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2009

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Articles 1771 - 1800 of 7616

Full-Text Articles in Physical Sciences and Mathematics

Nonideal Magnetohydrodynamic Turbulent Decay In Molecular Clouds, Turlough Downes, Stephen O'Sullivan Aug 2009

Nonideal Magnetohydrodynamic Turbulent Decay In Molecular Clouds, Turlough Downes, Stephen O'Sullivan

Articles

It is well known that non-ideal magnetohydrodynamic effects are important in the dynamics of molecular clouds: both ambipolar diffusion and possibly the Hall effect have been identified as significant. We present the results of a suite of simulations with a resolution of 512-cubed of turbulent decay in molecular clouds incorporating a simplified form of both ambipolar diffusion and the Hall effect simultaneously. The initial velocity field in the turbulence is varied from being super-Alfvénic and hypersonic, through to trans-Alfvénic but still supersonic.


T-Plausibility: Semantic Preserving Text Sanitization, Wei Jiang, Mummoorthy Murugesan, Chris Clifton, Luo Si Aug 2009

T-Plausibility: Semantic Preserving Text Sanitization, Wei Jiang, Mummoorthy Murugesan, Chris Clifton, Luo Si

Computer Science Faculty Research & Creative Works

Text documents play significant roles in decision making and scientific research. Under federal regulations, documents (e.g., pathology records) containing personally identifiable information cannot be shared freely, unless properly sanitized. Generally speaking, document sanitization consists of finding and hiding personally identifiable information. The first task has received much attention from the research community, but the main strategy for the second task has been to simply remove personal identifiers and very sensitive information (e.g., diseases and treatment). It is not hard to see that if important information (e.g., diagnoses and personal medical histories) is completely removed from pathology records, these records are …


Esperance Area Acid Sulfate Soil Hazard Mapping, Paul Galloway, Simon Clarendon Aug 2009

Esperance Area Acid Sulfate Soil Hazard Mapping, Paul Galloway, Simon Clarendon

Resource management technical reports

This project created a regional scale (1:100 000) acid sulfate soil (ASS) hazard map for the Lake Warden and Esperance town areas, using a combination of existing soil-landscape mapping information and elevation data, supported by field observations and laboratory data from 18 soil cores and 29 additional borelogs with descriptive information useful for identifying ASS and potential ASS materials. All data gathered during this project used common standards and protocols developed in Australia for identifying and mapping ASS materials. The project extends the mapping for acid sulfate soil in the region, complementing existing maps compiled for other parts of the …


Recent Applications Of Acyclic (Diene)Iron Complexes And (Dienyl)Iron Cations In Organic Synthesis, William Donaldson, Subhabrata Chaudhury Aug 2009

Recent Applications Of Acyclic (Diene)Iron Complexes And (Dienyl)Iron Cations In Organic Synthesis, William Donaldson, Subhabrata Chaudhury

Chemistry Faculty Research and Publications

Complexation of (tricarbonyl)iron to an acyclic diene serves to protect the ligand against oxidation, reduction, and cycloaddition reactions, whereas the steric bulk of this adjunct serves to direct the approaches of reagents to unsaturated groups attached to the diene onto the face opposite to iron. Furthermore, the Fe(CO)3 moiety can serve to stabilize carbocation centers adjacent to the diene (i.e. pentadienyl-iron cations). Recent applications of these reactivities to the synthesis of polyene-, cyclopropane-, cycloheptadiene-, and cyclohexenone-containing natural products or analogues are presented.


