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Articles 1 - 13 of 13
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A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
Electronic Theses and Dissertations
Nearly a century ago, the mathematicians Hardy and Ramanujan established their celebrated circle method to give a remarkable asymptotic expression for the unrestricted partition function. Following later improvements by Rademacher, the method was utilized by Niven, Lehner, Iseki, and others to develop rapidly convergent series representations of various restricted partition functions. Following in this tradition, we use the circle method to develop formulas for counting the restricted classes of partitions that arise in the Gollnitz-Gordon identities. We then show that our results are strongly supported by numerical tests. As a side note, we also derive and compare the asymptotic behavior …
Modification Of The Fundamental Properties Of Light Through Interaction With Nanostructured Materials, David W. Keene Ii
Modification Of The Fundamental Properties Of Light Through Interaction With Nanostructured Materials, David W. Keene Ii
Electronic Theses and Dissertations
The field of photonics has been growing rapidly over the last few decades as it has endeavored to harness the potential of nanostructured materials to utilize the energy and momentum of electromagnetic radiation on the nanoscale. Using metal nanostructures provides the ability to take advantage of the sub-field of plasmonics which holds the promise of opening the world to vast increases in computational power by circumventing the limitations of conventional current that plague today’s processors. With a thorough understanding of this subject we also get one step closer to increasing the efficiency of solar technology, developing a finer scale of …
Gorenstein Projective (Pre)Covers, Michael J. Fox
Gorenstein Projective (Pre)Covers, Michael J. Fox
Electronic Theses and Dissertations
The existence of the Gorenstein projective precovers is one of the main open problems in Gorenstein Homological algebra. We give sufficient conditions in order for the class of Gorenstein projective complexes to be special precovering in the category of complexes of R-modules Ch(R). More precisely, we prove that if every complex in Ch(R) has a special Gorenstein flat cover, every Gorenstein projective complex is Gorenstein flat, and every Gorenstein flat complex has finite Goenstein projective dimension, then the class of Gorenstein projective complexes, GP(C), is special precovering in Ch(R).
Gorenstein Projective Precovers In The Category Of Modules, Katelyn Coggins
Gorenstein Projective Precovers In The Category Of Modules, Katelyn Coggins
Electronic Theses and Dissertations
It was recently proved that if R is a coherent ring such that R is also left n-perfect, then the class of Gorenstein projective modules, GP, is precovering. We will prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring R such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes that of right coherent and left n-perfect rings.
Assessing Shoreline Change And Vegetation Cover Adjacent To Back-Barrier Shoreline Stabilization Structures In Georgia Estuaries, Katherine R. Wakefield
Assessing Shoreline Change And Vegetation Cover Adjacent To Back-Barrier Shoreline Stabilization Structures In Georgia Estuaries, Katherine R. Wakefield
Electronic Theses and Dissertations
Anthropogenic stabilization of erosional shorelines by hard-armoring structures is used for protection of property, especially if buildings, historical monuments, cultural resources, or other infrastructure are present. The post-installation effects of shoreline stabilization structures on adjacent shorelines in the back-barrier marshes of coastal Georgia are a concern, and interest in living shorelines as erosion control devices has increased because of their use of natural materials and vegetation. AMBUR shoreline analysis software was used to calculate pre-and post-installation shoreline change rates of shorelines adjacent to riprap and bulkhead structures. There was no significant difference between the post-installation shoreline change rates of the …
Up-Converted Emissions Of Er3+ Doped Gd2(Wo4)3 Phosphors, Grayson L. Wiggins
Up-Converted Emissions Of Er3+ Doped Gd2(Wo4)3 Phosphors, Grayson L. Wiggins
Electronic Theses and Dissertations
In this work, the up-conversion (UC) emissions of Er3+ in a gadolinium tungstate host was investigated to analyze the possible processes of up-conversion by 1500 nm and 980 nm excitation. Studies were conducted to see how the 4S3/2 -> 4I15/2 transition changed with varying current through the excitation source, varying excitation wavelength, and doping concentration. Power dependent studies revealed that under 1500 nm excitation the 4S3/2 -> 4I15/2 transition needed 3 photons, while 980 nm excitation could do the same transition with 2 photons. It was found that 1500 nm could produce more efficient red emission due to the 4I9/2 …
Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd
Garch(1,1) With Sifted Gamma-Distributed Errors, Alan C. Budd
Electronic Theses and Dissertations
Typical General Autoregressive Conditional Heteroskedastic (GARCH) processes involve normally-distributed errors, and they model strictly-positive error processes poorly. This thesis will present a method for estimating the parameters of a GARCH(1,1) process with shifted Gamma-distributed errors, conduct a simulation study to test the method, and apply the method to real time series data.
