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Mathematical Methods for Accident Reconstruction
This book demonstrates the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.
Eleven-Digit Regular Sexagesimals and Their Recipricols
This is a print on demand edition of an important, hard-to-find publication. Illustration.
Real Analysis - An Introduction
Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.
Compact Closed 2-Categories
While the Cobordism Hypothesis provides a translation between topological and categorical structures, the subject of fusion categories arising from representations of finite groups has shown the need for a robust theory of duality in monoidal 2-categories. This book intertwines 3-dimensional category theory with enriched and symmetric monoidal 2-categories to present a comprehensive foundation for duals in dimension two. This framework is presented using wire diagrams, a typographical tool that combines the geometric appeal of ordinary string diagrams with the clarity of standard commutative diagrams in category theory. Chapters on enriched 2-categories, closed 2-categories, and compact closed 2-categories build the theory from the ground up and in full detail. Shorter appendices on technical topics from higher category theory such as icons, strictification theorems, and computads provide readers with concise explanations of key results, as well as references for researchers interested in more depth. The book concludes with a chapter of examples from algebra and topology, including a detailed construction for the example of cobordisms.
7th Grade Arkansas Math for Beginners
Arkansas Grade 7 MathComprehensive & Aligned with Arkansas Math StandardsBuild strong math skills and confidence with this complete Grade 7 workbook designed for Arkansas students. Fully aligned with Arkansas Mathematics Standards, this resource supports classroom instruction, homeschooling, and independent study, while providing focused practice for the ATLAS (Arkansas Test of Learning and Academic Skills) math assessment.Inside, students will find clear, step-by-step lessons covering essential Grade 7 topics such as ratios, proportional relationships, expressions, equations, geometry, and data analysis. Real-world examples and ATLAS-style practice questions throughout help students sharpen problem-solving skills and prepare effectively for test day.✔️ Covers all key Grade 7 Arkansas math standards ✔️ Includes ATLAS-style practice problems for targeted test prep ✔️ Ideal for homeschoolers, tutors, and classroom learners ✔️ Supports independent study with clear explanations and review sectionsWhether used for ongoing learning or focused ATLAS prep, this workbook guides Arkansas students to math success with confidence.
Extreme-Scale Computing
Scientific computing is essential for tackling complex problems across many domains--but how can scientists develop high-performance and high-quality software that scales efficiently? This book serves as an accessible introduction to extreme-scale computing, specifically designed for domain scientists who may not have formal computer science training but need to harness the power of C++ and parallel computing for large-scale applications. The book begins by covering the fundamentals of scientific computing software management, including essential tools like Linux, Git, and CMake, before diving into a detailed exploration of C++ for extreme-scale computing. Readers familiar with languages like Python will gain the necessary skills to transition to C++ and build scalable, efficient software. Beyond basic programming, this book delves into hardware-aware computing, teaching readers how to optimize software performance by understanding the underlying architecture of modern computational systems. It then introduces parallel computing techniques, covering MPI for distributed memory parallelism, shared memory parallelism, CUDA for GPU programming, and Kokkos for performance portability. Further chapters focus on efficient I/O, debugging, and profiling, which all address aspects of the critical challenge of performance optimization in extreme-scale computing. The book concludes with an overview of popular libraries for extreme-scale computing, equipping readers with the tools they need to solve real-world computational problems. With a balance of theory, practical applications, and illustrative case studies, this book provides domain scientists with a comprehensive roadmap to mastering extreme-scale computing and developing highly parallel and performant software.
Exact Methods for Nonlinear Pdes
The book describes and illustrates how to apply effective analytical methods to obtain exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations.
Practical Geometry in the High Middle Ages
Contents: (I) The Place of Practical Geometry in the Middle Ages: The Nature of Practical Geometry; Practical Geometry in Education; Theory and Practice in Geometry; and Practical Geometry and Practical Concerns; (II) The Contents of "Artis cuiuslibet consummatio" and the "Pratike de geometrie"; (III) Procedures in the Editions, Translations, and Commentary: Editing "Artis cuiuslibet consummatio"; Editing the "Pratike de geometrie"; Translating the Texts; and About the commentary; and (IV) English translation of "Arts cuiuslibet consummatio" and of the "Pratike de geometrie." Selected Bibliography, Index of Latin Technical Terms, Index of Old French Technical Terms, and Index of Astronomical Parameters. Illus.
