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2013

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Articles 10501 - 10530 of 11462

Full-Text Articles in Physical Sciences and Mathematics

The Effect Of Neutron Irradiation On The Properties Of Tl_{0.6}Pb_{0.3}Cd_{0.1}Ba_2ca_2cu_{3}O_{9-Delta} Superconductors, Kareem Ali Jasim, Tariq Jaffar Alwan, Khalid Hadi Mahdi, Hazim Louis Mansour Jan 2013

The Effect Of Neutron Irradiation On The Properties Of Tl_{0.6}Pb_{0.3}Cd_{0.1}Ba_2ca_2cu_{3}O_{9-Delta} Superconductors, Kareem Ali Jasim, Tariq Jaffar Alwan, Khalid Hadi Mahdi, Hazim Louis Mansour

Turkish Journal of Physics

The effect of neutron irradiation on phase purity, crystal structure, and electrical resistivity of Tl_{0.6}Pb_{0.3}Cd_{0.1} Ba_2Ca_2Cu_3O_{9-delta} superconductors has been studied before and after irradiation by electrical resistance measurements and X-ray diffraction techniques. The zero-resistance superconducting transition temperature, T_{c(offset)}, of samples systematically decreases by about 5 K with the increase of neutron irradiation fluence up 18.12 \times 10^{10} n cm^{-2}. The crystalline phases showed that the compounds have 2 phases, a high-Tc phase (1223) and low-Tc phase (1212), in addition to the impurity phase. The irradiation led to a decrease in oxygen content and volume fraction of high-Tc phase (1223).


Development And Utilization Of A Retarding Analyzer For Field Emission Investigation Of Lab_6/W Emitter, Ahmed Abdurrahman Ahmed Al-Tabbakh, Mahendra A. More, Dilip S. Joag Jan 2013

Development And Utilization Of A Retarding Analyzer For Field Emission Investigation Of Lab_6/W Emitter, Ahmed Abdurrahman Ahmed Al-Tabbakh, Mahendra A. More, Dilip S. Joag

Turkish Journal of Physics

A cold field emission from LaB_6/W-coated cathodes has been investigated with a high-accuracy and low-cost retarding field analyzer instrument. Guidelines are provided for measurements of Fowler-Nordheim (FN) characteristics and total energy distributions using a single set-up and direct detection technique to address presumed shortages in sophisticated instrumental requirements for integral investigation. Electron emission from LaB_6 nanoprotrusions, deposited on a tungsten microtip, was successfully investigated. Results emphasize a metallic behavior of the emitter in accordance with the FN theory. No size effects were observed for protrusions of 300 nm in radii.


Chaos And Its Control In Semiconductor Laser With Delayed Negative Optoelectronic Feedback, Guang-Yu Jiang, Juan Zhang, Yan Huang Jan 2013

Chaos And Its Control In Semiconductor Laser With Delayed Negative Optoelectronic Feedback, Guang-Yu Jiang, Juan Zhang, Yan Huang

Turkish Journal of Physics

We reveal theoretically chaos and its control in a semiconductor laser with delayed negative optoelectronic feedback. Under nonperiodic or sinusoidal period optoelectronic current, the semiconductor laser exhibits rich nonlinear dynamics. For a given coupling constant, chaos is shown in a semiconductor laser directly injected by external light. For a photoelectric delayed negative-feedback scheme with sinusoidal period optoelectronic current, the laser can be controlled in single-periodic, dual-periodic, multi-periodic states, and even chaos. The results also illustrate what we think to be a new method to generate various period states in the chaos system.


