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 |
|---|---|
| A Dynamical Theory of the Electromagnetic Field | vector calculus in component form via predicate surface "usesMathematicalTool" ⓘ |
| A Treatise on Electricity and Magnetism | vector calculus (in proto-form) via predicate surface "usesMathematicalTool" ⓘ |
| Ampère–Maxwell law | curl operator ∇× via predicate surface "mathematicalOperator" ⓘ |
| BCS theory of superconductivity | BCS ground state wavefunction ⓘ |
| BCS theory of superconductivity | gap equation ⓘ |
| Bekenstein bound | S ≤ 2πkRE/ħc via predicate surface "hasMathematicalForm" ⓘ |
| Boltzmann distribution | P(E) ∝ exp(-E/(k_B T)) via predicate surface "hasMathematicalForm" ⓘ |
|
Born approximation in scattering theory
surface form:
Born approximation
|
Fourier transform of interaction potential via predicate surface "mathematicallyInvolves" ⓘ |
|
Born approximation in scattering theory
surface form:
Born approximation
|
Green’s function of free particle via predicate surface "mathematicallyInvolves" ⓘ |
| Chandrasekhar–Friedman–Schutz instability | eigenmode analysis of rotating relativistic stars via predicate surface "mathematicalDescription" ⓘ |
|
CTSS
surface form:
Communication Theory of Secrecy Systems
|
information entropy via predicate surface "usesMathematicalTool" ⓘ |
|
CTSS
surface form:
Communication Theory of Secrecy Systems
|
probability theory via predicate surface "usesMathematicalTool" ⓘ |
| Einstein tensor | Einstein field equations via predicate surface "appearsInEquation" ⓘ |
| Gaussian law of error | probability density proportional to exp(-x^2/(2σ^2)) via predicate surface "hasMathematicalForm" ⓘ |
| Iannis Xenakis |
Markov processes
via predicate surface "usedMathematicalConcept"
ⓘ
surface form:
Markov chains
|
| Iannis Xenakis | game theory via predicate surface "usedMathematicalConcept" ⓘ |
| Iannis Xenakis | set theory via predicate surface "usedMathematicalConcept" ⓘ |
| Iannis Xenakis | stochastic processes via predicate surface "usedMathematicalConcept" ⓘ |
| London equations | supercurrent proportional to vector potential via predicate surface "mathematicallyExpressedAs" ⓘ |
| London equations | time derivative of supercurrent proportional to electric field via predicate surface "mathematicallyExpressedAs" ⓘ |
| Meissner effect | exponential decay of magnetic field over penetration depth via predicate surface "mathematicalDescription" ⓘ |
| Newton's second law of motion | F = dp/dt via predicate surface "hasMathematicalForm" ⓘ |
| Newton's second law of motion | F = ma via predicate surface "hasMathematicalForm" ⓘ |
| Newtonian gravitational constant G |
Einstein field equations
via predicate surface "appearsInEquation"
ⓘ
surface form:
Einstein field equations (via κ = 8πG/c^4)
|
| Newtonian gravitational constant G | F = G m1 m2 / r^2 via predicate surface "appearsInEquation" ⓘ |
| Newtonian gravitational constant G | g = G M / r^2 via predicate surface "appearsInEquation" ⓘ |
| Newtonian gravitational constant G | ∇^2Φ = 4πGρ via predicate surface "appearsInEquation" ⓘ |
| Planck constant | Bohr model energy levels via predicate surface "appearsInEquation" ⓘ |
| Planck constant |
uncertainty principle
via predicate surface "appearsInEquation"
ⓘ
surface form:
Heisenberg uncertainty principle
|
| Planck constant | Planck radiation law via predicate surface "appearsInEquation" ⓘ |
| Planck constant | Planck–Einstein relation via predicate surface "appearsInEquation" ⓘ |
| Planck constant | Schrödinger equation via predicate surface "appearsInEquation" ⓘ |
| Planck constant | de Broglie wavelength formula via predicate surface "appearsInEquation" ⓘ |
| Q-balls | nonlinear solutions of scalar field equations with global symmetry via predicate surface "mathematicalDescription" ⓘ |
| RFC 3526 | large prime moduli via predicate surface "usesNumberTheoryConcept" ⓘ |
| RFC 3526 | safe primes via predicate surface "usesNumberTheoryConcept" ⓘ |
| RFC 3526 | subgroup order via predicate surface "usesNumberTheoryConcept" ⓘ |
| Ricci flow | blow-up techniques via predicate surface "singularityAnalysisUses" ⓘ |
| Ricci flow | rescaling arguments via predicate surface "singularityAnalysisUses" ⓘ |
| Rudolphine Tables | logarithms via predicate surface "usesMathematicalTool" ⓘ |
| Rudolphine Tables | sine tables via predicate surface "usesMathematicalTool" ⓘ |
| Rényi entropy | H_α(P) = 1/(1-α) log(∑_i p_i^α) for α ≠ 1 via predicate surface "hasMathematicalForm" ⓘ |
| S-matrix | Dyson series via predicate surface "computedUsing" ⓘ |
| S-matrix | perturbation theory via predicate surface "computedUsing" ⓘ |
| S-matrix | time-ordered exponentials via predicate surface "computedUsing" ⓘ |
| Shockley diode equation | I = I_s (e^{V/(n V_T)} - 1) via predicate surface "hasMathematicalForm" ⓘ |
| Stokes flow | ∇p = μ∇²u via predicate surface "hasMathematicalForm" ⓘ |
| Stokes flow | ∇·u = 0 for incompressible case via predicate surface "hasMathematicalForm" ⓘ |
| TLS 1.2 Finished message | TLS 1.2 PRF via predicate surface "computedUsing" ⓘ |
| Théorie analytique de la chaleur | differential equations via predicate surface "mathematicalToolUsed" ⓘ |