Structure - Property Relationships Of New Polystyrene Nanocomposites Prepared From Initiator-Containing Layered Double Hydroxides Of Zinc Aluminum And Magnesium Aluminum, Charles Manzi-Nshuti, Dan Chen, Shengpei Shu, Charles A. Wilkie Aug 2009

Structure - Property Relationships Of New Polystyrene Nanocomposites Prepared From Initiator-Containing Layered Double Hydroxides Of Zinc Aluminum And Magnesium Aluminum, Charles Manzi-Nshuti, Dan Chen, Shengpei Shu, Charles A. Wilkie

Chemistry Faculty Research and Publications

Polystyrene/layered double hydroxides (PS/LDHs) nanocomposites were prepared by free radical polymerization of styrene monomer in the presence of LDHs intercalated with 4,4′-azobis(4-cyanopentanoate) anions (LDH–ACPA). XRD and ATR-IR are used to confirm that the materials produced are layered and the presence of the azo-initiator anions in these LDHs. These LDHs were used successfully to polymerize styrene and both XRD and TEM images of the composites support the formation of a mixed exfoliated-intercalated nanocomposite for ZnAl–ACPA but a microcomposite for MgAl–ACPA. The magnesium-containing LDHs decreased the glass transition temperature (Tg) of the composites while ZnAl–ACPA did not affect T …


A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. Banks, Alex Capaldi, Alun Lloyd Aug 2009

A Sensitivity Matrix Methodology For Inverse Problem Formulation, Ariel Cintron-Arias, H. Banks, Alex Capaldi, Alun Lloyd

Mathematics and Statistics Faculty Publications

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects in a score for a vector parameter defined using the norm of the …


National Urban Database And Access Portal Tool, Nudapt, Jason Ching, Michael Brown, Steven Burian, Fei Chen, Ron Cionco, Adel Hanna, Torrin Hultgren, Timothy Mcpherson, David J. Sailor, Haider Taha, David Williams Aug 2009

National Urban Database And Access Portal Tool, Nudapt, Jason Ching, Michael Brown, Steven Burian, Fei Chen, Ron Cionco, Adel Hanna, Torrin Hultgren, Timothy Mcpherson, David J. Sailor, Haider Taha, David Williams

Mechanical and Materials Engineering Faculty Publications and Presentations

Based on the need for advanced treatments of high resolution urban morphological features (e.g., buildings, trees) in meteorological, dispersion, air quality and human exposure modeling systems for future urban applications, a new project was launched called the National Urban Database and Access Portal Tool (NUDAPT). NUDAPT is sponsored by the U.S. Environmental Protection Agency (USEPA) and involves collaborations and contributions from many groups including federal and state agencies and from private and academic institutions here and in other countries. It is designed to produce and provide gridded fields of urban canopy parameters for various new and advanced descriptions of model …


Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis Aug 2009

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis

Masters Theses & Specialist Projects

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between …


Green Employees: Organizational Identification In An Environmentally Friendly Company, Jenna Haugen Aug 2009

Green Employees: Organizational Identification In An Environmentally Friendly Company, Jenna Haugen

Masters Theses & Specialist Projects

Environmental sustainability is an issue facing our global society and one that must be addressed through communication in order to encourage change amongst individuals. The current research focuses on the organization, in this instance a “Green” printing company, and its role in building identification amongst employees. This study focuses on environmental sustainable practices initiated or continued by employees through the use of a directed mission statement and organizational rhetoric. Utilizing individual interviews, the findings suggest that by building organizational identification, more environmentally-friendly practices amongst organizational members may be achieved.


Increased Control Over Gold Colloid Adsorption On Substrates For Colloid Displacement Lithography, Vara Prasad Reddy Sakampally Aug 2009

Increased Control Over Gold Colloid Adsorption On Substrates For Colloid Displacement Lithography, Vara Prasad Reddy Sakampally

Masters Theses & Specialist Projects

Colloid displacement lithography is proving to be very effective in the designing of nanometer scale electronic devices. Precise control of the structure of matter at the nanometer scale has brought a revolutionary change in science and technology. The use of these nanometer scale devices ranges from the diagnosis of various diseases to cell repair to ultra strong materials. This research focused on optimizing the conditions for gold colloid particle adsorption for colloid displacement lithography, an expansion on gold colloid particle manipulation techniques using a scanned probe microscope. The system consists of a scrupulously cleaned glass surface that is coated with …


Synthesis And Characterization Of Bis-Phosphine Complexes With Transition Metals, Alicia L. Mcdaniel Aug 2009