Effect Of Microwave Sintering On Grain Size And Dielectric Properties Of Barium Titanate, Praveena Kuruva, Uma Maheshwara Singh Rajaputra, Srinath Sanyadanam, Ramana Murthy Sarabu Jan 2013

Effect Of Microwave Sintering On Grain Size And Dielectric Properties Of Barium Titanate, Praveena Kuruva, Uma Maheshwara Singh Rajaputra, Srinath Sanyadanam, Ramana Murthy Sarabu

Turkish Journal of Physics

In the present paper, nanosized barium titanate (BaTiO_3) powders were synthesized by microwave hydrothermal method. The structural characterization of as-prepared powders was investigated using X-ray diffraction and Fourier transform infrared spectroscopy. The particle size was estimated using a transmission electron microscope. The nanopowders were sintered at different temperatures using a microwave furnace, followed by characterizations such as X-ray diffraction and field emission scanning electron microscopy. The dielectric constant behavior was observed as a function of frequency (100 Hz to 1 MHz) and temperature. The ferroelectric nature was confirmed from polarization-electric field loops.


Level Structure Of ^{210}Po By Means Of Surface Delta Interaction, Ali Khalaf Hasan, Abdul Ridha Hussain Subber Jan 2013

Level Structure Of ^{210}Po By Means Of Surface Delta Interaction, Ali Khalaf Hasan, Abdul Ridha Hussain Subber

Turkish Journal of Physics

Within the framework of the shell model, we consider the residual interaction to be a surface delta interaction. This interaction has been applied in the calculation of the energy levels of ^{210}Po, which belong to N = 126 magic closed shell nuclei. The pure and the configuration mixings are applied in the calculations of matrix elements. The predicted energy levels are compared with experimental data.


Effects Of The Different Types Of Nuclear Radiations On The Optically Stimulated Luminescence, Ayşe Güneş Tanir, Mustafa Hi̇cabi̇ Bölükdemi̇r, Tülay Neşe Kizilirmak Jan 2013

Effects Of The Different Types Of Nuclear Radiations On The Optically Stimulated Luminescence, Ayşe Güneş Tanir, Mustafa Hi̇cabi̇ Bölükdemi̇r, Tülay Neşe Kizilirmak

Turkish Journal of Physics

This study aims to investigate the effects of different nuclear radiation fields on an optically stimulated luminescence (OSL) dosimeter using Al_2O_3:C material. The Al_2O_3:C material was exposed to alpha- and beta-particles and gamma-photons, and the luminescence signals were measured by stimulation with a blue light emitting diode. It is concluded that the OSL technique is suitable for obtaining an adequate blue light stimulated luminescence signal in alpha, beta, and gamma radiation fields, and if the source activity was low, the statistical distributions were large.


Magnetic Wiggler-Assisted Third-Harmonic Generation Of A Gaussian Laser Pulse In Plasma, Hirdesh Sharma, Harsha Jaloree, Jetendra Parashar Jan 2013

Magnetic Wiggler-Assisted Third-Harmonic Generation Of A Gaussian Laser Pulse In Plasma, Hirdesh Sharma, Harsha Jaloree, Jetendra Parashar

Turkish Journal of Physics

A Gaussian laser pulse propagating through plasma in the presence of a magnetic wiggler produces third-harmonic radiation. The wiggler's magnetic field provides additional momentum required for phase matching. The required wiggler wave number is sensitive to pulse duration and amplitude. The efficiency of the process is significant at the instant at which the phase matching condition is satisfied.


Analysis Of Amplitude And Slope Diffraction Coefficients, Mehmet Bariş Tabakcioğlu, Ahmet Cansiz Jan 2013

Analysis Of Amplitude And Slope Diffraction Coefficients, Mehmet Bariş Tabakcioğlu, Ahmet Cansiz

Turkish Journal of Physics

The diffraction mechanism is used for field prediction in both light and shadowed regions. Slope and amplitude diffraction coefficients are vital to predict the field strength at the receiver accurately. In this paper, amplitude and slope diffraction coefficients for one of the ray theoretical models, the slope uniform theory of diffraction with convex hull (S-UTD-CH) model, are analyzed. Moreover, diffraction coefficients are given for knife-edge and wedge structures.