Asclepius of Tralles
This is a print on demand edition of an important, hard-to-find publication.
Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling
The United States Air Force fighter training squadrons build weekly schedules using a long and tedious process. Very little of this process is automated and optimality of any kind is nearly impossible. Schedules are built to a feasible condition only to be changed with consideration of Wing level requirements. Weekly flying schedules are restricted by requirements for crew rest, days since a pilot's last sortie, sorties in the last 30 days, and sorties in the last 90 days. By providing a scheduling model to the pilot charged with creating the schedule, valuable pilot hours could be spent in the cockpit, simulator, or other required duty. This research effort presents a mathematical programming (MP) approach to the fighter squadron pilot training scheduling problem. The methodology presented is based on binary variables that will provide integer solutions to every feasible set of inputs. A simulator heuristic developed specifically for this problem assigns pilots to simulator sorties based on the feasible solutions obtained from two different formulation and solving approaches. One approach assigns training mission sorties and duties for the entire week, while the other approach breaks the week into ten successive sub-problems. The model constructs two feasible schedules in approximately 2.5 minutes.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
7th Grade North Carolina Math for Beginners
7th Grade North Carolina MathComprehensive & Aligned with North Carolina Math StandardsBoost math skills and build confidence with this complete 7th-grade workbook designed for North Carolina students. Fully aligned with the North Carolina Standard Course of Study, this resource supports classroom instruction, homeschooling, and independent study, while providing focused practice for the EOG (End-of-Grade) math assessment.Inside, students will find clear, step-by-step lessons covering essential 7th-grade topics such as ratios, proportional relationships, expressions, equations, geometry, and data analysis. Practical examples and EOG-style practice questions throughout help students sharpen problem-solving skills and prepare effectively for test day.✔️ Covers all key 7th-grade North Carolina math standards ✔️ Includes EOG-style practice problems for targeted test prep ✔️ Ideal for homeschoolers, tutors, and classroom learners ✔️ Supports independent study with clear explanations and review sectionsWhether used for ongoing learning or focused EOG prep, this workbook guides North Carolina students to math success with confidence.Mathfa - Trusted by families, recommended by educators.
Quadrature, Interpolation and Observability
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Basic Unit System
Basic Unit System, penned by Harry B. Clyatt, offers a comprehensive exploration of fundamental units of measurement. Published in 1921, this enduring work serves as a vital reference for scientists, engineers, and students seeking a robust understanding of foundational measurement principles. The book delves into the intricacies of establishing and utilizing basic units across various scientific and technical disciplines.Clyatt's clear and concise approach makes this book an invaluable resource for anyone working with quantitative data. Explore the establishment of standards and their applications in practical scenarios. This book provides a historical yet relevant perspective on the bedrock of metrology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Quadrature, Interpolation and Observability
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Investigation of the Effects of Correlation, Autocorrelation, and Sample Size in Classifier Fusion
This thesis extends the research found in Storm, Bauer, and Oxley, 2003. Data correlation effects and sample size effects on three classifier fusion techniques and one data fusion technique were investigated. Identification System Operating Characteristic Fusion (Haspert, 2000), the Receiver Operating Characteristic "Within" Fusion method (Oxley and Bauer, 2002), and a Probabilistic Neural Network were the three classifier fusion techniques; a Generalized Regression Neural Network was the data fusion technique. Correlation was injected into the data set both within a feature set (autocorrelation) and across feature sets for a variety of classification problems, and sample size was varied throughout. Total Probability of Misclassification (TPM) was calculated for some problems to show the effect of correlation on TPM.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Descartes's Theory of Light and Refraction
Contents: (1) Historical Overview; & Descartes's Perspectivist Sources; (2) Analysis of Refraction: Cartesian Light-Theory; & A Critical Evaluation; (3) The Foundations of Perspectivist Optics: Perspectivist Light-Theory; Quantization of Light; & Comparison with Descartes's Theory of Light; (4) The Perspectivist Analysis of Refraction: Physical Model; Physical "Explanation" & The Final Cause; (5) Perspectivist Grounds of the Cartesian Proof: Mathematical Implications; From Cosines to Sines; & Descartes Revisited; (6) Cartesian Light-Theory as a Culmination; Toward a Kinetic Theory of Light; & Epistemological Consequences. App.: The Sine-Law Before Descartes; The Fermat-Descartes Controversy; & Kepler, Descartes & the Anaclastic. Illustrations.
