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212 relations: Activation function, Affine curvature, Airy wave theory, Alexander Macfarlane, AlexNet, Alternating series, Angle, Angle of parallelism, Area of a circle, Argument of a function, Arthur E. Kennelly, Augustus De Morgan, Beltrami–Klein model, Benjamin–Bona–Mahony equation, Bernoulli number, Bogoliubov transformation, Bohr effect, C mathematical functions, Casio fx-3650P, Casio fx-39, Casio fx-7000G, Catenary, Centimorgan, CH, Characteristic polynomial, Cloth modeling, Cnoidal wave, Cofunction, Complex number, Computer, Contributions of Leonhard Euler to mathematics, Convolutional neural network, Cooperativity, Coordinate systems for the hyperbolic plane, CORDIC, Correlate summation analysis, Cosh, Cubic function, Curie's law, Darcy's law, De Moivre's formula, Derivations of the Lorentz transformations, Differentiation rules, Dispersion (water waves), Drag (physics), Edith Clarke, Elementary function, Entire function, Equal incircles theorem, Eugenio Beltrami, ..., Euler number, Euler's continued fraction formula, Even and odd functions, Exponential function, Exponentiation, Folded normal distribution, Foundations of mathematics, Four-vector, Fourier series, Fourier transform, Franz Taurinus, Functional determinant, Gated recurrent unit, Gateway Arch, Generalized trigonometry, Glossary of areas of mathematics, Glossary of calculus, GNU MPFR, Group of rational points on the unit circle, Gudermannian function, Gustav von Escherich, Gyrovector space, Hemoglobin, History of Lorentz transformations, Horocycle, HP 35s, HP-42S, Hyperbola, Hyperbolic, Hyperbolic angle, Hyperbolic equilibrium point, Hyperbolic geometry, Hyperbolic law of cosines, Hyperbolic secant distribution, Hyperbolic sector, Hyperbolic triangle, Hyperbolic trigonometry, Hyperboloid, Hyperboloid model, Hypercycle (geometry), Hypertranscendental function, IEEE 754, Inverse function, Inverse hyperbolic functions, ISO 80000-2, Jacobi elliptic functions, Jacopo Riccati, Janet Barnett, Johann Heinrich Lambert, Kepler orbit, Korteweg–de Vries equation, Lambert quadrilateral, Langmuir probe, Laplace transform, Law of cosines, Leonhard Euler, Light cone, Lindemann–Weierstrass theorem, Linear differential equation, List of calculus topics, List of exponential topics, List of integrals of hyperbolic functions, List of Laplace transforms, List of mathematical abbreviations, List of mathematical functions, List of representations of e, List of trigonometric identities, Logarithmic number system, Logistic distribution, Logistic function, Long short-term memory, Lorentz transformation, Mild-slope equation, Mittag-Leffler function, Mode-locking, Modern Arabic mathematical notation, Modified Morlet wavelet, Multilayer perceptron, Mxparser, Natural logarithm, Newton's theorem of revolving orbits, Noncentral chi-squared distribution, Nonlinear system, Normal moveout, Oblate spheroidal coordinates, Occurrences of Grandi's series, OpenPlaG, Optical autocorrelation, Outline of trigonometry, Parabolic arch, Pfaffian function, Photoluminescence, Plastic number, Poincaré disk model, Poinsot's spirals, Proper reference frame (flat spacetime), Proper velocity, Pythagorean theorem, Reciprocity (photography), Rectangular function, Rectifier (neural networks), Recursive neural network, Reflections of signals on conducting lines, Relativistic rocket, Resource fragmentation hypothesis, Right triangle, Risk aversion, RLC circuit, Scientific calculator, Sech (disambiguation), Self-phase modulation, Series multisection, SH, Sharp EL-5120, Shine, Siegmund Guenther, Sigmoid function, Silicon photonics, Simple suspension bridge, Sine, Singular boundary method, Sinh, Skerryvore, Slide rule, Softmax function, Soliton (optics), Spacetime, Special functions, Split-complex number, Squeeze mapping, Srinivasa Ramanujan, Stirling's approximation, Stjepan Horvat, Stumpff function, Support vector machine, Symmetry in mathematics, Synthetic-aperture radar, Tangent half-angle formula, Tanh-sinh quadrature, Taylor series, Terminal velocity, TI SR-50, TI-54, Tractrix, Transcendental function, Trigonometric functions, Trigonometric functions of matrices, Trigonometric integral, Trigonometric substitution, Trochoidal wave, Tsiolkovsky rocket equation, Tuning fork, Unary function, Unit hyperbola, Unit interval, Van Deemter equation, Vanishing gradient problem, Velocity-addition formula, Vincenzo Riccati, Visual acuity, Wrapped asymmetric Laplace distribution, XLfit. Expand index (162 more) »
Activation function
In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs.
