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Topics referred to by the same term
algebraic groups over global fields Weak weak approximation, a form of weak approximation for varieties Weak-field approximation, a solution in general relativity
Weak_approximation
in weak approximation is whether the embedding of G(k) in G(AS) has dense image. If the group G is connected and k-rational, then it satisfies weak approximation
Approximation in algebraic groups
Approximation_in_algebraic_groups
Hilbertian. The WWA property (weak 'weak approximation', sic) for a variety V over a number field is weak approximation (cf. approximation in algebraic groups)
Thin_set_(Serre)
Meteorological concept
In atmospheric science, the weak temperature gradient approximation (WTG) is a theoretical framework used to simplify the equations governing tropical
Weak temperature gradient approximation
Weak_temperature_gradient_approximation
Linear perturbations to solutions of nonlinear Einstein field equations
of these that preserve the small scale that is required by the weak-field approximation. One may thus define ϕ {\displaystyle \phi } to denote an arbitrary
Linearized_gravity
Problem of finding the longest simple path for a given graph
understanding its approximation hardness". The best polynomial time approximation algorithm known for this case achieves only a very weak approximation ratio, n
Longest_path_problem
Approximation for factorials
mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate
Stirling's_approximation
Mathematical concept
The approximation error in a given data value represents the significant discrepancy that arises when an exact, true value is compared against some approximation
Approximation_error
Concept in optimization
only holds in certain cases. Many primal-dual approximation algorithms are based on the principle of weak duality. Consider a linear programming problem
Weak_duality
1995 video game
gamer's shelf." They also criticized the Genesis version as being a weak approximation of the arcade version, particularly the character sprites and sound
Mortal_Kombat_3
Concept in number theory
provides a unified interpretation of approximation theorems and local-global questions. The weak approximation theorem says that, for finitely many inequivalent
Adele_ring
Mathematical theorem in the study of analysis
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly
Stone–Weierstrass_theorem
Averages of repeated trials converge to the expected value
numerical results. The larger the number of repetitions, the better the approximation tends to be. The reason that this method is important is mainly that
Law_of_large_numbers
Method for solving continuous operator problems (such as differential equations)
and approximation methods used: Ritz–Galerkin method (after Walther Ritz) typically assumes symmetric and positive-definite bilinear form in the weak formulation
Galerkin_method
Commutative ring with a well behaved theory of prime factorization
pairwise independent. As a consequence, there holds the so-called weak approximation theorem, an homologue of the Chinese remainder theorem: if p 1 , …
Krull_ring
Problem in number theory
Heath-Brown, D. R. (1992), "The density of zeros of forms for which weak approximation fails", Mathematics of Computation, 59 (200): 613–623, Bibcode:1992MaCom
Sums_of_three_cubes
Rational-number approximation of a real number
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus
Diophantine_approximation
Statistical estimation method
an order- β {\displaystyle \beta } weak approximation to x {\displaystyle \mathbf {x} } satisfying (10) and the weak convergence condition sup t k ≤ t
Innovation_method
2009 studio album by Handsome Furs
sludgy rock and tinsel-thin beats of 'Evangeline' to the couple's weak approximation of The Knife on '(White City)' to the half-assed 'Dancing In The Dark'
Face_Control
In algebraic topology, the cellular approximation theorem states that a map between CW-complexes can always be taken to be of a specific type. Concretely
Cellular approximation theorem
Cellular_approximation_theorem
finding a sequence of weak approximation of maps in W 1 , p ( M , N ) {\displaystyle W^{1,p}(M,N)} is equivalent to the strong approximation when p {\displaystyle
Sobolev_mapping
Model used in atom optics and magnetic resonance
The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate
Rotating-wave_approximation
Family of iterative methods
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive
Stochastic_approximation
Russian mathematician (1937–2023)
method. In 1978, Milstein introduced weak-sense approximations of SDEs for the first time and proposed a number of weak schemes. These papers became classics
Grigori_Milstein
Gravitational deflection of light
In astronomy, weak gravitational lensing is a technique to map the mass distribution of astronomical objects. As predicted by general relativity, the presence
Weak_gravitational_lensing
Mathematician
Brauer-Manin obstruction is the only obstruction to the Hasse principle and weak approximation for homogeneous spaces of connected linear algebraic groups over number
