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Effective particle coupling beyond tree level
In quantum electrodynamics, the vertex function describes the coupling between a photon and an electron beyond the leading order of perturbation theory
Vertex_function
Polynomial function of degree two
vertex of a parabola is the place where it turns; hence, it is also called the turning point. If the quadratic function is in vertex form, the vertex
Quadratic_function
Topics referred to by the same term
surface Vertex function, describing the interaction between a photon and an electron Vertex (anatomy), the highest point of the head Vertex (gastropod):
Vertex
Algebra used in 2D conformal field theories and string theory
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string
Vertex_operator_algebra
Type of discrete calculus
calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Quantum field theory of electromagnetism
self-energy function Σ {\displaystyle \Sigma } One-loop contribution to the vertex function Γ {\displaystyle \Gamma } that, being closed loops, imply the presence
Quantum_electrodynamics
Renormalization scheme in quantum field theory
of Π ( 0 ) {\displaystyle \Pi (0)} . A similar reasoning using the vertex function leads to the renormalization of the electric charge e r {\displaystyle
On-shell renormalization scheme
On-shell_renormalization_scheme
Pictorial representation of the behavior of subatomic particles
meet at a vertex, which contributes a delta-function that ensures that the sum of the momenta are all equal. To compute a correlation function in the interacting
Feynman_diagram
Functions of an angle
List of periodic functions Polar sine – a generalization to vertex angles Sinc function Klein, Felix (1924) [1902]. "Die goniometrischen Funktionen"
Trigonometric_functions
Multivalued function in mathematics
number of trees with a designated root vertex is n n − 1 {\displaystyle n^{n-1}} . The exponential generating function of this counting sequence is: T ( x
Lambert_W_function
Type of program in computer graphics
shaders. The first shader-capable GPUs only supported pixel shading, but vertex shaders were quickly introduced once developers realized the power of shaders
Shader
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
On points of extreme curvature in curves
point of the curvature function a vertex. This theorem has many generalizations, including a version for space curves where a vertex is defined as a point
Four_vertex_theorem
some fixed order). A vertex function fv for each vertex v. The vertex function maps the state of vertex v at time t to the vertex state at time t + 1 based
Graph_dynamical_system
Fast-growing function
a simple subcubic graph (SSCG) is a finite simple graph in which each vertex has a degree of at most three. Suppose we have a sequence of simple subcubic
Friedman's_SSCG_function
Feature of OpenGL for storing vertex data
via the Nvidia-created extension "vertex array range" or ATI's "vertex array object" extension. The following functions form the core of VBO access and
Vertex_buffer_object
Polynomial equation of degree two
for graphing a quadratic function. Since the graph is symmetric with respect to a vertical line through the vertex, the vertex's x-coordinate is located
Quadratic_equation
Directed graph with no directed cycles
vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed
Directed_acyclic_graph
Method in physics used to deal with infinities
number of photons is zero. For example, at the one-loop order, the vertex function has both ultraviolet and infrared divergences. In contrast to the ultraviolet
Renormalization
Value in quantum electrodynamics
mechanical correction—of the electron is found by calculating the vertex function shown in the adjacent diagram. The calculation is relatively straightforward
Anomalous magnetic dipole moment
Anomalous_magnetic_dipole_moment
Type of field appearing in the Lagrangian
corresponding correlator obtained from F [ J ] {\displaystyle F[J]} , known as vertex function, is given by G Γ [ J ] N , c = δ Γ [ ϕ ¯ ] δ ϕ ¯ ( x 1 ) ⋯ δ ϕ ¯
Source_field
Symmetric function invariant of graphs
G=(V,E)} with vertex set V = { v 1 , v 2 , … , v n } {\displaystyle V=\{v_{1},v_{2},\ldots ,v_{n}\}} , a vertex coloring is a function κ : V → C {\displaystyle
Chromatic_symmetric_function
Methodic assignment of colors to elements of a graph
is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems
Graph_coloring
energy; poles of this function determine the quasiparticle energy-momentum dispersion relation. The four-point vertex function Γ ( K 3 , K 4 ; K 1 , K