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Affine curvature
Special affine curvature, also known as the equi-affine curvature or affine curvature, is a particular type of curvature that is defined on a plane curve that remains unchanged under a special affine transformation (an affine transformation that preserves area).
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Airy wave theory
In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer.
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Alexander Macfarlane
Prof Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician.
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AlexNet
AlexNet is the name of a convolutional neural network, originally written with CUDA to run with GPU support, which competed in the ImageNet Large Scale Visual Recognition Challenge in 2012.
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Alternating series
In mathematics, an alternating series is an infinite series of the form with an > 0 for all n.
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Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Angle of parallelism
In hyperbolic geometry, the angle of parallelism \Pi(a), is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides.
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Area of a circle
In geometry, the area enclosed by a circle of radius is.
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Argument of a function
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
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Arthur E. Kennelly
Arthur Edwin Kennelly (December 17, 1861 – June 18, 1939), was an Irish-American electrical engineer.
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Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.
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Beltrami–Klein model
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 segments with ideal endpoints on the boundary sphere.
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Benjamin–Bona–Mahony equation
The Benjamin–Bona–Mahony equation (or BBM equation) – also known as the regularized long-wave equation (RLWE) – is the partial differential equation This equation was studied in as an improvement of the Korteweg–de Vries equation (KdV equation) for modeling long surface gravity waves of small amplitude – propagating uni-directionally in 1+1 dimensions.
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Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
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Bogoliubov transformation
In theoretical physics, the Bogoliubov transformation, also known as Bogoliubov-Valatin transformation, were independently developed in 1958 by Nikolay Bogolyubov and John George Valatin for finding solutions of BCS theory in a homogeneous system.
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Bohr effect
The Bohr effect is a physiological phenomenon first described in 1904 by the Danish physiologist Christian Bohr: hemoglobin's oxygen binding affinity (see Oxygen–haemoglobin dissociation curve) is inversely related both to acidity and to the concentration of carbon dioxide.
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C mathematical functions
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions.
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Casio fx-3650P
Casio fx-3650P is a programmable scientific calculator manufactured by Casio Computer Co., Ltd.
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Casio fx-39
The fx-39 is a scientific calculator manufactured by Casio released in 1978 and is one of several models to share the same physical design format.
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Casio fx-7000G
The Casio FX-7000G is a calculator which is widely known as being the world's first graphing calculator available to the public.
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Catenary
In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.
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Centimorgan
In genetics, a centimorgan (abbreviated cM) or map unit (m.u.) is a unit for measuring genetic linkage.
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CH
CH, Ch, cH, or ch may refer to.
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Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
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Cloth modeling
Cloth modeling is the term used for simulating cloth within a computer program; usually in the context of 3D computer graphics.
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Cnoidal wave
In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation.
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Cofunction
In mathematics, a function f is cofunction of a function g if f(A).
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Contributions of Leonhard Euler to mathematics
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field.
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Convolutional neural network
In machine learning, a convolutional neural network (CNN, or ConvNet) is a class of deep, feed-forward artificial neural networks, most commonly applied to analyzing visual imagery.
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Cooperativity
Cooperativity is a phenomenon displayed by systems involving identical or near-identical elements, which act dependently of each other, relative to a hypothetical standard non-interacting system in which the individual elements are acting independently.
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Coordinate systems for the hyperbolic plane
In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers.
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CORDIC
CORDIC (for COordinate Rotation DIgital Computer), also known as Volder's algorithm, is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions, typically converging with one digit (or bit) per iteration.
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Correlate summation analysis
Correlate summation analysis is a data mining method.
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Cosh
Cosh may refer to.
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Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
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Curie's law
In a paramagnetic material, the magnetization of the material is (approximately) directly proportional to an applied magnetic field.
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Darcy's law
Darcy's law is an equation that describes the flow of a fluid through a porous medium.
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De Moivre's formula
In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.
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Derivations of the Lorentz transformations
There are many ways to derive the Lorentz transformations utilizing a variety of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory.
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Differentiation rules
This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.
