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2013

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Articles 781 - 810 of 11462

Full-Text Articles in Physical Sciences and Mathematics

Mapping The Invisible: A Framework For Tracking Covid-19 Spread Among College Students With Google Location Data, Prajindra Sankar Krishnan, Chai Phing Chen, Gamal Alkawsi, Sieh Kiong Tiong, Luiz Fernando Capretz Nov 2013

Mapping The Invisible: A Framework For Tracking Covid-19 Spread Among College Students With Google Location Data, Prajindra Sankar Krishnan, Chai Phing Chen, Gamal Alkawsi, Sieh Kiong Tiong, Luiz Fernando Capretz

Electrical and Computer Engineering Publications

The COVID-19 pandemic and the implementation of social distancing policies have rapidly changed people's visiting patterns, as reflected in mobility data that tracks mobility traffic using location trackers on cell phones. However, the frequency and duration of concurrent occupancy at specific locations govern the transmission rather than the number of customers visiting. Therefore, understanding how people interact in different locations is crucial to target policies, inform contact tracing, and prevention strategies. This study proposes an efficient way to reduce the spread of the virus among on-campus university students by developing a self-developed Google History Location Extractor and Indicator software based …


Laser Induced Ignition With Resonant Multiphoton Absorption In Oxygen, Steven F. Adams Nov 2013

Laser Induced Ignition With Resonant Multiphoton Absorption In Oxygen, Steven F. Adams

Physics Seminars

A novel resonant laser-induced breakdown scheme has been demonstrated to provide precision spatial guidance of spark formation within an air flow and has been further demonstrated successfully in resonant laser-induced ignition of a moderate-speed flow of an air-propane mixture. This scheme could potentially provide ignition within a combustion system with a laser trigger leading to breakdown of an air-fuel flow within a high-voltage gap using a compact low power laser source. The laser scheme involves resonant enhanced multiphoton ionization (REMPI) in molecular oxygen and subsequent laser field-enhanced electron avalanche to generate a pre-ionized micro-plasma path between high voltage electrodes and …


Introduction To Special Section On The U.S. Ioos Coastal And Ocean Modeling Testbed, Richard A. Luettich Jr, L. Donelson Wright, Richard Signell, Carl T. Friedrichs, Marjorie A.M. Friedrichs, John Harding, Katja Fennel, Eoin Howlett, Sara Graves, Elizabeth Smith, Gary Crane, Rebecca Baltes Nov 2013

Introduction To Special Section On The U.S. Ioos Coastal And Ocean Modeling Testbed, Richard A. Luettich Jr, L. Donelson Wright, Richard Signell, Carl T. Friedrichs, Marjorie A.M. Friedrichs, John Harding, Katja Fennel, Eoin Howlett, Sara Graves, Elizabeth Smith, Gary Crane, Rebecca Baltes

VIMS Articles

Strong and strategic collaborations among experts from academia, federal operational centers, and industry have been forged to create a U.S. IOOS Coastal and Ocean Modeling Testbed (COMT). The COMT mission is to accelerate the transition of scientific and technical advances from the coastal and ocean modeling research community to improved operational ocean products and services. This is achieved via the evaluation of existing technology or the development of new technology depending on the status of technology within the research community. The initial phase of the COMT has addressed three coastal and ocean prediction challenges of great societal importance: estuarine hypoxia …


Review And Extension For The O’Brien Fleming Multiple Testing Procedure, Hanan Hammouri Nov 2013

Review And Extension For The O’Brien Fleming Multiple Testing Procedure, Hanan Hammouri

Theses and Dissertations

O'Brien and Fleming (1979) proposed a straightforward and useful multiple testing procedure (group sequential testing procedure) for comparing two treatments in clinical trials where subject responses are dichotomous (e.g. success and failure). O'Brien and Fleming stated that their group sequential testing procedure has the same Type I error rate and power as that of a fixed one-stage chi-square test, but gives the opportunity to terminate the trial early when one treatment is clearly performing better than the other. We studied and tested the O'Brien and Fleming procedure specifically by correcting the originally proposed critical values. Furthermore, we updated the O’Brien …