Pomeranchuk_instability
parameter gradients between vertex attributes as a prerequisite for rasterization. Triangle setup unit A fixed-function unit in a GPU that performs triangle
Glossary_of_computer_graphics
Class of graph dynamical systems
some fixed order). A vertex function fi for each vertex i. The vertex function maps the state of vertex i at time t to the vertex state at time t + 1 based
Sequential_dynamical_system
Path planning algorithm
A*. The only difference is the update _ vertex ( ) {\displaystyle {\text{update}}\_{\text{vertex}}()} function. Compared to A*, the parent of a node in
Theta*
Fundamental trigonometric functions
sine theorem Polar sine—a generalization to vertex angles Proofs of trigonometric identities Sinc function Sine and cosine transforms Sine integral Sine
Sine_and_cosine
Monster and modular connection
moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James
Monstrous_moonshine
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Deleting a graph edge and merging its nodes
f} be a function that maps every vertex in V ∖ { u , v } {\displaystyle V\setminus \{u,v\}} to itself, and otherwise, maps it to a new vertex w {\displaystyle
Edge_contraction
References Square brackets [ ] G[S] is the induced subgraph of a graph G for vertex subset S. Prime symbol ' The prime symbol is often used to modify notation
Glossary_of_graph_theory
Maximal biconnected subgraph
Specifically, it processes n vertex additions and m edge additions in O(m α(m, n)) total time, where α is the inverse Ackermann function. This time bound is proved
Biconnected_component
Well-quasi-ordering of finite trees
path from v {\displaystyle v} to w {\displaystyle w} contains no other vertex. Take ( X , ≤ X ) {\displaystyle (X,\leq _{X})} to be a partially ordered
Kruskal's_tree_theorem
S-shaped curve
and vertex at ( 2 , 1 ) {\displaystyle (2,1)} , corresponding to the range and midpoint ( 1 / 2 {\displaystyle 1/2} ) of the logistic function. Parametrically
Logistic_function
service function inside UK utility company United Utilities, Vertex was spun out as a separate company in 1996. In 2007, United Utilities sold Vertex to a
Vertex_(company)
Types of special mathematical functions
mentioned otherwise, the following is assumed: Sectors in C having their vertex at z = 0 often prove to be appropriate domains for complex expressions.
Incomplete_gamma_function
Plane curve: conic section
any parabola with the origin as vertex and the y axis as axis of symmetry can be considered as the graph of a function f ( x ) = a x 2 with a ≠ 0. {\displaystyle
Parabola
Fractal creation method
polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random on
Chaos_game
Algorithm for maximum cardinality matching
and right sides of the bipartite graph and NIL is a special null vertex */ function BFS() is for each u in U do if Pair_U[u] = NIL then Dist[u] := 0 Enqueue(Q
Hopcroft–Karp_algorithm
Cloud-based service and infrastructure
February 2021 – Google Kubernetes Engine Autopilot is introduced. May 2021 – Vertex AI announced at Google.io June 2021 – In 2021, Apple was Google Cloud's
Google_Cloud_Platform
Assignment of labels to elements of a graph
graph G = (V, E), a vertex labeling is a function of V to a set of labels; a graph with such a function defined is called a vertex-labeled graph. Likewise
Graph_labeling
Algorithm for finding shortest paths
v, then the distance of v is updated to alt. 1 function Dijkstra(Graph, source): 2 3 for each vertex v in Graph.Vertices: 4 dist[v] ← INFINITY 5 prev[v]
Dijkstra's_algorithm
Identity in abelian theories due to gauge invariance
Clive Ward and Yasushi Takahashi to relate the wave function renormalization of the electron to its vertex renormalization factor, guaranteeing the cancellation
Ward–Takahashi_identity
In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such
Ice-type_model
Component in electronic graphics processing units (GPUs)
The function of the vertex pipeline in any GPU is to take geometry data (usually supplied as vector points), work with it if needed with either fixed function
Vertex_pipeline
Dimensionality of space at which the character of the phase transition changes
invariance below this dimension. For small external wave vectors the vertex functions Γ {\displaystyle \Gamma } acquire additional exponents, for example
Critical_dimension
Mathematical function with no sudden changes
a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies
Continuous_function
Real-time rendering technique
