Preferred NV Field for Arbitrary Crossed-Gratings with Analytic Boundary

2013 ◽  
Vol 52 (1) ◽  
pp. 859-864 ◽  
Author(s):  
H. Deng ◽  
S. Chen
Keyword(s):  
Analytic Boundary

On the Vector Sum of Two Convex Sets in Space

1991 ◽  
Vol 43 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Steven G. Krantz ◽  
Harold R. Parks
Keyword(s):  
Convex Sets ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Vector Sum ◽  
Bounded Convex

In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

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