Ghost symmetry and an analogue of Steinitz’s theorem

2011 ◽  
Vol 52 (1) ◽  
pp. 205-219
Author(s):  
David A. Richter
Keyword(s):  
Ghost Symmetry ◽  
Steinitz’S Theorem

Steinitz’s Theorem and B-Convexity

1997 ◽  
pp. 87-100
Author(s):  
Mikhail I. Kadets ◽  
Vladimir M. Kadets
Keyword(s):  
Steinitz’S Theorem

scholarly journals Constrained lattice-field hierarchies and Toda system with Block symmetry

2016 ◽  
Vol 13 (05) ◽  
pp. 1650061 ◽  
Author(s):  
Chuanzhong Li
Keyword(s):  
Difference Equations ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Lie Symmetry ◽  
Toda System ◽  
One Dimensional ◽  
Toda Hierarchy ◽  
Lattice Field ◽  
The One ◽  
Ghost Symmetry

In this paper, we construct the additional [Formula: see text]-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new integrable difference equations. Under a further reduction, the constrained two-lattice integrable systems can be combined into one single integrable system, namely the well-known one-dimensional original Toda hierarchy. We prove that the one-dimensional original Toda hierarchy has a nice Block Lie symmetry.

scholarly journals Hypercompositional Algebra, Computer Science and Geometry

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1338 ◽  
Author(s):  
Gerasimos Massouros ◽  
Christos Massouros
Keyword(s):  
Computer Science ◽  
Formal Languages ◽  
Helly’S Theorem ◽  
Projective Geometries ◽  
Carathéodory’S Theorem ◽  
Close Relationship ◽  
Radon’S Theorem ◽  
Steinitz’S Theorem ◽  
Stone’S Theorem

The various branches of Mathematics are not separated between themselves. On the contrary, they interact and extend into each other’s sometimes seemingly different and unrelated areas and help them advance. In this sense, the Hypercompositional Algebra’s path has crossed, among others, with the paths of the theory of Formal Languages, Automata and Geometry. This paper presents the course of development from the hypergroup, as it was initially defined in 1934 by F. Marty to the hypergroups which are endowed with more axioms and allow the proof of Theorems and Propositions that generalize Kleen’s Theorem, determine the order and the grade of the states of an automaton, minimize it and describe its operation. The same hypergroups lie underneath Geometry and they produce results which give as Corollaries well known named Theorems in Geometry, like Helly’s Theorem, Kakutani’s Lemma, Stone’s Theorem, Radon’s Theorem, Caratheodory’s Theorem and Steinitz’s Theorem. This paper also highlights the close relationship between the hyperfields and the hypermodules to geometries, like projective geometries and spherical geometries.

Quantum Torus Lie Algebra in the q-Deformed Kadomtsev–Petviashvili System

2019 ◽  
Vol 26 (04) ◽  
pp. 579-588
Author(s):  
Chuanzhong Li ◽  
Xinyue Li ◽  
Fushan Li
Keyword(s):  
Lie Algebra ◽  
Kp Hierarchy ◽  
Quantum Torus ◽  
Tau Function ◽  
Ghost Symmetry

Based on the W∞ symmetry of the q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy, which is a q-deformation of the KP hierarchy, we construct the quantum torus symmetry of the q-KP hierarchy, which further leads to the quantum torus constraint of its tau function. Moreover, we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.

scholarly journals An analogue of a theorem of Steinitz for ball polyhedra in $$\mathbb {R}^3$$

2021 ◽  
Author(s):  
Sami Mezal Almohammad ◽  
Zsolt Lángi ◽  
Márton Naszódi
Keyword(s):  
Convex Polyhedron ◽  
3 Dimensional ◽  
Edge Graph ◽  
Steinitz’S Theorem

AbstractSteinitz’s theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if and only if, G is simple, plane and 3-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in $$\mathbb {R}^3$$ R 3 .

scholarly journals Local Particle-Ghost Symmetry

2015 ◽  
Vol 06 (12) ◽  
pp. 1721-1736
Author(s):  
Yoshiharu Kawamura
Keyword(s):  
Ghost Symmetry

scholarly journals The “ghost” symmetry of the BKP hierarchy

2010 ◽  
Vol 51 (5) ◽  
pp. 053514 ◽  
Author(s):  
Jipeng Cheng ◽  
Jingsong He ◽  
Sen Hu
Keyword(s):  
Bkp Hierarchy ◽  
Ghost Symmetry
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