Basic Unit System
Basic Unit System, penned by Harry B. Clyatt, offers a comprehensive exploration of fundamental units of measurement. Published in 1921, this enduring work serves as a vital reference for scientists, engineers, and students seeking a robust understanding of foundational measurement principles. The book delves into the intricacies of establishing and utilizing basic units across various scientific and technical disciplines.Clyatt's clear and concise approach makes this book an invaluable resource for anyone working with quantitative data. Explore the establishment of standards and their applications in practical scenarios. This book provides a historical yet relevant perspective on the bedrock of metrology.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Consistency Results for the ROC Curves of Fused Classifiers
The U.S. Air Force is researching the fusion of multiple classifiers. Given a finite collection of classifiers one seeks a new fused classifier with improved performance. An established performance quantifier is the Receiver Operating Characteristic (ROC) curve, which allows one to view the probability of detection versus the probability of false alarm in one graph. Previous research shows that one does not have to perform tests to determine the ROC curve of this new fused classifier. If the ROC curve for each individual classifier has been determined, then formulas for the ROC curve of the fused classifier exist for certain fusion rules. This will be an enormous saving in time and money since the performance of many fused classifiers can be determined analytically. In reality only finite data is available so only an estimated ROC curve can be constructed. It has been proven that estimated ROC curves will converge to the true ROC curve in probability. This research examines if convergence is preserved when these estimated ROC curves are fused. It provides a general result for fusion rules that are governed by a Lipschitz continuous ROC fusion function and establishes a metric that can be used to prove this convergence.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry and Trigonometry From the Works of A. M. Legendre
"Elements of Geometry and Trigonometry" presents a comprehensive exploration of fundamental geometric principles and trigonometric functions, derived from the esteemed works of A. M. Legendre. This enduring text, originally published in 1869, offers a rigorous and systematic approach to understanding Euclidean geometry and its applications in trigonometry. Legendre's clear and precise exposition makes this book an invaluable resource for students and scholars seeking a solid foundation in mathematical reasoning. The text covers a wide range of topics, from basic geometric constructions to advanced trigonometric identities, all presented with meticulous detail and clarity. This edition preserves the historical significance of Legendre's work while providing contemporary readers with access to essential mathematical knowledge.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Course in Algebra
"A First Course in Algebra," originally published in 1908, offers a comprehensive introduction to algebraic principles and problem-solving techniques. Designed for students beginning their study of algebra, this text provides a systematic approach to understanding fundamental concepts. Webster Wells, a prominent mathematics educator, presents clear explanations and numerous examples to aid comprehension. The book covers essential topics such as equations, polynomials, factoring, and radicals, laying a solid foundation for further mathematical studies. This edition retains the original content, ensuring that readers experience the timeless methods of teaching algebra that have proven effective for generations. This book is valuable for students, educators, and anyone interested in the historical development of mathematical education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Collected Mathematical Papers of James Joseph Sylvester ..
This collection brings together the seminal mathematical papers of James Joseph Sylvester, a prominent 19th-century mathematician. Sylvester's work spanned a range of mathematical fields, including algebra, number theory, and geometry. This compilation offers insights into the development of mathematical thought during a transformative period. Edited by H.F. Baker, this collection, titled "The Collected Mathematical Papers of James Joseph Sylvester," stands as a testament to Sylvester's enduring contributions to the field. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Collected Mathematical Papers of James Joseph Sylvester ..
