NONEXISTENCE OF H-CONVEX CUSPIDAL STANDARD FUNDAMENTAL DOMAIN

It was brought to our attention by Zoran Luicic and Milica Stojanovic, via Peter Gilkey, that some of the diagrams in our paper are not correct.The particular problems are the gluing diagrams for the pair of isospectral surfaces of genus 4, which occur on page 20. It is easy to check that the gluing diagrams given there give rise to a surface of the wrong genus. The problem arose because of carelessness in some of the identifications of some of the edges of the fundamental domain.

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CALCULATION OF MADELUNG CONSTANT OF VARIOUS IONIC STRUCTURES BASED ON THE SEMISIMPLE LIE ALGEBRAS

Modern Physics Letters B ◽

10.1142/s0217984996000523 ◽

1996 ◽

Vol 10 (11) ◽

pp. 475-485 ◽

Cited By ~ 2

Author(s):

M.A. JAFARIZADEH ◽

F. NAZERI ◽

A. KESHISHI

Keyword(s):

Boundary Conditions ◽

Lie Algebras ◽

Fundamental Domain ◽

Dirichlet Boundary ◽

Periodic Structures ◽

Dirichlet Boundary Conditions ◽

Ionic Crystals ◽

Madelung Constant ◽

Semisimple Lie Algebras ◽

Coordination Numbers

Periodic structures are constructed by using semisimple Lie algebras. Then these structures are generalized to ionic structures. Finally Madelung constant of these structures are calculated by solving Poisson equation in the fundamental domain of corresponding Lie algebras with Dirichlet boundary conditions. The obtained results are consistent with data of the ionic crystals with the same coordination numbers as our structures.

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Topological densities of periodic graphs

Zeitschrift für Kristallographie - Crystalline Materials ◽

10.1515/zkri-2020-0065 ◽

2020 ◽

Vol 235 (12) ◽

pp. 609-617

Author(s):

Anton Shutov ◽

Andrey Maleev

Keyword(s):

Fundamental Domain ◽

Layer Growth ◽

New Method ◽

Layer By Layer ◽

Carbon Allotrope ◽

Periodic Graphs ◽

Topological Density

AbstractWe propose a new method to calculate topological densities of periodic graphs based on the concept of layer-by-layer growth. Topological density is expressed in terms of metric characteristics: the volume of the fundamental domain and the volume of the growth polytope of the graph. Our method is universal (works for all d-periodic graphs) and is easily automated. As examples, we calculate topological densities of all 20 plane 2-uniform graphs and 14 carbon allotrope modifications.

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