Mikhail_Borovoi
Paradigm in machine learning
Weak supervision (also known as semi-supervised learning) is a paradigm in machine learning, the relevance and notability of which increased with the advent
Weak_supervision
Approximation valid for weakly non-linear and fairly long waves
the Boussinesq approximation for water waves is an approximation valid for weakly non-linear and fairly long waves. The approximation is named after Joseph
Boussinesq approximation (water waves)
Boussinesq_approximation_(water_waves)
Computational property
polynomially bounded objective function cannot have a fully polynomial-time approximation scheme (or FPTAS) unless P = NP. However, the converse fails: e.g. if
Strong_NP-completeness
Numerical method for solving physical or engineering problems
equations are often partial differential equations (PDEs). To explain the approximation of this process, FEM is commonly introduced as a special case of the
Finite_element_method
Theoretical electronic band structure model in which the potential is periodic and weak
The empty lattice approximation is a theoretical electronic band structure model in which the potential is periodic and weak (close to constant). One may
Empty_lattice_approximation
Method of approximation in general relativity
law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher-order terms can be added
Post-Newtonian_expansion
Physical model of solid metals as electron gases
cores can be modeled through the use of a "weak" perturbing potential. This may seem like a severe approximation, for the Coulomb attraction between these
Nearly_free_electron_model
Mathematical concept
sequence might represent an attempt to construct 'better and better' approximations to a desired measure μ that is difficult to obtain directly. The meaning
Convergence_of_measures
Quantity in quantum mechanics
In quantum mechanics (and computation), a weak value is a quantity related to a shift of a measuring device's pointer when usually there is pre- and postselection
Weak_value
Traditional form of Malagasy oral literature and poetry
an exemplar of the new wave of Malagasy poetry. "Proverb" offers a weak approximation of the meaning of ohabolana, which constitute no less than concise
Hainteny
Consonant sound change
alters consonants, making them "weaker" in some way. The word lenition means 'softening' or 'weakening' (from Latin lēnis 'weak'). Lenition can happen both
Lenition
Mathematical approach to quantum physics
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Indicator function of positive numbers
variance can serve as an approximation, in the limit as the variance approaches zero. For example, all three of the above approximations are cumulative distribution
Heaviside_step_function
Near-field diffraction
the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation
Fresnel_diffraction
Chemical compound involving ionic bonding
structural information, the Kapustinskii equation. Using an even simpler approximation of the ions as impenetrable hard spheres, the arrangement of anions
Salt_(chemistry)
Theory of forces and subatomic particles
describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying
Standard_Model
Computational quantum mechanical modelling method to investigate electronic structure
hard spheres and a term in a weak interaction such as the long range London dispersion force. In a local density approximation the local excess free energy
Density_functional_theory
Computational geometry and optimization concept
distinguishes between: Strong coresets: The approximation guarantee holds uniformly for all candidate solutions x. Weak coresets: The guarantee holds only for
Coreset
NP-hard problem in combinatorial optimization
optimal. It was one of the first approximation algorithms, and was in part responsible for drawing attention to approximation algorithms as a practical approach
Travelling_salesman_problem
Problem in combinatorial optimization
algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine
Knapsack_problem
Type of algorithm
A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Markovian master equation of a quantum system weakly coupled to its environment
connection to the Lindblad master equation. If a so-called secular approximation is performed, where only certain resonant interactions with the environment
Redfield_equation
In probability theory, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) refers
Komlós–Major–Tusnády approximation
Komlós–Major–Tusnády_approximation
Most basic type of physical force
four fundamental interactions known to exist: gravity, electromagnetism, weak interaction, and strong interaction. The gravitational and electromagnetic
Fundamental_interaction
Exercise in general relativity
are fully determined by some variant of this approach; from the weak-field approximation one arrives at the result: g 44 = K ( 1 + 1 S r ) ≈ − c 2 + 2 G
Derivation of the Schwarzschild solution
Derivation_of_the_Schwarzschild_solution
Darker version of the flag using RGB approximations of semiofficial Pantone approximations, and also the official 1997–2011 color scheme.