This collection brings together the seminal mathematical papers of James Joseph Sylvester, a prominent 19th-century mathematician. Sylvester's work spanned a range of mathematical fields, including algebra, number theory, and geometry. This compilation offers insights into the development of mathematical thought during a transformative period. Edited by H.F. Baker, this collection, titled "The Collected Mathematical Papers of James Joseph Sylvester," stands as a testament to Sylvester's enduring contributions to the field. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Traveling Salesman Problem for Surveillance Mission Using Particle Swarm Optimization
The surveillance mission requires aircraft to fly from a starting point through defended terrain to targets and return to a safe destination (usually the starting point). The process of selecting such a flight path is known as the Mission Route Planning (MRP) Problem and is a three-dimensional, multi-criteria (fuel expenditure, time required, risk taken, priority targeting, goals met, etc.) path search. Planning aircraft routes involves an elaborate search through numerous possibilities, which can severely task the resources of the system being used to compute the routes. Operational systems can take up to a day to arrive at a solution due to the combinatoric nature of the problem. This delay is not acceptable because timeliness of obtaining surveillance information is critical in many surveillance missions. Also, the information that the software uses to solve the MRP may become invalid during computation. An effective and efficient way of solving the MRP with multiple aircraft and multiple targets is desired. One approach to funding solutions is to simplify and view the problem as a two-dimensional, minimum path problem.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Application of Category Theory and Analysis of Receiver Operating Characteristics to Information Fusion
Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described . Definitions of fusion rules and fusors are introduced, along with functor categories, of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researchers choice. One such objective function, a functional on families of classification systems, and in particular receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument which minimizes it (a particular ROC), corresponds to the Bayes Optimal threshold, given certain assumptions, within a family of classification systems. This constraint is extended to ROC manifolds in higher dimensions. Under different data assumptions, the minimizing argument of the ROC functional is shown to be the point of a ROC manifold corresponding to the Neyman-Pearson criteria. A second functional is shown to determine the min-max threshold. A more robust functional is developed.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Cross-Resolution Combat Model Calibration Using Bootstrap Sampling
The US Air Force uses many combat simulation models to assist them in performing combat analyses. BRAWLER is a high-resolution air-to-air combat simulation model used for engagement-level analyses of few-on-few air combat. THUNDER is a low-resolution combat simulation model used for campaign-level analyses of theater-level warfare. BRAWLER is frequently used to ensure that THUNDER air-to-air inputs are valid. This thesis describes the confederation of THUNDER and BRAWLER by clearly showing how one particular BRAWLER output, the effectiveness of a missile type, is transformed into THUNDER air-to-air input data. Since BRAWLER is a stochastic simulation model, it is necessary to replicate a number of BRAWLER simulation runs in order to obtain a sufficiently accurate estimate of the mean missile effectiveness, a number that varies for each different BRAWLER combat scenario. This thesis focuses on using two different sequential methods to determine when the minimum number of BRAWLER runs has been performed to obtain a specified relative precision. One method uses classical statistical analysis techniques, while the other uses the more modern technique of bootstrap resampling. The performance of these two methods is compared.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A New Sequential Goodness of Fit Test for the Three-Parameter Gamma Distribution With Known Shape Based on Skewness and Kurtosis
This research presents a sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing the two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fits using parameter estimation methods such as MLE (maximum likelihood estimation) and MD (minimum distance estimation). This sequential goodness of fit tests using two test statistics above do not involve a substantial degree of computational complexity. Critical values are obtained using large Monte Carlo simulations, which use 'percentile' function, for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)50. Attained significance levels for all combinations of the two tests between = 0:01(0:01)0:20 are also approximated with Monte Carlo simulations. Extensive power studies are then conducted against two sets of alternatives. One is against common alternative distributions and the other is comparative study whose competitor are popular EDF test statistics such as the Anderson-Darling, Cramer-von Mises, and Komogrov-Smirove tests.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Boundary Value Problems
This new edition presents an updated and expanded exploration of boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. In a new chapter, the author introduces time scale calculus and fractional time scale calculus. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions. This second edition includes new and updated examples and problems.
