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In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical enti... | Wikipedia/Euler_equations |
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are a general setting for studying many of the concepts of mathematical analysis and geometry.
The most fam... | Wikipedia/Distance_function |
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/Eigenvalue,_eigenvector_and_eigenspace |
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which points are represented by points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space or by the displacement vectors from the origi... | Wikipedia/Hyperboloid_model |
In differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was announced in 2012 and published in 2014.
== Willmore energy ==
Let v : M → R... | Wikipedia/Willmore_conjecture |
In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements (in cases when this is indeed a submodule, such as when the ring is commutativ... | Wikipedia/Torsion_(algebra) |
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.
Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsic... | Wikipedia/Regular_surface_(differential_geometry) |
In mathematics, triangulation describes the replacement of topological spaces with simplicial complexes by the choice of an appropriate homeomorphism. A space that admits such a homeomorphism is called a triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exist... | Wikipedia/Triangulation_(topology) |
In Riemannian geometry, Gauss's lemma asserts that any sufficiently small sphere centered at a point in a Riemannian manifold is perpendicular to every geodesic through the point. More formally, let M be a Riemannian manifold, equipped with its Levi-Civita connection, and p a point of M. The exponential map is a mapp... | Wikipedia/Gauss's_lemma_(Riemannian_geometry) |
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivale... | Wikipedia/Elliptic_differential_operator |
In differential geometry, the Carathéodory conjecture is a mathematical conjecture attributed to Constantin Carathéodory by Hans Ludwig Hamburger in a session of the Berlin Mathematical Society in 1924. Carathéodory never committed the conjecture into writing, but did publish a paper on a related subject. In John Eden... | Wikipedia/Carathéodory_conjecture |
In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segm... | Wikipedia/Beltrami-Klein_model |
The Weingarten equations give the expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of a point on the surface. These formulas were established in 1861 by the German mathematician Julius Weingarten.
== Statement in classical differential geometr... | Wikipedia/Weingarten_equations |
In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and the Cayley–Klein model, is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk (or n-dimensional unit ball) and lines are represented by the chords, straight line segm... | Wikipedia/Klein_model |
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form
d
d
x
... | Wikipedia/Sturm–Liouville_equation |
Science of morality (also known as science of ethics or scientific ethics) may refer to various forms of ethical naturalism grounding morality and ethics in rational, empirical consideration of the natural world. It is sometimes framed as using the scientific approach to determine what is right and wrong, in contrast t... | Wikipedia/Science_of_morality |
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the re... | Wikipedia/Bellman_equation |
In mathematics, the method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase. The saddle... | Wikipedia/Method_of_steepest_descent |
Integrated nested Laplace approximations (INLA) is a method for approximate Bayesian inference based on Laplace's method. It is designed for a class of models called latent Gaussian models (LGMs), for which it can be a fast and accurate alternative for Markov chain Monte Carlo methods to compute posterior marginal dist... | Wikipedia/Integrated_nested_Laplace_approximations |
In mathematics, Laplace's principle is a basic theorem in large deviations theory which is similar to Varadhan's lemma. It gives an asymptotic expression for the Lebesgue integral of exp(−θφ(x)) over a fixed set A as θ becomes large. Such expressions can be used, for example, in statistical mechanics to determining the... | Wikipedia/Laplace_principle_(large_deviations_theory) |
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold
of much smaller d... | Wikipedia/Integrable_model |
In mathematics, the inverse Laplace transform of a function
F
(
s
)
{\displaystyle F(s)}
is a real function
f
(
t
)
{\displaystyle f(t)}
that is piecewise-continuous, exponentially-re... | Wikipedia/Inverse_Laplace_transform |
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to functions given by integration against a rapidly-varying complex exponential.
This method originates from the 19th century, and is due to George Gabriel Stokes and Lord Kelvin.
It is closely related to Laplace's ... | Wikipedia/Stationary_phase_approximation |
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f
(
x
)
=
exp
(
−
x
2
)
{\displaysty... | Wikipedia/Gaussian_function |
Laplace's approximation provides an analytical expression for a posterior probability distribution by fitting a Gaussian distribution with a mean equal to the MAP solution and precision equal to the observed Fisher information. The approximation is justified by the Bernstein–von Mises theorem, which states that, under ... | Wikipedia/Laplace's_approximation |
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cramér and Lundberg. A unified f... | Wikipedia/Large_deviations_theory |
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Par... | Wikipedia/Partition_function_(quantum_field_theory) |
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree. That i... | Wikipedia/Homogeneous_function |
In mathematics, a piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments.