Flag_of_South_Korea
Design technique
graphical perspective projections, but there is attendant distortion in the approximation. Because pictorial projections innately contain this distortion, in
3D_projection
Approximation in many-body systems
The GW approximation is a method used to calculate the self-energy of a many-body system of electrons. The approximation is that the expansion of the
GW_approximation
Swedish mathematician
Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. (2001). "Adaptive weak approximation of stochastic differential equations". Communications on Pure and
Anders_Szepessy
Mathematical problem
viz. monotone polygons and polygons weakly visible from an edge. Krohn & Nilsson (2013) presented an approximation algorithm that computes in polynomial
Art_gallery_problem
computational complexity, an NP-complete (or NP-hard) problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose running
Weak_NP-completeness
Type of weak interaction in nuclear and atomic physics
Q_{\epsilon }\,} is the electric charge. The approximation for the weak charge is usually valid, since the weak mixing angle typically is 29° ≈ 30° , and
Weak_charge
Mathematical formalism used in quantum field theory
The random phase approximation (RPA) is an approximation method in condensed matter physics and nuclear physics. It was first introduced by David Bohm
Random_phase_approximation
Concept in topology
to N {\displaystyle N} . It can be equipped with the weak or strong topology. A basic approximation theorem says that C W s ( M , N ) {\displaystyle {\mathcal
Mapping_space
Approximations in density functional theory
Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT)
Local-density_approximation
Machine learning technique
traditional boosting. It gives a prediction model in the form of an ensemble of weak prediction models, i.e., models that make very few assumptions about the
Gradient_boosting
Partition of a graph's nodes into cliques
there can be no polynomial time approximation algorithm for any ε > 0 that, on n-vertex graphs, achieves an approximation ratio better than n1 − ε. In graphs
Clique_cover
Weakly bound complex of atoms or molecules
adiabatic approximation or Born–Oppenheimer approximation has been adapted to separate angular and radial motions. Despite the challenges posed by the weak interactions
Van_der_Waals_molecule
Matrix decomposition
applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix. The SVD
Singular_value_decomposition
Base that does not associate completely with hydrogen ions
A weak base is a base that does not accept all the available H+ ions, and forms an equilibrium between the base and its conjugate acid. Upon dissolution
Weak_base
Numerical integration method
left and right Riemann sums and is sometimes defined this way. The approximation becomes more accurate as the resolution of the partition increases (that
Trapezoidal_rule
Decision problem in computer science
where r is a number in (0,1) called the approximation ratio. The following very simple algorithm has an approximation ratio of 1/2: Order the inputs by descending
Subset_sum_problem
NP-complete problem in computer science
are not sorted, then the runtime is O(n) and the approximation ratio is at most 3/2 ("approximation ratio" means the larger sum in the algorithm output
Partition_problem
Type of radioactive decay
consequence of the weak force, which is characterized by relatively long decay times. Nucleons are composed of up quarks and down quarks, and the weak force allows
Beta_decay
Word modified to convey a slighter degree
affection (Stevie or Stevey, derived from Steven). The suffix -y can signal approximation rather than literal smallness (a bluey color meaning somewhat blue)
Diminutive
Uniform approximation theorem in mathematics
convex spaces with the approximation property". Séminaire Paul Krée Tome 4: 1–7. Zbl 0401.46024. Noguchi, Junjiro (2019), "A Weak Coherence Theorem and
Oka–Weil_theorem
Computer-aided geometric design
In mathematics, the progressive-iterative approximation method is an iterative method of data fitting with geometric meanings. Given a set of data points
Progressive-iterative approximation method
Progressive-iterative_approximation_method
Italian mathematician and professor
of the same University. Stefano has made contributions to approximation theory, such as Weakly Admissible Meshes, Barycentric rational interpolation, Stability
Stefano_De_Marchi
general the first few terms of the Born series are good approximation to the expanded quantity for "weak" interaction V {\displaystyle V} and large collision
Born_series
Quantum chemistry rule regarding vibronic transitions
of a series of approximations, principally the electrical dipole transition assumption and the Born–Oppenheimer approximation. Weaker magnetic dipole
Franck–Condon_principle
Scattering of an electromagnetic plane wave by a sphere
the wavelength of the scattered light there are simple and accurate approximations that suffice to describe the behavior of the system. But for objects
Mie_scattering
Point set triangulation minimizing total length
Kirkpatrick (1980). A weaker bound was given by Manacher & Zobrist (1979). A family of examples proving that the approximation ratio is Ω ( n ) {\displaystyle
Minimum-weight_triangulation
Task of computing complete subgraphs
maximum. Although the approximation ratio of this algorithm is weak, it is the best known to date. The results on hardness of approximation described below
Clique_problem
Solution concept of a non-cooperative game