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Dispersion (water waves)
In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds.
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Drag (physics)
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.
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Edith Clarke
Edith Clarke (February 10, 1883 – October 29, 1959) was the first female electrical engineer and the first female professor of electrical engineering at the University of Texas at Austin.
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Elementary function
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
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Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
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Equal incircles theorem
In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal.
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Eugenio Beltrami
Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics.
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Euler number
In mathematics, the Euler numbers are a sequence En of integers defined by the Taylor series expansion where is the hyperbolic cosine.
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Euler's continued fraction formula
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction.
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Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
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Folded normal distribution
No description.
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Foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.
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Four-vector
In special relativity, a four-vector (also known as a 4-vector) is an object with four components, which transform in a specific way under Lorentz transformation.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Franz Taurinus
Franz Adolph Taurinus (15 November 1794 – 13 February 1874) was a German mathematician who is known for his work on non-Euclidean geometry.
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Functional determinant
In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself.
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Gated recurrent unit
Gated recurrent units (GRUs) are a gating mechanism in recurrent neural networks, introduced in 2014 by Kyunghyun Cho et al.
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Gateway Arch
The Gateway Arch is a monument in St. Louis, Missouri, United States.
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Generalized trigonometry
Ordinary trigonometry studies triangles in the Euclidean plane R2.
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Glossary of areas of mathematics
This is a glossary of terms that are or have been considered areas of study in mathematics.
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Glossary of calculus
Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself.
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GNU MPFR
GNU MPFR (GNU Multiple Precision Floating-Point Reliably) is a GNU portable C library for arbitrary-precision binary floating-point computation with correct rounding, based on GNU Multi-Precision Library.
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Group of rational points on the unit circle
In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x2 + y2.
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Gudermannian function
The Gudermannian function, named after Christoph Gudermann (1798–1852), relates the circular functions and hyperbolic functions without explicitly using complex numbers.
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Gustav von Escherich
Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician.
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Gyrovector space
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry.
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Hemoglobin
Hemoglobin (American) or haemoglobin (British); abbreviated Hb or Hgb, is the iron-containing oxygen-transport metalloprotein in the red blood cells of all vertebrates (with the exception of the fish family Channichthyidae) as well as the tissues of some invertebrates.
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History of Lorentz transformations
The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_0^2+\cdots+x_n^2 and the Minkowski inner product -x_0^2 y_0^2+\cdots+x_n^2 y_n^2.
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Horocycle
In hyperbolic geometry, a horocycle (ὅριον + κύκλος — border + circle, sometimes called an oricycle, oricircle, or limit circle) is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction.
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HP 35s
The HP 35s (F2215A) is the latest in Hewlett-Packard's long line of non-graphing programmable scientific calculators.
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HP-42S
The HP-42S RPN Scientific is a programmable RPN Scientific hand held calculator introduced by Hewlett Packard in 1988.
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Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
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Hyperbolic
Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry.
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Hyperbolic angle
In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola. The science of hyperbolic angle parallels the relation of an ordinary angle to a circle. The hyperbolic angle is first defined for a "standard position", and subsequently as a measure of an interval on a branch of a hyperbola. A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to (x, 1/x) where x > 1. The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is ln x. Note that unlike circular angle, hyperbolic angle is unbounded, as is the function ln x, a fact related to the unbounded nature of the harmonic series. The hyperbolic angle in standard position is considered to be negative when 0 a > 1 so that (a, b) and (c, d) determine an interval on the hyperbola xy.
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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 law of cosines
In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry.
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Hyperbolic secant distribution
In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function.
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Hyperbolic sector
A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy.
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Hyperbolic triangle
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.
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Hyperbolic trigonometry
In mathematics, hyperbolic trigonometry can mean.
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Hyperboloid
In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.
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Hyperboloid model
In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+.
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Hypercycle (geometry)
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis).
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Hypertranscendental function
A hypertranscendental function or transcendentally transcendental function is an analytic function which is not the solution of an algebraic differential equation with coefficients in Z (the integers) and with algebraic initial conditions.
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IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Inverse hyperbolic functions
In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions.
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ISO 80000-2
ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO), superseding ISO 31-11.
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Jacobi elliptic functions
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance.
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Jacopo Riccati
Jacopo Francesco Riccati (28 May 1676 – 15 April 1754) was an Venetian mathematician and jurist from Venice.
