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113 relations: Action (physics), Allegheny Mountain (Pennsylvania), Anchor, Shropshire, Angular defect, Anti-de Sitter space, Azeotrope, Bifurcation theory, Big Round Top, Cation–pi interaction, Cellular model, Chicago Portage, Church Stretton, Church Stretton railway station, Clarke's Gap, Cottonwood Pass, Critical point (mathematics), Crunode, Darwin–Fowler method, Derivative test, Differential calculus, Earnshaw's theorem, Eastern Continental Divide, Energy minimization, Envelope theorem, Equilibrium point, Espartel Sill, Evolutionary invasion analysis, Expectation–maximization algorithm, Feasible region, Finite difference, Function of several real variables, Gaussian curvature, Gear, Hagere Selam (Degua Tembien), Hessian matrix, History of variational principles in physics, Homoclinic bifurcation, Hyperbolic equilibrium point, Hyperbolic geometry, Hyperbolic space, Infinite-period bifurcation, Instanton, Lagrange multiplier, Lagrange point colonization, Least squares support vector machine, List of differential geometry topics, List of mathematical artists, List of mathematical properties of points, List of multivariable calculus topics, List of passes of the Rocky Mountains, ..., List of Rocky Mountain passes on the continental divide, Lotka–Volterra equations, Magnetic anisotropy, Magnetocrystalline anisotropy, Marching squares, Mark Child, Mathematical and theoretical biology, Mathematical optimization, Max–min inequality, Maxima and minima, Maximum principle, McPherson Ridge, Mechanical equilibrium, Method of steepest descent, Minimal surface, Minimax eversion, Monkey saddle, Monterey Pass, Morse theory, Mountain pass, Mountain pass theorem, Newton's method in optimization, Normal plane (geometry), Palais–Smale compactness condition, Paraboloid, Peeler Lake, Peixoto's theorem, Penning trap, Periodic point, Phase plane, Pizzo Coca, Potential energy surface, Principle of least action, Pseudosphere, Ramsey–Cass–Koopmans model, Reaction mechanism, Reeb graph, Robert Longhurst, Round window, Saddle (disambiguation), Saddle roof, Saddle-node bifurcation, Saddleback, Second partial derivative test, Singular point of a curve, Sion's minimax theorem, Somatic evolution in cancer, Sphaleron, Stationary point, Theta model, Topographic prominence, Transition state theory, Trapped ion quantum computer, Triangle, Utah teapot, Uzawa iteration, Van Hove singularity, Variational transition-state theory, Vector calculus, Wald's maximin model, Washington & Old Dominion Railroad Regional Park, Wet electrons, 3-manifold. Expand index (63 more) »
Action (physics)
In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived.
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Allegheny Mountain (Pennsylvania)
Allegheny Mountain is a stratigraphic ridge that extends northeast to southwest from south of Blue Knob (Pennsylvania) to a saddle point at the Savage Mountain anticline. It merges with Negro Mountain just north of the Cambria County line where the Berlin-Salisbury basin expires.;Eastern Continental Divide (ECD): The ECD enters Allegheny Mountain south of Fraziers Pass and follows the Allegheny Backbone southwest where it leaves the escarpment toward the saddle point to the southeast between headwaters of Flaugherty and Wills Creeks, at which the ECD enters the Savage Mountain anticline.
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Anchor, Shropshire
Anchor is a remote hamlet in southwest Shropshire, England.
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Angular defect
In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.
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Anti-de Sitter space
In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.
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Azeotrope
An azeotrope (gK, US) or a constant boiling point mixture is a mixture of two or more liquids whose proportions cannot be altered or changed by simple distillation.
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Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
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Big Round Top
Big Round Top is a boulder-strewn hill notable as the topographic high point of the Gettysburg Battlefield and for 1863 American Civil War engagements for which Medals of Honor were awarded.
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Cation–pi interaction
Cation–π interaction is a noncovalent molecular interaction between the face of an electron-rich π system (e.g. benzene, ethylene, acetylene) and an adjacent cation (e.g. Li+, Na+).
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Cellular model
Creating a cellular model has been a particularly challenging task of systems biology and mathematical biology.
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Chicago Portage
The Chicago Portage is a water gap, and in the past a sometime wind-gap portage, connecting the watersheds (BrE: drainage basins) and the navigable waterways of the Mississippi River and the Great Lakes.
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Church Stretton
Church Stretton is a small town in Shropshire, England, south of Shrewsbury and north of Ludlow.
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Church Stretton railway station
Church Stretton railway station in Church Stretton, Shropshire, England, is a station on the Welsh Marches Line, south of Shrewsbury railway station; trains on the Heart of Wales Line also serve the station.
