On global extensions of Dynkin diagrams and singular surfaces of the topological type of 𝐏²

1983 ◽  
pp. 145-151 ◽  
Author(s):  
Lawrence Brenton ◽  
David Bindschadler ◽  
Daniel Drucker ◽  
Geert C. E. Prins
Keyword(s):  
Topological Type ◽  
Singular Surfaces ◽  
Dynkin Diagrams

The influence of singular surfaces and morphological changes on coarsening

2005 ◽  
Vol 96 (2) ◽  
pp. 191-196 ◽  
Author(s):  
Gregory S. Rohrer ◽  
Chang-Soo Kim
Keyword(s):  
Morphological Changes ◽  
Singular Surfaces

scholarly journals 2, 12, 117, 1959, 45171, 1170086, …: a Hilbert series for the QCD chiral Lagrangian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lukáš Gráf ◽  
Brian Henning ◽  
Xiaochuan Lu ◽  
Tom Melia ◽  
Hitoshi Murayama
Keyword(s):  
Hilbert Series ◽  
Charge Conjugation ◽  
External Fields ◽  
Dynkin Diagrams ◽  
Non Linear ◽  
Very High ◽  
Chiral Lagrangian

Abstract We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $$ \mathfrak{su}(n) $$ su n Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order p8, as well as enumeration of CP-even, CP-odd, C-odd, and P-odd terms beginning from order p6. The method is extendable to very high orders, and we present results up to order p16.(The title sequence is the number of independent C-even and P-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions p2, p4, p6, …)

scholarly journals Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

Growth Kinetics of Molecular Beam Epitaxy on Non-Singular Surfaces

1992 ◽  
Vol 280 ◽  
Author(s):  
J. F. Egler ◽  
N. Otsuka ◽  
K. Mahalingam
Keyword(s):  
Surface Roughness ◽  
Monte Carlo ◽  
Growth Kinetics ◽  
Molecular Beam ◽  
Singular Surface ◽  
Sticking Coefficient ◽  
Singular Surfaces ◽  
Vicinal Surfaces ◽  
Kinetics Of ◽  
Multiple Configurations

ABSTRACTGrowth kinetics on non-singular surfaces were studied by Monte Carlo simulations. In contrast to the growth on singular and vicinal surfaces, the sticking coefficient on the non-singular surfaces was found to decrease with increase of the surface roughness. Simulations of annealing processes showed that surface diffusion of atoms leads to a stationary surface roughness, which is explained by multiple configurations having the lowest energy in the non-singular surface.

scholarly journals Local invariants of singular surfaces in an almost complex four-manifold

1993 ◽  
Vol 11 (2) ◽  
pp. 125-133 ◽  
Author(s):  
Goo Ishikawa ◽  
Toru Ohmoto
Keyword(s):  
Singular Surfaces ◽  
Almost Complex ◽  
Local Invariants

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

Root spaces and Dynkin diagrams

2010 ◽  
pp. 159-171
Author(s):  
Robert Gilmore
Keyword(s):  
Dynkin Diagrams
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