== Definition ==
A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals ... | Wikipedia/Piecewise_linear_function |
The governing equations of a mathematical model describe how the values of the unknown variables (i.e. the dependent variables) change when one or more of the known (i.e. independent) variables change.
Physical systems can be modeled phenomenologically at various levels of sophistication, with each level capturing a d... | Wikipedia/Governing_equation |
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of... | Wikipedia/Malthusian_growth_model |
"All models are wrong" is a common aphorism and anapodoton in statistics. It is often expanded as "All models are wrong, but some are useful". The aphorism acknowledges that statistical models always fall short of the complexities of reality but can still be useful nonetheless. The aphorism is generally attributed to G... | Wikipedia/All_models_are_wrong |
In mathematics, statistics, and computational modelling, a grey box model combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information on the smoothness of results, to models that need only parameter values from data or existing literature. Thus, almost a... | Wikipedia/Grey_box_model |
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases an... | Wikipedia/Mathematical_modelling_of_infectious_disease |
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation
f
(
x
)
=
L
1
+
e
−
... | Wikipedia/Logistic_function |
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | Wikipedia/Loss_function |
Cliodynamics () is a transdisciplinary area of research that integrates cultural evolution, economic history/cliometrics, macrosociology, the mathematical modeling of historical processes during the longue durée, and the construction and analysis of historical databases.
Cliodynamics treats history as science. Its prac... | Wikipedia/Cliodynamics |
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applie... | Wikipedia/Constitutive_equation |
Optimal foraging theory (OFT) is a behavioral ecology model that helps predict how an animal behaves when searching for food. Although obtaining food provides the animal with energy, searching for and capturing the food require both energy and time. To maximize fitness, an animal adopts a foraging strategy that provide... | Wikipedia/Optimal_foraging_theory |
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that ap... | Wikipedia/Model_fitting |
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965.
Newton's method for solving f(x) = 0 uses the Jacobian matrix, J, at every iteration. However, computing this Jacobian can be a difficult and expensive operation; for ... | Wikipedia/Broyden's_method |
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities... | Wikipedia/Statistical_model |
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called a... | Wikipedia/Model_inversion |
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, 'a measure'.
Models can be divided into physical models (e.g. a ship model or a fashion model) and... | Wikipedia/Model |
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies. Wassily Leontief (1906–1999) is credited with developing this type of analysis and earned the Nobel Prize in Economics for his devel... | Wikipedia/Input–output_model |
In statistics, the term linear model refers to any model which assumes linearity in the system. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In ... | Wikipedia/Linear_model |
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | Wikipedia/Objective_function |
In classical mechanics, a constraint on a system is a parameter that the system must obey. For example, a box sliding down a slope must remain on the slope. There are two different types of constraints: holonomic and non-holonomic.
== Types of constraint ==
First class constraints and second class constraints
Primary... | Wikipedia/Constraint_(classical_mechanics) |
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a funct... | Wikipedia/Surrogate_model |
Microscale models form a broad class of computational models that simulate fine-scale details, in contrast with macroscale models, which amalgamate details into select categories. Microscale and macroscale models can be used together to understand different aspects of the same problem.
== Applications ==
Macroscale m... | Wikipedia/Microscale_and_macroscale_models |
A molecular model is a physical model of an atomistic system that represents molecules and their processes. They play an important role in understanding chemistry and generating and testing hypotheses. The creation of mathematical models of molecular properties and behavior is referred to as molecular modeling, and the... | Wikipedia/Molecular_model |
The neighbour-sensing mathematical model of hyphal growth is a set of interactive computer models that simulate the way fungi hyphae grow in three-dimensional space. The three-dimensional simulation is an experimental tool which can be used to study the morphogenesis of fungal hyphal networks.