Synthesis And Characterization Of Bis-Phosphine Complexes With Transition Metals, Alicia L. Mcdaniel

Masters Theses & Specialist Projects

Extractants and extraction methodologies play a vital role in many industrial processes, from the concentration of precious metals from ores to the separation of longlived nuclei from radioactive waste as well as the removal of heavy metals from soils and water for remediation. The vast majority of extractants rely on the use of nitrogen, oxygen, sulfur or selenium as Lewis base donor atoms to form coordination complexes with the metal ions of interest. These extractants often make use of the chelate effect and/or the macrocyclic effect in order to form stable complexes. Some of the best known types of chelate …


Synthesis And Characterization Of Some Rhenium Complexes, Joseph Brian Scott Aug 2009

Synthesis And Characterization Of Some Rhenium Complexes, Joseph Brian Scott

Masters Theses & Specialist Projects

Plastics or polymers are thought to behave oppositely from metals. Ideally, polymers behave as insulators while metals conduct electricity. Shirakawa and coworkers discovered conductive polymers in 1977.1 These conductor polymers have been extensively studied, discovering that charge transfer oxidative doping of polyacteylene could increase its conductivity by 12 orders of magnitude. Polyacetylene, although showing promise as an organic conductor, because it is highly air-sensitive and oxidizes when exposed to molecular oxygen, therefore making this an unattractive use for commercial products. Attention has been focused on heterocylic aromatic polymers such as polythiophene and polypyrrole, in efforts to produce conductive polymers that …


A Survey Of Drought Impacts And Mitigation Planning In Kentucky, Crystal Jane Bergman Aug 2009

A Survey Of Drought Impacts And Mitigation Planning In Kentucky, Crystal Jane Bergman

Masters Theses & Specialist Projects

Drought is a well-known and costly climate-related natural hazard. Unlike other climate-related natural hazards, droughts are usually long in duration and may cover a large region, the physical boundaries of areas affected by drought are sometimes arbitrary, and the impacts are sometimes difficult to identify. Climate records since 1895 show that drought has occurred periodically in Kentucky. The drought of 2007 was the most recent drought to affect Kentucky and is the primary focus of this research. The purpose of this research is to identify impacts of drought and potential vulnerabilities to various drought impact sectors in Kentucky so that …


The Study Of Variations In The Properties Of Biodiesel On Addition Of Antioxidants, Hiranmayee Kandala Aug 2009

The Study Of Variations In The Properties Of Biodiesel On Addition Of Antioxidants, Hiranmayee Kandala

Masters Theses & Specialist Projects

This research studies variations in biodiesel upon addition of different concentrations of antioxidant and petrodiesel additives. Oxidation onset temperature, oxidation induction time, oxidative stability, thermal stability, crystallization onset temperature and moisture retention properties of the biodiesel, with and without antioxidants have been studied. Antioxidants like BHT, BHA, PrG, Vit E and Vit C were added to the biodiesel during the study. These samples were analyzed using the PDSC, TGA, DSC and TGA-SA instrumentation.

The results of this research show an improvement in the OOT, OIT and Oxidative stability of biodiesel with the addition of antioxidants and by blending the biodiesel …


Climate Justice: Towards A Proactive Response To Social Inequities, Vivek Shandas Aug 2009

Climate Justice: Towards A Proactive Response To Social Inequities, Vivek Shandas

Institute for Sustainable Solutions Publications and Presentations

Discussions about climate change have taken center stage. Claims of 'carbon neutral', and strategies for calculating and mitigating green house gas emissions (GHGs) have become common place from Beaverton to Bali. The discourse on climate change, however, remains largely an environmental one, with increasingly precise definitions of parts per million, downscaling climate models, and regional assessments for reducing carbon dioxide (CO2) emissions. These discussions are essential for understanding connections between local sources of GHGs and global consequences of our actions. But health and equity are equally critical dimensions of climate change, although these dimensions have had only limited investigation. Regional …


Multi-Task Transfer Learning For Weakly-Supervised Relation Extraction, Jing Jiang Aug 2009

