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In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for comparison of the topologies.
== Definition ==
A topology on a set may be defined as the collection of subsets which are considered to be "open". (An alter... | Wikipedia/Finer_topology |
In mathematics, a path in a topological space
X
{\displaystyle X}
is a continuous function from a closed interval into
X
.
{\displaystyle X.}
Paths play an important role in the fields of topology and mathematical analysis.... | Wikipedia/Path_(topology) |
In topology, the cartesian product of topological spaces can be given several different topologies. One of the more natural choices is the box topology, where a base is given by the Cartesian products of open sets in the component spaces. Another possibility is the product topology, where a base is also given by the Ca... | Wikipedia/Box_topology |
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, wh... | Wikipedia/Equation_(mathematics) |
A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.
A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed... | Wikipedia/System_of_polynomial_equations |
In mathematics and computer science, an algorithm ( ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use co... | Wikipedia/Algorithms |
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of stud... | Wikipedia/Equational_theory |
Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlap... | Wikipedia/Control_system_engineering |
Fractional-order control (FOC) is a field of control theory that uses the fractional-order integrator as part of the control system design toolkit. The use of fractional calculus can improve and generalize well-established control methods and strategies.
The fundamental advantage of FOC is that the fractional-order int... | Wikipedia/Fractional-order_control |
A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, machines, robotic devices, or any activity that requires high reliability, ease of programming, and process fault diagnosis.... | Wikipedia/Programmable_logic_controller |
In cybernetics and control theory, a setpoint (SP; also set point) is the desired or target value for an essential variable, or process value (PV) of a control system, which may differ from the actual measured value of the variable. Departure of such a variable from its setpoint is one basis for error-controlled regul... | Wikipedia/Setpoint_(control_system) |
In control theory, the linear–quadratic–Gaussian (LQG) control problem is one of the most fundamental optimal control problems, and it can also be operated repeatedly for model predictive control. It concerns linear systems driven by additive white Gaussian noise. The problem is to determine an output feedback law that... | Wikipedia/Linear-quadratic-Gaussian_control |
Industrial process control (IPC) or simply process control is a system used in modern manufacturing which uses the principles of control theory and physical industrial control systems to monitor, control and optimize continuous industrial production processes using control algorithms. This ensures that the industrial m... | Wikipedia/Process_control |
In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their curren... | Wikipedia/State_(controls) |
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circum... | Wikipedia/Catastrophe_theory |
A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, but often called a Mason graph after Samuel Jefferson Mason who coined the term, is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections betw... | Wikipedia/Signal-flow_graph |
Positive systems constitute a class of systems that has the important property that its state variables are never negative, given a positive initial state. These systems appear frequently in practical applications, as these variables represent physical quantities, with positive sign (levels, heights, concentrations, et... | Wikipedia/Positive_systems |
A proportional–integral–derivative controller (PID controller or three-term controller) is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications wh... | Wikipedia/PID_algorithm |
A fuzzy control system is a control system based on fuzzy logic – a mathematical system that analyzes analog input values in terms of logical variables that take on continuous values between 0 and 1, in contrast to classical or digital logic, which operates on discrete values of either 1 or 0 (true or false, respectiv... | Wikipedia/Fuzzy_control |
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such rel... | Wikipedia/Differential_equations |
In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their curren... | Wikipedia/State_space_(controls) |
Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing condit... | Wikipedia/Adaptive_control |
Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, ... | Wikipedia/Controller_(control_theory) |
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation.
It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). This... | Wikipedia/Z-transform |
Charles François (5 September 1922 – 31 July 2019) was a Belgian administrator, editor and scientist in the fields of cybernetics, systems theory and systems science, internationally known for his main work the International Encyclopedia of Systems and Cybernetics.
== Biography ==
Charles François was born in Belgium... | Wikipedia/Charles_François_(systems_scientist) |
A plant in control theory is the combination of process and actuator. A plant is often referred to with a transfer function
(commonly in the s-domain) which indicates the relation between an input signal and the output signal of a system without feedback, commonly determined by physical properties of the system. An exa... | Wikipedia/Plant_(control_theory) |
The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers.
