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- Algebraic combinatorics|commutative algebra|Möbius function|poset topology|representation theory (1)
- Algebraic topology|Burnside ring|representation ring|elementary abelian p-group|cyclic p-group (1)
- Cyclic subgroups (1)
- Direct product (1)
- Eigenvalues of the Laplacian|isoperimetric inequalities|Payne-P'olya-Weinberger conjecture|Szegö-Weinberger inequality|Faber-Krahn inequality (1)
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Eigenvalue Inequalities For A Family Of Spherically Symmetric Riemannian Manifolds, Julie Miker
Eigenvalue Inequalities For A Family Of Spherically Symmetric Riemannian Manifolds, Julie Miker
University of Kentucky Doctoral Dissertations
This thesis considers two isoperimetric inequalities for the eigenvalues of the Laplacian on a family of spherically symmetric Riemannian manifolds. The Payne-Pólya-Weinberger Conjecture (PPW) states that for a bounded domain Ω in Euclidean space Rn, the ratio λ1(Ω)/λ0(Ω) of the first two eigenvalues of the Dirichlet Laplacian is bounded by the corresponding eigenvalue ratio for the Dirichlet Laplacian on the ball BΩof equal volume. The Szegö-Weinberger inequality states that for a bounded domain Ω in Euclidean space Rn, the first nonzero eigenvalue of the Neumann Laplacian μ1(Ω) is maximized on the ball BΩ …
The Generalized Burnside And Representation Rings, Eric B. Kahn
The Generalized Burnside And Representation Rings, Eric B. Kahn
University of Kentucky Doctoral Dissertations
Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module …
Aspects Of The Geometry Of Metrical Connections, Matthew J. Wells
Aspects Of The Geometry Of Metrical Connections, Matthew J. Wells
University of Kentucky Doctoral Dissertations
Differential geometry is about space (a manifold) and a geometric structure on that space. In Riemann’s lecture (see [17]), he stated that “Thus arises the problem, to discover the matters of fact from which the measure-relations of space may be determined...”. It is key then to understand how manifolds differ from one another geometrically. The results of this dissertation concern how the geometry of a manifold changes when we alter metrical connections. We investigate how diverse geodesics are in different metrical connections. From this, we investigate a new class of metrical connections which are dependent on the class of smooth …
Rees Products Of Posets And Inequalities, Tricia Muldoon Brown
Rees Products Of Posets And Inequalities, Tricia Muldoon Brown
University of Kentucky Doctoral Dissertations
In this dissertation we will look at properties of two different posets from different perspectives. The first poset is the Rees product of the face lattice of the n-cube with the chain. Specifically we study the Möbius function of this poset. Our proof techniques include straightforward enumeration and a bijection between a set of labeled augmented skew diagrams and barred signed permutations which label the maximal chains of this poset. Because the Rees product of this poset is Cohen-Macaulay, we find a basis for the top homology group and a representation of the top homology group over the symmetric …
Iterative Methods For Computing Eigenvalues And Exponentials Of Large Matrices, Ping Zhang
Iterative Methods For Computing Eigenvalues And Exponentials Of Large Matrices, Ping Zhang
University of Kentucky Doctoral Dissertations
In this dissertation, we study iterative methods for computing eigenvalues and exponentials of large matrices. These types of computational problems arise in a large number of applications, including mathematical models in economics, physical and biological processes. Although numerical methods for computing eigenvalues and matrix exponentials have been well studied in the literature, there is a lack of analysis in inexact iterative methods for eigenvalue computation and certain variants of the Krylov subspace methods for approximating the matrix exponentials. In this work, we proposed an inexact inverse subspace iteration method that generalizes the inexact inverse iteration for computing multiple and clustered …
Direct Products And The Intersection Map Of Certain Classes Of Finite Groups, Julia Chifman
Direct Products And The Intersection Map Of Certain Classes Of Finite Groups, Julia Chifman
University of Kentucky Doctoral Dissertations
The main goal of this work is to examine classes of finite groups in which normality, permutability and Sylow-permutability are transitive relations. These classes of groups are called T , PT and PST , respectively. The main focus is on direct products of T , PT and PST groups and the behavior of a collection of cyclic normal, permutable and Sylow-permutable subgroups under the intersection map. In general, a direct product of finitely many groups from one of these classes does not belong to the same class, unless the orders of the direct factors are relatively prime. Examples suggest that …