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Clarke's Gap
Clarke's Gap, also known as Clarks Gap, is a pass through Catoctin Mountain west of Leesburg, Virginia.
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Cottonwood Pass
Cottonwood Pass (elevation) is a high mountain pass in the Rocky Mountains of south-central Colorado, United States.
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Critical point (mathematics)
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.
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Crunode
In mathematics, a crunode (archaic) or node is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines at the point of intersection.
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Darwin–Fowler method
In statistical mechanics, the Darwin–Fowler method is used for deriving the distribution functions with mean probability.
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Derivative test
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point.
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Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.
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Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges.
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Eastern Continental Divide
The Eastern Continental Divide (ECD) or Appalachian Divide or Eastern Divide, in conjunction with other continental divides of North America, demarcates two watersheds of the Atlantic Ocean: the Gulf of Mexico watershed and the Atlantic Seaboard watershed.
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Energy minimization
In the field of computational chemistry, energy minimization (also called energy optimization, geometry minimization, or geometry optimization) is the process of finding an arrangement in space of a collection of atoms where, according to some computational model of chemical bonding, the net inter-atomic force on each atom is acceptably close to zero and the position on the potential energy surface (PES) is a stationary point (described later).
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Envelope theorem
The envelope theorem is a result about the differentiability properties of the objective function of a parameterized optimization problem.
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Equilibrium point
In mathematics, specifically in differential equations, an equilibrium point is a constant solution to a differential equation.
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Espartel Sill
The Spartel or Espartel Sill is one of the sills separating the Mediterranean Sea and the Atlantic Ocean.
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Evolutionary invasion analysis
Evolutionary invasion analysis, also known as adaptive dynamics, is a set of mathematical modeling techniques that use differential equations to study the long-term evolution of traits in asexually reproducing populations.
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Expectation–maximization algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables.
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Feasible region
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.
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Finite difference
A finite difference is a mathematical expression of the form.
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Function of several real variables
In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables.
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Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.
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Gear
A gear or cogwheel is a rotating machine part having cut like teeth, or cogs, which mesh with another toothed part to transmit torque.
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Hagere Selam (Degua Tembien)
Hagere Selam (meaning place of peace) is a town in northern Ethiopia.
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Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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History of variational principles in physics
A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an extremum (minimum, maximum or saddle point) of a function or functional.
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Homoclinic bifurcation
A homoclinic bifurcation is a global bifurcation which often occurs when a periodic orbit collides with a saddle point.
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Hyperbolic equilibrium point
In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Hyperbolic space
In mathematics, hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional curvature.
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Infinite-period bifurcation
In mathematics, an infinite-period bifurcation is a global bifurcation that can occur when two fixed points emerge on a limit cycle.
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Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics.
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Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
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Lagrange point colonization
Lagrange point colonization is the colonization of the five equilibrium points in the orbit of a planet or its primary moon, called Lagrangian points.
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Least squares support vector machine
Least squares support vector machines (LS-SVM) are least squares versions of support vector machines (SVM), which are a set of related supervised learning methods that analyze data and recognize patterns, and which are used for classification and regression analysis.
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List of differential geometry topics
This is a list of differential geometry topics.
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List of mathematical artists
This is a list of artists who actively explored mathematics in their artworks.
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List of mathematical properties of points
In mathematics, the following appear.
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List of multivariable calculus topics
This is a list of multivariable calculus topics.
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List of passes of the Rocky Mountains
The Rocky Mountains of North America include more than one thousand named mountain passes (topographic saddle points).
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List of Rocky Mountain passes on the continental divide
This is a list of Rocky Mountain passes on the Continental Divide.
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Lotka–Volterra equations
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
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Magnetic anisotropy
Magnetic anisotropy is the directional dependence of a material's magnetic properties.
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Magnetocrystalline anisotropy
In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others.
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Marching squares
Marching squares is a computer graphics algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values).
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Mark Child
Mark Sheard Child FRS (born 17 August 1937) is a British chemist, and Emeritus Fellow of St Edmund Hall, Oxford.
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Mathematical and theoretical biology
Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Max–min inequality
In mathematics, the max–min inequality is as follows: for any function f: Z × W → ℝ, \sup_ \inf_ f(z, w) \leq \inf_ \sup_ f(z, w).
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Maximum principle
In mathematics, the maximum principle is a property of solutions to certain partial differential equations, of the elliptic and parabolic types.
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McPherson Ridge
McPherson Ridge is a landform used for military engagements during the 1863 Battle of Gettysburg, First Day, when the I Corps (Union Army) had a headquarters on the ridge and was defeated by the Confederate division of Major General Henry Heth.
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Mechanical equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero.
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Method of steepest descent
In mathematics, the method of steepest descent or stationary-phase method 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.
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Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area.
