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Topics referred to by the same term
Look up parametrization in Wiktionary, the free dictionary. Parametrization, also spelled parameterization, parametrisation or parameterisation, is the
Parametrization
Describing something mathematical with variables
indexed). The length of the curve is therefore a parametrization-invariant quantity. In such cases parametrization is a mathematical tool employed to extract
Parametrization_(geometry)
Parametrization used for loop integrals
Feynman parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes
Feynman_parametrization
Self-intersecting compact surface, an immersion of the real projective plane
of this parametrization centered on the triple point, one obtains a complete minimal surface with three ends (that's how this parametrization was discovered
Boy's_surface
Study of curves from a differential point of view
Because of this, –γ is called an arc-length parametrization, natural parametrization, unit-speed parametrization. The parameter s(t) is called the natural
Differentiable_curve
Surface specified with parameters
can be easily parametrized. If the graph z = f(x), a ≤ x ≤ b is rotated about the z-axis then the resulting surface has a parametrization 𝐫(u,ϕ)=(ucosϕ
Parametric_surface
Loop integral parametrization
Schwinger parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. It is named after Julian
Schwinger_parametrization
Mathematical measure of how much a curve or surface deviates from flatness
second derivative of an arc-length parametrization 𝜸¯: 𝐊(s)=𝜸¯″(s). The curvature vector of a general parametrization, 𝜸, is the perpendicular component
Curvature
Parametrization (or parameterization) in an atmospheric model (either weather model or climate model) is a method of replacing processes that are too
Parametrization (atmospheric modeling)
Parametrization_(atmospheric_modeling)
Representation of a curve by a function of a parameter
representation, or parametric system, or parameterization (also spelled parametrization, parametrisation) of the object. For example, the equations x=costy=sint
Parametric_equation
Non-orientable mathematical surface
cross section. With the above parametrization the cross section is a 2:1 Lissajous curve. A non-intersecting 4-D parametrization can be modeled after that
Klein_bottle
Branch of computational complexity theory
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according
Parameterized_complexity
Mathematical spiral-type surface
Seashell surface with parametrization on left
Seashell_surface
Mathematical concept
This mapping is called a modular parametrization of level N. If N is the smallest integer for which such a parametrization can be found (which by the modularity
Modular_elliptic_curve
Topics referred to by the same term
In mathematics and related areas, a natural parameter or natural parameterization can refer to: The natural parameter of a differentiable curve, its arc
Natural parameter (disambiguation)
Natural_parameter_(disambiguation)
Formulaic parametrization
In control theory, the Youla–Kučera parametrization (also simply known as Youla parametrization) is a formula that describes all possible stabilizing
Youla–Kucera_parametrization
Network scheduling algorithm
Weighted fair queueing (WFQ) is a network scheduling algorithm. WFQ is both a packet-based implementation of the generalized processor sharing (GPS) policy
Weighted_fair_queueing
Integration over a non-flat region in 3D space
surface integral obtained using one parametrization is the negative of the one obtained via the other parametrization. It follows that given a surface,
Surface_integral
Plane algebraic curve
y=(j2+16)3j2 parametrizes X0(2) in terms of rational functions of j2. It is not necessary to actually compute j2 to use this parametrization; it can be
Classical_modular_curve
only on the chosen values for a set of parameters. Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc
Parametric_family
In mathematics, the trigonometric moment problem is formulated as follows: given a sequence {ck}k∈ℕ0, does there exist a distribution function σ on the
Trigonometric_moment_problem
Definite integral of a scalar or vector field along a path
the parametrization r in absolute value, but they do depend on its orientation. Specifically, a reversal in the orientation of the parametrization changes
Line_integral
Computational method for constructing 3D models
In computer vision, the inverse depth parametrization is a parametrization used in methods for 3D reconstruction from multiple images such as simultaneous
Inverse_depth_parametrization
and third quartiles are respectively μ − σ and μ + σ. McCullagh's parametrization, introduced by Peter McCullagh, professor of statistics at the University
McCullagh's parametrization of the Cauchy distributions
McCullagh's_parametrization_of_the_Cauchy_distributions
Four integers where the sum of the squares of three equals the square of the fourth
b are odd, in which case no solutions exist as can be seen by the parametrization in the previous section. The largest number that always divides the
Pythagorean_quadruple
Two-parameter family of continuous probability distributions
