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Algebraic Geometry is an algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977.
== Importance ==
It was the first extended treatment of scheme theory written as a text intended to be accessible to graduate students, and is considered to be the standard reference. This book w... | Wikipedia/Algebraic_Geometry_(book) |
In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).
Semialgebraic geometry is the study of semialgebraic sets, i.... | Wikipedia/Real_algebraic_geometry |
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of pr... | Wikipedia/Projective_linear_transformation |
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined. In case of varieties defined over the reals, this notion generalizes the not... | Wikipedia/Regular_point_of_an_algebraic_variety |
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without 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 matching in a bipartite graph can be treated as ... | Wikipedia/Matching_(graph_theory) |
In mathematics, cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraic sets called ... | Wikipedia/Cylindrical_algebraic_decomposition |
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An... | Wikipedia/Lattice_theory |
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a ... | Wikipedia/Valuation_theory |
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates.
== Description ==
Calculus on Manifolds is a brief monograph o... | Wikipedia/Calculus_on_Manifolds_(book) |
In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively,
schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using t... | Wikipedia/Algebraic_space |
The concept of a Projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and to describe some basic uses of projective spaces.
== Homogeneous polynomial ideals ==
Let k be an algebraically closed field, and V be a finite-dimensional v... | Wikipedia/Algebraic_geometry_of_projective_spaces |
In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function.
A regular map whose inverse is also regular is called biregu... | Wikipedia/Morphism_of_algebraic_varieties |
Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.
Traditionally, algebraic statistics has been associated with the design of experiments and multivariate analysis (especially time series). In recent years, the... | Wikipedia/Algebraic_statistics |
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross it... | Wikipedia/Singularity_theory |
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory m... | Wikipedia/Intersection_theory |
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by
f
−
1
... | Wikipedia/Function_inverse |
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the su... | Wikipedia/Riemann-Roch_theorem_for_algebraic_curves |
In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm uses the same mathematical principles as the Buchberger algorithm, but computes many normal forms in one go by forming a generally sparse matrix and using fast... | Wikipedia/Faugère_F5_algorithm |
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized a... | Wikipedia/Geometric_Group_Theory |
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical analysis to study and manipulate the solutions of systems of polynomial equations.
== Homotopy continuation ==
The primary computational method used in numerical alge... | Wikipedia/Numerical_algebraic_geometry |
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizin... | Wikipedia/Plane_algebraic_curve |
In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm uses the same mathematical principles as the Buchberger algorithm, but computes many normal forms in one go by forming a generally sparse matrix and using fast... | Wikipedia/Faugère's_F4_and_F5_algorithms |
In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the r... | Wikipedia/Birational_transformation |
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGam... | Wikipedia/Elliptic-curve_cryptography |
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certain axioms relating them. These abstract from the category of topological spaces or of chain complexes (derived ca... | Wikipedia/Quillen_model_category |
In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety
with n hyperplanes in general position. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. ... | Wikipedia/Degree_of_an_algebraic_variety |
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts... | Wikipedia/Differential_manifold |
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.
The shapes studied in geometric modeling are mostly two- or three-dimensional (solid figures), although many of its tools and principles can be applied to sets... | Wikipedia/Geometric_modelling |
In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.
Some of these definitions are of geometric nature, while some other are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply ... | Wikipedia/Dimension_of_an_algebraic_variety |
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, tra... | Wikipedia/Wiley-Interscience |
In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.
Classical elimination theory culminated with the work of Francis Macaulay on multi... | Wikipedia/Elimination_theory |
In mathematics, a parametric equation expresses several quantities, such as the coordinates of a point, as functions of one or several variables called parameters.
In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is ofte... | Wikipedia/Parametric_equation |
In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex
v
{\displaystyle v}
is denoted
... | Wikipedia/Degree_(graph_theory) |
A notable molecule editor is a computer program for creating and modifying representations of chemical structures.
Molecule editors can manipulate chemical structure representations in either a simulated two-dimensional space or three-dimensional space, via 2D computer graphics or 3D computer graphics, respectively. Tw... | Wikipedia/Molecule_editor |
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs
G
{\displaystyle G}
and
H
{\displaystyle H}
are given as input, and one must determine whether
G
... | Wikipedia/Subgraph_isomorphism_problem |
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges, vertices and by contracting edges.
The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K5 nor the complete bipartite... | Wikipedia/Minor_(graph_theory) |
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.
Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognitio... | Wikipedia/Graph_algorithm |
In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumera... | Wikipedia/Graph_enumeration |
In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering (software construction and also software verification) to layout algorithms and picture generation.
Grap... | Wikipedia/Graph_transformation |
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither odd holes (odd-length induced cycles of length at least 5) nor odd antiholes (complements of odd holes). It was conjectured by Claude Berge in 1961. A proof by Mari... | Wikipedia/Strong_perfect_graph_theorem |
In graph theory, the Kelmans–Seymour conjecture states that every 5-vertex-connected graph that is not planar contains a subdivision of the 5-vertex complete graph K5. It is named for Paul Seymour and Alexander Kelmans, who independently described the conjecture; Seymour in 1977 and Kelmans in 1979. A proof was announc... | Wikipedia/Kelmans–Seymour_conjecture |
In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v.