techniques use SH to encode multiple functions—usually the global lighting environment and a per-vertex radiance transfer function. The generalized lighting equation
Spherical_harmonic_lighting
In physics, proton and neutron magnetism
first-order and largest correction in QED, is found by calculating the vertex function shown in the diagram on the right. The calculation was discovered by
Nucleon_magnetic_moment
Node ordering for directed acyclic graphs
ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of
Topological_sorting
Central object in linear algebra; mapping vectors to vectors
{e} _{2})&\cdots &T(\mathbf {e} _{n})\end{bmatrix}}} For example, the function T ( x ) = 5 x {\displaystyle T(x)=5x} is a linear transformation. Applying
Transformation_matrix
Generalization of finite element method
these functions restricted to a single element. All these functions are defined in the entire element interior. Vertex function. Edge function. Face function
Hp-FEM
Mathematical function
complete graph Kn + 1 for odd n. In such a graph, any single vertex v has n possible choices of vertex that it can be matched to, and once this choice is made
Double_factorial
Length of shortest path between two nodes of a graph
over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph
Distance_(graph_theory)
Generalization of the ice-type (six-vertex) models
In statistical mechanics, the eight-vertex model is a generalization of the ice-type (six-vertex) models. It was discussed by T. Bill Sutherland and C
Eight-vertex_model
Theoretical physicist (1939–2023)
Thesis Nonperturbative solutions of the Bethe-Salpeter equation for the vertex function (1966) Doctoral advisor Hans Bethe Kenneth G. Wilson Doctoral students
Roman_Jackiw
Set of edges without common vertices
common vertices. In other words, a subset of the edges is a matching if each vertex appears in at most one edge of that matching. Finding a largest matching
Matching_(graph_theory)
Method for finding minimum spanning trees
the pseudocode below. function Prim(vertices, edges) is for each vertex in vertices do cheapestCost[vertex] ← ∞ cheapestEdge[vertex] ← null explored ← empty
Prim's_algorithm
Figure formed by two rays meeting at a common point
line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and
Angle
Method for solving quadratic equations
a < 0) of the quadratic function. One way to see this is to note that the graph of the function f(x) = x2 is a parabola whose vertex is at the origin (0, 0)
Completing_the_square
n-vertex cubic graph? The reconstruction conjecture and new digraph reconstruction conjecture on whether a graph is uniquely determined by its vertex-deleted
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Vertices connected in pairs by edges
and v and to be incident on them. A vertex may belong to no edge, in which case it is not joined to any other vertex and is called isolated. When an edge
Graph_(discrete_mathematics)
Type of computer science algorithm
simply start at one vertex and perform a random walk of about 20n3 steps, the chance that we will stumble across the other vertex provided that it is
In-place_algorithm
Shading language
only included support for vertex shaders and pixel shaders ("fragment" in GLSL). A vertex shader is executed for each vertex that is submitted by the application
High-Level_Shader_Language
Property of functions which is weaker than continuity
is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f {\displaystyle f} is upper (respectively
Semi-continuity
Min-max theorem in graph theory
collection of vertex-disjoint cycles contained in the graph; The size of the smallest feedback vertex set in the graph: a set that contains one vertex from every
Erdős–Pósa_theorem
Graphs of d-dimensional polytopes are d-connected
maximum of a linear function on a convex polytope (the linear programming problem). The simplex method starts at an arbitrary vertex of the polytope and
Balinski's_theorem
Method to solve optimization problems
a vertex of the polytope and then walking along a path on the edges of the polytope to vertices with non-decreasing values of the objective function until
Linear_programming
Type of dominating set in graph theory
A Roman dominating function (RDF) is a function f : V → { 0 , 1 , 2 } {\displaystyle f:V\to \{0,1,2\}} such that for every vertex v {\displaystyle v}
Roman_dominating_set
Maximum size of an independent set of the matroid
Then the rank function r(B) is the number of vertices in the graph, minus the number of connected components of B (including single-vertex components).