Updating Optimal Decisions Using Game Theory and Exploring Risk Behavior Through Response Surface Methodology
This thesis utilizes game theory within a framework for updating optimal decisions based on new information as it becomes available. Methodology is developed that allows a decision maker to change his perceived optimal policy based on available knowledge of the opponents strategy, where the opponent is a rational decision maker or a random component nature. Utility theory is applied to account for the different risk preferences of the decision makers. Furthermore, response surface methodology is used to explore good risk strategies for the decision maker to approach each situation with. The techniques are applied to a combat scenario, a football game, and a terrorist resource allocation problem, providing a decision maker with the best possible strategy given the information available to him. The results are intuitive and exemplify the benefits of using the methods.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Elements Of Descriptive Geometry
"The Elements Of Descriptive Geometry" by Joseph Woolley is a detailed exposition on the principles of descriptive geometry and its practical applications, particularly in shipbuilding. This first part of the treatise offers a comprehensive introduction to the fundamental concepts, providing readers with a solid foundation in the subject. Woolley meticulously explains the methods of representing three-dimensional objects in two dimensions, essential for accurate drafting and design. The book is invaluable for students, engineers, and naval architects seeking a thorough understanding of descriptive geometry's role in technical fields. Its historical context adds to its significance, offering insights into the practices of 19th-century shipbuilding and engineering.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Anderson-Darling and Cramer-Von Mises Based Goodness-of-Fit Tests for the Weibull Distribution With Known Shape Using Normalized Spacings
Two new goodness-of-_t tests are developed for the three-parameter Weibull distribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling A2 s and Cram_er-von Mises W2 S statistics based on the normalized spacings of the sample data. Critical values of A2 s and W2 s are obtained for common signi_cance levels by large Monte Carlo simulations for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)40 with up to 40% censoring (type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z_, and the modi_ed Kolmogorov-Smirnov (KS), Cram_er- von Mises (W2) and Anderson-Darling (A2) EDF tests. The power results indicate that no one test is superior in all situations. When the alternatives considered are tested against a skewed Weibull null distribution, A2 s and W2 s achieve considerably higher power than the other EDF tests, but do not perform as well as Z_. On the other hand, when the null distribution is symmetric, Z_ loses all of its power, while A2 s and W2 s yield power comparable to the other EDF tests. Results also show A2 s generally outperforms W2 s, and for these reasons, A2 s is the preferred test for the three-parameter Weibull with known shape.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Investigation of the Effects of Correlation, Autocorrelation, and Sample Size in Classifier Fusion
This thesis extends the research found in Storm, Bauer, and Oxley, 2003. Data correlation effects and sample size effects on three classifier fusion techniques and one data fusion technique were investigated. Identification System Operating Characteristic Fusion (Haspert, 2000), the Receiver Operating Characteristic "Within" Fusion method (Oxley and Bauer, 2002), and a Probabilistic Neural Network were the three classifier fusion techniques; a Generalized Regression Neural Network was the data fusion technique. Correlation was injected into the data set both within a feature set (autocorrelation) and across feature sets for a variety of classification problems, and sample size was varied throughout. Total Probability of Misclassification (TPM) was calculated for some problems to show the effect of correlation on TPM.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
The Application of Category Theory and Analysis of Receiver Operating Characteristics to Information Fusion
Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described . Definitions of fusion rules and fusors are introduced, along with functor categories, of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researchers choice. One such objective function, a functional on families of classification systems, and in particular receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument which minimizes it (a particular ROC), corresponds to the Bayes Optimal threshold, given certain assumptions, within a family of classification systems. This constraint is extended to ROC manifolds in higher dimensions. Under different data assumptions, the minimizing argument of the ROC functional is shown to be the point of a ROC manifold corresponding to the Neyman-Pearson criteria. A second functional is shown to determine the min-max threshold. A more robust functional is developed.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Solid Geometry
This classic text, "Solid Geometry," by Franz Hocevar, translated and adapted by C. Godfrey and E.A. Price, offers a comprehensive exploration of three-dimensional geometry. Designed for students and educators alike, the book provides a rigorous yet accessible approach to understanding the fundamental principles of solid geometry.Through clear explanations and detailed diagrams, Hocevar's work covers a wide range of topics, including the properties of polyhedra, the calculation of volumes and surface areas, and the relationships between geometric figures in space. This edition, carefully adapted for English-speaking audiences, retains the original's precision while enhancing its clarity and usability, making it an invaluable resource for anyone studying or teaching this essential branch of mathematics. A timeless contribution to mathematical literature, "Solid Geometry" continues to inspire and educate generations of learners.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Group Theoretic Tabu Search Methodology for Solving the Theater Distribution Vehicle Routing and Scheduling Problem