Exact Solution Of Frw Perfect Fluid Model Interacting With Zero-Rest-Mass Scalar Field And Electromagnetic Field In B-D Theory, Kangujam Priyokumar Singh, Chungkham Gokulchandra Singh Jan 2013

Exact Solution Of Frw Perfect Fluid Model Interacting With Zero-Rest-Mass Scalar Field And Electromagnetic Field In B-D Theory, Kangujam Priyokumar Singh, Chungkham Gokulchandra Singh

Turkish Journal of Physics

Considering a spherically symmetric nonstatic cosmological flat model of the Robertson-Walker universe, the problem of perfect fluid distribution interacting with the gravitational field in the presence of a zero-rest-mass scalar field and electromagnetic field in Brans-Dicke (B-D) theory has been investigated. Exact solutions are obtained by using a general approach of solving the partial differential equations and it has been observed that the electromagnetic field cannot survive the cosmological flat model due to the action caused by the presence of the zero-rest-mass scalar field, and the isotropic pressure p turns out to be negative. The pressure and density are found …


Uncertainties In Modelling Heterogeneous Chemistry And Arctic Ozone Depletion In The Winter 2009/2010, I. Wohltmann, T. Wegner, R. Müller, R. Lehmann, M. Rex, G. L. Manney, M. L. Santee, P. Bernath, O. Suminska-Ebersoldt Jan 2013

Uncertainties In Modelling Heterogeneous Chemistry And Arctic Ozone Depletion In The Winter 2009/2010, I. Wohltmann, T. Wegner, R. Müller, R. Lehmann, M. Rex, G. L. Manney, M. L. Santee, P. Bernath, O. Suminska-Ebersoldt

Chemistry & Biochemistry Faculty Publications

Stratospheric chemistry and denitrification are simulated for the Arctic winter 2009/2010 with the Lagrangian Chemistry and Transport Model ATLAS. A number of sensitivity runs is used to explore the impact of uncertainties in chlorine activation and denitrification on the model results. In particular, the efficiency of chlorine activation on different types of liquid aerosol versus activation on nitric acid trihydrate clouds is examined. Additionally, the impact of changes in reaction rate coefficients, in the particle number density of polar stratospheric clouds, in supersaturation, temperature or the extent of denitrification is investigated. Results are compared to satellite measurements of MLS and …


Intersection Number Of Plane Curves, Margaret E. Nichols Jan 2013

Intersection Number Of Plane Curves, Margaret E. Nichols

Honors Papers

In algebraic geometry, seemingly geometric problems can be solved using algebraic techniques. Some of the most basic geometric objects we can study are polynomial curves in the plane. In this paper we focus on the intersections of two curves. We address both the number of times two curves intersect at a given point, counting multiplicity (whatever that means), and the total number of intersections of the curves, again counting multiplicity. The former is known as the intersection number of the curves at the point. This concept, although geometrically motivated, can be described in algebraic terms; it is this relationship which …


Oligomers Of Beta-L-Arabinosides Of Hydroxyproline : Synthesis Of The Carbohydrate Epitope Of The Art V 1 Allergen, Ning Xie Jan 2013

Oligomers Of Beta-L-Arabinosides Of Hydroxyproline : Synthesis Of The Carbohydrate Epitope Of The Art V 1 Allergen, Ning Xie

LSU Doctoral Dissertations

The pollen of mugwort is a major contributor to hay fever in Europe and North America. The chemical structure of Art v 1, the major allergen of mugwort, has been elucidated. A notable motif in Art v 1 – characterized by clusters of contiguous â-arabinosides of hydroxyproline – was found to be a key recognition element for antibodies generated in response to the natural protein. This dissertation details the chemical synthesis of oligomers of â-arabinosides of hydroxyproline and the search to establish the minimal carbohydrate epitope of Art v 1. The â-arabinoside motif, being a 1,2-cis glycoside, presents a considerable …


High Resolution Tephra And U/Pb Chronology Of The 3.33 – 3.26 Ga Mendon Formation, Barberton, Greenstone Belt, South Africa, Nicholas Burns Decker Jan 2013

High Resolution Tephra And U/Pb Chronology Of The 3.33 – 3.26 Ga Mendon Formation, Barberton, Greenstone Belt, South Africa, Nicholas Burns Decker