Matroid_rank
Graph where all pairs of vertices are automorphic
the Rado graph Two countable vertex-transitive graphs are called quasi-isometric if the ratio of their distance functions is bounded from below and from
Vertex-transitive_graph
Every graph has evenly many odd vertices
class PPA encapsulates the difficulty of finding a second odd vertex, given one such vertex in a large implicitly-defined graph. An undirected graph consists
Handshaking_lemma
Data structure representing a finite set of strings
single source vertex (a vertex with no incoming edges), in which each edge of the graph is labeled by a letter or symbol, and in which each vertex has at most
Deterministic acyclic finite state automaton
Deterministic_acyclic_finite_state_automaton
Coordinate system that is defined by points instead of vectors
but not at a vertex, one of the area coordinates λ 1...3 {\displaystyle \lambda _{1...3}} (the one associated with the opposite vertex) is zero, while
Barycentric_coordinate_system
Shape with three sides
an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the
Triangle
High-level shading language
rendering pipeline at the vertex and fragment level. Programmability at this level is achieved with the use of fragment and vertex shaders. Originally, this
OpenGL_Shading_Language
Putting fermions on a lattice with chiral symmetry results in more fermions than expected
theory with non-covariant contributions to the fermion self-energy and vertex function, rendering the theory non-renormalizable and difficult to work with
Fermion_doubling
Path in a graph that visits each vertex exactly once
directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian
Hamiltonian_path
Planar movement within a Euclidean space without rotation
For example, taking the quadratic function y = x 2 {\displaystyle y=x^{2}} , whose graph is a parabola with vertex at ( 0 , 0 ) {\displaystyle (0
Translation_(geometry)
Area of discrete mathematics
two graphs that respects their structure, or equivalently, a function between the vertex sets of two graphs that maps adjacent vertices to adjacent vertices
Graph_theory
Terminology used in computer graphics
means that host CPUs have no direct influence on how its GPUs will process vertex and rasterization operations, beyond issuing indirect commands and transferring
Fixed-function (computer graphics)
Fixed-function_(computer_graphics)
Function in algebraic graph theory
colors for the first vertex, any of the k − 1 {\displaystyle k-1} remaining colors for the second vertex, and lastly for the third vertex, any of the k − 1
Chromatic_polynomial
Quantum field theory
to obtain all the n-point functions with perturbation theory. Using LSZ reduction formula we get from the n-point functions the corresponding process
Yang–Mills_theory
Shading language for WebGPU
@binding(0) var<uniform> mvp : mat4x4f; @vertex fn main(v_in : VertexInput) -> VertexOutput { var v_out : VertexOutput; v_out.clip_position = mvp * vec4f(v_in
WebGPU_Shading_Language
Organ in vertebrates that collects and stores urine from the kidneys before disposal
broad fundus (base), a body, an apex, and a neck. The apex (also called the vertex) is directed forward toward the upper part of the pubic symphysis, and from
Bladder
theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector
Edge_and_vertex_spaces
Property of all triangles on a Euclidean plane
facets that meet at a vertex, divided by the hyperarea of the facet opposite the vertex is independent of the choice of the vertex. Writing V for the hypervolume
Law_of_sines
Extremal graph theory bound on clique-free graph edges
example of an n {\displaystyle n} -vertex graph that does not contain any ( r + 1 ) {\displaystyle (r+1)} -vertex clique K r + 1 {\displaystyle K_{r+1}}
Turán's_theorem
Binary tree of rational numbers
parents of a vertex. Each vertex a/b has one child whose value is less than 1, a/a + b (because a + b > a). Similarly, each vertex a/b has one
Calkin–Wilf_tree
Set of hypergraph nodes to which every hyperedge is connected
graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that set.
Vertex_cover_in_hypergraphs
Algorithm for finding the shortest paths in graphs
algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's
Bellman–Ford_algorithm
Result in combinatorics and graph theory
a perfect matching—that is, a way to match each vertex from one group uniquely to an adjacent vertex from the other group. Hall's condition is that any
Hall's_marriage_theorem
Sparse graph with strong connectivity
sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research
Expander_graph
Object relationship in programming language
insert(vertex.get()); } void removeVertex(SharedPtr<Vertex> vertex) { vertices.erase(vertex); } void addEdge(SharedPtr<Vertex> from, SharedPtr<Vertex> to)
Friend_class
Partial differential equations of correlation functions
satisfied by the N-point functions of affine primary fields and can be derived using either the formalism of Lie algebras or that of vertex algebras. The structure
Knizhnik–Zamolodchikov equations
Knizhnik–Zamolodchikov_equations
Natural number, composite number
between all its vertices. There are fourteen polygons that can fill a plane-vertex tiling, where five polygons tile the plane uniformly, and nine others only
14_(number)
perfect matching) has a vertex cover of size n + k {\displaystyle n+k} . The odd cycle transversal can be transformed into a vertex cover by including both
Odd_cycle_transversal
Graph with at most one cycle per component
pairs of vertices, such that no two cycles of consecutive edges share any vertex with each other, nor can any two cycles be connected to each other by a
Pseudoforest
Mean position of all the points in a shape
intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side). For other properties of a triangle's
Centroid
VERTEX FUNCTION
VERTEX FUNCTION
Female
Hebrew
(וֶרֶד) Hebrew unisex name VERED means "rose."
Male
German
German form of Latin Valentinus, VELTEN means "healthy, strong."
Boy/Male
Shakespearean
Much Ado About Nothing' A Headborough.
Male
English
Variant spelling of English Vern, VERNE means "place of alder trees."