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Minimax eversion
In geometry, minimax eversions are a class of sphere eversions, constructed by using half-way models.
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Monkey saddle
In mathematics, the monkey saddle is the surface defined by the equation It belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail.
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Monterey Pass
Monterey Pass is a mountain pass located in Franklin County, southern Pennsylvania.
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Morse theory
"Morse function" redirects here.
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Mountain pass
A mountain pass is a navigable route through a mountain range or over a ridge.
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Mountain pass theorem
The mountain pass theorem is an existence theorem from the calculus of variations.
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Newton's method in optimization
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to), also known as the stationary points of.
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Normal plane (geometry)
A normal plane is any plane containing the normal vector of a surface at a particular point.
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Palais–Smale compactness condition
The Palais–Smale compactness condition, named after Richard Palais and Stephen Smale, is a hypothesis for some theorems of the calculus of variations.
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Paraboloid
In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.
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Peeler Lake
Peeler Lake is a California landform within the Toiyabe National Forest and on the west edge of the Hoover Wilderness.
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Peixoto's theorem
In the theory of dynamical systems, Peixoto theorem, proved by Maurício Peixoto, states that among all smooth flows on surfaces, i.e. compact two-dimensional manifolds, structurally stable systems may be characterized by the following properties.
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Penning trap
A Penning trap is a device for the storage of charged particles using a homogeneous axial magnetic field and an inhomogeneous quadrupole electric field.
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Periodic point
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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Phase plane
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc.
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Pizzo Coca
Pizzo Coca is a mountain that straddles the Val Seriana and the Valtellina in Lombardy, Italy.
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Potential energy surface
A potential energy surface (PES) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms.
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Principle of least action
The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system.
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Pseudosphere
In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature.
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Ramsey–Cass–Koopmans model
The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans.
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Reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.
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Reeb graph
A Reeb graph (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolution of the level sets of a real-valued function on a manifold.
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Robert Longhurst
Robert Longhurst is an American sculptor who was born in Schenectady, New York in 1949.
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Round window
The round window is one of the two openings from the middle ear into the inner ear.
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Saddle (disambiguation)
A saddle is a supportive structure for a rider or other load, fastened to an animal's back by a girth.
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Saddle roof
A saddle roof is a roof form which follows a convex curve about one axis and a concave curve about the other.
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Saddle-node bifurcation
In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical system collide and annihilate each other.
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Saddleback
Saddleback may refer to.
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Second partial derivative test
In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum, maximum or saddle point.
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Singular point of a curve
In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.
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Sion's minimax theorem
In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion.
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Somatic evolution in cancer
Somatic evolution is the accumulation of mutations and epimutations in somatic cells (the cells of a body, as opposed to germplasm and stem cells) during a lifetime, and the effects of those mutations and epimutations on the fitness of those cells.
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Sphaleron
A sphaleron (σφαλερός "slippery") is a static (time-independent) solution to the electroweak field equations of the Standard Model of particle physics, and is involved in certain hypothetical processes that violate baryon and lepton numbers.
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Stationary point
In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.
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Theta model
The theta model, or Ermentrout–Kopell canonical model, is a biological neuron model originally developed to model neurons in the animal Aplysia, and later used in various fields of computational neuroscience.
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Topographic prominence
In topography, prominence characterizes the height of a mountain or hill's summit by the vertical distance between it and the lowest contour line encircling it but containing no higher summit within it.
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Transition state theory
Transition state theory (TST) explains the reaction rates of elementary chemical reactions.
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Trapped ion quantum computer
A trapped ion quantum computer is one proposed approach to a large-scale quantum computer.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Utah teapot
The Utah teapot, or the Newell teapot, is a 3D test model that has become a standard reference object and an in-joke within the computer graphics community.
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Uzawa iteration
In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems.
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Van Hove singularity
A Van Hove singularity is a singularity (non-smooth point) in the density of states (DOS) of a crystalline solid.
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Variational transition-state theory
Variational transition-state theory is a refinement of transition-state theory.
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Vector calculus
Vector calculus, or vector analysis, is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3.
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Wald's maximin model
In decision theory and game theory, Wald's maximin model is a non-probabilistic decision-making model according to which decisions are ranked on the basis of their worst-case outcomes – the optimal decision is one with the least worst outcome.
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Washington & Old Dominion Railroad Regional Park
The Washington & Old Dominion Railroad Regional Park is a linear regional park in Northern Virginia.
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Wet electrons
Wet electrons, which occur on the surface of metal oxides, are a transition state for electrons between the solid and liquid states of matter.
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3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.
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Redirects here:
Saddle points, Saddle surface, Saddle value, Saddle-node, Saddle-point, Saddlepoint.
References
[1] https://en.wikipedia.org/wiki/Saddle_point
