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.
All labels observed (36)
| Label | Occurrences |
|---|---|
| hasMathematicalForm | 56 |
| appearsInEquation | 37 |
| usesMathematics | 20 |
| mathematicallyExpressedAs | 19 |
| hasMathematicalTool | 16 |
| usesMathematicalConcept | 16 |
| usesMathematicalTool | 16 |
| mathematicalDescription | 10 |
| mathematicalFoundation | 9 |
| usesMathematicalObject | 9 |
| usesMathematicalStructure | 9 |
| roleInMathematics | 8 |
| usesMathematicalTools | 7 |
| mathematicalConceptUsed | 6 |
| computedUsing | 5 |
| hasMathematicalFramework | 5 |
| mathematicalFormalism | 5 |
| containsMathematics | 4 |
| mathematicalFormulationUses | 4 |
| mathematicalOperation | 4 |
| usedMathematicalConcept | 4 |
| usedMathematicalTool | 4 |
| calculationUses | 3 |
| mathematicalToolUsed | 3 |
| mathematicallyInvolves | 3 |
| usesNumberTheoryConcept | 3 |
| mathematicalDescriptionUses | 2 |
| mathematicallyUses canonical | 2 |
| singularityAnalysisUses | 2 |
| usesMathematicalConcepts | 2 |
| usesMathematicsOf | 2 |
| forComplexExponent | 1 |
| forRealExponent | 1 |
| mathematicalOperator | 1 |
| usesMathematicalForm | 1 |
| usesMathematicsLevel | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: mathematicallyUses
Generated description
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
Sample triples (300)
| Subject | Object |
|---|---|
|
textbook "Quantum Electronics"
surface form:
Quantum Electronics
|
rate equations via predicate surface "containsMathematics" ⓘ |
| double-slit experiment | superposition of two coherent waves via predicate surface "mathematicalDescription" ⓘ |
| double-slit experiment | interference term proportional to cosine of phase difference via predicate surface "mathematicalDescription" ⓘ |
| RMM1 | empirical orthogonal function analysis via predicate surface "computedUsing" ⓘ |
| HITS algorithm | spectral graph theory via predicate surface "mathematicalFoundation" ⓘ |
| HITS algorithm | linear algebra via predicate surface "mathematicalFoundation" ⓘ |
| Fibonacci search |
Fibonacci sequence
via predicate surface "usesMathematicalConcept"
ⓘ
surface form:
Fibonacci numbers
|
| Fibonacci search | properties of Fibonacci sequence indices via predicate surface "usesMathematicalConcept" ⓘ |
| Ledoux criterion | inequality involving temperature and composition gradients via predicate surface "hasMathematicalForm" ⓘ |
| The Cosmographic Mystery | tetrahedron via predicate surface "usesMathematicalObject" ⓘ |
| The Cosmographic Mystery | cube via predicate surface "usesMathematicalObject" ⓘ |
| The Cosmographic Mystery | octahedron via predicate surface "usesMathematicalObject" ⓘ |
| The Cosmographic Mystery | dodecahedron via predicate surface "usesMathematicalObject" ⓘ |
| The Cosmographic Mystery | icosahedron via predicate surface "usesMathematicalObject" ⓘ |
| stress–energy tensor | Einstein field equations via predicate surface "appearsInEquation" ⓘ |
| stress–energy tensor | conservation of energy–momentum equations via predicate surface "appearsInEquation" ⓘ |
| Einstein–Yang–Mills equations | G_{μν} = 8πG T^{YM}_{μν} via predicate surface "hasMathematicalForm" ⓘ |
| Einstein–Yang–Mills equations | D_{μ} F^{a μν} = 0 in curved spacetime via predicate surface "hasMathematicalForm" ⓘ |
| Gutenberg–Richter law | log10 N = a − bM via predicate surface "hasMathematicalForm" ⓘ |
| Laspeyres formula | L = (Σ p_t q_0) / (Σ p_0 q_0) via predicate surface "hasMathematicalForm" ⓘ |
| Yukawa coupling | dimensionless coupling constant in four spacetime dimensions via predicate surface "hasMathematicalForm" ⓘ |
| Kramers degeneracy | T^2 = -1 on half-integer spin states via predicate surface "mathematicallyExpressedAs" ⓘ |
| Zhu Shijie | counting rods via predicate surface "usedMathematicalTool" ⓘ |
| Alain Badiou | set theory via predicate surface "usesMathematics" ⓘ |
| Alain Badiou | Cantorian set theory via predicate surface "usesMathematics" ⓘ |
| Alain Badiou | forcing via predicate surface "usesMathematics" ⓘ |
| Natural Policy Gradient | information geometry via predicate surface "mathematicalFoundation" ⓘ |
| Natural Policy Gradient | Riemannian optimization via predicate surface "mathematicalFoundation" ⓘ |
| Bianchi type cosmologies | orthonormal frame formalism via predicate surface "hasMathematicalFramework" ⓘ |
| Bianchi type cosmologies | Hamiltonian formulation of cosmology via predicate surface "hasMathematicalFramework" ⓘ |
| Shunya (void) | placeholder in positional notation via predicate surface "roleInMathematics" ⓘ |
| Shunya (void) | number representing null quantity via predicate surface "roleInMathematics" ⓘ |
|
Hubble constant H₀
surface form:
Hubble constant
|
v = H₀ d via predicate surface "appearsInEquation" ⓘ |
|
PMAC message authentication code
surface form:
PMAC
|
finite field over block size via predicate surface "usesMathematicalStructure" ⓘ |
| Verdet constant | θ = V B L via predicate surface "appearsInEquation" ⓘ |
| Langmuir adsorption isotherm | θ = (K P) / (1 + K P) via predicate surface "hasMathematicalForm" ⓘ |
| Langmuir adsorption isotherm | θ = (K C) / (1 + K C) via predicate surface "hasMathematicalForm" ⓘ |
| von Kármán constant | u+ = (1/κ) ln y+ + B via predicate surface "appearsInEquation" ⓘ |
| von Kármán constant | U(z) = (u*/κ) ln(z/z0) for neutral atmospheric stratification via predicate surface "appearsInEquation" ⓘ |
| Urbach tail | exponential dependence of absorption coefficient on photon energy via predicate surface "hasMathematicalForm" ⓘ |
| Hamming window | w[n] = α − β cos(2πn/(N−1)) via predicate surface "hasMathematicalForm" ⓘ |
| Schrödinger picture | complex Hilbert space via predicate surface "usesMathematicalStructure" ⓘ |
| Schrödinger picture | self-adjoint operators for observables via predicate surface "usesMathematicalStructure" ⓘ |
| Schrödinger picture | unitary operators for time evolution via predicate surface "usesMathematicalStructure" ⓘ |
| Debye relaxation | complex permittivity epsilon(omega) = epsilon_infinity + (epsilon_s - epsilon_infinity) / (1 + i omega tau) via predicate surface "hasMathematicalForm" ⓘ |
| Leontief production function | Q(x) = min_i (x_i / a_i) via predicate surface "mathematicallyExpressedAs" ⓘ |
| Rayleigh–Sommerfeld diffraction theory | surface integral over aperture via predicate surface "hasMathematicalForm" ⓘ |
| theory of unparticles | quantum field theory with non-integer operator dimensions via predicate surface "hasMathematicalFramework" ⓘ |
| Arrhenius equation | ln k = ln A - E_a/(R T) via predicate surface "hasMathematicalForm" ⓘ |
| Arrhenius equation for temperature dependence of reaction rates | k = A · exp(−Ea / (R · T)) via predicate surface "hasMathematicalForm" ⓘ |