Th... | Wikipedia/Neighbourhood_(graph_theory) |
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license.
== History ==
NetworkX began development in 2002 by Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart. It is supported by the National Nuclear Security Administration of the U.S. Departmen... | Wikipedia/NetworkX |
In graph theory, two graphs
G
{\displaystyle G}
and
G
′
{\displaystyle G'}
are homeomorphic if there is a graph isomorphism from some subdivision of
G
{\displayst... | Wikipedia/Subdivision_(graph_theory) |
Graph Theory, 1736–1936 is a book in the history of mathematics on graph theory. It focuses on the foundational documents of the field, beginning with the 1736 paper of Leonhard Euler on the Seven Bridges of Königsberg and ending with the first textbook on the subject, published in 1936 by Dénes Kőnig. Graph Theory, 17... | Wikipedia/Graph_Theory,_1736–1936 |
In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumera... | Wikipedia/Enumeration_of_graphs |
In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs.
Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for examp... | Wikipedia/Topological_graph_theory |
In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972. It says:
If k complete graphs, each having exactly k vertices, have the property that every pair of complete graphs has at most one shared vertex, th... | Wikipedia/Erdős–Faber–Lovász_conjecture |
In computer science, persistence refers to the characteristic of state of a system that outlives (persists for longer than) the process that created it. This is achieved in practice by storing the state as data in computer data storage. Programs have to transfer data to and from storage devices and have to provide mapp... | Wikipedia/Persistence_(computer_science) |
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding ... | Wikipedia/Planarity_(graph_theory) |
Graphviz (short for Graph Visualization Software) is a package of open-source tools initiated by AT&T Labs Research for drawing graphs (as in nodes and edges, not as in bar charts) specified in DOT language scripts having the file name extension "gv". It also provides libraries for software applications to use the tool... | Wikipedia/Graphviz |
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning c... | Wikipedia/Percolation_theory |
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nod... | Wikipedia/Flow_network |
In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph, but some important special classes of graphs can be defined by the types of sets that are used to form an intersection representation of them.
== F... | Wikipedia/Intersection_graph |
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and is often ... | Wikipedia/Sparse_graph |
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a ... | Wikipedia/Random_graph |
Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure.
Results in extremal graph theory deal with quantitative c... | Wikipedia/Extremal_graph_theory |
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuro... | Wikipedia/Statistical_physics |
A semantic network, or frame network is a knowledge base that represents semantic relations between concepts in a network. This is often used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent semantic relations betwee... | Wikipedia/Semantic_network |
igraph is a library collection for creating and manipulating graphs and analyzing networks. It is written in C and also exists as Python and R packages. There exists moreover an interface for Mathematica. The software is widely used in academic research in network science and related fields. The publication that introd... | Wikipedia/Igraph |
In graph theory, a factor of a graph G is a spanning subgraph, i.e., a subgraph that has the same vertex set as G. A k-factor of a graph is a spanning k-regular subgraph, and a k-factorization partitions the edges of the graph into disjoint k-factors. A graph G is said to be k-factorable if it admits a k-factorization.... | Wikipedia/Graph_factorization |
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly inter... | Wikipedia/Geometric_graph_theory |
In graph theory, the Hadwiger conjecture states that if
G
{\displaystyle G}
is loopless and has no
K
t
{\displaystyle K_{t}}
minor then its chromatic number satisfies
... | Wikipedia/Hadwiger_conjecture_(graph_theory) |
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the st... | Wikipedia/Algebraic_graph_theory |
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling. In its simplest form, it is a way of c... | Wikipedia/Graph_coloring |
In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the graph. These problems may be solved either exactly (as an algebraic enumera... | Wikipedia/Graphical_enumeration |
Microsoft Automatic Graph Layout (MSAGL) is a .NET library for automatic graph layout.
It was created by Lev Nachmanson at Microsoft Research.
Earlier versions carried the name GLEE (Graph Layout Execution Engine).
== Contents ==
The MSAGL software supplies four programming libraries:
Microsoft.MSAGL.dll, a device-... | Wikipedia/Microsoft_Automatic_Graph_Layout |
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set
S
{\displaystyle S}
of vertices such that for every two vertices in
S
{\displays... | Wikipedia/Independent_set_(graph_theory) |
In graph theory, two graphs
G
{\displaystyle G}
and
G
′
{\displaystyle G'}
are homeomorphic if there is a graph isomorphism from some subdivision of
G
{\displayst... | Wikipedia/Homeomorphism_(graph_theory) |
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics.
