scholarly journals Second order backward SDE with random terminal time

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Yiqing Lin ◽  
Zhenjie Ren ◽  
Nizar Touzi ◽  
Junjian Yang
Keyword(s):  
Second Order ◽  
Terminal Time ◽  
Backward Sde

scholarly journals HOMOGENIZATION OF A PERIODIC DEGENERATE SEMILINEAR ELLIPTIC PDE

2011 ◽  
Vol 11 (02n03) ◽  
pp. 475-493 ◽  
Author(s):  
ÉTIENNE PARDOUX ◽  
AHMADOU BAMBA SOW
Keyword(s):  
Differential Operator ◽  
Weak Convergence ◽  
Diffusion Processes ◽  
Probabilistic Method ◽  
Second Order ◽  
Elliptic Pde ◽  
Semilinear Elliptic ◽  
Terminal Time ◽  
Oscillating Coefficients ◽  
Order Part

In this paper, a semilinear elliptic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of ℝd. Our fully probabilistic method is based on the connection between PDEs and BSDEs with random terminal time and the weak convergence of a class of diffusion processes.

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
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