Rule-Based Conditional Trust With Openpgp., Andrew Jackson Nov 2013

Rule-Based Conditional Trust With Openpgp., Andrew Jackson

Theses

This thesis describes a new trust model for OpenPGP encryption. This trust model uses conditional rule-based trust to establish key validity and trust. This thesis describes "Trust Rules" that may be used to sort and categorize keys automatically without user interaction. "Trust Rules" are also capable of integrating key revocation status into its calculations so it too is automated. This thesis presents that conditional trust established through "Trust Rules" can enforce stricter security while reducing the burden of use and automating the process of key validity, trust, and revocation.


Double Resonance Spectroscopy Of The D1Πu+ And B''B-Bar 1Σu+ States Near The Third Dissociation Threshold Of H2, R. C. Ekey, A. E. Cordova, W. Duan, Alexander M. Chartrand, Elizabeth Mccormack Nov 2013

Double Resonance Spectroscopy Of The D1Πu+ And B''B-Bar 1Σu+ States Near The Third Dissociation Threshold Of H2, R. C. Ekey, A. E. Cordova, W. Duan, Alexander M. Chartrand, Elizabeth Mccormack

Physics Faculty Research and Scholarship

Double-resonance laser spectroscopy via the E, F 1Σg+, v' = 6, J' state was used to probe the energy region below the third dissociation limit of molecular hydrogen. Resonantly enhanced multi-photon ionization spectra were recorded by detecting ion production as a function of energy using a time-of-flight mass spectrometer. Energies and line widths for the v = 14–17 levels of the D1Πu+ state of H2 are reported and compared to experimental data obtained by using VUV synchrotron light excitation (Dickenson et al. 2010 J. Chem. Phys. 133 144317) and fully ab …


Physics-Based Surface Energy Model Optimization For Water Bodies In Cold Climates Using Visible And Calibrated Thermal Infrared Imagery, May V. Casterline Nov 2013

Physics-Based Surface Energy Model Optimization For Water Bodies In Cold Climates Using Visible And Calibrated Thermal Infrared Imagery, May V. Casterline

Theses

When tasked with accurately modeling a water body in a cold climate environment, the complexity of the system being simulated and the numerous parameters affecting the observable outcome pose an arduous task for any modeling effort. The task is increasingly complicated when the body of water is serving as a cooling pond for a power plant and can become partially frozen. The introduction of a heat effluent into the water creates a highly dynamic system whose physical state is not only reactionary to the surrounding environmental conditions, but the industrial facility's operating parameters as well. Both calibrated thermal and visible …


Symplectomorphism Groups Of Weighted Projective Spaces And Related Embedding Spaces, Martin L. Vanhoof Nov 2013

Symplectomorphism Groups Of Weighted Projective Spaces And Related Embedding Spaces, Martin L. Vanhoof

Electronic Thesis and Dissertation Repository

In this thesis, we study 4-dimensional weighted projective spaces and homotopy properties of their symplectomorphism groups. Using these computations, we also investigate some homotopy theoretic properties of a few associated embedding spaces. In the classical case of the complex projective plane, Gromov observed that its symplectomorphism group is homotopy equivalent to its subgroup of Kahler isometries. We find that in the case of one singularity, the symplectomorphism group is weakly homotopy equivalent to the Kahler isometry group of a certain Hirzebruch surface, which corresponds to the resolution of the singularity. In the case of multiple singularities, the symplectomorphism groups are …


The Pseudo-Rigid-Body Model For Fast, Accurate, Non-Linear Elasticity, Anthony R. Hall Nov 2013

The Pseudo-Rigid-Body Model For Fast, Accurate, Non-Linear Elasticity, Anthony R. Hall

Theses and Dissertations

We introduce to computer graphics the Pseudo-Rigid-Body Mechanism (PRBM) and the chain algorithm from mechanical engineering, with a unified tutorial from disparate source materials. The PRBM has been used successfully to simplify the simulation of non-linearly elastic beams, using deflections of an analogous spring and rigid-body linkage. It offers computational efficiency as well as an automatic parameterization in terms of physically measurable, intuitive inputs which fit naturally into existing animation work flows for character articulation. The chain algorithm is a technique for simulating the deflection of complicated elastic bodies in terms of straight elastic elements, which has recently been extended …