LSU Master's Theses

The Mendon Formation in the Barberton Greenstone Belt of South Africa marks the boundary between the Onverwacht and Fig Tree Groups. These groups are characterized by mafic to ultramafic volcanism and felsic volcanism with related epiclastic sedimentation, respectively. This transition marks the end of komatiitic volcanism in the Barberton Greenstone Belt and is accompanied by numerous impact-related spherule layers. This study characterizes the upper Mendon Formation texturally and geochemically over a wide areal extent and across structure and facies change in an attempt to better understand the evolution of tectonic processes at this boundary. A suite of whole rock and …


Cross-Boundary Water Transfers In The Colorado River Basin: A Review Of Efforts And Issues Associated With Marketing Water Across State Lines Or Reservation Boundaries, Colorado River Governance Initiative, University Of Colorado Boulder. Getches-Wilkinson Center For Natural Resources, Energy, And The Environment, Western Water Policy Program Jan 2013

Cross-Boundary Water Transfers In The Colorado River Basin: A Review Of Efforts And Issues Associated With Marketing Water Across State Lines Or Reservation Boundaries, Colorado River Governance Initiative, University Of Colorado Boulder. Getches-Wilkinson Center For Natural Resources, Energy, And The Environment, Western Water Policy Program

Books, Reports, and Studies

65 p. : charts ; 29 cm


Strongly Correlated Ultra-Cold Bosonic Atoms In Optical Lattices, Kalani Hettiarachchilage Jan 2013

Strongly Correlated Ultra-Cold Bosonic Atoms In Optical Lattices, Kalani Hettiarachchilage

LSU Doctoral Dissertations

A major focus in condensed matter physics is to study the origin of exotic quantum phases such as coexistent and inhomogeneous phases, quantum criticality, and secondary ordered phases close to quantum critical points. Exotic phenomena in strongly correlated systems occur due to competing complex interactions of spin, charge, lattice, and orbital degrees of freedom. Complex quantum phases in strongly correlated systems are challenging, but they might be very useful due to their possible functionality to make advance devices. In order to understand, utilize, and optimize such behaviors, we need to improve our understanding of these systems. Studies in cold atom …


Patterns And Pathways Of Wetland Sedimentation And Landscape Change In Coastal Louisiana, Andrew William Tweel Jan 2013

Patterns And Pathways Of Wetland Sedimentation And Landscape Change In Coastal Louisiana, Andrew William Tweel

LSU Doctoral Dissertations

Coastal Louisiana wetlands exist in a dynamic physical environment and retracted dramatically in the last century. Here I examine the spatial and temporal variability of this landscape with an emphasis on the interactions between anthropogenic landscape modifications and geological processes.

The Mississippi River watershed underwent drastic changes during the past 200 years, beginning with widespread land clearing and, later, large-scale reservoir construction. These modifications caused increases in suspended sediment concentrations, then sharp decreases, and have remained relatively stable since 1960. I show how changes in land area of the Mississippi River birdfoot delta reflect these fluctuations, and that they are …


Exploring Student Perseverance In Problem Solving, Angelique Renee (Treadway) Duncker Jan 2013

Exploring Student Perseverance In Problem Solving, Angelique Renee (Treadway) Duncker

LSU Master's Theses

ABSTRACT Many high school Geometry students lack the perseverance required to complete complex and time-consuming problems. This project tests the hypothesis that if students were provided with a means of organizing their problem solving work they will be less apt to quit when faced with complex and time-consuming mathematical problems. This study involved students enrolled in 10th grade Geometry and 10th grade Honors Geometry in two similar high schools. After trying unsuccessfully to implement methods adapted from an engineering workshop, I designed a graphic organizer that was simple to use and acceptable to the students. Ultimately, I did not detect …


Spatial Structure And Dynamics Of The Plant Communities In A Pro-Grading River Delta : Wax Lake Delta, Atchafalaya Bay, Louisiana, Melissa Carle Jan 2013

Spatial Structure And Dynamics Of The Plant Communities In A Pro-Grading River Delta : Wax Lake Delta, Atchafalaya Bay, Louisiana, Melissa Carle