This form of model is also well-suited for modelling objects with complex material behavior such as those with nonlinearity or viscoelasticity.
As well as engineering s... | Wikipedia/Mass-spring-damper_model |
In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form
a
0
(
x
)
y
+
a... | Wikipedia/Linear_differential_equation |
In the subject area of control theory, an internal model is a process that simulates the response of the system in order to estimate the outcome of a system disturbance. The internal model principle was first articulated in 1976 by B. A. Francis and W. M. Wonham as an explicit formulation of the Conant and Ashby good ... | Wikipedia/Internal_model_(motor_control) |
This is an alphabetical list of people who have made significant contributions in the fields of system analysis and control theory.
== Eminent researchers ==
The eminent researchers (born after 1920) include the winners of at least one award of the IEEE Control Systems Award, the Giorgio Quazza Medal, the Hendrik W. ... | Wikipedia/People_in_systems_and_control |
Cruise control (also known as speed control, cruise command, autocruise, or tempomat) is a system that automatically controls the speed of an automobile. The system is a servomechanism that takes over the car's throttle to maintain a steady speed set by the driver.
== History ==
Speed control existed in early automo... | Wikipedia/Cruise_control |
A control loop is the fundamental building block of control systems in general and industrial control systems in particular. It consists of the process sensor, the controller function, and the final control element (FCE) which controls the process necessary to automatically adjust the value of a measured process variab... | Wikipedia/Control_loop |
A distributed control system (DCS) is a computerized control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either... | Wikipedia/Distributed_control_system |
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems via biologic... | Wikipedia/Genetic_algorithms |
Motion control is a sub-field of automation, encompassing the systems or sub-systems involved in moving parts of machines in a controlled manner. Motion control systems are extensively used in a variety of fields for automation purposes, including precision engineering, micromanufacturing, biotechnology, and nanotechno... | Wikipedia/Motion_control |
A bond graph is a graphical representation of a physical dynamic system. It allows the conversion of the system into a state-space representation. It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while tho... | Wikipedia/Bond_graph |
A proportional–integral–derivative controller (PID controller or three-term controller) is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications wh... | Wikipedia/PID_controller |
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability d... | Wikipedia/Stochastic_control |
Vector control, also called field-oriented control (FOC), is a variable-frequency drive (VFD) control method in which the stator currents of a three-phase AC motor are identified as two orthogonal components that can be visualized with a vector. One component defines the magnetic flux of the motor, the other the torque... | Wikipedia/Vector_control_(motor) |
A fire-control system (FCS) is a number of components working together, usually a gun data computer, a director and radar, which is designed to assist a ranged weapon system to target, track, and hit a target. It performs the same task as a human gunner firing a weapon, but attempts to do so faster and more accurately.... | Wikipedia/Fire-control_system |
An industrial control system (ICS) is an electronic control system and associated instrumentation used for industrial process control. Control systems can range in size from a few modular panel-mounted controllers to large interconnected and interactive distributed control systems (DCSs) with many thousands of field co... | Wikipedia/Industrial_control_systems |
In linear algebra, an eigenvector ( EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector
v
{\displaystyle \mathbf {v} }
of a linear transformation
... | Wikipedia/Eigenvalues |
Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlap... | Wikipedia/Control_Systems_Engineering |
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and ... | Wikipedia/Model_Predictive_Control |
In mathematics, a transformation, transform, or self-map is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X.
Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and ... | Wikipedia/Transform_(mathematics) |
Intelligent control is a class of control techniques that use various artificial intelligence computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, reinforcement learning, evolutionary computation and genetic algorithms.
== Overview ==
Intelligent control can be divided into ... | Wikipedia/Intelligent_control |
Digital control is a branch of control theory that uses digital computers to act as system controllers.
Depending on the requirements, a digital control system can take the form of a microcontroller to an ASIC to a standard desktop computer.
Since a digital computer is a discrete system, the Laplace transform is replac... | Wikipedia/Digital_control |
In mathematics a radial basis function (RBF) is a real-valued function
φ
{\textstyle \varphi }
whose value depends only on the distance between the input and some fixed point, either the origin, so that
φ
(
x
... | Wikipedia/Radial_basis_function |
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z-domain or z-plane) representation.