Abstract Modular Systems And Solvers, Yuliya Lierler, Miroslaw Truszczyński Nov 2013

Abstract Modular Systems And Solvers, Yuliya Lierler, Miroslaw Truszczyński

Yuliya Lierler

Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study general principles behind the design and analysis of modelfinding programs, or solvers, for integrated heterogeneous multi-logic systems. We show how abstract modules and abstract modular systems give rise to transition systems, which are a natural and convenient representation of solvers pioneered by the SAT community. We illustrate our approach by showing how it applies to answer set programming and propositional logic, and to multi-logic systems based on these two formalisms.


Asp-Based Problem Solving With Cutting-Edge Tools, Marcello Balduccini, Yuliya Lierler Nov 2013

Asp-Based Problem Solving With Cutting-Edge Tools, Marcello Balduccini, Yuliya Lierler

Yuliya Lierler

In the development of practical applications of answer set programming (ASP), encodings that use well-established solvers such as CLASP and DLV are sometimes affected by scalability issues. In those situations, one can resort to more sophisticated ASP tools exploiting, for instance, incremental and constraint ASP. However, today there is no specific methodology for the selection or use of such tools. In this paper we describe how we used such cutting-edge ASP tools on challenging problems from the Third Answer Set Programming Competition, and outline the methodology we followed. We view this paper as a first step in the development of …


A Transition System For Ac Language Algorithms, Yuliya Lierler, Yaunlin Zhang Nov 2013

A Transition System For Ac Language Algorithms, Yuliya Lierler, Yaunlin Zhang

Yuliya Lierler

Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming (ASP) and constraint logic programming. In a similar vein, Gebser et al. (2009) proposed a CLINGCON language integrating ASP and finite domain constraints. A distinguishing feature of these languages is their capacity to allow new efficient inference algorithms that combine traditional ASP procedures and other efficient methods in constraint programming. In this paper we show that a transition system introduced by Nieuwenhuis et al. (2006) can be extended to model the “hybrid” ACSOLVER algorithm, by Mellarkod et al., designed for processing a …


Hybrid Automated Reasoning Tools: From Black-Box To Clear-Box Integration, Marcello Balduccini, Yuliya Lierler Nov 2013

Hybrid Automated Reasoning Tools: From Black-Box To Clear-Box Integration, Marcello Balduccini, Yuliya Lierler

Yuliya Lierler

Recently, researchers in answer set programming and constraint programming spent significant efforts in the development of hybrid languages and solving algorithms combining the strengths of these traditionally separate fields. These efforts resulted in a new research area: constraint answer set programming (CASP). CASP languages and systems proved to be largely successful at providing efficient solutions to problems involving hybrid reasoning tasks, such as scheduling problems with elements of planning. Yet, the development of CASP systems is difficult, requiring non-trivial expertise in multiple areas. This suggests a need for a study identifying general development principles of hybrid systems. Once these principles …


Representing Synonymity In Causal Logic And In Logic Programming, Joohyung Lee, Yuliya Lierler, Vladimir Lifschitz, Fangkai Yang Nov 2013

Representing Synonymity In Causal Logic And In Logic Programming, Joohyung Lee, Yuliya Lierler, Vladimir Lifschitz, Fangkai Yang

Yuliya Lierler

We investigate the relationship between rules representing synonymity in nonmonotonic causal logic and in answer set programming. This question is of interest in connection with current work on modular languages for describing actions.


A Sat-Based Polynomial Space Algorithm For Answer Set Programming, Enrico Giunchiglia, Marco Maratea, Yuliya Lierler Nov 2013

A Sat-Based Polynomial Space Algorithm For Answer Set Programming, Enrico Giunchiglia, Marco Maratea, Yuliya Lierler

Yuliya Lierler

The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a one-to-one correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SAT-Based decision procedure for …


Fages' Theorem And Answer Set Programming, Yuliya Lierler, Esta Erdem, Vladimir Lifschitz Nov 2013

Fages' Theorem And Answer Set Programming, Yuliya Lierler, Esta Erdem, Vladimir Lifschitz

Yuliya Lierler

We generalize a theorem by François Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negotiation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as SMODELS and DLV is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelä is discussed as an example.


