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.

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All labels observed (36)

Label Occurrences
hasMathematicalForm 56
appearsInEquation 37
usesMathematics 20

Sample triples (300)

Subject Object
BCS theory of superconductivity BCS ground state wavefunction ⓘ
BCS theory of superconductivity gap equation ⓘ
binomial theorem (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 via predicate surface "forRealExponent" ⓘ
binomial theorem (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 and α ∈ ℂ via predicate surface "forComplexExponent" ⓘ
Théorie analytique de la chaleur trigonometric series via predicate surface "mathematicalToolUsed" ⓘ
Théorie analytique de la chaleur integral calculus via predicate surface "mathematicalToolUsed" ⓘ
Théorie analytique de la chaleur differential equations via predicate surface "mathematicalToolUsed" ⓘ
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 Einstein field equations via predicate surface "appearsInEquation" ⓘ
surface form: Einstein field equations (via κ = 8πG/c^4)
Newtonian gravitational constant G ∇^2Φ = 4πGρ via predicate surface "appearsInEquation" ⓘ
Rényi entropy H_α(P) = 1/(1-α) log(∑_i p_i^α) for α ≠ 1 via predicate surface "hasMathematicalForm" ⓘ
Tsallis entropy S_q = (1 - \sum_i p_i^q) / (q - 1) via predicate surface "hasMathematicalForm" ⓘ
Chandrasekhar–Friedman–Schutz instability eigenmode analysis of rotating relativistic stars via predicate surface "mathematicalDescription" ⓘ
Meissner effect exponential decay of magnetic field over penetration depth via predicate surface "mathematicalDescription" ⓘ
London equations time derivative of supercurrent proportional to electric field via predicate surface "mathematicallyExpressedAs" ⓘ
London equations supercurrent proportional to vector potential via predicate surface "mathematicallyExpressedAs" ⓘ
Einstein tensor Einstein field equations via predicate surface "appearsInEquation" ⓘ
S-matrix time-ordered exponentials via predicate surface "computedUsing" ⓘ
S-matrix Dyson series via predicate surface "computedUsing" ⓘ
S-matrix perturbation theory via predicate surface "computedUsing" ⓘ
A Treatise on Electricity and Magnetism vector calculus (in proto-form) via predicate surface "usesMathematicalTool" ⓘ
CTSS
surface form: Communication Theory of Secrecy Systems
probability theory via predicate surface "usesMathematicalTool" ⓘ
CTSS
surface form: Communication Theory of Secrecy Systems
information entropy via predicate surface "usesMathematicalTool" ⓘ
Q-balls nonlinear solutions of scalar field equations with global symmetry via predicate surface "mathematicalDescription" ⓘ
Bekenstein bound S ≤ 2πkRE/ħc via predicate surface "hasMathematicalForm" ⓘ
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" ⓘ
Planck constant Schrödinger equation via predicate surface "appearsInEquation" ⓘ
Planck constant uncertainty principle via predicate surface "appearsInEquation" ⓘ
surface form: Heisenberg uncertainty principle
Planck constant Planck–Einstein relation via predicate surface "appearsInEquation" ⓘ
Planck constant Planck radiation law via predicate surface "appearsInEquation" ⓘ
Planck constant de Broglie wavelength formula via predicate surface "appearsInEquation" ⓘ
Planck constant Bohr model energy levels via predicate surface "appearsInEquation" ⓘ
Gaussian law of error probability density proportional to exp(-x^2/(2σ^2)) via predicate surface "hasMathematicalForm" ⓘ
Ampère–Maxwell law curl operator ∇× via predicate surface "mathematicalOperator" ⓘ
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" ⓘ
TLS 1.2 Finished message TLS 1.2 PRF via predicate surface "computedUsing" ⓘ
Stokes flow ∇p = μ∇²u via predicate surface "hasMathematicalForm" ⓘ
Stokes flow ∇·u = 0 for incompressible case via predicate surface "hasMathematicalForm" ⓘ
Ricci flow blow-up techniques via predicate surface "singularityAnalysisUses" ⓘ
Ricci flow rescaling arguments via predicate surface "singularityAnalysisUses" ⓘ
Boltzmann distribution P(E) ∝ exp(-E/(k_B T)) via predicate surface "hasMathematicalForm" ⓘ
Shockley diode equation I = I_s (e^{V/(n V_T)} - 1) via predicate surface "hasMathematicalForm" ⓘ
k_B U = (f/2) N k_B T via predicate surface "appearsInEquation" ⓘ
k_B S = k_B ln Ω via predicate surface "appearsInEquation" ⓘ
k_B pV = N k_B T via predicate surface "appearsInEquation" ⓘ
k_B ⟨E⟩ = k_B T for a classical degree of freedom via predicate surface "appearsInEquation" ⓘ