scholarly journals Correction to: Group invariance of integrable Pfaffian systems

2019 ◽  
Vol 198 (5) ◽  
pp. 1885-1885
Author(s):  
A. Kumpera
Keyword(s):  
Pfaffian Systems ◽  
Group Invariance

scholarly journals Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

2015 ◽  
Vol 78 (12) ◽  
pp. 126201 ◽  
Author(s):  
Xing-Gang Wu ◽  
Yang Ma ◽  
Sheng-Quan Wang ◽  
Hai-Bing Fu ◽  
Hong-Hao Ma ◽  
...  
Keyword(s):  
Renormalization Group ◽  
Renormalization Scale ◽  
Group Invariance ◽  
Key Issues

scholarly journals Investigations of Laser Produced Plasmas Generated by Laser Ablation on Geomaterials. Experimental and Theoretical Aspects

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1391 ◽  
Author(s):  
Enescu ◽  
Irimiciuc ◽  
Cimpoesu ◽  
Bedelean ◽  
Bulai ◽  
...  
Keyword(s):  
Morphological Structure ◽  
Optical Emission ◽  
Ionic Species ◽  
Plasma Parameters ◽  
Mineral Contents ◽  
Plasma Dynamics ◽  
Time Resolved ◽  
Type Group ◽  
Group Invariance ◽  
Ablation Plasma

Several surface investigation techniques, such as X-ray diffraction (XRD), EDX, and optical microscopy, were employed in order to describe the mineral contents in several geomaterials. Space and time resolved optical emission spectroscopy was implemented to analyze the plasma generated by the laser–geomaterial interaction. The values of the plasma parameters (velocity and temperature) were discussed with respect to the nature of the minerals composing the geomaterials and the morphological structure of the samples. Correlations were found between the excitation temperatures of the atomic and ionic species of the plasmas and the presence of calcite in the samples. A mathematical model was built to describe the dynamics in ablation plasma using various mathematical operational procedures: multi structuring of the ablation plasma by means of the fractal analysis and synchronizations of the ablation plasma entities through SL (2R) type group invariance and in a particular case, through self-modulation in the form of Stoler type transformations. Since Stoler type transformations are implied in general, in the charge creation and annihilation processes, then the SL (2R) type group invariance become fundamental in the description of ablation plasma dynamics.

scholarly journals Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

2010 ◽  
Vol 50 (1-4) ◽  
pp. 247-250 ◽  
Author(s):  
V. S. Timóteo ◽  
S. Szpigel ◽  
F. O. Durães
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Field ◽  
Group Invariance

scholarly journals GROUP INVARIANCE AND POHOZAEV IDENTITY IN MOSER-TYPE INEQUALITIES

2013 ◽  
Vol 15 (02) ◽  
pp. 1250054 ◽  
Author(s):  
DANIELE CASSANI ◽  
BERNHARD RUF ◽  
CRISTINA TARSI
Keyword(s):  
Bounded Domain ◽  
Best Constants ◽  
Pohozaev Identity ◽  
Lagrange Equations ◽  
Group Invariance ◽  
Type Identity ◽  
Zygmund Spaces ◽  
Pohozaev Type Identity

We study the so-called limiting Sobolev cases for embeddings of the spaces [Formula: see text], where Ω ⊂ ℝn is a bounded domain. Differently from J. Moser, we consider optimal embeddings into Zygmund spaces: we derive related Euler–Lagrange equations, and show that Moser's concentrating sequences are the solutions of these equations and thus realize the best constants of the corresponding embedding inequalities. Furthermore, we exhibit a group invariance, and show that Moser's sequence is generated by this group invariance and that the solutions of the limiting equation are unique up to this invariance. Finally, we derive a Pohozaev-type identity, and use it to prove that equations related to perturbed optimal embeddings do not have solutions.

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