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Janet Barnett
Janet Heine Barnett is a professor of mathematics at Colorado State University–Pueblo, interested in set theory, mathematical logic, the history of mathematics, women in mathematics, and mathematics education.
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Johann Heinrich Lambert
Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.
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Kepler orbit
In celestial mechanics, a Kepler orbit (or Keplerian orbit) is the motion of one body relative to another, as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space.
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Korteweg–de Vries equation
In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces.
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Lambert quadrilateral
In geometry, a Lambert quadrilateral, named after Johann Heinrich Lambert, is a quadrilateral in which three of its angles are right angles.
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Langmuir probe
A Langmuir probe is a device used to determine the electron temperature, electron density, and electric potential of a plasma.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Law of cosines
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Light cone
In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.
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Lindemann–Weierstrass theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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List of calculus topics
This is a list of calculus topics.
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List of exponential topics
This is a list of exponential topics, by Wikipedia page.
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List of integrals of hyperbolic functions
The following is a list of integrals (anti-derivative functions) of hyperbolic functions.
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List of Laplace transforms
The following is a list of Laplace transforms for many common functions of a single variable.
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List of mathematical abbreviations
This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology.
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List of mathematical functions
In mathematics, some functions or groups of functions are important enough to deserve their own names.
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List of representations of e
The mathematical constant ''e'' can be represented in a variety of ways as a real number.
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List of trigonometric identities
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.
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Logarithmic number system
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.
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Logistic distribution
In probability theory and statistics, the logistic distribution is a continuous probability distribution.
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Logistic function
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where.
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Long short-term memory
Long short-term memory (LSTM) units (or blocks) are a building unit for layers of a recurrent neural network (RNN).
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Lorentz transformation
In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.
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Mild-slope equation
In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines.
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Mittag-Leffler function
In mathematics, the Mittag-Leffler function Eα,β is a special function, a complex function which depends on two complex parameters α and β.
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Mode-locking
Mode-locking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds (10−12 s) or femtoseconds (10−15 s).
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Modern Arabic mathematical notation
Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education.
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Modified Morlet wavelet
Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic (sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses.
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Multilayer perceptron
A multilayer perceptron (MLP) is a class of feedforward artificial neural network.
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Mxparser
mXparser is an open-source mathematical expressions parser/evaluator providing abilities to calculate various expressions at a run time.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Newton's theorem of revolving orbits
In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor k without affecting its radial motion (Figures 1 and 2).
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Noncentral chi-squared distribution
No description.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Normal moveout
In reflection seismology, normal moveout (NMO) describes the effect that the distance between a seismic source and a receiver (the offset) has on the arrival time of a reflection in the form of an increase of time with offset.
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Oblate spheroidal coordinates
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci.
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Occurrences of Grandi's series
Guido Grandi illustrated the series with a parable involving two brothers who share a gem.
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OpenPlaG
openPlaG is a PHP based function graph plotter for use on websites.
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Optical autocorrelation
In optics, various autocorrelation functions can be experimentally realized.
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Outline of trigonometry
Trigonometry is a branch of mathematics that studies the relationships between the sides and the angles in triangles.
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Parabolic arch
A parabolic arch is an arch shaped like a parabola.
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Pfaffian function
In mathematics, Pfaffian functions are a certain class of functions whose derivative can be written in terms of the original function.
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Photoluminescence
Photoluminescence (abbreviated as PL) is light emission from any form of matter after the absorption of photons (electromagnetic radiation).
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Plastic number
In mathematics, the plastic number (also known as the plastic constant, the minimal Pisot number, the platin number, Siegel's number or, in French, le nombre radiant) is a mathematical constant which is the unique real solution of the cubic equation It has the exact value Its decimal expansion begins with.
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Poincaré disk model
In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
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Poinsot's spirals
In mathematics, Poinsot's spirals are two spirals represented by the polar equations where csch is the hyperbolic cosecant, and sech is the hyperbolic secant.
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Proper reference frame (flat spacetime)
A proper reference frame in the theory of relativity is a particular form of accelerated reference frame, that is, a reference frame in which an accelerated observer can be considered as being at rest.
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Proper velocity
In relativity, proper velocity, also known as celerity, is an alternative to velocity for measuring motion.
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Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
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Reciprocity (photography)
In photography reciprocity is the inverse relationship between the intensity and duration of light that determines the reaction of light-sensitive material.
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Rectangular function
The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as: 0 & \mbox |t| > \frac \\ \frac & \mbox |t|.
