Mathematics Commons^™

Approximation Of Invariant Subspaces, Faruk Yilmaz

Doctoral Dissertations

For a real number α [alpha] the Dirichlet-type spaces 𝔇_α [script D sub alpha] are the family of Hilbert spaces consisting of all analytic functions f(z) = ∑_n=0^∞[sum over n equals zero to infinity] ˆf(n) [f hat of n] zⁿ [z to the n] defined on the open unit disc 𝔻 [unit disc] such that

∑_n=0^∞ (n+1)^α | ˆf(n) |²

[sum over n equals 0 to infinity] [(n+1) to α] [ | f hat of n | to 2]

is finite.

For α < 0, the spaces 𝔇_α are known as weighted Bergman spaces. When …

Construction And Classification Results For Commuting Squares Of Finite Dimensional *-Algebras, Chase Thomas Worley

Doctoral Dissertations

In this dissertation, we present new constructions of commuting squares, and we investigate finiteness and isolation results for these objects. We also give applications to the classification of complex Hadamard matrices and to Hopf algebras.

In the first part, we recall the notion of commuting squares which were introduced by Popa and arise naturally as invariants in Jones' theory of subfactors. We review some of the main known examples of commuting squares such as those constructed from finite groups and from complex Hadamard matrices. We also recall Nicoara's notion of defect which gives an upper bound for the number of …

Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, Joel Anthony Mazer

Doctoral Dissertations

In relativistic heavy ion collisions at the Large Hadron Collider (LHC), a hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced. Quarks and gluons from incoming nuclei collide to produce partons at high momenta early in the collisions. By fragmenting into collimated sprays of hadrons, these partons form 'jets'. Within the framework of perturbative Quantum Chromodynamics (pQCD), jet production is well understood in pp collisions. We can use jets measured in pp interactions as a baseline reference for comparing to heavy ion collision systems to detect and study jet quenching. The jet quenching mechanism …

The Loewner Equation And Weierstrass' Function, Gavin Ainsley Glenn

Chancellor’s Honors Program Projects

No abstract provided.