Multi-Task Transfer Learning For Weakly-Supervised Relation Extraction, Jing Jiang

Research Collection School Of Computing and Information Systems

Creating labeled training data for relation extraction is expensive. In this paper, we study relation extraction in a special weakly-supervised setting when we have only a few seed instances of the target relation type we want to extract but we also have a large amount of labeled instances of other relation types. Observing that different relation types can share certain common structures, we propose to use a multi-task learning method coupled with human guidance to address this weakly-supervised relation extraction problem. The proposed framework models the commonality among different relation types through a shared weight vector, enables knowledge learned from …


Ssnetviz: A Visualization Engine For Heterogeneous Semantic Social Networks, Ee Peng Lim, Maureen Maureen, Nelman Lubis Ibrahim, Aixin Sun, Anwitaman Datta, Kuiyu Chang Aug 2009

Ssnetviz: A Visualization Engine For Heterogeneous Semantic Social Networks, Ee Peng Lim, Maureen Maureen, Nelman Lubis Ibrahim, Aixin Sun, Anwitaman Datta, Kuiyu Chang

Research Collection School Of Computing and Information Systems

SSnetViz is an ongoing research to design and implement a visualization engine for heterogeneous semantic social networks. A semantic social network is a multi-modal network that contains nodes representing di®erent types of people or object entities, and edges representing relationships among them. When multiple heterogeneous semantic social networks are to be visualized together, SSnetViz provides a suite of functions to store heterogeneous semantic social networks, to integrate them for searching and analysis. We will illustrate these functions using social networks related to terrorism research, one crafted by domain experts and another from Wikipedia.


Essential Spreadsheet Modeling Course For Business Students, Thin Yin Leong, Michelle L. F. Cheong Aug 2009

Essential Spreadsheet Modeling Course For Business Students, Thin Yin Leong, Michelle L. F. Cheong

Research Collection School Of Computing and Information Systems

Ask any student at the Singapore Management University (SMU) to name one of the most practical and useful courses offered by the university. The answer would inevitably include CAT. CAT stands for the "Computer as an Analysis Tool" course. Originally based on a course of the same title offered by the Wharton Business School, the focus of CAT was shifted to provide business students the essential practical skills and necessary "real-world" exposure to better use personal computers for resolving business problems. The course is basically centered on using the Excel spreadsheet to work on ambiguous ill-defined problems.


Evaluating Straddle Carrier Deployment Policies: A Simulation Study For The Piraeus Container Terminal, Eleni Hadjiconstantinou, Nang Laik Ma Aug 2009

Evaluating Straddle Carrier Deployment Policies: A Simulation Study For The Piraeus Container Terminal, Eleni Hadjiconstantinou, Nang Laik Ma

Research Collection School Of Computing and Information Systems

Most container terminals in the world today are operating up to their capacities. In this paper, we have developed a decision support system to optimise yard operations by considering all container flows (import, export and transshipment) through the yard with the view to improving the terminal performance and efficiency. In another paper, we proposed an optimisation model that determines optimal container locations and straddle carrier (SC) movements with the objective of minimising the overall storage and handling cost of containers. In this paper, a discrete event simulation tool for container terminal operations has been developed with three objectives: (i) to …


Dartmouth Internet Security Testbed (Dist): Building A Campus-Wide Wireless Testbed, Sergey Bratus, David Kotz, Keren Tan, William Taylor, Anna Shubina, Bennet Vance, Michael E. Locasto Aug 2009

Dartmouth Internet Security Testbed (Dist): Building A Campus-Wide Wireless Testbed, Sergey Bratus, David Kotz, Keren Tan, William Taylor, Anna Shubina, Bennet Vance, Michael E. Locasto

Dartmouth Scholarship

We describe our experiences in deploying a campus-wide wireless security testbed. The testbed gives us the capability to monitor security-related aspects of the 802.11 MAC layer in over 200 diverse campus locations. We describe both the technical and the social challenges of designing, building, and deploying such a system, which, to the best of our knowledge, is the largest such testbed in academia (with the UCSD's Jigsaw infrastructure a close competitor). In this paper we focus on the \em testbed setup, rather than on the experimental data and results.


