mathematicallyExpressedBy
P12675
predicate
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
Observed surface forms (43)
- expressedAs ×12
- mathematicalTool ×7
- entersEquation ×5
- mathematicalType ×5
- enterEquation ×3
- expressibleIn ×3
- givesFormulaFor ×3
- hasMathematicalDescription ×3
- symbolicForm ×3
- differentialForm ×2
- equation ×2
- governingEquation ×2
- hasEquation ×2
- hasMathematicalBasis ×2
- mathematicalDefinition ×2
- DirichletSeriesDefinition ×1
- EulerProduct ×1
- GSEFormula ×1
- RiemannHypothesisStatement ×1
- coefficientOf ×1
- commutationRelations ×1
- entryFormula ×1
- equationContext ×1
- equationForm ×1
- equations ×1
- expressibleAs ×1
- expressibleInTermsOf ×1
- formulaInPrincipalDirections ×1
- formulaInWavelengthForm ×1
- functionalEquation ×1
- hasMathematicalFormulation ×1
- integralForm ×1
- integrand ×1
- introducedFormula ×1
- isMathematicallyRepresentedAs ×1
- localExpression ×1
- mathematicalCondition ×1
- mathematicalRole ×1
- mathematicallyFormalizedIn ×1
- obeysEquation ×1
- occursInEquation ×1
- probabilityDensityFunction ×1
- relatedFormula ×1
Sample triples (85)
| Subject | Object |
|---|---|
|
Einstein's annus mirabilis papers
surface form: ""Does the Inertia of a Body Depend Upon Its Energy Content?""
|
E = mc^2 via predicate surface "introducedFormula" → |
| AdS/CFT correspondence | correspondence between boundary correlators and bulk on-shell action via predicate surface "mathematicalTool" → |
| Bardeen–Stephen model of flux flow in superconductors | flux-flow resistivity ρ_ff ≈ ρ_n (B / Hc2) via predicate surface "givesFormulaFor" → |
| Boltzmann equation | integro-differential equation in 7 variables via predicate surface "mathematicalType" → |
| Boltzmann equation | nonlinear equation via predicate surface "mathematicalType" → |
| Christoffel symbols | covariant derivative ∇_μ V^ν = ∂_μ V^ν + Γ^ν_{μρ} V^ρ via predicate surface "enterEquation" → |
| Christoffel symbols | covariant derivative ∇_μ ω_ν = ∂_μ ω_ν − Γ^ρ_{μν} ω_ρ via predicate surface "enterEquation" → |
| Christoffel symbols | first derivatives of the metric via predicate surface "expressibleInTermsOf" → |
| Christoffel symbols | geodesic equation d^2x^μ/dτ^2 + Γ^μ_{νρ}(dx^ν/dτ)(dx^ρ/dτ) = 0 via predicate surface "enterEquation" → |
| Economic Confidence Model | cyclical periodicity via predicate surface "hasMathematicalBasis" → |
| Einstein synchronization convention | t_B = (t_A1 + t_A2) / 2 via predicate surface "mathematicalCondition" → |
| Einstein tensor | G_{\mu\nu} = 8\pi G T_{\mu\nu} / c^{4} via predicate surface "equationContext" → |
| Einstein tensor | G_{\mu\nu} = R_{\mu\nu} - \tfrac{1}{2} R g_{\mu\nu} via predicate surface "equation" → |
| Einstein–Maxwell equations | G_{μν} = 8π T_{μν}^{(EM)} + 8π T_{μν}^{(matter)} via predicate surface "expressedAs" → |
| Einstein–Maxwell equations | ∇_{[α} F_{βγ]} = 0 via predicate surface "expressedAs" → |
| Einstein–Maxwell equations | ∇_{μ} F^{μν} = 4π J^{ν} via predicate surface "expressedAs" → |
| Ekman transport | M = τ / (ρ f) via predicate surface "governingEquation" → |
| Eliashberg theory |
Eliashberg theory
via predicate surface "equations"
self-linksurface differs
→
surface form: "Eliashberg equations"
|
| Euler equations | hyperbolic system via predicate surface "mathematicalType" → |
| Euler equations | nonlinear partial differential equation via predicate surface "mathematicalType" → |
| Faraday's law of induction | ∮_C E · dl = - d/dt ∫_S B · dA via predicate surface "differentialForm" → |
| Faraday's law of induction | ∮_C E · dl = - dΦ_B/dt via predicate surface "integralForm" → |
| Fermi liquid theory | Green's functions via predicate surface "mathematicalTool" → |
| Fermi liquid theory | renormalization of quasiparticle parameters via predicate surface "mathematicalTool" → |
| Fermi liquid theory | self-energy via predicate surface "mathematicalTool" → |
| Fourier's law of heat conduction | q = -k ∇T via predicate surface "expressedAs" → |
| Fourier's law of heat conduction | q_i = -k_{ij} ∂T/∂x_j via predicate surface "expressedAs" → |
| Galilean relativity | Galilean group symmetry via predicate surface "hasMathematicalFormulation" → |
|
Gauss’s law
surface form: "Gauss's law"
|
∇ · E = ρ / ε₀ via predicate surface "differentialForm" → |
| Gaussian curvature | K = k1 * k2 via predicate surface "formulaInPrincipalDirections" → |
| Gaussian distribution | f(x) = (1/(σ√(2π))) · exp(−(x−μ)²/(2σ²)) via predicate surface "probabilityDensityFunction" → |
| Gaussian integral | e^{−x^2} via predicate surface "integrand" → |
| Gibbons–Hawking temperature | T = \frac{\hbar}{2\pi k_B} \sqrt{\frac{\Lambda}{3}} via predicate surface "relatedFormula" → |
| Hawking radiation | Bogoliubov transformations between in and out states via predicate surface "hasMathematicalDescription" → |
| Hawking radiation | quantum field modes on Schwarzschild background via predicate surface "hasMathematicalDescription" → |