A Beautiful Mind, Simon & Schuster. Aviad Rubinstein: "Hardness of Approximation Between P and NP", ACM, ISBN 978-1-947487-23-9 (May 2019), DOI: https://doi
Nash_equilibrium
Technique in statistics
not finite sample, properties, and inference is based on asymptotic approximations to the sampling distribution of the estimator. Even when the instruments
Instrumental_variables
Relation between vapour pressure and temperature
application. The August–Roche–Magnus formula provides a solution under that approximation: e s ( T ) = 6.1094 exp ( 17.625 T T + 243.04 ) , {\displaystyle e_{\text{s}}(T)=6
Clausius–Clapeyron_relation
Unitary matrix containing information on the weak interaction
weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions
Cabibbo–Kobayashi–Maskawa matrix
Cabibbo–Kobayashi–Maskawa_matrix
Concept in physics
image points of infinite amplification. In weak lensing by large-scale structure, the thin-lens approximation may break down, and low-density extended structures
Gravitational lensing formalism
Gravitational_lensing_formalism
Dimensionless quantity in fluid dynamics
surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium
Mach_number
Punctuation and accent mark (~, ◌̃)
most common in English, is used in modern texts mainly to indicate approximation. The tilde was originally one of a variety of marks written over an
Tilde
Fundamental theorem in probability theory and statistics
version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is the de Moivre–Laplace theorem. Let
Central_limit_theorem
Estimate of time taken for running an algorithm
arise in approximation algorithms; a famous example is the directed Steiner tree problem, for which there is a quasi-polynomial time approximation algorithm
Time_complexity
Method of logical reasoning
Libertarians. Therefore, about 60% of people are Libertarians." The argument is weak because the sample is non-random and the sample size is very small. Statistical
Inductive_reasoning
Technique in quantum mechanics for solving scattering problems
components dominate. At high energy, where scattering is weak, an alternative called the Born approximation is used. A steady beam of particles scatters off a
Partial-wave_analysis
Elementary particle involved with rest mass
and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. Its "sombrero potential" leads it to take a nonzero
Higgs_boson
Class of numerical techniques
n and the original function. Following is the process to derive an approximation for the first derivative of the function f by first truncating the Taylor
Finite_difference_method
Normed vector space that is complete
{\displaystyle X} satisfies the bounded approximation property. The first example by Enflo of a space failing the approximation property was at the same time the
Banach_space
Effective theory of gravity
over time. By definition, the post-Newtonian expansion assumes a weak field approximation. Within the first order perturbation to the metric g μ ν = η μ
Non-relativistic general relativity
Non-relativistic_general_relativity
Field-equations in general relativity
to Newton's law of gravity by using both the weak-field approximation and the low-velocity approximation. The constant G {\displaystyle G} appearing in
Einstein_field_equations
Theorem in complex analysis
numerical approximation of solutions of ordinary and partial differential equations and in the determination of bounds for the errors in such approximations. In
Maximum_principle
complex numbers Gamma function: Lanczos approximation Spouge's approximation — modification of Stirling's approximation; easier to apply than Lanczos AGM method
List of numerical analysis topics
List_of_numerical_analysis_topics
Type of stochastic process
\end{aligned}}} So { z t } {\displaystyle \{z_{t}\}} is a white noise in the weak sense (the mean and cross-covariances are zero, and the variances are all
Stationary_process
Number of orderings allowing ties
ordered Bell numbers or Fubini numbers count the weak orderings on a set of n {\displaystyle n} elements. Weak orderings arrange their elements into a sequence
Ordered_Bell_number
Instantaneous rate of change (mathematics)
of the function at that point. The tangent line is the best linear approximation of the function near that input value. The derivative is often described
Derivative
WEAK APPROXIMATION
WEAK APPROXIMATION
Boy/Male
Hindu
Peak
Surname or Lastname
English
English : topographic name for someone living by a pointed hill (or regional name from the Peak District (Old English Pēaclond) in Derbyshire), named with Old English pēac ‘peak’, ‘pointed hill’ (found only in place names). This word is not directly related to Old English pīc ‘point’, ‘pointed hill’, which yielded Pike; there is, however, some evidence of confusion between the two surnames.Possibly also Irish : reduced form of McPeak.Major concentrations of the surname Peak are found in Staffordshire and the West Country of England. Among the earliest known bearers are Richard del Pech or del Pek (d. 1196), son of Rannulf, sheriff of Nottingham, and Willielmus Piec (Winchester 1194). A century later, c.1284, a certain Richard del Peke settled in Denbighshire (now part of Clwyd), Wales, receiving lands from Henry de Lacey, earl of Lincoln, in return for helping to control the region. His descendants, who bear the name Peak(e), can be traced to the present day, and are found in New Zealand and Canada as well as in Britain. Peake is also the name of a family descended from John Pyke, who paid rent to the abbot of Leicester in 1477. The name took various forms, such as Peke and Pick, eventually becoming established as Peak in the 17th century.
