Appendix F: Geometric Aspects of Complex Vector Relationships

2011 ◽  
pp. 525-526
Keyword(s):  
Complex Vector

scholarly journals Magnetic-field effects on p-wave phase transition in Gauss–Bonnet gravity

2014 ◽  
Vol 29 (20) ◽  
pp. 1450094 ◽  
Author(s):  
Ya-Bo Wu ◽  
Jun-Wang Lu ◽  
Yong-Yi Jin ◽  
Jian-Bo Lu ◽  
Xue Zhang ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
P Wave ◽  
Vector Model ◽  
Magnetic Field Effects ◽  
Complex Vector ◽  
Bonnet Gravity ◽  
Yang Mills ◽  
Wave Phase ◽  
Lowest Landau Level

In the probe limit, we study the holographic p-wave phase transition in the Gauss–Bonnet gravity via numerical and analytical methods. Concretely, we study the influences of the external magnetic field on the Maxwell complex vector model in the five-dimensional Gauss–Bonnet–AdS black hole and soliton backgrounds, respectively. For the two backgrounds, the results show that the magnetic field enhances the superconductor phase transition in the case of the lowest Landau level, while the increasing Gauss–Bonnet parameter always hinders the vector condensate. Moreover, the Maxwell complex vector model is a generalization of the SU(2) Yang–Mills model all the time. In addition, the analytical results backup the numerical results. Furthermore, this model might provide a holographic realization for the QCD vacuum instability.

Lectures on Real and Complex Vector Spaces.

1968 ◽  
Vol 75 (8) ◽  
pp. 925
Author(s):  
Homer Bechtell ◽  
Frank S. Cater
Keyword(s):  
Vector Spaces ◽  
Complex Vector

Grid Synchronization Systems of Three-Phase Grid-Connected Power Converters: A Complex-Vector-Filter Perspective

2014 ◽  
Vol 61 (4) ◽  
pp. 1855-1870 ◽  
Author(s):  
Weiwei Li ◽  
Xinbo Ruan ◽  
Chenlei Bao ◽  
Donghua Pan ◽  
Xuehua Wang
Keyword(s):  
Power Converters ◽  
Complex Vector ◽  
Grid Synchronization ◽  
Three Phase

scholarly journals Strong unique continuation for systems of complex vector fields

2014 ◽  
Vol 138 (4) ◽  
pp. 457-469 ◽  
Author(s):  
R.F. Barostichi ◽  
P.D. Cordaro ◽  
G. Petronilho
Keyword(s):  
Vector Fields ◽  
Unique Continuation ◽  
Complex Vector

On the local solvability of vector fields with critical points

2011 ◽  
Vol 10 (3) ◽  
pp. 785-808
Author(s):  
François Treves
Keyword(s):  
Critical Points ◽  
Vector Fields ◽  
Local Solvability ◽  
Complex Vector ◽  
Base Manifold ◽  
Smooth Complex ◽  
Empty Subset

AbstractThe article discusses the local solvability (or lack thereof) of various classes of smooth, complex vector fields that vanish on some non-empty subset of the base manifold.

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