LSU Doctoral Dissertations

River deltas are dynamic depositional environments that are controlled to varying degrees by coastal and fluvial forces. Plant communities in deltas respond to many of the same allogenic forces that shape delta geomorphology. This study examines the factors that influence plant community development, productivity, and species distributions in the Wax Lake delta, a young, actively pro-grading river delta in coastal Louisiana, USA. A species distribution map created using high-resolution 8-band WorldView-2 imagery was found to have an overall accuracy of 75 percent. Classification tree analysis suggested that most of the observed variation in plant species distributions within the delta can …


Evaluating The Effectiveness Of Response To Intervention In Ela And Math For Sixth, Seventh, And Eighth Grade Students, Shehla Khan Jan 2013

Evaluating The Effectiveness Of Response To Intervention In Ela And Math For Sixth, Seventh, And Eighth Grade Students, Shehla Khan

LSU Master's Theses

Abstract This study examined the combined effectiveness of Tier I and Tier II instruction in the context of a Response to Intervention framework with sixth, seventh and eighth grade students both in ELA and Math. The Tier I interventions emphasized topics from the Grade Level Expectations that the students were having difficulties grasping during regular classroom instruction. Tier II instruction mainly emphasized preparing students for the standardized iLEAP and LEAP tests. These students were then compared with a group of similar students who did not receive tiered instructions (control group). Students who participated in Tier I or Tier II instructions …


Charge And Discharge Behaviour Of Li-Ion Batteries At Various Temperatures Containing Licoo2 Nanostructured Cathode Produced By Ccso, Y. Y. Mamyrbayeva, R. E. Beissenov, Mkhitar A. Hobosyan, S. E. Kumekov, Karen S. Martirosyan Jan 2013

Charge And Discharge Behaviour Of Li-Ion Batteries At Various Temperatures Containing Licoo2 Nanostructured Cathode Produced By Ccso, Y. Y. Mamyrbayeva, R. E. Beissenov, Mkhitar A. Hobosyan, S. E. Kumekov, Karen S. Martirosyan

Physics and Astronomy Faculty Publications and Presentations

There are technical barriers for penetration market requesting rechargeable lithium-ion battery packs for portable devices that operate in extreme hot and cold environments. Many portable electronics are used in very cold (-40 °C) environments, and many medical devices need batteries that operate at high temperatures. Conventional Li-ion batteries start to suffer as the temperature drops below 0 °C and the internal impedance of the battery increases. Battery capacity also reduced during the higher/lower temperatures. The present work describes the laboratory made lithium ion battery behaviour features at different operation temperatures. The pouch-type battery was prepared by exploiting LiCoO2 cathode material …


The Development Of Capillary Electrophoresis Assays To Study Enzyme Inhibition, Sherrisse Kelly Bryant Jan 2013

The Development Of Capillary Electrophoresis Assays To Study Enzyme Inhibition, Sherrisse Kelly Bryant

LSU Doctoral Dissertations

New methods for studying enzymes and enzyme inhibition using capillary electrophoresis (CE) were developed and applied. Because CE is a separation technique, spectral interference is minimized by separation of substrates, products, inhibitors, and sample matrix components. Two types of CE enzyme assays were explored in this dissertation research. The first assay was based on optically gated vacancy capillary electrophoresis (OGVCE) with laser-induced fluorescence detection (LIF). This approach involves periodic photobleaching of fluorescent substrates and products. The initial goal of the study was to develop an assay for adenosine deaminase (ADA). A fluorescent ADA substrate was synthesized; however, the substrate was …


Refining The Characterization Of Projective Graphs, Perry K. Iverson Jan 2013

Refining The Characterization Of Projective Graphs, Perry K. Iverson

LSU Doctoral Dissertations

Archdeacon showed that the class of graphs embeddable in the projective plane is characterized by a set of 35 excluded minors. Robertson, Seymour and Thomas in an unpublished result found the excluded minors for the class of k-connected graphs embeddable on the projective plane for k = 1,2,3. We give a short proof of that result and then determine the excluded minors for the class of internally 4-connected projective graphs. Hall showed that a 3-connected graph diff_x000B_erent from K5 is planar if and only if it has K3,3 as a minor. We provide two analogous results for projective graphs. For …