A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points), together with a set of un... | Wikipedia/Graph_(data_structure) |
In graph theory, a graph property or graph invariant is a property of graphs that depends only on the abstract structure, not on graph representations such as particular labellings or drawings of the graph.
== Definitions ==
While graph drawing and graph representation are valid topics in graph theory, in order to fo... | Wikipedia/Graph_properties |
Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.
The pioneers of chemical graph theory are Alexandru Balaban, Ante Graovac, Iván Gutman, Haruo Hosoya, Milan Randić and Nenad Trinajstić (also Harry Wiener and others).
In 19... | Wikipedia/Chemical_graph_theory |
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many ... | Wikipedia/Condensed_matter_physics |
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the crossing number continues to be of great importance in graph drawing, as user studies have shown t... | Wikipedia/Crossing_number_(graph_theory) |
In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space
R
n
{\displaystyle \mathbb {R} ^{n}}
, forms a regular tiling. This implies th... | Wikipedia/Lattice_graph |
Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to Kelly and Ulam.
== Formal statements ==
Given a graph
G
=
(
V
,
E
)
{\displaystyle G=(V,E)}
,... | Wikipedia/Reconstruction_conjecture |
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges.
== Symbols ==
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 for graph inva... | Wikipedia/Weighted_graph |
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges, from the original graph, connecting pairs of vertices in that subset.
== Definition ==
Formally, let
G
=
(
V
,
E
... | Wikipedia/Induced_subgraph |
In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.
There are 2 distinct notions of multiple edges:
Edges without ow... | Wikipedia/Pseudograph |
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.
The problem is not known to be solvable in polynomial time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism proble... | Wikipedia/Graph_isomorphism_problem |
In chemical graph theory and in mathematical chemistry, a molecular graph or chemical graph is a representation of the structural formula of a chemical compound in terms of graph theory. A chemical graph is a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. I... | Wikipedia/Molecular_graph |
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor.
A prototypical example of this phe... | Wikipedia/Forbidden_graph_characterization |
This partial list of graphs contains definitions of graphs and graph families. For collected definitions of graph theory terms that do not refer to individual graph types, such as vertex and path, see Glossary of graph theory. For links to existing articles about particular kinds of graphs, see Category:Graphs. Some of... | Wikipedia/Gallery_of_named_graphs |
An electric power system is a network of electrical components deployed to supply, transfer, and use electric power. An example of a power system is the electrical grid that provides power to homes and industries within an extended area. The electrical grid can be broadly divided into the generators that supply the po... | Wikipedia/Power_systems |
Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley Classics series (ISBN 0-471-60839-4).
In 1962 Algèbre Géométrique, a translation into French by Michel Lazard, was published by Gauthier-Villars, and reprinted in 1996. ... | Wikipedia/Geometric_Algebra_(book) |
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are rigid (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the c... | Wikipedia/Rigid_body_dynamics |
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and... | Wikipedia/Computational_fluid_dynamics |
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations a... | Wikipedia/Lorentz_transformation |
The Navier–Stokes equations ( nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of p... | Wikipedia/Navier–Stokes_equations |
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is.
== Usage in science and engineering ==
In formal expressions, the ordinal number used before the word order refers to the highest power in the series expan... | Wikipedia/First-order_approximation |
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables.
For example,
{
3
x
+
... | Wikipedia/Homogeneous_system_of_linear_equations |
In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that
B
=
P
−
1
A
P
.
{\displaystyle B=P^{-1}AP.}
Simi... | Wikipedia/Similar_(linear_algebra) |
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of pr... | Wikipedia/Homography |
Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas pigeon post is not. Ancient signalling systems, although sometimes quite extensi... | Wikipedia/Telegraph |
A graphics processing unit (GPU) is a specialized electronic circuit designed for digital image processing and to accelerate computer graphics, being present either as a discrete video card or embedded on motherboards, mobile phones, personal computers, workstations, and game consoles. GPUs were later found to be usefu... | Wikipedia/Graphics_processing_units |
Renewable energy (also called green energy) is energy made from renewable natural resources that are replenished on a human timescale. The most widely used renewable energy types are solar energy, wind power, and hydropower. Bioenergy and geothermal power are also significant in some countries. Some also consider nucle... | Wikipedia/Renewable_energy |
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.: 3
Originally applied to water (hydromechanics), it found applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as w... | Wikipedia/Fluid_mechanics |
Control Data Corporation (CDC) was a mainframe and supercomputer company that in the 1960s was one of the nine major U.S. computer companies, which group included IBM, the Burroughs Corporation, and the Digital Equipment Corporation (DEC), the NCR Corporation (NCR), General Electric, Honeywell, RCA, and UNIVAC. For mos... | Wikipedia/Control_Data_Corporation |
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex-valued. For example, a wave function mi... | Wikipedia/Wave_function |
In mathematics, for a function
f
:
X
→
Y
{\displaystyle f:X\to Y}
, the image of an input value
x
{\displaystyle x}
is the single output value produced by
f
{\di... | Wikipedia/Image_(function) |
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