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 |
|---|---|
| Leavitt law | linear relation between absolute magnitude and logarithm of period via predicate surface "mathematicallyExpressedAs" ⓘ |
| Pay As You Earn | adjusted gross income via predicate surface "calculationUses" ⓘ |
| Pay As You Earn | family size via predicate surface "calculationUses" ⓘ |
| Pay As You Earn | state of residence via predicate surface "calculationUses" ⓘ |
| Dirac string | A_φ potential of Dirac monopole in spherical coordinates via predicate surface "appearsInEquation" ⓘ |
| no-cloning theorem | no unitary U exists such that U(|ψ⟩|0⟩) = |ψ⟩|ψ⟩ for all |ψ⟩ via predicate surface "mathematicallyExpressedAs" ⓘ |
| Rindler horizon | boundary of the Rindler wedge in Minkowski spacetime via predicate surface "mathematicalDescription" ⓘ |
| Kubo–Martin–Schwinger condition | φ(A α_{iβ}(B)) = φ(BA) for all A,B in the algebra via predicate surface "mathematicallyExpressedAs" ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
fundamental in linear algebra via predicate surface "roleInMathematics" ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
central in representation theory via predicate surface "roleInMathematics" ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
basic example in Lie theory via predicate surface "roleInMathematics" ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
basic example in algebraic geometry via predicate surface "roleInMathematics" ⓘ |
| Coulomb constant | F = k_e q_1 q_2 / r^2 via predicate surface "appearsInEquation" ⓘ |
| Coulomb constant | E = k_e q / r^2 via predicate surface "appearsInEquation" ⓘ |
| Coulomb constant | U = k_e q_1 q_2 / r via predicate surface "appearsInEquation" ⓘ |
| Successive Under-Relaxation | x^{k+1} = x^{k} + omega (x^{k+1}_{*} - x^{k}) via predicate surface "hasMathematicalForm" ⓘ |
| gauge theory | Lie group via predicate surface "mathematicalFormalism" NERFINISHED ⓘ |
| gauge theory | Lie algebra via predicate surface "mathematicalFormalism" ⓘ |
| gauge theory | principal G-bundle via predicate surface "mathematicalFormalism" ⓘ |
| gauge theory | connection one-form via predicate surface "mathematicalFormalism" ⓘ |
| gauge theory | curvature two-form via predicate surface "mathematicalFormalism" ⓘ |
| Gamow factor | G(E) = exp(-2π η) via predicate surface "hasMathematicalForm" ⓘ |
| Hamilton's rule | ΔW > 0 if rb − c > 0 via predicate surface "mathematicallyExpressedAs" ⓘ |
| CPT theorem | Wightman axioms via predicate surface "hasMathematicalFramework" NERFINISHED ⓘ |
| CPT theorem | axiomatic quantum field theory via predicate surface "hasMathematicalFramework" ⓘ |
| Slater determinant | determinant of a matrix of spin-orbitals evaluated at electron coordinates via predicate surface "hasMathematicalForm" ⓘ |
| Slater determinant | 1/sqrt(N!) times determinant of orbital matrix for N electrons via predicate surface "hasMathematicalForm" ⓘ |
|
Volterra integral equations
surface form:
Volterra integral equation
|
y(t) = f(t) + ∫_a^t K(t,s) y(s) ds via predicate surface "hasMathematicalForm" ⓘ |
| Eyring reverberation formula | T = 0.161 V / (-S ln(1 - ᾱ)) in SI units via predicate surface "hasMathematicalForm" ⓘ |
| Wythoff Nim | Beatty sequences via predicate surface "hasMathematicalTool" NERFINISHED ⓘ |
| collective electrodynamics | path integrals via predicate surface "usesMathematicalTool" ⓘ |
| collective electrodynamics | Lagrangian formalism via predicate surface "usesMathematicalTool" ⓘ |
| Square cipher | finite field arithmetic via predicate surface "usesMathematics" ⓘ |
| Square cipher | linear algebra over GF(2^8) via predicate surface "usesMathematics" ⓘ |
| Van Vleck paramagnetism | sum over excited states of squared magnetic-moment matrix elements divided by energy separations via predicate surface "mathematicallyExpressedAs" ⓘ |
| Sparrow criterion | condition where derivative of combined intensity has an inflection at midpoint between sources via predicate surface "mathematicallyExpressedAs" ⓘ |
| Hermann | dissemination of Bourbaki’s works via predicate surface "roleInMathematics" ⓘ |
| Hermann | support of modern mathematical formalism via predicate surface "roleInMathematics" ⓘ |
| Alfvén waves | linearized MHD equations via predicate surface "mathematicalDescription" ⓘ |
| Alfvén’s theorem in magnetohydrodynamics | dΦ_B/dt = 0 for a surface moving with the fluid via predicate surface "mathematicallyExpressedAs" ⓘ |
| Alfvén’s theorem in magnetohydrodynamics | ∂B/∂t = ∇ × (v × B) in ideal MHD via predicate surface "mathematicallyExpressedAs" ⓘ |
| Navier boundary condition | u_t = b (∂u_t/∂n) via predicate surface "hasMathematicalForm" ⓘ |
| Optimization over Time | Markov decision process formulation via predicate surface "hasMathematicalTool" ⓘ |
| Optimization over Time | dynamic programming recursion via predicate surface "hasMathematicalTool" ⓘ |
| Optimization over Time | stochastic process theory via predicate surface "hasMathematicalTool" ⓘ |
| Optimization over Time | measure-theoretic probability via predicate surface "hasMathematicalTool" ⓘ |
| Optimization over Time | functional equations via predicate surface "hasMathematicalTool" ⓘ |
| Optimization over Time | convex analysis via predicate surface "hasMathematicalTool" ⓘ |
| Batch Normalization | standardization of activations via predicate surface "mathematicalOperation" ⓘ |
| Instance Normalization | x_hat = (x - mu_{n,c}) / sqrt(sigma_{n,c}^2 + epsilon) via predicate surface "mathematicalOperation" ⓘ |