Structural Role Of Pseudouridines In The Peptidyl Transferase Center Of Human 28s Ribosomal Rna, Chris Mart Aug 2009

Structural Role Of Pseudouridines In The Peptidyl Transferase Center Of Human 28s Ribosomal Rna, Chris Mart

All Theses

The human ribosome is an RNA-protein complex responsible for protein synthesis in the cell. Crystal structures of bacterial ribosomes solved to date depict no protein sidechains within the catalytic core, or peptidyl transferase center (PTC). This region of the human ribosome comprises approximately 230 highly conserved nucleotides. Notably, several of the uridine bases clustered within the human PTC are post-transcriptionally modified to pseudouridines, as compared with bacterial analogues. Pseudouridines are base-rotated uridines, linked to their sugar moieties through C5-C1' linkages, affording additional hydrogen-bond donor groups at the N1 position of their rings. A connection was recently made between the absence …


Optimal-Location-Selection Query Processing In Spatial Databases, Yunjun Gao, Baihua Zheng, Gencai Chen, Qing Li Aug 2009

Optimal-Location-Selection Query Processing In Spatial Databases, Yunjun Gao, Baihua Zheng, Gencai Chen, Qing Li

Research Collection School Of Computing and Information Systems

This paper introduces and solves a novel type of spatial queries, namely, Optimal-Location-Selection (OLS) search, which has many applications in real life. Given a data object set D_A, a target object set D_B, a spatial region R, and a critical distance d_c in a multidimensional space, an OLS query retrieves those target objects in D_B that are outside R but have maximal optimality. Here, the optimality of a target object b \in D_B located outside R is defined as the number of the data objects from D_A that are inside R and meanwhile have their distances to b not exceeding …


A Fair Assignment Algorithm For Multiple Preference Queries, Leong Hou U, Nikos Mamoulis, Kyriakos Mouratidis Aug 2009

A Fair Assignment Algorithm For Multiple Preference Queries, Leong Hou U, Nikos Mamoulis, Kyriakos Mouratidis

Research Collection School Of Computing and Information Systems

Consider an internship assignment system, where at the end of each academic year, interested university students search and apply for available positions, based on their preferences (e.g., nature of the job, salary, office location, etc). In a variety of facility, task or position assignment contexts, users have personal preferences expressed by different weights on the attributes of the searched objects. Although individual preference queries can be evaluated by selecting the object in the database with the highest aggregate score, in the case of multiple simultaneous requests, a single object cannot be assigned to more than one users. The challenge is …


Scalable Verification For Outsourced Dynamic Databases, Hwee Hwa Pang, Jilian Zhang, Kyriakos Mouratidis Aug 2009

Scalable Verification For Outsourced Dynamic Databases, Hwee Hwa Pang, Jilian Zhang, Kyriakos Mouratidis

Research Collection School Of Computing and Information Systems

Query answers from servers operated by third parties need to be verified, as the third parties may not be trusted or their servers may be compromised. Most of the existing authentication methods construct validity proofs based on the Merkle hash tree (MHT). The MHT, however, imposes severe concurrency constraints that slow down data updates. We introduce a protocol, built upon signature aggregation, for checking the authenticity, completeness and freshness of query answers. The protocol offers the important property of allowing new data to be disseminated immediately, while ensuring that outdated values beyond a pre-set age can be detected. We also …


A Distributed Spatial Index For Error-Prone Wireless Data Broadcast, Baihua Zheng, Wang-Chien Lee, Ken C. K. Lee, Dik Lun Lee, Min Shao Aug 2009

A Distributed Spatial Index For Error-Prone Wireless Data Broadcast, Baihua Zheng, Wang-Chien Lee, Ken C. K. Lee, Dik Lun Lee, Min Shao

