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 |
|---|---|
| k_B | k_B T as thermal energy scale 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 |
Fermi–Dirac statistics
via predicate surface "appearsInEquation"
ⓘ
surface form:
Fermi–Dirac distribution
|
| k_B |
Bose–Einstein statistics
via predicate surface "appearsInEquation"
ⓘ
surface form:
Bose–Einstein distribution
|
| k_B | Helmholtz free energy F = -k_B T ln Z via predicate surface "appearsInEquation" ⓘ |
| k_B | Gibbs free energy in statistical form via predicate surface "appearsInEquation" ⓘ |
| A Dynamical Theory of the Electromagnetic Field | vector calculus in component form via predicate surface "usesMathematicalTool" ⓘ |
|
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" ⓘ |
| Rudolphine Tables | logarithms via predicate surface "usesMathematicalTool" ⓘ |
| Rudolphine Tables | sine tables via predicate surface "usesMathematicalTool" ⓘ |
| Iannis Xenakis | stochastic processes via predicate surface "usedMathematicalConcept" ⓘ |
| Iannis Xenakis |
Markov processes
via predicate surface "usedMathematicalConcept"
ⓘ
surface form:
Markov chains
|
| Iannis Xenakis | set theory via predicate surface "usedMathematicalConcept" ⓘ |
| Iannis Xenakis | game theory via predicate surface "usedMathematicalConcept" ⓘ |
| Yukawa potential | V(r) = - g^2 e^{-\mu r} / (4 \pi r) via predicate surface "hasMathematicalForm" ⓘ |
| Wigner–Eckart theorem | group representation theory via predicate surface "mathematicalFormulationUses" ⓘ |
| Wigner–Eckart theorem | spherical harmonics via predicate surface "mathematicalFormulationUses" ⓘ |
| uncertainty principle | Δx · Δp ≥ ħ/2 via predicate surface "hasMathematicalForm" ⓘ |
| uncertainty principle | ΔE · Δt ≥ ħ/2 via predicate surface "hasMathematicalForm" ⓘ |
| Lorentz ether theory | Lorentz transformations between inertial frames via predicate surface "usesMathematicalTool" ⓘ |
|
book "Probabilistic Robotics"
surface form:
Probabilistic Robotics
|
probability theory via predicate surface "usesMathematicalTools" ⓘ |
|
book "Probabilistic Robotics"
surface form:
Probabilistic Robotics
|
Bayesian statistics via predicate surface "usesMathematicalTools" ⓘ |
|
book "Probabilistic Robotics"
surface form:
Probabilistic Robotics
|
linear algebra via predicate surface "usesMathematicalTools" ⓘ |
|
book "Probabilistic Robotics"
surface form:
Probabilistic Robotics
|
stochastic processes via predicate surface "usesMathematicalTools" ⓘ |
| Weyl’s gauge theory | Weyl geometry via predicate surface "usesMathematicalStructure" ⓘ |
| Weyl’s gauge theory | connection on a fiber bundle via predicate surface "usesMathematicalStructure" ⓘ |
| Heisenberg operator formulation of quantum mechanics | Hilbert space via predicate surface "usesMathematicalObject" ⓘ |
| Heisenberg operator formulation of quantum mechanics | linear operators via predicate surface "usesMathematicalObject" ⓘ |
| Heisenberg operator formulation of quantum mechanics | self-adjoint operators via predicate surface "usesMathematicalObject" ⓘ |
| Heisenberg operator formulation of quantum mechanics | unitary operators via predicate surface "usesMathematicalObject" ⓘ |
| GIM mechanism | unitary 2×2 quark mixing matrix for two generations via predicate surface "mathematicalFormulationUses" ⓘ |
| principle of least action | calculus of variations via predicate surface "mathematicalFormulationUses" ⓘ |
| Regge theory | complex J-plane analysis via predicate surface "hasMathematicalTool" ⓘ |
| Regge theory | Sommerfeld-Watson transform via predicate surface "hasMathematicalTool" ⓘ |
| Regge theory | analytic continuation of partial waves via predicate surface "hasMathematicalTool" ⓘ |
| Schwinger effect | imaginary part of the effective action via predicate surface "mathematicalDescription" ⓘ |
| Schwinger effect | instanton solutions in Euclidean spacetime via predicate surface "mathematicalDescription" ⓘ |
| Laplace equation | ∇²u = 0 via predicate surface "hasMathematicalForm" ⓘ |
| Superstring Theory, Volume 1: Introduction | quantum field theory via predicate surface "usesMathematicalTools" ⓘ |
| Superstring Theory, Volume 1: Introduction | differential geometry via predicate surface "usesMathematicalTools" ⓘ |
| Superstring Theory, Volume 1: Introduction | group theory via predicate surface "usesMathematicalTools" ⓘ |
| An Introduction to Mechanics | calculus via predicate surface "usesMathematics" ⓘ |
| An Introduction to Mechanics | vector calculus via predicate surface "usesMathematics" ⓘ |
| forgetting curve | negatively accelerated function via predicate surface "hasMathematicalForm" ⓘ |
| forgetting curve | exponential decay function via predicate surface "hasMathematicalForm" ⓘ |
| Rydberg constant | 1/λ = R∞ (1/n₁² − 1/n₂²) via predicate surface "appearsInEquation" ⓘ |
| Stefan–Boltzmann constant | P = σ A T^4 for a perfect black body via predicate surface "appearsInEquation" ⓘ |
| Noether charge | integral of time component of Noether current over a spatial hypersurface via predicate surface "mathematicallyExpressedAs" ⓘ |