Boy/Male
Danish, Finnish, German, Scandinavian, Swedish
Bright; Skillful
Girl/Female
British, English
Beaver-stream
Boy/Male
Swedish American Teutonic
Friend protector.
Surname or Lastname
English
English : variant of Varney.
Male
German
Low German form of French Martin, MERTEN means "of/like Mars."
Male
English
English surname transferred to forename use, from a Norman baronial name VERE means "alder."
Surname or Lastname
English
English : variant of Varley.Dutch : reduced form of van der Leye, a topographic name for someone living near the river Leie.French : habitational name from a place called Verlée in Liège province, Belgium.
Boy/Male
Hindu, Indian
Brave; Smart
Boy/Male
French
From the alder grove.
Surname or Lastname
English (Kent and London)
English (Kent and London) : from Old French verge ‘half-acre’, hence a status name for the owner of that amount of land.Catalan (Vergé) : variant of Verger, topographic name from Catalan verger ‘orchard’ (Latin viridiarium)Catalan : possibly also a nickname from verge ‘maiden’ (Latin virgo ‘maiden’).
Boy/Male
Scandinavian
Bright.
Male
Scandinavian
Scandinavian form of German Werner, VERNER means "Warin warrior," i.e. "covered warrior."
Boy/Male
Australian, Danish, Dutch, Finnish, German, Swedish, Teutonic
Army Defender; Army Warrior
Surname or Lastname
English
English : see Fern.French : topographic name for someone who lived near a grove of alders, French verne, a word of Gaulish origin.
Surname or Lastname
English and Scottish (of Norman origin)
English and Scottish (of Norman origin) : habitational name from any of numerous places named in France named Vert or Le Vert.
Male
English
Short form of English Sylvester, VESTER means "from the forest."
VERTEX FUNCTION
VERTEX FUNCTION
Boy/Male
Arabic, Muslim
Torch
Female
English
Variant spelling of German Annemarie, ANNE-MARIE means "favor; grace," and "obstinate, rebellious."
Surname or Lastname
English
English : habitational name from places in Hampshire and Shropshire named Elson. The former is named from the Old English personal name Æ{dh}elswī{dh} (composed of the elements æ{dh}el ‘noble’ + swī{dh} ‘strong’) + Old English tūn ‘enclosure’, ‘settlement’; the latter from the genitive case of the Old English personal name Elli (see Ellington) + Old English tūn ‘settlement’ or dūn ‘hill’.English : variant spelling of Ellson.Jewish (Ashkenazic) : patronymic from the Yiddish male personal name Elye, from Hebrew Eliyahu ‘Elijah’ (see Elias).
Female
Greek
(Ολυμπιάς) Ancient Greek name of the mother of Alexander the Great. It is a feminine form of Greek Olympos ("home of the gods"), OLYMPIAS means "of Olympus."Â
Girl/Female
Indian, Tamil
Goddess Amman
Girl/Female
Arabic, Muslim
Light
Boy/Male
Hindu, Indian, Punjabi, Sanskrit, Sikh
Satisfying the Mind
Biblical
his kingdom; his counselor
Girl/Female
German
War goddess.
Girl/Female
Arabic
Meaningful Ceremony
VERTEX FUNCTION
VERTEX FUNCTION
VERTEX FUNCTION
VERTEX FUNCTION
VERTEX FUNCTION
n.
The outer or superficial part of an organ; as, the cortex or gray exterior substance of the brain.
n.
A verse.
v. i.
To make verses; to versify.
v. t.
To tell in verse, or poetry.
n.
A pregnant woman; a mother; as, A has a son B by one venter, and a daughter C by another venter; children by different venters.
n.
One who carries a verge, or emblem of office.
imp. & p. p.
of Verse
a.
Not in a state of contingency or suspension; fixed; as, vested rights; vested interests.
pl.
of Vertex
n.
The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base.
n.
A stanza; a stave; as, a hymn of four verses.
n.
An edible European marine fish (Sparus dentex, or Dentex vulgaris) of the family Percidae.
n.
A belly, or protuberant part; a broad surface; as, the venter of a muscle; the venter, or anterior surface, of the scapula.
pl.
of Vertex
imp. & p. p.
of Verge
n.
The zenith, or the point of the heavens directly overhead.
n. sing. & pl.
A verse or verses. See Verse.
n.
The top, or crown, of the head.
n.
Any one of numerous species of small Turbellaria belonging to Vortex and allied genera. See Illustration in Appendix.
v. i.
To tend downward; to bend; to slope; as, a hill verges to the north.