AROUND THE NEARBY CYCLE FUNCTOR FOR ARITHMETIC -MODULES

2019 ◽  
Vol 236 ◽  
pp. 1-28
Author(s):  
TOMOYUKI ABE
Keyword(s):  
Module Theory ◽  
Nearby Cycle ◽  
Vanishing Cycle ◽  
Smooth Objects

We will establish a nearby and vanishing cycle formalism for the arithmetic $\mathscr{D}$-module theory following Beilinson’s philosophy. As an application, we define smooth objects in the framework of arithmetic $\mathscr{D}$-modules whose category is equivalent to the category of overconvergent isocrystals.

scholarly journals Determination of the refractive index profile and surface topography of optically smooth objects using interference of optical vortices

2021 ◽  
Vol 2103 (1) ◽  
pp. 012166
Author(s):  
B V Sokolenko ◽  
N V Shostka ◽  
D A Poletaev
Keyword(s):  
Refractive Index Profile ◽  
Optical Path Difference ◽  
Path Difference ◽  
Reference Plane ◽  
Optical Vortices ◽  
Vortex Beams ◽  
Singly Charged ◽  
Longitudinal Resolution ◽  
Smooth Objects

Abstract In this paper, we present the results of the propagational dynamics of vortex beams in the scope of their possible applications for interferometric non-contact robust and precision optical surface profilometry with nanoscale longitudinal resolution. The result of coaxial superposition of the reference plane wave with singly charged vortex beams represents a dynamically changing intensity distribution. The nature of this changes, namely, rotational effects of intensity zeros, allows to determine directly the optical path difference which is introduced by the surfaces and internal structure of test object. We have proposed the experimental setup for examination of reflecting and transmitting objects.

Impulse characteristics of smooth objects in bistatic case

1996 ◽  
Vol 10 (12) ◽  
pp. 1613-1622 ◽  
Author(s):  
O.I. Sukharevsky ◽  
V.A. Vasilets
Keyword(s):  
Smooth Objects ◽  
Impulse Characteristics

Module Theory

1998 ◽  
Author(s):  
Alberto Facchini
Keyword(s):  
Module Theory
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