mathematicallyUses
P4746
predicate
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
Observed surface forms (15)
- appearsInEquation ×22
- hasMathematicalForm ×11
- usesMathematicalTool ×6
- computedUsing ×4
- usedMathematicalConcept ×4
- mathematicalDescription ×3
- mathematicalToolUsed ×3
- usesNumberTheoryConcept ×3
- mathematicalFormulationUses ×2
- mathematicallyExpressedAs ×2
- mathematicallyInvolves ×2
- singularityAnalysisUses ×2
- forComplexExponent ×1
- forRealExponent ×1
- mathematicalOperator ×1
Sample triples (69)
| Subject | Object |
|---|---|
| Théorie analytique de la chaleur | integral calculus via predicate surface "mathematicalToolUsed" ⓘ |
| Théorie analytique de la chaleur | trigonometric series via predicate surface "mathematicalToolUsed" ⓘ |
| Tsallis entropy | S_q = (1 - \sum_i p_i^q) / (q - 1) via predicate surface "hasMathematicalForm" ⓘ |
| Wigner–Eckart theorem | group representation theory via predicate surface "mathematicalFormulationUses" ⓘ |
| Wigner–Eckart theorem | spherical harmonics via predicate surface "mathematicalFormulationUses" ⓘ |
| Yukawa potential | V(r) = - g^2 e^{-\mu r} / (4 \pi r) via predicate surface "hasMathematicalForm" ⓘ |
| binomial theorem | (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 via predicate surface "forRealExponent" ⓘ |
| binomial theorem | (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ via predicate surface "forComplexExponent" ⓘ |
| k_B |
Bose–Einstein statistics
via predicate surface "appearsInEquation"
ⓘ
surface form:
Bose–Einstein distribution
|
| k_B |
Fermi–Dirac statistics
via predicate surface "appearsInEquation"
ⓘ
surface form:
Fermi–Dirac distribution
|
| k_B | Gibbs free energy in statistical form via predicate surface "appearsInEquation" ⓘ |
| k_B | Helmholtz free energy F = -k_B T ln Z via predicate surface "appearsInEquation" ⓘ |
| k_B | Johnson–Nyquist noise: ⟨V²⟩ = 4 k_B T R Δf via predicate surface "appearsInEquation" ⓘ |
| k_B |
Maxwell–Boltzmann statistics
via predicate surface "appearsInEquation"
ⓘ
surface form:
Maxwell–Boltzmann distribution
|
| k_B | S = k_B ln Ω via predicate surface "appearsInEquation" ⓘ |
| k_B | U = (f/2) N k_B T via predicate surface "appearsInEquation" ⓘ |
| k_B | k_B T as thermal energy scale via predicate surface "appearsInEquation" ⓘ |
| k_B | pV = N k_B T via predicate surface "appearsInEquation" ⓘ |
| k_B | ⟨E⟩ = k_B T for a classical degree of freedom via predicate surface "appearsInEquation" ⓘ |