required. It is common among some Bayesians to consider an alternative parametrization of the normal distribution in terms of the precision, defined as the
Inverse-gamma_distribution
Algebraic variety
In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension
Rational_variety
Generalized processor sharing (GPS) is an ideal scheduling algorithm for process schedulers and network schedulers. It is related to the fair-queuing principle
Generalized_processor_sharing
Type of perceptual phenomenon
Looming is a term found in the study of perception, as it relates directly to psychology. Looming occurs when an object begins moving closer to the eye
Looming
Ways to represent 3D rotations
qi=exsinθ2qj=eysinθ2qk=ezsinθ2qr=cosθ2 Inspection shows that the quaternion parametrization obeys the following constraint: qi2+qj2+qk2+qr2=1 The last term (in
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Computer hacking technique
are processed as unexpected input rather than executable code. With parametrized queries, SQL code remains separate from user input, and each parameter
SQL_injection
Geometric figure
Gregoire de Saint-Vincent led to the logarithm function and the modern parametrization of the hyperbola by sector areas. When the notions of conjugate hyperbolas
Unit_hyperbola
Locus of the zeros of a polynomial of degree two
its tangent hyperplane at A. In the affine case, the parametrization is a rational parametrization of the form xi=fi(t1,…,tn−1)f0(t1,…,tn−1)for i=1,…,n
Quadric
In mathematics, the monopole moduli space is a space parametrizing monopoles (solutions of the Bogomolny equations). Atiyah and Hitchin (1988) studied
Monopole_moduli_space
Validating the behavior of isolated source code
framework that supports parametrized tests supports a way to encode parameter sets and to run the test with each set. Use of parametrized tests can reduce test
Unit_testing
real functions they parametrize the cubic Fermat curve x3+y3=1, just as the trigonometric functions sine and cosine parametrize the unit circle x2+y2=1
Dixon_elliptic_functions
Representation of water movement in unsaturated soils
The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931
Richards_equation
Postulate in particle physics
Bethe–Feynman formula Hellmann–Feynman theorem Feynman slash notation Feynman parametrization Path integral formulation Parton model Sticky bead argument One-electron
One-electron_universe
Mathematics of smooth surfaces
assignment, to each local parametrization f : V → S with p ∈ f(V), of two numbers X1 and X2, such that for any other local parametrization f ′ : V → S with p
Differential geometry of surfaces
Differential_geometry_of_surfaces
Distribution of variables which satisfies a stability property under linear combinations
In the first parametrization ("1"), this is done by defining the new variable: y={x−μcα≠1x−μc−β2πlncα=1 For the second parametrization ("0"), simply
Stable_distribution
Ensemble forecasting Model output statistics Meteorological reanalysis Parametrization Specific models Climate IGCM HadCM3 HadGEM1 GFDL CM2.X CGCM CCSM CESM
Earth System Modeling Framework
Earth_System_Modeling_Framework
Problem of finding the optimal shape under given conditions
faced using standard optimization methods if a parametrization of the geometry is defined. Such parametrization is very important in CAE field where goal functions
Shape_optimization
Quadratic form related to curvatures of surfaces
parametric surface is defined as follows. Let r = r(u,v) be a regular parametrization of a surface in R3, where r is a smooth vector-valued function of two
Second_fundamental_form
Geometric space whose points represent algebro-geometric objects of some fixed kind
genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this
Moduli_space
Special functions of several complex variables
the lattice is dictated by a matrix; in general, theta functions are parametrized by points in a tube domain inside a complex Lagrangian Grassmannian,
Theta_function
Use of various control systems for operating equipment
flexible, and offer greater scope for more sophisticated configuration, parametrization, and operation. This was accompanied by the fieldbus revolution which
Automation
Probability distribution
(in the shape–rate parametrization), then X has an exponential distribution with rate parameter β. In the shape-scale parametrization, X ~ Gamma(1, θ) has
Gamma_distribution
Algebraic variety
the extended complex upper-half plane). The points of a modular curve parametrize isomorphism classes of elliptic curves, together with some additional
Modular_curve
Problem in celestial mechanics
extrapolation of these two position fixes is obtained. It is possible to parametrize all possible orbits passing through the two points 𝐫1 and 𝐫2 using
Lambert's_problem
Topic in probability theory and statistics
This is the central limit theorem (CLT). Special case of distribution parametrization: X is a hypergeometric (m, N, n) random variable. If n and m are large
Relationships among probability distributions
Relationships_among_probability_distributions
Equation in fluid dynamics
In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to viscous shear forces along