The Fierce Green Fire: Vol. 4 Issue 11, Wofford College Environmental Studies Program Nov 2013

The Fierce Green Fire: Vol. 4 Issue 11, Wofford College Environmental Studies Program

The Fierce Green Fire

No abstract provided.


Fixed-Point Free Circle Actions On 4-Manifolds, Weimin Chen Chen Nov 2013

Fixed-Point Free Circle Actions On 4-Manifolds, Weimin Chen Chen

Weimin Chen

This paper is concerned with fixed-point free S1-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, there are at most finitely many distinct smooth (resp. topological) 4-manifolds which support a fixed-point free smooth (resp. locally linear) S1-action and realize the given group as the fundamental group. A similar statement holds for the number of equivalence classes of fixed-point free S1-actions under some further conditions on the fundamental group. The connection …


Above-Threshold Ionization As Temporal Multi-Slit Interference, William B. Laing Iii Nov 2013

Above-Threshold Ionization As Temporal Multi-Slit Interference, William B. Laing Iii

Faculty Works

When atoms are subjected to a laser pulse of sufficiently high intensity, electrons are ionized by absorbing multiple photons in excess of the ionization potential. The resulting sequence of peaks in the photoelectron spectrum separated by the energy of one photon is called “above-threshold ionization” (ATI). This time-independent description of ATI invokes the language of photons, even though calculations are performed using the time-dependent Schrodinger equation with a classical electric field. We demonstrate that the energy-periodic structure of ATI can be understood from the interference of ionized electron wavepackets produced periodically each half-cycle of the laser field. Using this simple …


Above-Threshold Ionization As Temporal Multi-Slit Interference, William B. Laing Iii, B.D. Esry Nov 2013

Above-Threshold Ionization As Temporal Multi-Slit Interference, William B. Laing Iii, B.D. Esry

Faculty Works

When atoms are subjected to a laser pulse of sufficiently high intensity, electrons are ionized by absorbing multiple photons in excess of the ionization potential. The resulting sequence of peaks in the photoelectron spectrum separated by the energy of one photon is called ``above-threshold ionization'' (ATI). This time-independent description of ATI invokes the language of photons, even though calculations are performed using the time-dependent Schrodinger equation with a classical electric field. We demonstrate that the energy-periodic structure of ATI can be understood from the interference of ionized electron wavepackets produced periodically each half-cycle of the laser field. Using this simple …


Imls Place Grant: Campus Journal Press Release, Place Project Group Nov 2013

Imls Place Grant: Campus Journal Press Release, Place Project Group

PLACE Project

Campus Journal press release describing the PLACE (Position-based Location Archive Coordinate Explorer) project that is funded by the Institute for Museum and Library Services. The University of New Hampshire (UNH) library partnered with the UNH Earth Systems Research Center to develop a geospatial interface that is searchable by geospatial coordinates.


New Bis(Imino)Pyridine Complexes Of Iron(Ii) And Iron(Iii), And Their Catalytic­ Activity In The Mukaiyama Aldol Reaction, Pushkar Shejwalkar, Nigam Rath, Eike Bauer Nov 2013

New Bis(Imino)Pyridine Complexes Of Iron(Ii) And Iron(Iii), And Their Catalytic­ Activity In The Mukaiyama Aldol Reaction, Pushkar Shejwalkar, Nigam Rath, Eike Bauer

Chemistry & Biochemistry Faculty Works

New iron(II) and iron(III) complexes bearing bis(imino)pyridine ligands were synthesized and successfully applied to the Mukaiyama aldol reaction. The two complexes [FeCl2 L] (L = bis(imino)pyridine ligand, 55% isolated yield) and [LFe(μCl)3FeCl3] (76%) were obtained employing FeCl2 and FeCl3 iron sources, respectively, and characterized by elemental analyses, mass spectrometry, IR spectroscopy and, one example, by X-ray diffraction. The two new iron complexes were subsequently employed as catalysts in the Mukaiyama aldol reaction after abstraction of two chlorides by AgSbF6 to obtain the aldol products in 43% to virtually quantitative yield (CH2Cl2 solvent, room temperature, 3.5 to 16 h reaction time). …


