scholarly journals Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms

2022 ◽  
Vol 19 (1) ◽  
pp. 163
Author(s):  
Yan-Xia Ren ◽  
Renming Song ◽  
Ting Yang
Keyword(s):  
Local Branching ◽  
Non Local ◽  
L Log L

scholarly journals L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms

2019 ◽  
Vol 62 (8) ◽  
pp. 1439-1462 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Yan-Xia Ren ◽  
Renming Song
Keyword(s):  
Local Branching ◽  
Non Local ◽  
L Log L

scholarly journals Non local branching Brownian motions with annihilation and free boundary problems

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Anna De Masi ◽  
Pablo A. Ferrari ◽  
Errico Presutti ◽  
Nahuel Soprano-Loto
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
Brownian Motions ◽  
Local Branching ◽  
Non Local

Stochastic solutions to evolution equations of non-local branching processes

2020 ◽  
Vol 200 ◽  
pp. 112021 ◽  
Author(s):  
Lucian Beznea ◽  
Oana Lupaşcu-Stamate ◽  
Cătălin Ioan Vrabie
Keyword(s):  
Evolution Equations ◽  
Branching Processes ◽  
Local Branching ◽  
Non Local

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

Magic of signs: a non-local interpretation of homeopathy

2000 ◽  
Vol 89 (3) ◽  
pp. 127-140 ◽  
Author(s):  
H Walach
Keyword(s):  
Non Local
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