Analysis Of Protein Aggregates And Synthetic Nanoparticles Using Capillary Electrophoresis With Light Scattering And Fluorescence Detection, Suresh Chandra Regmi Jan 2013

Analysis Of Protein Aggregates And Synthetic Nanoparticles Using Capillary Electrophoresis With Light Scattering And Fluorescence Detection, Suresh Chandra Regmi

LSU Doctoral Dissertations

The goal of the research presented in this dissertation is to develop capillary electrophoresis (CE) based analysis techniques for the characterization of individual particles including amyloid beta (Aâ) peptide aggregates and to apply these methods to study the aggregation of Aâ peptides. Protein self-assembly into ordered aggregates is a common and important process in normal biological function, but this process is also involved in several diseases. Amyloid beta peptide aggregation is linked to Alzheimer’s disease. Thioflavin T (ThT) has been used as a fluorescent probe for the detection of Aâ aggregation. Based on previous observations of false positive fluorescent signals …


Project Haiti 2012: Providing An Experiential Learning Experience Through The Design And Delivery Of A Water Purifier In Haiti, Yung Wong, Johnathon Camp, Shavin Pinto, Kyle Fennesy, Marc Compere, Yan Tang Jan 2013

Project Haiti 2012: Providing An Experiential Learning Experience Through The Design And Delivery Of A Water Purifier In Haiti, Yung Wong, Johnathon Camp, Shavin Pinto, Kyle Fennesy, Marc Compere, Yan Tang

Publications

In this paper, we share our experiences and lessons learned from Project Haiti 2012, a project to design and install a water purification system serving 20,000 people per day in the largest tent city in Haiti. Project Haiti 2012 was the third and largest system we have built for Haitians and represents a huge success for all participants and stakeholders. This paper discusses the unique experiential learning opportunity involved in the design and delivery of the water purifier in a foreign developing country. Multiple positive educational, social, and economic outcomes were achieved including students applying knowledge gained from coursework towards …


Book Review: Weird Worlds: Bizarre Bodies Of The Solar System And Beyond, T. D. Oswalt Jan 2013

Book Review: Weird Worlds: Bizarre Bodies Of The Solar System And Beyond, T. D. Oswalt

Publications

This document is Dr. Oswalt’s review of Weird Worlds : Bizarre Bodies of the Solar System and Beyond by David A. J. Seargent. Springer, 2013 309p, 1461470633 $34.95, 9781461470632 $34.95.


James-Stein Type Compound Estimation Of Multiple Mean Response Functions And Their Derivatives, Limin Feng Jan 2013

James-Stein Type Compound Estimation Of Multiple Mean Response Functions And Their Derivatives, Limin Feng

Theses and Dissertations--Statistics

Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates.

James and Stein proposed an estimator of the mean vector of a p dimensional multivariate normal distribution, which produces a smaller risk than the maximum …


On The Norm Closure Problem For Complex Symmetric Operators, Stephan Ramon Garcia, Daniel E. Poore '11 Jan 2013

On The Norm Closure Problem For Complex Symmetric Operators, Stephan Ramon Garcia, Daniel E. Poore '11

Pomona Faculty Publications and Research

We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.


A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan Jan 2013

A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan

Pomona Faculty Publications and Research

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices …


The Graphic Nature Of Gaussian Periods, William Duke, Stephan Ramon Garcia, Bob Lutz '13 Jan 2013

The Graphic Nature Of Gaussian Periods, William Duke, Stephan Ramon Garcia, Bob Lutz '13

Pomona Faculty Publications and Research

Recent work has shown that the study of supercharacters on abelian groups provides a natural framework with which to study the properties of certain exponential sums of interest in number theory. Our aim here is to initiate the study of Gaussian periods from this novel perspective. Among other things, this approach reveals that these classical objects display a dazzling array of visual patterns of great complexity and remarkable subtlety.


Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14 Jan 2013

Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14

Pomona Faculty Publications and Research

The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.