isLimitOf
P9149
predicate
Indicates that one quantity, function, or sequence approaches a particular value as its input or index approaches some specified point or condition.
All labels observed (37)
| Label | Occurrences |
|---|---|
| hasLimitingCase | 12 |
| isLimitOf canonical | 10 |
| isLowEnergyLimitOf | 6 |
| hasLimitingBehavior | 3 |
| isLimitCaseOf | 3 |
| limitingCase | 3 |
| scalingLimit | 3 |
| approachedAsLimit | 2 |
| becomesExactInLimit | 2 |
| hasLimitCase | 2 |
| haveLimit | 2 |
| isCutoffFor | 2 |
| limitObject | 2 |
| concernsLimit | 1 |
| hasChiralLimit | 1 |
| hasClassicalLimit | 1 |
| hasContinuousLimitAt | 1 |
| hasLimitForm | 1 |
| hasLimitRelation | 1 |
| hasSeriesLimit | 1 |
| involvesLimit | 1 |
| isClassicalLimitOf | 1 |
| isIsingLikeLimit | 1 |
| isIsotropicLimit | 1 |
| isLimitIn | 1 |
| isLimitType | 1 |
| isLimitingCaseOf | 1 |
| isPlanarLimit | 1 |
| limitDefinition | 1 |
| limitOf | 1 |
| limitProcess | 1 |
| limitProperty | 1 |
| limitRegime | 1 |
| recoveredAsLimitOf | 1 |
| seriesLimitTransition | 1 |
| spectralMeasureLimit | 1 |
| usesLimit | 1 |
Sample triples (76)
| Subject | Object |
|---|---|
| Bekenstein–Hawking entropy | entanglement entropy across a horizon in quantum field theory ⓘ |
| Minkowski space-time | curved space-times in general relativity ⓘ |
| de Sitter spacetime | Minkowski spacetime for Λ → 0 via predicate surface "hasLimitCase" ⓘ |
| Gaussian distribution | central limit theorem via predicate surface "isLimitIn" ⓘ |
| Galilean relativity | special relativity at low velocities via predicate surface "recoveredAsLimitOf" ⓘ |
| Rayleigh–Jeans law at low frequencies |
Planck radiation law
via predicate surface "isClassicalLimitOf"
ⓘ
surface form:
Planck’s radiation law
|
| Euler equations |
Navier–Stokes equations
via predicate surface "isLimitCaseOf"
ⓘ
surface form:
Navier–Stokes equations with zero viscosity
|
| Bardeen black hole model | de Sitter spacetime at the center via predicate surface "hasLimitingCase" ⓘ |
| Rényi divergence | α → 1 to KL divergence via predicate surface "hasContinuousLimitAt" ⓘ |
| Kerr–Newman black hole | naked singularity when M^2 < a^2 + Q^2 via predicate surface "hasLimitingCase" ⓘ |
| Riemann–Liouville integral | identity operator when α → 0^+ via predicate surface "hasLimitingCase" ⓘ |
| Riemann sums | definite integral as limit of Riemann sums via predicate surface "limitDefinition" ⓘ |
| Fermi constant | W boson exchange interaction via predicate surface "isLowEnergyLimitOf" ⓘ |
| Compton effect | Thomson scattering via predicate surface "hasClassicalLimit" ⓘ |
| Jacobi ellipsoid | Maclaurin spheroid at lower rotation via predicate surface "hasLimitingCase" ⓘ |
| Dirac Lagrangian | massless Dirac Lagrangian with m = 0 via predicate surface "hasChiralLimit" ⓘ |
| Thomson cross section | Klein–Nishina formula via predicate surface "isLowEnergyLimitOf" ⓘ |
| Laplace law of error | difference of two independent exponential distributions ⓘ |
| Jacobi elliptic functions | trigonometric functions as m → 0 via predicate surface "haveLimit" ⓘ |
| Jacobi elliptic functions | hyperbolic functions as m → 1 via predicate surface "haveLimit" ⓘ |
| Jacobi polynomials | limit cases yield Bessel-type functions under scaling via predicate surface "hasLimitRelation" ⓘ |
