle
Linear operator related to topological vector spaces
unless otherwise stated). The projective tensor product of two locally convex TVSs X and Y is denoted by X ⊗ π Y {\displaystyle X\otimes _{\pi }Y} and
Nuclear_operator
Graph which remains connected when k or fewer nodes removed
Connectivity (graph theory) Menger's theorem Structural cohesion Tutte embedding Vertex separator Schrijver (12 February 2003), Combinatorial Optimization
Vertex_connectivity
Alternative mathematical ordering
repeating an element: p ↪ r ↪ q ↪ p. ^embeddingNovák (1984, p. 332) calls an embedding an "isomorphic embedding". ^rollIn this case, Giraudet & Holland
Cyclic_order
2004 drama film by Chazz Palminteri
using Lidrock disks, another technology owned by Convex Group. These were CDs and DVDs that were embedded in the lids of soda cups. On review aggregate website
Noel_(film)
various restrictions on f-vectors of convex simplicial polytopes, to this more general setting. The face lattice of a convex polytope, consisting of its faces
Eulerian_poset
Generalization of the tangent space to a manifold to the case of certain spaces
contingent cone, and the Clarke tangent cone. These three cones coincide for a convex set, but they can differ on more general sets. Let A {\displaystyle A} be
Tangent_cone
Polyhedron associated with another by swapping vertices for faces
geometric transformation that, when applied to a convex polyhedron, realizes the dual polyhedron as another convex polyhedron. There are many kinds of duality
Dual_polyhedron
Study of graphs defined by geometric means
or polytope. The skeleton of any convex polyhedron is a planar graph, and the skeleton of any k-dimensional convex polytope is a k-connected graph. Conversely
Geometric_graph_theory
CONVEX EMBEDDING
CONVEX EMBEDDING
Surname or Lastname
English
English : habitational name from a place named Cove, examples of which are found in Devon, Hampshire, and Suffolk, from Old English cofa ‘cove’, ‘bay’, ‘inlet’, also ‘shelter’, ‘hut’, or a topographic name with the same meaning.
Male
English
Variant spelling of English Connor, CONNER means "hound-lover."
Boy/Male
American, British, English
Shepherd
Boy/Male
American, British, English
Dove
Male
English
Anglicized form of Irish Gaelic Conláed, CONLEY means "purifying fire."
Boy/Male
American, Christian, German, Indian
High Desire
Boy/Male
Irish
Hero.
Surname or Lastname
English
English : unexplained.
Surname or Lastname
English
English : from Old French covine ‘fraud’, ‘deceit’, hence a derogatory nickname for a trickster.English : habitational name from a place in Staffordshire named Coven ‘(place) at the huts or shelters (Old English cofa, dative plural cofum)’.
Boy/Male
British, Christian, English
Wagoner; To Convey
Boy/Male
Irish American
Hound lover. Full of desire; much desire.
Boy/Male
Irish
Hound of the plains.
Surname or Lastname
Italian
Italian : from the title of rank conte ‘count’ (from Latin comes, genitive comitis ‘companion’). Probably in this sense (and the Late Latin sense of ‘traveling companion’), it was a medieval personal name; as a title it was no doubt applied ironically as a nickname for someone with airs and graces or simply for someone who worked in the service of a count.English : variant of Count, cognate with 1.French : nickname for someone in the service of a count or for someone who behaved pretentiously, from Old French conte, cunte ‘count’ (of the same derivation as 1).French (Conté) : variant of Comté (see Comte).
Surname or Lastname
Irish
Irish : variant spelling of Connor, now common in Scotland.English : occupational name for an inspector of weights and measures, Middle English connere, cunnere ‘inspector’, an agent derivative of cun(nen) ‘to examine’.
Boy/Male
Irish American
Strong willed or wise. Also a : Hero.
Boy/Male
Indian, Kannada, Tamil
God Murugan
Surname or Lastname
English
English : from Middle English cony ‘rabbit’ (a back-formation from conies, from Old French conis, plural of conil), a nickname for someone thought to resemble a rabbit in some way or a metonymic occupational name for a dealer in rabbits or rabbit skins.
Surname or Lastname
English (Leicestershire)
English (Leicestershire) : variant of Culver.
Surname or Lastname
Spanish and Portuguese
Spanish and Portuguese : nickname from the title of rank conde ‘count’, a derivative of Latin comes, comitis ‘companion’.English : unexplained.
Surname or Lastname
English
English : metathesized form of the occupational name Coyner.English : possibly an occupational name for a dealer in rabbits or rabbit skins, from an agent derivative of Middle English cony ‘rabbit’ (see Coney).
CONVEX EMBEDDING
CONVEX EMBEDDING
Biblical
banishment of grace
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Moon; Son of Abhimanyu
Girl/Female
Tamil
Aprajita | அபராஜிதா
Undefeated, A flower, One name of devis names
Girl/Female
Hindu
The best, Saintly
Male
German
Variant form of German Hugubert, HUPPRECHT means "bright heart/mind/spirit."
Surname or Lastname
English
English : nickname from Old French bon homme (Latin bonus homo). This had two senses relevant to surname formation; partly it had the literal meaning ‘good man’, and partly it came to mean ‘peasant farmer’.Americanized form of French Bonhomme.
Girl/Female
Indian
Speech, Powerful, Heaven and earth
Boy/Male
Hindu, Indian, Punjabi, Sikh
The One Taking Shelter in God
Girl/Female
English, Swedish
Life
Girl/Female
Christian, French, Hindu, Indian
Idol; A Small Bird; Little Lake
CONVEX EMBEDDING
CONVEX EMBEDDING
CONVEX EMBEDDING
CONVEX EMBEDDING
CONVEX EMBEDDING
a.
Convex on one side, and flat on the other; plano-convex.
v. t.
To accompany; to convoy.
v. t.
To call before a judge or judicature; to summon; to convene.
a.
Concave on one side and convex on the other, as an eggshell or a crescent.
v. t.
To exchange for some specified equivalent; as, to convert goods into money.
n.
The conger eel; -- called also congeree.
n.
A convex body or surface.
v. t.
To context.
a.
Convex on one side, and concave on the other. The curves of the convex and concave sides may be alike or may be different. See Meniscus.
a.
Specifically, having such a combination of concave and convex sides as makes the focal axis the shortest line between them. See Illust. under Lens.
imp. & p. p.
of Cove
dv.
In a convex form; convexly.
a.
Convex on both sides; double convex. See under Convex, a.
a.
Plane or flat on one side, and convex on the other; as, a plano-convex lens. See Convex, and Lens.
a.
Made convex; protuberant in a spherical form.
v. t.
To impart or communicate; as, to convey an impression; to convey information.
n. & v.
See Conge, Conge.
adv.
In a convex form; as, a body convexly shaped.
a.
Convex on both sides; as, a biconvex lens.
v. t.
To cause to pass from one place or person to another; to serve as a medium in carrying (anything) from one place or person to another; to transmit; as, air conveys sound; words convey ideas.