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Rectifier (neural networks)
In the context of artificial neural networks, the rectifier is an activation function defined as the positive part of its argument: f(x).
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Recursive neural network
A recursive neural network (RNN) is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order.
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Reflections of signals on conducting lines
A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if the far end of the line is not terminated in its characteristic impedance.
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Relativistic rocket
Relativistic rocket refers to any spacecraft that travels at a velocity close enough to light speed for relativistic effects to become significant.
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Resource fragmentation hypothesis
The resource fragmentation hypothesis was first proposed by Janzen & Pond (1975), and says that as species richness becomes large there is not a linear increase in the number of parasitoid species that can be supported.
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Right triangle
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).
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Risk aversion
In economics and finance, risk aversion is the behavior of humans (especially consumers and investors), when exposed to uncertainty, in attempting to lower that uncertainty.
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RLC circuit
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel.
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Scientific calculator
A scientific calculator is a type of electronic calculator, usually but not always handheld, designed to calculate problems in science, engineering, and mathematics.
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Sech (disambiguation)
Sech, seich, and similar words, can mean.
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Self-phase modulation
Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction.
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Series multisection
In mathematics, a multisection of a power series is a new power series composed of equally spaced terms extracted unaltered from the original series.
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SH
SH, Sh, sH or sh may refer to.
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Sharp EL-5120
The Sharp EL-5120 is a scientific programmable calculator.
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Shine
Shine may refer to.
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Siegmund Guenther
Adam Wilhelm Siegmund Günther (6 February 1848 – 3 February 1923) was a German geographer, mathematician, historian of mathematics and natural scientist.
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Sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
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Silicon photonics
Silicon photonics is the study and application of photonic systems which use silicon as an optical medium.
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Simple suspension bridge
A simple suspension bridge (also rope bridge, swing bridge (in New Zealand), suspended bridge, hanging bridge and catenary bridge) is a primitive type of bridge that is supported entirely from anchors at either end and has no towers or piers.
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Sine
In mathematics, the sine is a trigonometric function of an angle.
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Singular boundary method
In numerical analysis, the singular boundary method (SBM) belongs to a family of meshless boundary collocation techniques which include the method of fundamental solutions (MFS), boundary knot method (BKM), regularized meshless method (RMM), boundary particle method (BPM), modified MFS, and so on.
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Sinh
Sinh may refer to.
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Skerryvore
Skerryvore (from the Gaelic An Sgeir Mhòr meaning "The Great Skerry") is a remote reef that lies off the west coast of Scotland, 12 miles (19 kilometres) south-west of the island of Tiree.
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Slide rule
The slide rule, also known colloquially in the United States as a slipstick, is a mechanical analog computer.
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Softmax function
In mathematics, the softmax function, or normalized exponential function, is a generalization of the logistic function that "squashes" a -dimensional vector \mathbf of arbitrary real values to a -dimensional vector \sigma(\mathbf) of real values, where each entry is in the range (0, 1, and all the entries add up to 1. The function is given by In probability theory, the output of the softmax function can be used to represent a categorical distribution – that is, a probability distribution over different possible outcomes. In fact, it is the gradient-log-normalizer of the categorical probability distribution. The softmax function is also the gradient of the LogSumExp function. The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression), multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of distinct linear functions, and the predicted probability for the 'th class given a sample vector and a weighting vector is: This can be seen as the composition of linear functions \mathbf \mapsto \mathbf^\mathsf\mathbf_1, \ldots, \mathbf \mapsto \mathbf^\mathsf\mathbf_K and the softmax function (where \mathbf^\mathsf\mathbf denotes the inner product of \mathbf and \mathbf). The operation is equivalent to applying a linear operator defined by \mathbf to vectors \mathbf, thus transforming the original, probably highly-dimensional, input to vectors in a -dimensional space \mathbb^K.
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Soliton (optics)
In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium.
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Split-complex number
In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z.
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Squeeze mapping
In linear algebra, a squeeze mapping is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping.
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Srinivasa Ramanujan
Srinivasa Ramanujan (22 December 188726 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems considered to be unsolvable.
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Stirling's approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.
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Stjepan Horvat
Stjepan Horvat (November 29, 1895 – March 12, 1985) was a Croatian patriot, geodesist and professor, dean of the Technical Faculty in Zagreb, head of the University of Zagreb, editor of the journals Geodetski list and Hrvatska državna izmjera, manager of the Department for State Survey in the Croatian Headquarters for Public Affairs, member of the State Land Consolidation Commission, colonel in the time of the Independent State of Croatia, adviser at the Military-Geography Institute in Argentina for 40 years and an honorary member of the Argentine Association of Geophysicists.
