scholarly journals The topology of the monodromy map of a second order ODE

2006 ◽  
Vol 227 (2) ◽  
pp. 581-597 ◽  
Author(s):  
Dan Burghelea ◽  
Nicolau C. Saldanha ◽  
Carlos Tomei
Keyword(s):  
Second Order ◽  
Monodromy Map

scholarly journals On the monodromy of the deformed cubic oscillator

2022 ◽  
Author(s):  
Tom Bridgeland ◽  
Davide Masoero
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Second Order ◽  
Painlevé Equation ◽  
Order Linear Differential Equation ◽  
Isomonodromic Deformations ◽  
Order Linear ◽  
Linear Differential ◽  
Monodromy Map ◽  
Invent Math

AbstractWe study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Invent Math 216(1):69–124, 2019) arising from the Donaldson-Thomas theory of the A$$_2$$ 2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Second order interference in two photon absorption

1996 ◽  
Vol 43 (9) ◽  
pp. 1765-1771 ◽  
Author(s):  
M. W. HAMILTON and D. S. ELLIOTT
Keyword(s):  
Second Order ◽  
Photon Absorption ◽  
Two Photon Absorption ◽  
Two Photon

Die faktorielle Struktur des Partnerschaftsfragebogens

2012 ◽  
Vol 41 (2) ◽  
pp. 109-113 ◽  
Author(s):  
Sören Kliem ◽  
Christoph Kröger ◽  
Yve Stöbel-Richter ◽  
Kurt Hahlweg ◽  
Elmar Brähler
Keyword(s):  
Maximum Likelihood ◽  
Second Order ◽  
Bundesrepublik Deutschland

Zusammenfassung. Theoretischer Hintergrund: Der Partnerschaftsfragebogen (PFB) wird im deutschen Sprachraum zur Erfassung der Partnerschafts- und Ehequalität bevorzugt eingesetzt. Fragestellung: Neben der Überprüfung der Eindimensionalität der PFB-Subskalen (Streitverhalten, Zärtlichkeit, Gemeinsamkeit/Kommunikation) wird in der vorliegenden Arbeit überprüft, ob das Zusammenfassen der PFB-Subskalen zu einem Generalfaktor „Partnerschaftsqualität” angemessen ist. Methoden: Es wurden Daten einer Bevölkerungsstichprobe für die Bundesrepublik Deutschland genutzt (N = 1.289). Aufgrund der Abweichung von einer multivariaten Normalverteilung wurden konfirmatorische Faktorenanalysen mittels Maximum-Likelihood-Methode mit robusten Standardfehlern und einem mittelwertsadjustierten Chi2-Wert (Satorra-Bentler-scaled-χ2) durchgeführt. Ergebnisse: Es ergaben sich sowohl für die Eindimensionalität der PFB-Subskalen als auch für die Second-Order-Faktorenanalyse sehr gute Modellanapassungen. Schlussfolgerungen: Die Subsumierung der PFB-Items zu Skalenwerten sowie der PFB-Subskalen zu einem Gesamtwert kann als angemessen eingestuft werden.

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