Stokes lines
E620766
concept in asymptotic analysis
concept in complex analysis
concept in differential equations
mathematical concept
Stokes lines are specific curves in the complex plane across which the asymptotic behavior of solutions to differential equations changes, playing a key role in asymptotic analysis and complex function theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Stokes lines canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T6788235 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Stokes lines Context triple: [George Gabriel Stokes, knownFor, Stokes lines]
-
A.
Fraunhofer lines
Fraunhofer lines are the dark absorption lines observed in the solar spectrum that reveal the presence and properties of elements in the Sun’s atmosphere and intervening gases.
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B.
Stark effect
The Stark effect is the splitting and shifting of atomic or molecular spectral lines caused by an external electric field.
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C.
Stokes
Stokes is a surname most famously associated with George Gabriel Stokes, a 19th-century Irish mathematician and physicist known for his foundational work in fluid dynamics and optics.
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D.
K-lines
K-lines are a cognitive theory construct proposed by Marvin Minsky in "The Society of Mind," representing memory traces that, when activated, re-evoke networks of mental agents involved in past problem-solving.
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E.
Stokes shift
Stokes shift is a phenomenon in spectroscopy where the wavelength of emitted light is longer (lower energy) than that of the absorbed light, commonly observed in fluorescence and phosphorescence.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Stokes lines Target entity description: Stokes lines are specific curves in the complex plane across which the asymptotic behavior of solutions to differential equations changes, playing a key role in asymptotic analysis and complex function theory.
-
A.
Fraunhofer lines
Fraunhofer lines are the dark absorption lines observed in the solar spectrum that reveal the presence and properties of elements in the Sun’s atmosphere and intervening gases.
-
B.
Stark effect
The Stark effect is the splitting and shifting of atomic or molecular spectral lines caused by an external electric field.
-
C.
Stokes
Stokes is a surname most famously associated with George Gabriel Stokes, a 19th-century Irish mathematician and physicist known for his foundational work in fluid dynamics and optics.
-
D.
K-lines
K-lines are a cognitive theory construct proposed by Marvin Minsky in "The Society of Mind," representing memory traces that, when activated, re-evoke networks of mental agents involved in past problem-solving.
-
E.
Stokes shift
Stokes shift is a phenomenon in spectroscopy where the wavelength of emitted light is longer (lower energy) than that of the absorbed light, commonly observed in fluorescence and phosphorescence.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in asymptotic analysis
ⓘ
concept in complex analysis ⓘ concept in differential equations ⓘ mathematical concept ⓘ |
| appearsIn |
saddle point analysis of contour integrals
ⓘ
theory of linear ODEs with irregular singular points ⓘ uniform asymptotic approximations near turning points ⓘ |
| context |
complex plane of the independent variable
ⓘ
complex plane of the phase function in integral representations ⓘ |
| definition |
curves in the complex plane across which the dominant asymptotic behavior of a solution changes
ⓘ
loci in the complex plane where exponentially small contributions in an asymptotic expansion switch on or off ⓘ |
| distinguishedFrom | anti-Stokes lines, where the real part of the exponent is constant ⓘ |
| effect |
cause discontinuous changes in asymptotic coefficients across them
ⓘ
control the activation of exponentially small terms in asymptotic series ⓘ |
| field |
asymptotic analysis
ⓘ
complex analysis ⓘ ordinary differential equations ⓘ special functions ⓘ |
| mathematicalFormulation |
for exponentials e^{
phi(z)/
ε}, Stokes lines satisfy Im(φ(z)) = constant where Re(φ(z)) changes sign
ⓘ
often defined by conditions on the argument of a complex phase function ⓘ |
| namedAfter |
George Gabriel Stokes
ⓘ
linked to:
George Stokes
|
| property |
are defined relative to a particular asymptotic expansion or solution
ⓘ
are typically curves along which the imaginary part of an exponent is constant ⓘ depend on the choice of branch of multivalued functions ⓘ mark where exponentially subdominant terms become comparable to dominant terms ⓘ often emanate from singularities or turning points of the differential equation ⓘ |
| relatedTo |
Stokes phenomenon
ⓘ
WKB approximation ⓘ analytic continuation ⓘ anti-Stokes lines ⓘ asymptotic expansion ⓘ connection formulas ⓘ saddle point method ⓘ singular points of differential equations ⓘ steepest descent paths ⓘ turning points of differential equations ⓘ |
| role |
determine sectors of validity of asymptotic expansions
ⓘ
govern the switching of asymptotic contributions in Stokes phenomenon ⓘ guide analytic continuation of asymptotic solutions ⓘ separate regions with different asymptotic dominance of terms ⓘ |
| usedIn |
WKB analysis of Schrödinger-type equations
ⓘ
analysis of Bessel functions ⓘ analysis of special functions such as Airy functions ⓘ asymptotic analysis of linear differential equations ⓘ exponential asymptotics ⓘ matched asymptotic expansions ⓘ resurgent analysis ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Stokes lines Description of subject: Stokes lines are specific curves in the complex plane across which the asymptotic behavior of solutions to differential equations changes, playing a key role in asymptotic analysis and complex function theory.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.