Gallai-Ramsey Number Of An 8-Cycle, Jonathan Gregory
Gallai-Ramsey Number Of An 8-Cycle, Jonathan Gregory
Electronic Theses and Dissertations
Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge-coloring of Kn contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this work, we establish the Gallai-Ramsey number of an 8-cycle for all positive integers.
Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat
Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat
Electronic Theses and Dissertations
In this thesis, we discuss the Gross Pitaevskii Equation (GPE) with harmonic potential and with an angular momentum rotational term in space R^2, which describes the model for Bose-Einstein Condensation. Local Well-Posedness of the equation and the conservation identities for mass, energy and angular momentum are presented. Using the virial identities, we derive the condition for blow-up solution in finite time. Then a threshold of L^2 norm of wave function is obtained for global existence, of GPE in term of ground state solution. This method allows us to obtain our main result ``Sharp sufficient condition for global …
Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko
Geometric-Based Algorithm For A Full Row-Rank System Matrix Along Multiple Directions In Dt, Igor Lutsenko
Electronic Theses and Dissertations
Discrete tomography (DT) is an image reconstruction procedure that deals with computational synthesis of a cross-sectional image of an object from either transmission or reflection data collected by penetrating an object with X-rays from a small number of different directions, and whose range of the underlying function is discrete. Image reconstruction using algebraic approach is time consuming and the computation cost depends on the size of the system matrix. More scanning directions provide an increase in the reconstructed image quality, however they increase the size of the system matrix dramatically. Deletion of linearly dependent rows of this matrix is necessary …
Combinatorial Optimization Of Subsequence Patterns In Words, Matthew R. Just
Combinatorial Optimization Of Subsequence Patterns In Words, Matthew R. Just
Electronic Theses and Dissertations
Packing patterns in words concerns finding a word with the maximum number of a prescribed pattern. The majority of the work done thus far is on packing patterns into permutations. In 2002, Albert, Atkinson, Handley, Holton and Stromquist showed that there always exists a layered permutation containing the maximum number of a layered pattern among all permutations of length n. Consequently, the packing density for all but two (up to equivalence) permutation patterns up to length 4 can be obtained. In this thesis we consider the analogous question for colored patterns and permutations. By introducing the concept of colored blocks …
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
Stereographic Visualization Of Bose-Einstein Condensate Clouds To Measure The Gravitational Constant, Ed Wesley Wells
Electronic Theses and Dissertations
This thesis describes a set of tools that can be used for the rapid design of atom interferometer schemes suitable for measuring Newton's Universal Gravitation constant also known as "Big G". This tool set is especially applicable to Bose--Einstein--condensed systems present in NASA's Cold Atom Laboratory experiment to be deployed to the International Space Station in 2017. These tools include a method of approximating the solutions of the nonlinear Schrödinger or Gross--Pitaevskii equation (GPE) using the Lagrangian Variational Method. They also include a set of software tools for translating the approximate solutions of the GPE into images of the optical …
Missing Data In Clinical Trial: A Critical Look At The Proportionality Of Mnar And Mar Assumptions For Multiple Imputation, Theophile B. Dipita
Missing Data In Clinical Trial: A Critical Look At The Proportionality Of Mnar And Mar Assumptions For Multiple Imputation, Theophile B. Dipita
Electronic Theses and Dissertations
Randomized control trial is a gold standard of research studies. Randomization helps reduce bias and infer causality. One constraint of these studies is that it depends on participants to obtain the desired data. Whatever the researcher can do, there is a possibility to end up with incomplete data. The problem is more relevant in clinical trials when missing data can be related to the condition under study. The benefits of randomization is compromised by missing data. Multiple imputation is a valid method of treating missing data under the assumption of MAR. Unfortunately this is an unverified assumptions. Current practice advise …