Space-For-Time Substitution Works In Everglades Ecological Forecasting Models, Amanda I. Banet, Joel C. Trexler Nov 2013

Space-For-Time Substitution Works In Everglades Ecological Forecasting Models, Amanda I. Banet, Joel C. Trexler

Department of Biological Sciences

Space-for-time substitution is often used in predictive models because long-term time-series data are not available. Critics of this method suggest factors other than the target driver may affect ecosystem response and could vary spatially, producing misleading results. Monitoring data from the Florida Everglades were used to test whether spatial data can be substituted for temporal data in forecasting models. Spatial models that predicted bluefin killifish (Lucania goodei) population response to a drying event performed comparably and sometimes better than temporal models. Models worked best when results were not extrapolated beyond the range of variation encompassed by the original …


Spectral Energy Distributions Of Type 1 Agn In Xmm-Cosmos – Ii. Shape Evolution, Heng Hao, Martin Elvis, Francesca Civano, Gianni Zamorani Nov 2013

Spectral Energy Distributions Of Type 1 Agn In Xmm-Cosmos – Ii. Shape Evolution, Heng Hao, Martin Elvis, Francesca Civano, Gianni Zamorani

Dartmouth Scholarship

The mid-infrared to ultraviolet (0.1 -- 10 μm) spectral energy distribution (SED) shapes of 407 X-ray-selected radio-quiet type 1 AGN in the wide-field ``Cosmic Evolution Survey" (COSMOS) have been studied for signs of evolution. For a sub-sample of 200 radio-quiet quasars with black hole mass estimates and host galaxy corrections, we studied their mean SEDs as a function of a broad range of redshift, bolometric luminosity, black hole mass and Eddington ratio, and compared them with the Elvis et al. (1994, E94) type 1 AGN mean SED. We found that the mean SEDs in each bin are closely similar to …


New Bis(Imino)Pyridine Complexes Of Iron(Ii) And Iron(Iii), And Their Catalytic­ Activity In The Mukaiyama Aldol Reaction, Pushkar Shejwalkar, Nigam P. Rath, Eike B. Bauer Nov 2013

New Bis(Imino)Pyridine Complexes Of Iron(Ii) And Iron(Iii), And Their Catalytic­ Activity In The Mukaiyama Aldol Reaction, Pushkar Shejwalkar, Nigam P. Rath, Eike B. Bauer

Nigam Rath

New iron(II) and iron(III) complexes bearing bis(imino)pyridine ligands were synthesized and successfully applied to the Mukaiyama aldol reaction. The two complexes [FeCl2 L] (L = bis(imino)pyridine ligand, 55% isolated yield) and [LFe(μCl)3FeCl3] (76%) were obtained employing FeCl2 and FeCl3 iron sources, respectively, and characterized by elemental analyses, mass spectrometry, IR spectroscopy and, one example, by X-ray diffraction. The two new iron complexes were subsequently employed as catalysts in the Mukaiyama aldol reaction after abstraction of two chlorides by AgSbF6 to obtain the aldol products in 43% to virtually quantitative yield (CH2Cl2 solvent, room temperature, 3.5 to 16 h reaction time). …


Interplay Of Hydrogen Bonds And N→Π* Interactions In Proteins, Gail J. Bartlett, Robert W. Newberry, Brett Vanveller, Ronald T. Raines, Derek N. Woolfson Nov 2013

Interplay Of Hydrogen Bonds And N→Π* Interactions In Proteins, Gail J. Bartlett, Robert W. Newberry, Brett Vanveller, Ronald T. Raines, Derek N. Woolfson