It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). This... | Wikipedia/Z_transform |
A proportional–integral–derivative controller (PID controller or three-term controller) is a feedback-based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It is typically used in industrial control systems and various other applications wh... | Wikipedia/PID_control |
A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller.
A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inp... | Wikipedia/Closed-loop_controller |
Automation and Remote Control (Russian: Автоматика и Телемеханика, romanized: Avtomatika i Telemekhanika) is a Russian scientific journal published by MAIK Nauka/Interperiodica Press and distributed in English by Springer Science+Business Media.
The journal was established in April 1936 by the USSR Academy of Sciences ... | Wikipedia/Automation_and_remote_control |
In discrete-time control theory, the dead-beat control problem consists of finding what input signal must be applied to a system in order to bring the output to the steady state in the smallest number of time steps.
For an Nth-order linear system it can be shown that this minimum number of steps will be at most N (depe... | Wikipedia/Deadbeat_controller |
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the in... | Wikipedia/Nonlinear_control |
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abili... | Wikipedia/Computational_neuroscience |
A networked control system (NCS) is a control system wherein the control loops are closed through a communication network. The defining feature of an NCS is that control and feedback signals are exchanged among the system's components in the form of information packages through a network.
== Overview ==
The functiona... | Wikipedia/Networked_control_system |
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution co... | Wikipedia/Viscosity_solutions |
In mathematics, a function
f
{\displaystyle f}
defined on some set
X
{\displaystyle X}
with real or complex values is called bounded if the set of its values (its image) is bounded. In other words, there exists a real number
... | Wikipedia/Bounded_function |
In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equa... | Wikipedia/Distributed_parameter_systems |
In control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action ("input" to the system) is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its o... | Wikipedia/Open-loop_controller |
Integral windup, also known as integrator windup or reset windup, refers to the situation in a PID controller where a large change in setpoint occurs (say a positive change) and the integral term accumulates a significant error during the rise (windup), thus overshooting and continuing to increase as this accumulated e... | Wikipedia/Anti-wind_up_system_(control) |
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. It is widely used in electronic engineering tools like circuit simulators and control systems. In simple cases... | Wikipedia/Transfer_function |
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the in... | Wikipedia/Nonlinear_control_theory |
In control theory, the coefficient diagram method (CDM) is an algebraic approach applied to a polynomial loop in the parameter space. A special diagram called a "coefficient diagram" is used as the vehicle to carry the necessary information and as the criterion of good design. The performance of the closed-loop system ... | Wikipedia/Coefficient_diagram_method |
Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines".
The term "real-time" is also used in si... | Wikipedia/Real-time_control |
Control theory in sociology is the idea that two control systems—inner controls and outer controls—work against our tendencies to deviate. Control theory can either be classified as centralized or decentralized. Decentralized control is considered market control. Centralized control is considered bureaucratic control.... | Wikipedia/Control_theory_(sociology) |
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a f... | Wikipedia/Bang-bang_control |
In control theory, a closed-loop transfer function is a mathematical function describing the net result of the effects of a feedback control loop on the input signal to the plant under control.
== Overview ==
The closed-loop transfer function is measured at the output. The output signal can be calculated from the clo... | Wikipedia/Closed-loop_transfer_function |
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonli... | Wikipedia/Nonlinear_differential_equation |
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The contro... | Wikipedia/Linear_control_theory |
A hierarchical control system (HCS) is a form of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system.
== Overview ==
A hum... | Wikipedia/Hierarchical_control_system |
In linguistics, control is a construction in which the understood subject of a given predicate is determined by some expression in context. Stereotypical instances of control involve verbs. A superordinate verb "controls" the arguments of a subordinate, nonfinite verb. Control was intensively studied in the government ... | Wikipedia/Control_(linguistics) |
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks.
A neural network consists of connected units or nodes called artificial neurons, which loosely model the neurons in ... | Wikipedia/Artificial_neural_networks |
Automation and Remote Control (Russian: Автоматика и Телемеханика, romanized: Avtomatika i Telemekhanika) is a Russian scientific journal published by MAIK Nauka/Interperiodica Press and distributed in English by Springer Science+Business Media.