The modelling process st... | Wikipedia/Neighbour-sensing_model |
A mathematical model may mean a description of a physical system using mathematical concepts and language. "Mathematical model" may also refer to:
Model theory, a branch of mathematical logic, in which a model is an abstract structure that satisfies a set of logical sentences
Physical models of mathematical objects, c... | Wikipedia/Mathematical_model_(disambiguation) |
Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real ... | Wikipedia/Scientific_model |
The World in the Model: How Economists Work and Think is a work by Mary S. Morgan published by Cambridge University Press in 2012.
== Content ==
Mary S. Morgan, defined by Robert Sugden "a major philosopher and historian of economics", analyzes with examples how economists work and think using models. Her book recon... | Wikipedia/The_World_in_the_Model:_How_Economists_Work_and_Think |
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together is called the "physical sciences".
== Definition ==
Physical science can be described as all of the following:
A branch of sci... | Wikipedia/Physical_sciences |
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations and are converse to discrete modelling.
Modelling is generally broken down into several steps:
Making assumptio... | Wikipedia/Continuous_model |
Power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. Power is a scalar quantity.
Specifying power in particular systems may require attention to other quantities; for example, the power involved in movin... | Wikipedia/Mechanical_power_(physics) |
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark di... | Wikipedia/Applied_mechanics |
In classical mechanics, Routh's procedure or Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. Although Routhian mechanics is equivalent ... | Wikipedia/Routhian_mechanics |
A moment is a mathematical expression involving the product of a distance and a physical quantity such as a force or electric charge. Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. For example, the moment of force, oft... | Wikipedia/Moment_(physics) |
A fictitious force, also known as an inertial force or pseudo-force, is a force that appears to act on an object when its motion is described or experienced from a non-inertial frame of reference. Unlike real forces, which result from physical interactions between objects, fictitious forces occur due to the acceleratio... | Wikipedia/Fictitious_force |
In classical mechanics, a reactive centrifugal force forms part of an action–reaction pair with a centripetal force.
In accordance with Newton's first law of motion, an object moves in a straight line in the absence of a net force acting on the object. A curved path ensues when a force that is orthogonal to the object'... | Wikipedia/Reactive_centrifugal_force |
Centrifugal force is a fictitious force in Newtonian mechanics (also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It appears to be directed radially away from the axis of rotation of the frame. The magnitude of the centrifugal force F on an obj... | Wikipedia/Centrifugal_force |
Centripetal force (from Latin centrum, "center" and petere, "to seek") is the force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton coined the term... | Wikipedia/Centripetal_force |
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.
The Hamilton–Jacobi equation is a formulation... | Wikipedia/Hamilton–Jacobi_equation |
In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the ... | Wikipedia/Coriolis_force |
In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p1, and a subsequent momentum is p2, the object has received an impulse J:
J
=
p
... | Wikipedia/Impulse_(physics) |
A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position. Whe... | Wikipedia/Pendulum_(mechanics) |
In classical mechanics, Appell's equation of motion (aka the Gibbs–Appell equation of motion) is an alternative general formulation of classical mechanics described by Josiah Willard Gibbs in 1879 and Paul Émile Appell in 1900.
== Statement ==
The Gibbs-Appell equation reads
Q
... | Wikipedia/Appell's_equation_of_motion |
A fictitious force, also known as an inertial force or pseudo-force, is a force that appears to act on an object when its motion is described or experienced from a non-inertial frame of reference. Unlike real forces, which result from physical interactions between objects, fictitious forces occur due to the acceleratio... | Wikipedia/Fictitious_forces |
The following is a timeline of the history of classical mechanics:
== Antiquity ==
4th century BC – Aristotle invents the system of Aristotelian physics, which is later largely disproved
4th century BC – Babylonian astronomers calculate Jupiter's position using the Trapezoidal rule
260 BC – Archimedes works out the p... | Wikipedia/Timeline_of_classical_mechanics |
The Koopman–von Neumann (KvN) theory is a description of classical mechanics as an operatorial theory similar to quantum mechanics, based on a Hilbert space of complex, square-integrable wavefunctions. As its name suggests, the KvN theory is related to work: 220 by Bernard Koopman and John von Neumann.
== History ==... | Wikipedia/Koopman–von_Neumann_classical_mechanics |
In physics and engineering, kinetics is the branch of classical mechanics that is concerned with the relationship between the motion and its causes, specifically, forces and torques. Since the mid-20th century, the term "dynamics" (or "analytical dynamics") has largely superseded "kinetics" in physics textbooks, though... | Wikipedia/Kinetics_(physics) |
Rotation around a fixed axis or axial rotation is a special case of rotational motion around an axis of rotation fixed, stationary, or static in three-dimensional space. This type of motion excludes the possibility of the instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobb... | Wikipedia/Rotational_dynamics |
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler.
