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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Speedups And Orbit Equivalence Of Finite Extensions Of Ergodic Zᵈ-Actions, Aimee S.A. Johnson, D. M. Mcclendon
Speedups And Orbit Equivalence Of Finite Extensions Of Ergodic Zᵈ-Actions, Aimee S.A. Johnson, D. M. Mcclendon
Mathematics & Statistics Faculty Works
We classify n-point extensions of ergodic Zᵈ-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Zᵈ-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Zᵈ-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgroups of the symmetric group on n elements.
Generalized Cokähler Geometry And An Application To Generalized Kähler Structures, Ralph R. Gomez, Janet Talvacchia
Generalized Cokähler Geometry And An Application To Generalized Kähler Structures, Ralph R. Gomez, Janet Talvacchia
Mathematics & Statistics Faculty Works
In this paper, we propose a generalization of classical coKähler geometry from the point of view of generalized contact metric geometry. This allows us to generalize a theorem of Capursi (1984), Goldberg (1968) and show that the product M1×M2M1×M2 of generalized contact metric manifolds (Mi,Φi,E±,i,Gi)(Mi,Φi,E±,i,Gi), i=1,2i=1,2, where M1×M2M1×M2 is endowed with the product (twisted) generalized complex structure induced from Φ1Φ1 and Φ2Φ2, is (twisted) generalized Kähler if and only if View the MathML source(Mi,Φi,E±,i,Gi),i=1,2 are (twisted) generalized coKähler structures. As an application of our theorem we construct new examples of twisted generalized Kähler structures on manifolds that do not admit …
Low-Rank Network Decomposition Reveals Structural Characteristics Of Small-World Networks, Victor J. Barranca, D. Zhou, D. Cai
Low-Rank Network Decomposition Reveals Structural Characteristics Of Small-World Networks, Victor J. Barranca, D. Zhou, D. Cai
Mathematics & Statistics Faculty Works
Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering …
Directional Recurrence For Infinite Measure Preserving Zᵈ Actions, Aimee S.A. Johnson, A. A. Şahin
Directional Recurrence For Infinite Measure Preserving Zᵈ Actions, Aimee S.A. Johnson, A. A. Şahin
Mathematics & Statistics Faculty Works
We define directional recurrence for infinite measure preserving Zd actions both intrinsically and via the unit suspension flow and prove that the two definitions are equivalent. We study the structure of the set of recurrent directions and show it is always a Gδ set. We construct an example of a recurrent action with no recurrent directions, answering a question posed in a 2007 paper of Daniel J. Rudolph. We also show by example that it is possible for a recurrent action to not be recurrent in an irrational direction even if all its sub-actions are recurrent.
On Products Of Generalized Geometries, Ralph R. Gomez, Janet Talvacchia
On Products Of Generalized Geometries, Ralph R. Gomez, Janet Talvacchia
Mathematics & Statistics Faculty Works
In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a generalized almost contact structure, and then subsequently, the product of an odd dimensional space that admits a generalized almost contact structure and an even dimensional space that admits a generalized almost complex structure. We also draw attention to the relationship of the Courant bracket to the classical notion of normality for almost contact structures.
Resonance Problems For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama
Resonance Problems For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, M. N. Nkashama
Mathematics & Statistics Faculty Works
We study the solvability of nonlinear second order elliptic partial differential equations with nonlinear boundary conditions where we impose asymptotic conditions on both nonlinearities in the differential equation and on the boundary in such a way that resonance occurs at a generalized eigenvalue; which is an eigenvalue of the linear problem in which the spectral parameter is both in the differential equation and on the boundary. The proofs are based on some variational techniques and topological degree arguments.
Positivity Of Equivariant Gromov–Witten Invariants, D. Anderson, Linda Chen
Positivity Of Equivariant Gromov–Witten Invariants, D. Anderson, Linda Chen
Mathematics & Statistics Faculty Works
We show that the equivariant Gromov–Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients.
Numerical Solutions Of American Options With Dividends Using Finite Difference Methods, Nsoki Mavinga, Chi Zhang , '15
Numerical Solutions Of American Options With Dividends Using Finite Difference Methods, Nsoki Mavinga, Chi Zhang , '15
Mathematics & Statistics Faculty Works
We study the Black-Scholes model for American options with dividends. We cast the problem as a free-boundary problem for heat equations and use transformations to rewrite the problem in linear complementarity form. We use explicit and implicit finite difference methods to obtain numerical solutions. We implement and test the methods on a particular example in MATLAB. The effects of dividend payments on option pricing are also considered.