Darcy–Weisbach_equation
Mathematical strategy
for example.) One must be aware of singularities in the Euler angle parametrization when the pitch approaches ±90° (north/south pole). These cases must
Conversion between quaternions and Euler angles
Conversion_between_quaternions_and_Euler_angles
Connected series of line segments
chain is typically parametrized linearly, using linear interpolation between successive vertices. For the whole chain, two parametrizations are common in practical
Polygonal_chain
Immersion of the Klein bottle
the image are double curves of the immersion, not artifacts of the parametrization. Rendering the Ida surface poses a problem that ordinary shading models
Ida_surface
Approximation method for general relativity in physics
gravitation Tests of general relativity Will, Clifford M., ed. (1993), "The Parametrized Post-Newtonian Formalism", Theory and Experiment in Gravitational Physics
Parameterized post-Newtonian formalism
Parameterized_post-Newtonian_formalism
S-shaped curve
transformations (and rescaling the parametrization) of the hyperbola xy=1, with parametrization (e−t,et): the parametrization of the hyperbola for the logistic
Logistic_function
Mathematics award
existence and structure of varieties of moduli, varieties whose points parametrize isomorphism classes of some type of geometric object. Also made several
Fields_Medal
Theorem in vector calculus
continuous map to our surface in ℝ3. But we already have such a map: the parametrization of Σ. Suppose ψ:D→ℝ3 is piecewise smooth at the neighborhood of D
Stokes'_theorem
Number, approximately 3.14
is the winding number about the origin of the hodograph of the curve parametrized by arclength, a new curve lying on the unit circle, described by the
Pi
Doughnut-shaped surface of revolution
commonly used to discuss magnetic confinement fusion devices. Using the parametrization of the torus given at the beginning of the section, it is straight
Torus
Software testing framework
tests, end-to-end tests, and functional tests. Its features include parametrized testing, fixtures, and assert re-writing. Pytest fixtures provide the
Pytest
Triangle whose side lengths and area are integers
parametrization was discovered by Brahmagupta (598-668 A.D.), who did not prove that all Heronian triangles can be generated by the parametrization.
Heronian_triangle
Regulation of nonlinear systems
parameter-varying systems, a class of nonlinear systems which can be modelled as parametrized linear systems whose parameters change with their state. In designing
Linear parameter-varying control
Linear_parameter-varying_control
American theoretical physicist (1918–1988)
checkerboard Feynman diagrams Feynman gauge Feynman–Kac formula Feynman parametrization Feynman point Feynman propagator Feynman slash notation Feynman sprinkler
Richard_Feynman
Three-dimensional coordinate system
coordinates. An alternative (but non-orthogonal) parametrization exists that closely follows the angular parametrization of spherical coordinates: x = a s sin
Ellipsoidal_coordinates
Graver basis method described above. So the table width m provides a parametrization of all integer programming problems. Denote by G(m,n) the Graver basis
Graver_basis
American professor of physics emeritus at University of Florida
doi:10.1103/PhysRevD.15.2590. Field, R.D.; Feynman, R.P. (1978). "A Parametrization of the Properties of Quark Jets". Nuclear Physics. B136 (1): 1–76.
Richard_D._Field
Transformation method within a three-dimensional space
transformation (named after Friedrich Robert Helmert, 1843–1917) is a method of parametrization of geometric similarities, which is used in geodesy to compute transformations
Helmert_transformation
Probability distribution
by F(x;λ)={1−e−λxx≥0,0x<0. The exponential distribution is sometimes parametrized in terms of the scale parameter β = 1/λ, which is also the mean: f(x;β)={1βe−x/βx≥0
Exponential_distribution
Retrieved 2024-11-12. Cabré, P.; Fontich, E.; de la Llave, R. (2003). "The parametrization method for invariant manifolds I: manifolds associated to non-resonant
Spectral_submanifold
Quantitative methods used to simulate climate
higher throughput in terms of simulated years per wall clock day." Parametrization (or parameterization) in an atmospheric model (either weather model
Climate_model
Weather prediction and a climate model
Ensemble forecasting Model output statistics Meteorological reanalysis Parametrization Specific models Climate IGCM HadCM3 HadGEM1 GFDL CM2.X CGCM CCSM CESM
Climate Forecast System (NCEP)
Climate_Forecast_System_(NCEP)
Problem optimization method
However, there is an even faster solution that involves a different parametrization of the problem: Let k be the total number of floors such that the eggs
Dynamic_programming
Formulas in differential geometry
by the trajectory of the particle a natural parametrization by arc length (i.e. arc-length parametrization), since many different particle paths may trace
Frenet–Serret_formulas
Family of continuous probability distributions
proposed to use the (μ,φ) and (φ,λ) parametrizations in addition to the standard (μ,λ) parametrization (“Each of these forms is convenient or suggestive
