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Some graphical aspects of Frobenius structures
graphical aspects Frobenius structures Rings and Algebras
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2012/3/1
We survey some aspects of Frobenius algebras, Frobenius structures and their relation to finite Hopf algebras using graphical calculus. We focus on the `yanking' moves coming from a closed structure i...
A note on rings with the summand sum property
SSP SIP C3 regular ring semisimple ring
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2011/8/23
Abstract: A ring $R$ is called right SSP (SIP) if the sum (intersection) of any two direct summands of $R_{R}$ is also a direct summand. Left sides can be defined similarly. The following are equivale...
Secant Degree of Toric Surfaces and Delightful Planar Toric Degenerations
Toric varieties secant varieties degenerations polytopes
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2011/1/20
The k-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface X corresponds to a regular unimodular trian-gulation D of the polytope definin...
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
Chaos and Dynamical Systems 4D surfaces of section Hopf Bifurcation Galactic
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2011/3/2
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D
autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits
from stab...
Toric CFTs, Permutation Triples, and Belyi Pairs
Toric CFTs Permutation Triples Belyi Pairs
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2011/3/2
Four-dimensional CFTs dual to branes transverse to toric Calabi{Yau threefolds have been described by bipartite graphs on a torus (dimer models). We use the theory of dessins d'enfants to describe the...
Tricyclic graphs with exactly two main eigenvalues
Main eigenvalues Tricyclic graphs 2-walk (a, b)-linear graphs
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2011/1/18
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected tricyclic graphs with exactly two main eigen...
Universal deformation rings and dihedral blocks with two simple modules
Universal deformation rings dihedral defect groups special biserial algebras
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2011/1/19
Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG with a dihedral
defect group D su...
Jet schemes of toric surfaces (a short version)
Jet schemes toric surfaces
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2011/1/21
For m 2 N,m 1, we determine the irreducible components of the m − th jet scheme of a toric
surface S. For m big enough, we connect the number of a class of these irreducible components to the...
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
Laplacian matrix Laplacian spectral radius girth unicyclic graph
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2011/1/18
In this paper we consider the following problem: Over the class of all simple con-nected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral ra...
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
Chaos and Dynamical Systems 4D surfaces of section Hopf Bifurcation
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2010/12/28
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D
autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits
from stab...
Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus
logarithmic Sobolev inequality sharp constants remainder terms lattice sums
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2011/1/20
We give a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals,best constants, various re...
Linear groups over a locally linear division ring
Division ring algebraic strongly algebraic locally linear linear groups
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2011/2/28
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivi...
Universal Polynomials for Severi Degrees of Toric Surfaces
Enumerative geometry toric surfaces Gromov-Witten theory
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2011/2/25
The Severi variety parameterizes plane curves of degree d with nodes.Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of CP2....
The Brush Number of the Two-Dimensional Torus
Brush Number Two-Dimensional Torus
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2011/2/24
In this paper we are interested in the brush number of a graph - a concept introduced by McKeil and by Messinger, Nowakowski and Pralat. Our main aim in this paper is to determine the brush number of ...
The zero-divisor graphs of semirings
zero-divisor graphs semirings
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2011/1/20
In this paper we study zero-divisor graphs of semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We charact...