The journal was established in April 1936 by the USSR Academy of Sciences ... | Wikipedia/Automation_and_Remote_Control |
Control reconfiguration is an active approach in control theory to achieve fault-tolerant control for dynamic systems. It is used when severe faults, such as actuator or sensor outages, cause a break-up of the control loop, which must be restructured to prevent failure at the system level. In addition to loop restructu... | Wikipedia/Control_reconfiguration |
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, ... | Wikipedia/Lyapunov's_theory |
A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback controller.
A closed-loop controller uses feedback to control states or outputs of a dynamical system. Its name comes from the information path in the system: process inp... | Wikipedia/Closed-loop_control |
In control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action ("input" to the system) is independent of the "process output", which is the process variable that is being controlled. It does not use feedback to determine if its o... | Wikipedia/Open-loop_control |
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and ... | Wikipedia/Model_predictive_control |
In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some (typically compact) set. Robust methods aim to achieve robust performance and/or... | Wikipedia/Robust_control |
In applied physics, the concept of controlling self-organized criticality refers to the control of processes by which a self-organized system dissipates energy. The objective of the control is to reduce the probability of occurrence of and size of energy dissipation bursts, often called avalanches, of self-organized sy... | Wikipedia/Self-organized_criticality_control |
Too often systems fail, sometimes leading to significant loss of life, fortunes and confidence in the provider of a product or service. It was determined that a simple and useful tool was needed to help in the analysis of interactions of groups and systems to determine possible unexpected consequences. The tool didn’t ... | Wikipedia/Control–feedback–abort_loop |
A feed forward (sometimes written feedforward) is an element or pathway within a control system that passes a controlling signal from a source in its external environment to a load elsewhere in its external environment. This is often a command signal from an external operator.
In control engineering, a feedforward cont... | Wikipedia/Feed_forward_(control) |
In numerical methods for stochastic differential equations, the Markov chain approximation method (MCAM) belongs to the several numerical (schemes) approaches used in stochastic control theory. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as the Runge–Kutta me... | Wikipedia/Markov_chain_approximation_method |
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feed... | Wikipedia/Sliding_mode_control |
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a f... | Wikipedia/Bang–bang_control |
In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximatio... | Wikipedia/Describing_function |
In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical s... | Wikipedia/Lyapunov_function |
Computer numerical control (CNC) or CNC machining is the automated control of machine tools by a computer. It is an evolution of numerical control (NC), where machine tools are directly managed by data storage media such as punched cards or punched tape. Because CNC allows for easier programming, modification, and rea... | Wikipedia/Numerical_control |
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a numbe... | Wikipedia/Dimension_(mathematics_and_physics) |
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth.
== History ==
Geometric measure the... | Wikipedia/Geometric_measure_theory |
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at l... | Wikipedia/Resolution_of_singularities |
Compositio Mathematica is a monthly peer-reviewed mathematics journal established by L.E.J. Brouwer in 1935. It is owned by the Foundation Compositio Mathematica, and since 2004 it has been published on behalf of the Foundation by the London Mathematical Society in partnership with Cambridge University Press. According... | Wikipedia/Algebraic_Geometry_(journal) |
In mathematics, noncommutative topology is a term used for the relationship between topological and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark theorem, which implies the duality of the category of locally compact Hausdorff spaces and the category of commutative C*-algebras. Noncommutative to... | Wikipedia/Noncommutative_topology |
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of point... | Wikipedia/Algebraic_stack |
In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could be the ring of continuous functions defined on that open set. S... | Wikipedia/Sheaf_theory |
In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic graph. Such sets and functions are mainly studied in real algebraic geometry... | Wikipedia/Semi-algebraic_set |
Discrete differential geometry is the study of discrete counterparts of notions in differential geometry. Instead of smooth curves and surfaces, there are polygons, meshes, and simplicial complexes. It is used in the study of computer graphics, geometry processing and topological combinatorics.
== See also ==
Discret... | Wikipedia/Discrete_differential_geometry |
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/Regular_function |
In mathematics – particularly in homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often used to capture information about a topological or geometric space. Explicitly, a differential graded algebra is a graded associative a... | Wikipedia/Differential_graded_commutative_algebra |
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