| Menger sponge | sequence of polyhedral approximations ⓘ |
| Ayón-Beato–García regular black hole solutions | extremal regular black hole configuration via predicate surface "hasLimitCase" ⓘ |
| Rabi frequency | generalized Rabi frequency at zero detuning via predicate surface "isLimitCaseOf" ⓘ |
| Dulong–Petit law for molar heat capacity of many solids at high temperature | high-temperature limit of the Einstein model via predicate surface "approachedAsLimit" ⓘ |
| Dulong–Petit law for molar heat capacity of many solids at high temperature | high-temperature limit of the Debye model via predicate surface "approachedAsLimit" ⓘ |
| Bose gas | ideal Bose gas via predicate surface "hasLimitingCase" ⓘ |
| Bose gas | non-interacting Bose gas via predicate surface "hasLimitingCase" ⓘ |
| Carnap's continuum of inductive methods | methods that ignore new evidence (extreme caution) via predicate surface "hasLimitingCase" ⓘ |
| Carnap's continuum of inductive methods | methods that follow observed frequencies closely (extreme boldness) via predicate surface "hasLimitingCase" ⓘ |
| XXZ spin chain | XXX Heisenberg spin chain at Δ = 1 via predicate surface "isIsotropicLimit" ⓘ |
| XXZ spin chain | XX spin chain at Δ = 0 via predicate surface "isPlanarLimit" ⓘ |
| XXZ spin chain | Ising chain in a transverse field for |Δ| → ∞ (up to scaling) via predicate surface "isIsingLikeLimit" ⓘ |
| Khinchin–Lévy constant | for almost all real x, lim_{n→∞} (q_n)^{1/n} = L where q_n are denominators of convergents of x via predicate surface "limitProperty" ⓘ |
| Lyman series in hydrogen spectrum | n=∞ to n=1 via predicate surface "seriesLimitTransition" ⓘ |
| Balmer series of hydrogen | n → ∞ to n = 2 via predicate surface "hasSeriesLimit" ⓘ |
| Gaussian orthogonal ensemble | sine kernel in the bulk via predicate surface "scalingLimit" ⓘ |
| Gaussian orthogonal ensemble | Airy kernel at the soft edge via predicate surface "scalingLimit" NERFINISHED ⓘ |
| Gaussian orthogonal ensemble | semicircle distribution via predicate surface "spectralMeasureLimit" ⓘ |
|
Poisson distribution has P(s) = e^{-s}
surface form:
Poisson distribution with P(s) = e^{-s}
|
Poisson process inter-arrival time distribution with λ = 1 via predicate surface "isLimitingCaseOf" ⓘ |
| Thomson scattering | Compton scattering NERFINISHED ⓘ |
| Thomson scattering | classical limit of photon–electron scattering via predicate surface "isLimitType" ⓘ |
| Dirichlet distribution | degenerate distribution on simplex as concentration goes to infinity via predicate surface "hasLimitingCase" ⓘ |
| Dirichlet distribution | distribution concentrated on vertices of simplex as concentration goes to zero via predicate surface "hasLimitingCase" ⓘ |
| Roche ellipsoid | Roche lobe filling configuration via predicate surface "hasLimitingCase" ⓘ |
| Dynamical Mean-Field Theory | infinite lattice coordination number via predicate surface "becomesExactInLimit" ⓘ |
| Dynamical Mean-Field Theory | infinite spatial dimensions via predicate surface "becomesExactInLimit" ⓘ |
| Debye temperature | phonon wave vectors in Debye model via predicate surface "isCutoffFor" ⓘ |
| Debye temperature | phonon frequencies in Debye model via predicate surface "isCutoffFor" ⓘ |
| Erdős–Kac theorem | x tends to infinity via predicate surface "limitProcess" ⓘ |