Research Collection School Of Computing and Information Systems

Information is valuable to users when it is available not only at the right time but also at the right place. To support efficient location-based data access in wireless data broadcast systems, a distributed spatial index (called DSI) is presented in this paper. DSI is highly efficient because it has a linear yet fully distributed structure that naturally shares links in different search paths. DSI is very resilient to the error-prone wireless communication environment because interrupted search operations based on DSI can be resumed easily. It supports search algorithms for classical location-based queries such as window queries and kNN queries …


Scene-Based Nonuniformity Correction With Reduced Ghosting Using A Gated Lms Algorithm, Russell C. Hardie, Frank Orion Baxley, Brandon J. Brys, Patrick C. Hytla Aug 2009

Scene-Based Nonuniformity Correction With Reduced Ghosting Using A Gated Lms Algorithm, Russell C. Hardie, Frank Orion Baxley, Brandon J. Brys, Patrick C. Hytla

Electrical and Computer Engineering Faculty Publications

In this paper, we present a scene-based nouniformity correction (NUC) method using a modified adaptive least mean square (LMS) algorithm with a novel gating operation on the updates. The gating is designed to significantly reduce ghosting artifacts produced by many scene-based NUC algorithms by halting updates when temporal variation is lacking. We define the algorithm and present a number of experimental results to demonstrate the efficacy of the proposed method in comparison to several previously published methods including other LMS and constant statistics based methods. The experimental results include simulated imagery and a real infrared image sequence. We show that …


Setting Discrete Bid Levels Adaptively In Repeated Auctions, Jilian Zhang, Hoong Chuin Lau, Jialie Shen Aug 2009

Setting Discrete Bid Levels Adaptively In Repeated Auctions, Jilian Zhang, Hoong Chuin Lau, Jialie Shen

Research Collection School Of Computing and Information Systems

The success of an auction design often hinges on its ability to set parameters such as reserve price and bid levels that will maximize an objective function such as the auctioneer revenue. Works on designing adaptive auction mechanisms have emerged recently, and the challenge is in learning different auction parameters by observing the bidding in previous auctions. In this paper, we propose a non-parametric method for determining discrete bid levels dynamically so as to maximize the auctioneer revenue. First, we propose a non-parametric kernel method for estimating the probabilities of closing price with past auction data. Then a greedy strategy …


Inferring Player Rating From Performance Data In Massively Multiplayer Online Role-Playing Games (Mmorpgs), Kyong Jin Shim, Muhammad Aurangzeb Ahmad, Nishith Pathak, Jaideep Srivastava Aug 2009

Inferring Player Rating From Performance Data In Massively Multiplayer Online Role-Playing Games (Mmorpgs), Kyong Jin Shim, Muhammad Aurangzeb Ahmad, Nishith Pathak, Jaideep Srivastava

Research Collection School Of Computing and Information Systems

This paper examines online player performance in EverQuest II, a popular massively multiplayer online role-playing game (MMORPG) developed by Sony Online Entertainment. The study uses the game's player performance data to devise performance metrics for online players. We report three major findings. First, we show that the game's point-scaling system overestimates performances of lower level players and underestimates performances of higher level players. We present a novel point-scaling system based on the game's player performance data that addresses the underestimation and overestimation problems. Second, we present a highly accurate predictive model for player performance as a function of past behavior. …


Transparency In Formal Proof, Cap Petschulat Aug 2009

Transparency In Formal Proof, Cap Petschulat

Boise State University Theses and Dissertations

The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant.


Solvability Characterizations Of Pell Like Equations, Jason Smith Aug 2009

Solvability Characterizations Of Pell Like Equations, Jason Smith

Boise State University Theses and Dissertations

Pell's equation has intrigued mathematicians for centuries. First stated as Archimedes' Cattle Problem, Pell's equation, in its most general form, X2PY2 = 1, where P is any square free positive integer and solutions are pairs of integers, has seen many approaches but few general solutions. The eleventh century Indian mathematician Bhaskara solved X2 – 61 • Y2 = 1 and, in response to Fermat's challenge, Wallis and Brouncker gave solutions to X2 – 151 • Y2 = 1 and X2 –313 • Y2 = 1. Fermat claimed to …