Removeability of a codimension four singular set for solutions of a Yang–Mills–Higgs equation with small energy

2019 ◽  
Vol 24 (1) ◽  
pp. 257-291
Author(s):  
Penny Smith ◽  
Karen Uhlenbeck
Keyword(s):  
Singular Set ◽  
Small Energy ◽  
Yang Mills

scholarly journals Global well-posedness for the Yang-Mills equation in 4+1 dimensions. Small energy

2017 ◽  
Vol 185 (3) ◽  
pp. 831-893 ◽  
Author(s):  
Joachim Krieger ◽  
Daniel Tataru
Keyword(s):  
Well Posedness ◽  
Small Energy ◽  
Yang Mills

Use of LaB6 for a High Quality, Small Energy Spread Beam in an Electron Velocity Spectrometer

1976 ◽  
Vol 34 ◽  
pp. 534-535 ◽  
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
High Temperature ◽  
Energy Resolution ◽  
Electron Velocity ◽  
Electronic Excitations ◽  
Small Energy ◽  
Small Intensity ◽  
Good Energy ◽  
Spectrometer System ◽  
Electron Energy Loss ◽  
Very High

Electron energy loss experiments combined with microscopy have proven to be a valuable tool for the exploration of the structure of electronic excitations in materials. These types of excitations, however, are difficult to measure because of their small intensity. In a usual situation, the filament of the microscope is run at a very high temperature in order to present as much intensity as possible at the specimen. This results in a degradation of the ultimate energy resolution of the instrument due to thermal broadening of the electron beam.We report here observations and measurements on a new LaB filament in a microscope-velocity spectrometer system. We have found that, in general, we may retain a good energy resolution with intensities comparable to or greater than those available with the very high temperature tungsten filament. We have also explored the energy distribution of this filament.

Performance and applications of a field-emission gun TEM/STEM

1992 ◽  
Vol 50 (2) ◽  
pp. 942-943
Author(s):  
Judith M. Brock ◽  
Max T. Otten ◽  
Marc. J.C. de Jong
Keyword(s):  
Field Emission ◽  
High Resolution Imaging ◽  
High Quality ◽  
Small Energy ◽  
High Brightness ◽  
Small Probe ◽  
Resolution Imaging ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

A Field Emission Gun (FEG) on a TEM/STEM instrument provides a major improvement in performance relative to one equipped with a LaB6 emitter. The improvement is particularly notable for small-probe techniques: EDX and EELS microanalysis, convergent beam diffraction and scanning. The high brightness of the FEG (108 to 109 A/cm2srad), compared with that of LaB6 (∼106), makes it possible to achieve high probe currents (∼1 nA) in probes of about 1 nm, whilst the currents for similar probes with LaB6 are about 100 to 500x lower. Accordingly the small, high-intensity FEG probes make it possible, e.g., to analyse precipitates and monolayer amounts of segregation on grain boundaries in metals or ceramics (Fig. 1); obtain high-quality convergent beam patterns from heavily dislocated materials; reliably detect 1 nm immuno-gold labels in biological specimens; and perform EDX mapping at nm-scale resolution even in difficult specimens like biological tissue.The high brightness and small energy spread of the FEG also bring an advantage in high-resolution imaging by significantly improving both spatial and temporal coherence.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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