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Stumpff function
In celestial mechanics, the Stumpff functions ck(x), developed by Karl Stumpff, are used for analyzing orbits using the universal variable formulation.
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Support vector machine
In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis.
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Symmetry in mathematics
Symmetry occurs not only in geometry, but also in other branches of mathematics.
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Synthetic-aperture radar
Synthetic-aperture radar (SAR) is a form of radar that is used to create two- or three-dimensional images of objects, such as landscapes.
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Tangent half-angle formula
In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle.
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Tanh-sinh quadrature
Tanh-sinh quadrature is a method for numerical integration introduced by Hidetosi Takahasi and Masatake Mori in 1974.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Terminal velocity
Terminal velocity is the highest velocity attainable by an object as it falls through a fluid (air is the most common example).
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TI SR-50
The SR-50 was Texas Instruments' first scientific pocket calculator with trigonometric and logarithm functions.
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TI-54
The TI-54 was a scientific calculator produced by Texas Instruments, primarily marketed towards engineers and science professionals.
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Tractrix
A tractrix (from the Latin verb trahere "pull, drag"; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor (pulling) point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed.
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Transcendental function
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Trigonometric functions of matrices
The trigonometric functions (especially sine and cosine) for real or complex square matrices occur in solutions of second-order systems of differential equations.
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Trigonometric integral
In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions.
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Trigonometric substitution
In mathematics, Trigonometric substitution is the substitution of trigonometric functions for other expressions.
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Trochoidal wave
In fluid dynamics, a trochoidal wave or Gerstner wave is an exact solution of the Euler equations for periodic surface gravity waves.
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Tsiolkovsky rocket equation
The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation, describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and thereby move due to the conservation of momentum.
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Tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel).
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Unary function
A unary function is a function that takes one argument.
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Unit hyperbola
In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfy the implicit equation x^2 - y^2.
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Unit interval
In mathematics, the unit interval is the closed interval, that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1.
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Van Deemter equation
The Van Deemter equation in chromatography relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation.
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Vanishing gradient problem
In machine learning, the vanishing gradient problem is a difficulty found in training artificial neural networks with gradient-based learning methods and backpropagation.
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Velocity-addition formula
In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames.
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Vincenzo Riccati
Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was a Venetian mathematician and physicist.
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Visual acuity
Visual acuity (VA) commonly refers to the clarity of vision.
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Wrapped asymmetric Laplace distribution
In probability theory and directional statistics, a wrapped asymmetric Laplace distribution is a wrapped probability distribution that results from the "wrapping" of the asymmetric Laplace distribution around the unit circle. For the symmetric case (asymmetry parameter κ.
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XLfit
XLfit is a Microsoft Excel-based plug-in which performs Regression, curve fitting and statistical analysis.
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Ch (mathematical function), Cosecans hyperbolicus, Cosech, Cosh (mathematical function), Cosh(x), Cosinus hyperbolicus, Cotangens hyperbolicus, Coth, Coth(x), Csch, Ctanh, Cth, Cth (mathematical function), Hyberbolic cosecant, Hyberbolic cosine, Hyberbolic cotangent, Hyberbolic secant, Hyberbolic sine, Hyberbolic tangent, Hyperbolic cosecant, Hyperbolic cosine, Hyperbolic cotangent, Hyperbolic curve, Hyperbolic functions, Hyperbolic identities, Hyperbolic map, Hyperbolic polar sine, Hyperbolic secant, Hyperbolic sin, Hyperbolic sine, Hyperbolic sinus, Hyperbolic sinusoid, Hyperbolic tan, Hyperbolic tangent, Hyperbolic tangent function, Hyperbolic trig functions, Hyperbolic trig identities, Hyperbolic trigonometric function, Hyperbolic trigonometric functions, Hypersine, Osborn's Rule, Osborn's rule, Osborne rule, Osborne's rule, Secans hyperbolicus, Sech, Sh (mathematical function), Sinh (mathematical function), Sinh(x), Sinus hyperbolicus, Tangens hyperbolicus, Tanh, Tanh(x), Th (mathematical function).
References
[1] https://en.wikipedia.org/wiki/Hyperbolic_function