Inverse_Gaussian_distribution
Generalization of the one-dimensional normal distribution to higher dimensions
with mean vector μ = [μ1, μ2, μ3] and covariance matrix Σ (standard parametrization for multivariate normal distributions). Then the joint distribution
Multivariate normal distribution
Multivariate_normal_distribution
Protein design algorithm
can be directly analyzed on screen. In version 5.0, the possibility to parametrize previously not recognized molecules in JSON format was added into the
FoldX
Mathematical rule for inverting probabilities
for each point in the domain. In practice, these instances might be parametrized by writing the specified probability densities as a function of x and
Bayes'_theorem
Family of continuous probability distributions
In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions
Generalized inverse Gaussian distribution
Generalized_inverse_Gaussian_distribution
Probability distribution
"uniform" depends on the parametrization, led Jeffreys to seek a form of prior that would be invariant under different parametrizations. Harold Jeffreys proposed
Beta_distribution
Formula for 3D vector rotation
It is based on Rodrigues' rotation formula, but uses a different parametrization. The rotation is described by four Euler parameters due to Leonhard
Euler–Rodrigues_formula
Type of surface patch used in computer graphics
mathematics, a Coons patch, is a type of surface patch or manifold parametrization used in computer graphics to smoothly join other surfaces together
Coons_patch
Relates rational elliptic curves to modular forms
This mapping is called a modular parametrization of level N. If N is the smallest integer for which such a parametrization can be found (which by the modularity
Modularity_theorem
Fewest graph edges whose removal breaks all cycles
In graph theory, a branch of mathematics, the cyclomatic number, circuit rank, cycle rank, corank or nullity of an undirected graph is the minimum number
Cyclomatic_number
Concept in statistics
from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves
Compound probability distribution
Compound_probability_distribution
Continuous probability distribution
− m ) {\displaystyle s=\operatorname {sgn}(x-m)} . An alternative parametrization is made possible by the characteristic function: φ ( t ; μ , σ , β
Asymmetric Laplace distribution
Asymmetric_Laplace_distribution
Probability distribution
In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform
Circular_uniform_distribution
Type of artificial neural network
neural network), is a mathematical field that is fully or partially parametrized by a neural network. Initially developed to tackle visual computing tasks
Neural_field
Concept in probability theory
random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel. Consider two random
Regular conditional probability
Regular_conditional_probability
Change of variable for integrals involving trigonometric functions
This is the one-dimensional stereographic projection of the unit circle parametrized by angle measure onto the real line. The general transformation formula
Tangent half-angle substitution
Tangent_half-angle_substitution
Spherical triangle with three right angles
spherical triangles, the octant is its own polar triangle. The octant can be parametrized using a rational quartic Bézier triangle. The solid angle subtended by
Octant_of_a_sphere
Mathematical idealization of the surface of a body
point becomes regular, if one changes the parametrization. This is the case of the poles in the parametrization of the unit sphere by Euler angles: it suffices
Surface_(mathematics)
Unproven computational hardness assumption
the weighted feedback arc set problem on tournaments does not have a parametrized algorithm with running time O(2o(OPT)nO(1)). It does however have a parameterized
Exponential_time_hypothesis
In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Geometrically, it generalizes a quotient of a scheme or a variety
Quotient_stack
Mathematical abstraction of level sets
topological simplification and cleaning, surface segmentation and parametrization, efficient computation of level sets, neuroscience, and geometrical
Reeb_graph
1983 simulation of a simple planetary ecosystem
Ensemble forecasting Model output statistics Meteorological reanalysis Parametrization Specific models Climate IGCM HadCM3 HadGEM1 GFDL CM2.X CGCM CCSM CESM
Daisyworld
Continuous probability distribution
μX(k)=(d2d1)kΓ(d12+k)Γ(d12)Γ(d22−k)Γ(d22). The F-distribution is a particular parametrization of the beta prime distribution, which is also called the beta distribution
F-distribution
Concept on molecular modeling
field parametrization strategies. An important differentiation is 'component-specific' and 'transferable'. For a component-specific parametrization, the
Force_field_(chemistry)
Calculus of functions of several variables
limits and derivatives define the limit and differential along a 1D parametrized curve, reducing the problem to the 1D case. Further higher-dimensional
Multivariable_calculus
Canadian-American mathematician (born 1974)
forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study
Manjul_Bhargava
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