In the absence of app... | Wikipedia/Euler's_equations_(rigid_body_dynamics) |
Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies.
Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body ... | Wikipedia/Wrench_(screw_theory) |
In physics, a couple or torque is a pair of forces that are equal in magnitude but opposite in their direction of action. A couple produce a pure rotational motion without any translational form.
== Simple couple ==
The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coi... | Wikipedia/Couple_(mechanics) |
Inverse dynamics is an inverse problem. It commonly refers to either inverse rigid body dynamics or inverse structural dynamics. Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics (motion) of a body and the body's inertial properties (mass and moment o... | Wikipedia/Inverse_dynamics |
In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kern... | Wikipedia/Fredholm_theory |
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite expectation. A renewal-reward process addit... | Wikipedia/Renewal_theory |
In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. A useful method to solve such equations, the Adomian decomposition method, is due to George Ado... | Wikipedia/Fredholm_integral_equation |
In mathematical physics, more specifically the one-dimensional inverse scattering problem, the Marchenko equation (or Gelfand-Levitan-Marchenko equation or GLM equation), named after Israel Gelfand, Boris Levitan and Vladimir Marchenko, is derived by computing the Fourier transform of the scattering relation:
... | Wikipedia/Marchenko_equation |
In mathematics, the inverse scattering transform is a method that solves the initial value problem for a nonlinear partial differential equation using mathematical methods related to wave scattering.: 4960 The direct scattering transform describes how a function scatters waves or generates bound-states.: 39–43 The ... | Wikipedia/Inverse_scattering_transform |
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on th... | Wikipedia/Wiener–Hopf_method |
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviat... | Wikipedia/Boundary_element_method |
In actuarial science and applied probability, ruin theory (sometimes risk theory or collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and def... | Wikipedia/Ruin_theory |
In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind.
A linear Volterra equation of the first kind is
f
(
t
)
=
∫
... | Wikipedia/Volterra_integral_equation |
The electric-field integral equation is a relationship that allows the calculation of an electric field (E) generated by an electric current distribution (J).
== Derivation ==
When all quantities in the frequency domain are considered, a time-dependency
e
j
... | Wikipedia/Electric-field_integral_equation |
The calculus ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned characteristica universalis, a universal conceptual language.
== Two views ==
There are two contrasting points of view on wha... | Wikipedia/Calculus_ratiocinator |
In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output th... | Wikipedia/Truth_function |
In computer science, a production or production rule is a rewrite rule that replaces some symbols with other symbols. A finite set of productions
P
{\displaystyle P}
is the main component in the specification of a formal grammar (specifically a generative grammar). The other ... | Wikipedia/Production_(computer_science) |
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variable... | Wikipedia/Predicate_calculus |
In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
It was introduced in 1961 by Martin Davis, George Logema... | Wikipedia/DPLL_algorithm |
In mathematical logic, a proof calculus or a proof system is built to prove statements.
== Overview ==
A proof system includes the components:
Formal language: The set L of formulas admitted by the system, for example, propositional logic or first-order logic.
Rules of inference: List of rules that can be employed ... | Wikipedia/Proof_calculus |
In classical propositional logic, material implication is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not-
P
{\displaystyle P}
or... | Wikipedia/Material_implication_(rule_of_inference) |
In proof theory, the semantic tableau (; plural: tableaux), also called an analytic tableau, truth tree, or simply tree, is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at e... | Wikipedia/Method_of_analytic_tableaux |
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of excluded middle and doub... | Wikipedia/Intuitionistic_propositional_calculus |
Destructive dilemma is the name of a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either Q is false or S is false, then either P or R must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents ... | Wikipedia/Destructive_dilemma |
This is a list of topics around Boolean algebra and propositional logic.
== Articles with a wide scope and introductions ==
Algebra of sets
Boolean algebra (structure)
Boolean algebra
Field of sets
Logical connective
Propositional calculus
== Boolean functions and connectives ==
Ampheck
Analysis of B... | Wikipedia/Boolean_algebra_topics |
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