Boy/Male
Australian, Hindu, Indian
Peak
Biblical
weak; slacked
Boy/Male
Arabic, Muslim
Weak
Girl/Female
Indian
Peak
Boy/Male
Arabic
One who has Weak Eyes
Boy/Male
Biblical
Weak, slacked.
Surname or Lastname
English
English : variant of Week.
Surname or Lastname
English
English : variant spelling of Leake.
Girl/Female
Australian, Christian, French, German, Hebrew
Hair; Lovelorn; Delicate; Weak
Boy/Male
Tamil
Peak
Boy/Male
Arabic, Muslim
Weak
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Peak
Boy/Male
Hindu, Indian
Week
Surname or Lastname
English (Northumbria)
English (Northumbria) : topographic name for someone who lived by the Wear river in northern England. The river name is ancient, occuring in the form Vedra in Ptolemy’s Geographia; it is probably a Celtic word meaning ‘water’.English (Northumbria) : topographic name for someone who lived near a dam or weir, a variant spelling of Ware 1, or a habitational name from a place called Weare, in Devon and Somerset, from Old English wær, wer ‘weir’.
Girl/Female
Hindu, Indian, Traditional
Peak
Surname or Lastname
English
English : variant of Wick, specifically a habitational name from any of various places called Week or Weeke, notably in Cornwall, Hampshire, and Somerset.Americanized spelling of Norwegian or Swedish Vik.
Girl/Female
Tamil
Peak
Boy/Male
Spanish
Weak.
WEAK APPROXIMATION
WEAK APPROXIMATION
Girl/Female
Australian, British, English, German
Queen of Heaven
Girl/Female
Muslim
Crown.
Girl/Female
Indian, Telugu
King of Wisdom
Girl/Female
Gujarati, Hindu, Indian
Love or the One who is Loved by All; Lover; Beloved; Form of Pia
Boy/Male
Indian, Sanskrit
Lean; A Sage Endowed with Divine Powers
Boy/Male
Latin Russian
Lion.
Boy/Male
Tamil
Servant
Girl/Female
Hindu
Famous or glorious
Boy/Male
German, Polish
Helmet Protection; Will Desire
Girl/Female
Tamil
Minor deity
WEAK APPROXIMATION
WEAK APPROXIMATION
WEAK APPROXIMATION
WEAK APPROXIMATION
WEAK APPROXIMATION
v. i.
Lacking ability for an appropriate function or office; as, weak eyes; a weak stomach; a weak magistrate; a weak regiment, or army.
v. i.
Feeble of mind; wanting discernment; lacking vigor; spiritless; as, a weak king or magistrate.
v. i.
Not able to withstand temptation, urgency, persuasion, etc.; easily impressed, moved, or overcome; accessible; vulnerable; as, weak resolutions; weak virtue.
v. i.
Not stiff; pliant; frail; soft; as, the weak stalk of a plant.
v. i.
To rise or extend into a peak or point; to form, or appear as, a peak.
v. i.
Not able to resist external force or onset; easily subdued or overcome; as, a weak barrier; as, a weak fortress.
v. i.
Tending towards lower prices; as, a weak market.
a.
Having a weak mind, either naturally or by reason of disease; feebleminded; foolish; idiotic.
v. i.
Wanting in point or vigor of expression; as, a weak sentence; a weak style.
v. i.
Wanting in power to influence or bind; as, weak ties; a weak sense of honor of duty.
v. i.
Not having power to convince; not supported by force of reason or truth; unsustained; as, a weak argument or case.
v. i.
Lacking in elements of political strength; not wielding or having authority or energy; deficient in the resources that are essential to a ruler or nation; as, a weak monarch; a weak government or state.
a.
Having weak knees; hence, easily yielding; wanting resolution.
v.
A crack, crevice, fissure, or hole which admits water or other fluid, or lets it escape; as, a leak in a roof; a leak in a boat; a leak in a gas pipe.
v. i.
Not thoroughly or abundantly impregnated with the usual or required ingredients, or with stimulating and nourishing substances; of less than the usual strength; as, weak tea, broth, or liquor; a weak decoction or solution; a weak dose of medicine.
v. i.
Not able to sustain a great weight, pressure, or strain; as, a weak timber; a weak rope.
a.
To make or become weak; to weaken.
n.
The upper aftermost corner of a fore-and-aft sail; -- used in many combinations; as, peak-halyards, peak-brails, etc.
v. i.
Not firmly united or adhesive; easily broken or separated into pieces; not compact; as, a weak ship.
v. t.
To cause or make by friction or wasting; as, to wear a channel; to wear a hole.