Brett VanVeller

Protein structures are stabilized by multiple weak interactions, including the hydrophobic effect, hydrogen bonds, electrostatic effects, and van der Waals interactions. Among these interactions, the hydrogen bond is distinct in having its origins in electron delocalization. Recently, another type of electron delocalization, the n→π* interaction between carbonyl groups, has been shown to play a role in stabilizing protein structure. Here we examine the interplay between hydrogen bonding and n→π* interactions. To address this issue, we used data available from high-resolution protein crystal structures to interrogate asparagine side-chain oxygen atoms that are both acceptors of a hydrogen bond and donors of …


Multiperiodicity, Modulations And Flip-Flops In Variable Star Light Curves Ii. Analysis Of Ii Pegasus Photometry During 1979–2010, Marjaana Lindborg, Maarit J. Mantere, Nigul Olspert, Jaan Pelt, Thomas Hackman, Gregory W. Henry, Lauri Jetsu, Klaus G. Strassmeier Nov 2013

Multiperiodicity, Modulations And Flip-Flops In Variable Star Light Curves Ii. Analysis Of Ii Pegasus Photometry During 1979–2010, Marjaana Lindborg, Maarit J. Mantere, Nigul Olspert, Jaan Pelt, Thomas Hackman, Gregory W. Henry, Lauri Jetsu, Klaus G. Strassmeier

Information Systems and Engineering Management Research Publications

Aims. According to previously published Doppler images of the magnetically active primary giant component of the RS CVn binary II Peg, the surface of the star was dominated by one single active longitude that was clearly drifting in the rotational frame of the binary system during 1994-2002; later imaging for 2004–2010, however, showed decreased and chaotic spot activity, with no signs of the drift pattern. Here we set out to investigate from a more extensive photometric dataset whether this drift is a persistent phenomenon, in which case it could be caused either by an azimuthal dynamo wave or be an …


Non-Potential Fields In The Quiet Sun Network: Extreme-Ultraviolet And Magnetic Footpoint Observations, David L. Chesney, Hakeem M. Oluseyi, Norton B. Orange Nov 2013

Non-Potential Fields In The Quiet Sun Network: Extreme-Ultraviolet And Magnetic Footpoint Observations, David L. Chesney, Hakeem M. Oluseyi, Norton B. Orange

Aerospace, Physics, and Space Science Faculty Publications

The quiet Sun (QS) magnetic network is known to contain dynamics which are indicative of non-potential fields. Non-potential magnetic fields forming “S-shaped” loop arcades can lead to the breakdown of static activity and have only been observed in high temperature X-ray coronal structures—some of which show eruptive behavior. Thus, analysis of this type of atmospheric structuring has been restricted to large-scale coronal fields. Here we provide the first identification of non-potential loop arcades exclusive to the QS supergranulation network. High-resolution Atmospheric Imaging Assembly data from the Solar Dynamics Observatory have allowed for the first observations of fine-scale “S-shaped” loop arcades …


Assessing Functional Deficits At Optic Neuritis Onset In Eae Mice Using Manganese-Enhanced Mri (Memri) And Diffusion Fmri, Tsen-Hsuan Lin Nov 2013

Assessing Functional Deficits At Optic Neuritis Onset In Eae Mice Using Manganese-Enhanced Mri (Memri) And Diffusion Fmri, Tsen-Hsuan Lin

All Theses and Dissertations (ETDs)

Optic neuritis: ON) is frequently a first sign of multiple sclerosis: MS), which is an inflammatory demyelinative disease of the central nerve system: CNS), including brain, optic nerve, and spinal cord. Investigating ON provides an approach to improve MS diagnosis and treatment monitoring. Experimental autoimmune encephalomyelitis: EAE) is a widely used animal model of MS and exhibits pathologies similar to the human disease. Magnetic resonance imaging: MRI) is a non-invasive tool to detect disease progress and as a standard diagnose procedure for MS in the clinic. In biological samples, the hydrogen nuclei are used to produce the MR signal due …


The Kronecker-Weber Theorem: An Exposition, Amber Verser Nov 2013

The Kronecker-Weber Theorem: An Exposition, Amber Verser

Lawrence University Honors Projects

This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …