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 |
|---|---|
| Schrödinger equation with point interactions | (-ħ^2/2m) Δψ + V ψ = E ψ with V a sum of delta functions via predicate surface "hasMathematicalForm" ⓘ |
| Fear of Physics | minimal via predicate surface "usesMathematics" ⓘ |
| Hammett equation | log(k/k0) = ρσ via predicate surface "hasMathematicalForm" ⓘ |
| Hammett equation | log(K/K0) = ρσ via predicate surface "hasMathematicalForm" ⓘ |
| Sears and Zemansky’s University Physics | calculus via predicate surface "usesMathematicsLevel" ⓘ |
| Regular Division of the Plane | wallpaper groups via predicate surface "mathematicalConceptUsed" ⓘ |
| Regular Division of the Plane | symmetry groups via predicate surface "mathematicalConceptUsed" ⓘ |
| Regular Division of the Plane | translation symmetry via predicate surface "mathematicalConceptUsed" ⓘ |
| Regular Division of the Plane | rotation symmetry via predicate surface "mathematicalConceptUsed" ⓘ |
| Regular Division of the Plane | reflection symmetry via predicate surface "mathematicalConceptUsed" ⓘ |
| Regular Division of the Plane | glide reflection symmetry via predicate surface "mathematicalConceptUsed" ⓘ |
| Alhambra tilings | symmetry via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | tessellation via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | periodicity via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | translation symmetry via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | rotation symmetry via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | reflection symmetry via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | glide reflection symmetry via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | wallpaper groups via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | plane symmetry groups via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | Euclidean geometry via predicate surface "usesMathematicalConcept" NERFINISHED ⓘ |
| Alhambra tilings | regular polygons via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | star polygons via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | interlacing patterns via predicate surface "usesMathematicalConcept" ⓘ |
| Alhambra tilings | repetition via predicate surface "usesMathematicalConcept" ⓘ |
| law of diminishing returns | declining first derivative of output with respect to a variable input beyond some point via predicate surface "mathematicallyExpressedAs" ⓘ |
| Paczynski–Wiita potential | Φ(r) = -GM / (r - r_s) via predicate surface "hasMathematicalForm" ⓘ |
| Peres–Horodecki criterion | matrix transposition on one subsystem via predicate surface "mathematicalOperation" ⓘ |
| Coulomb potential | V(r) = k q_1 q_2 / r via predicate surface "hasMathematicalForm" ⓘ |
| Coulomb potential | V(r) = (1 / (4π ε_0)) (q_1 q_2 / r) via predicate surface "hasMathematicalForm" ⓘ |
| Sérsic index | I(R) = I_e * exp{-b_n[(R/R_e)^{1/n} - 1]} via predicate surface "appearsInEquation" ⓘ |
| Anatoly Vlasov | partial differential equations via predicate surface "usedMathematicalTool" ⓘ |
| Anatoly Vlasov | distribution functions in phase space via predicate surface "usedMathematicalTool" ⓘ |
| Richardson–Dushman equation | J = A T^2 exp(-\phi / k_B T) via predicate surface "hasMathematicalForm" ⓘ |
| Partitions for Piano | combinatorics via predicate surface "usesMathematicalConcepts" ⓘ |
| Partitions for Piano | set partitions via predicate surface "usesMathematicalConcepts" ⓘ |
| Wess–Zumino–Witten model | Lie group via predicate surface "usesMathematicalStructure" ⓘ |
| Wess–Zumino–Witten model | Lie algebra via predicate surface "usesMathematicalStructure" ⓘ |
| Wess–Zumino–Witten model | affine Kac–Moody algebra via predicate surface "usesMathematicalStructure" ⓘ |
| Reichenbach epsilon | t_B = t_A + ε (t_A' − t_A) via predicate surface "appearsInEquation" ⓘ |
| Kroupa initial mass function | multi-part power-law via predicate surface "hasMathematicalForm" ⓘ |
| Lax–Wendroff method | Taylor series expansion via predicate surface "usesMathematicalTool" NERFINISHED ⓘ |
| Dzyaloshinskii–Moriya interaction | D · (S_i × S_j) via predicate surface "hasMathematicalForm" ⓘ |
| Bondi mass | surface integral over cuts of null infinity via predicate surface "mathematicallyExpressedAs" ⓘ |
| Ostwald dilution law | K = [A⁻][H⁺] / [HA] for a weak acid HA via predicate surface "hasMathematicalForm" ⓘ |
| Albatenius | sine function via predicate surface "usedMathematicalTool" ⓘ |
| R-matrix | element of End(V ⊗ V) for a vector space V via predicate surface "hasMathematicalForm" ⓘ |
| non-Abelian Berry connection | matrix-valued one-form on parameter space via predicate surface "hasMathematicalForm" ⓘ |
|
Hutchinson–Rice–Rosengren singularity in fracture mechanics
surface form:
Hutchinson–Rice–Rosengren singularity
|
power-law singularity in radial distance from crack tip via predicate surface "hasMathematicalForm" ⓘ |
| Elo-type rating system (men) | probabilistic model of match results via predicate surface "mathematicalFoundation" ⓘ |