| Higgs field | complex scalar doublet field φ via predicate surface "isMathematicallyRepresentedAs" → |
| Higgs mechanism | gauge theories with spontaneous symmetry breaking via predicate surface "mathematicallyFormalizedIn" → |
| Huang–Rhys factor | average number of phonons involved in an electronic transition via predicate surface "mathematicalRole" → |
| Karush–Kuhn–Tucker conditions | system of equations and inequalities via predicate surface "expressedAs" → |
| Klein quartic | x^3 y + y^3 z + z^3 x = 0 via predicate surface "equation" → |
| Lemaître–Hubble law | v = H₀ d via predicate surface "expressedAs" → |
| Levi-Civita connection | Christoffel symbols of the second kind via predicate surface "localExpression" → |
| London penetration depth | B(x) = B(0) exp(-x / λ) via predicate surface "occursInEquation" → |
| Lorentz contraction | L = L0 / gamma via predicate surface "expressedAs" → |
| Lorentz contraction | Lorentz factor gamma = 1/sqrt(1 - v^2/c^2) via predicate surface "mathematicalTool" → |
| Lorentz force | F = q(E + v × B) via predicate surface "expressedAs" → |
|
Newtonian fluids
surface form: "Newtonian fluid"
|
τ = μ (du/dy) via predicate surface "obeysEquation" → |
| On the Curvature of Space | Riemannian geometry via predicate surface "mathematicalTool" → |
| On the Curvature of Space | differential equations via predicate surface "mathematicalTool" → |
| Pascal's triangle | C(n,k) = n choose k via predicate surface "entryFormula" → |
| Poisson spot | Bessel function intensity distribution via predicate surface "hasMathematicalDescription" → |
| Rayleigh–Jeans law at low frequencies | B_λ(T) = (2ckT)∕λ⁴ via predicate surface "formulaInWavelengthForm" → |
| Ricci flow | ∂g_ij/∂t = -2 Ric_ij via predicate surface "governingEquation" → |
| Riemann zeta function | all nontrivial zeros lie on Re(s) = 1/2 via predicate surface "RiemannHypothesisStatement" → |
| Riemann zeta function | ζ(s) = 2^s π^{s-1} sin(πs/2) Γ(1-s) ζ(1-s) via predicate surface "functionalEquation" → |
| Riemann zeta function | ζ(s) = Σ_{n=1}^{∞} 1/n^s via predicate surface "DirichletSeriesDefinition" → |
| Riemann zeta function | ζ(s) = ∏_{p prime} (1 - p^{-s})^{-1} via predicate surface "EulerProduct" → |
| Riemann–Roch theorem | dimension of the space of global sections of a line bundle via predicate surface "givesFormulaFor" → |
| Riemann–Roch theorem | dimension of the space of meromorphic functions with prescribed zeros and poles via predicate surface "givesFormulaFor" → |
| Rosseland mean opacity | harmonic mean of monochromatic opacity weighted by derivative of Planck function with respect to temperature via predicate surface "mathematicalDefinition" → |
| SU(2)_L | [T^a, T^b] = i ε^{abc} T^c via predicate surface "commutationRelations" → |
| Sackur–Tetrode equation | molar form via predicate surface "expressibleIn" → |
| Sackur–Tetrode equation | per-particle form via predicate surface "expressibleIn" → |
| Snell’s law of refraction | n = c / v via predicate surface "expressibleAs" → |
| Snell’s law of refraction | n1 * sin(θ1) = n2 * sin(θ2) via predicate surface "equationForm" → |
| Snell’s law of refraction | trigonometric relation via predicate surface "mathematicalType" → |
| Tomonaga–Schwinger equation | functional differential equation via predicate surface "expressedAs" → |
| Wien displacement law | λ_max = b / T via predicate surface "hasEquation" → |
| Wien displacement law | λ_max T = b via predicate surface "symbolicForm" → |
| Wien displacement law | ν_max ≈ (k_B T)/h (for frequency form, approximate) via predicate surface "hasEquation" → |
| Wigner surmise | P(s) = (2^{18}/3^6 π^3) s^4 exp(-64 s^2 / 9π) via predicate surface "GSEFormula" → |
| axiom of choice | every family of nonempty sets admits a choice function via predicate surface "expressedAs" → |
| axiom schema of separation | first-order logic with equality and membership via predicate surface "expressibleIn" → |
| axiom schema of separation | ∀A ∀p1 … ∀pn ∃B ∀x (x ∈ B ↔ x ∈ A ∧ φ(x, p1, …, pn)) via predicate surface "expressedAs" → |
| ideal gas law | PV = nRT via predicate surface "symbolicForm" → |
| ideal gas law | pV = nRT via predicate surface "symbolicForm" → |
| moment magnitude scale | seismic moment tensor via predicate surface "hasMathematicalBasis" → |
| multinomial theorem | x1^{k1}...xm^{km} equals n!/(k1!...km!) via predicate surface "coefficientOf" → |
| reduced Planck constant | L̂ = -iħ r × ∇ via predicate surface "entersEquation" → |
| reduced Planck constant | Ŝ = ħ σ/2 via predicate surface "entersEquation" → |
| reduced Planck constant | [x̂, p̂] = iħ via predicate surface "entersEquation" → |
| reduced Planck constant | iħ ∂ψ/∂t = Ĥψ via predicate surface "entersEquation" → |
| reduced Planck constant | ħ = h / (2π) via predicate surface "mathematicalDefinition" → |
| reduced Planck constant | Δx Δp ≥ ħ/2 via predicate surface "entersEquation" → |
| relativity of simultaneity | time component of Lorentz transformation → |