The application of Group Theory to Tabu Search is a new and exciting field of research. This dissertation applies and extends some of Colletti's (1999) seminal work in group theory and metaheuristics in order to solve the theater distribution vehicle routing and scheduling problem (TDVRSP). This research produced a robust, efficient, effective and flexible generalized theater distribution model that prescribes the routing and scheduling of multi-modal theater transportation assets to provide economically efficient time definite delivery of cargo to customers. In doing so, advances are provided in the field of group theoretic tabu search and its application to difficult combinatorial optimization problems, e.g., the multiple trip multiple services vehicle routing and scheduling problem with hubs and other defining constraints.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A New Sequential Goodness of Fit Test for the Three-Parameter Gamma Distribution With Known Shape Based on Skewness and Kurtosis
This research presents a sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing the two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fits using parameter estimation methods such as MLE (maximum likelihood estimation) and MD (minimum distance estimation). This sequential goodness of fit tests using two test statistics above do not involve a substantial degree of computational complexity. Critical values are obtained using large Monte Carlo simulations, which use 'percentile' function, for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)50. Attained significance levels for all combinations of the two tests between = 0:01(0:01)0:20 are also approximated with Monte Carlo simulations. Extensive power studies are then conducted against two sets of alternatives. One is against common alternative distributions and the other is comparative study whose competitor are popular EDF test statistics such as the Anderson-Darling, Cramer-von Mises, and Komogrov-Smirove tests.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Comparison Of Weights And Measures Of Length And Capacity
This is a valuable historical document, "Comparison Of Weights And Measures Of Length And Capacity," a report presented to the United States Senate by the Treasury Department in 1832. Authored by Ferdinand Rudolph Hassler, this report provides a detailed snapshot of the standards of measurement used in the early 19th century. It offers insights into the complexities of standardization efforts and the variations present across different regions and industries at the time.A vital resource for historians, metrologists, and anyone interested in the development of scientific standards in the United States, this document is a testament to the ongoing quest for precision and uniformity. Its enduring appeal lies in its meticulous detail and its contribution to understanding the foundations of modern measurement systems.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Anderson-Darling and Cramer-Von Mises Based Goodness-of-Fit Tests for the Weibull Distribution With Known Shape Using Normalized Spacings
Two new goodness-of-_t tests are developed for the three-parameter Weibull distribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling A2 s and Cram_er-von Mises W2 S statistics based on the normalized spacings of the sample data. Critical values of A2 s and W2 s are obtained for common signi_cance levels by large Monte Carlo simulations for shapes of 0.5(0.5)4.0 and sample sizes of 5(5)40 with up to 40% censoring (type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z_, and the modi_ed Kolmogorov-Smirnov (KS), Cram_er- von Mises (W2) and Anderson-Darling (A2) EDF tests. The power results indicate that no one test is superior in all situations. When the alternatives considered are tested against a skewed Weibull null distribution, A2 s and W2 s achieve considerably higher power than the other EDF tests, but do not perform as well as Z_. On the other hand, when the null distribution is symmetric, Z_ loses all of its power, while A2 s and W2 s yield power comparable to the other EDF tests. Results also show A2 s generally outperforms W2 s, and for these reasons, A2 s is the preferred test for the three-parameter Weibull with known shape.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Updating Optimal Decisions Using Game Theory and Exploring Risk Behavior Through Response Surface Methodology
This thesis utilizes game theory within a framework for updating optimal decisions based on new information as it becomes available. Methodology is developed that allows a decision maker to change his perceived optimal policy based on available knowledge of the opponents strategy, where the opponent is a rational decision maker or a random component nature. Utility theory is applied to account for the different risk preferences of the decision makers. Furthermore, response surface methodology is used to explore good risk strategies for the decision maker to approach each situation with. The techniques are applied to a combat scenario, a football game, and a terrorist resource allocation problem, providing a decision maker with the best possible strategy given the information available to him. The results are intuitive and exemplify the benefits of using the methods.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Error Functions - Approximations and Implementations with modern FORTRAN. Volume I
The Error Function is used in many areas of mathematics, statistics, science and scientific applications such as error probability in signal detection, option pricing, diffusion, heat equation, modeling of magnetization, transitions between two planes, nonlinearities in the amplifier, rubbery materials and soft tissue. Error Functions, Volume I: erf, erfc and erfcx is the first comprehensive collection of multi-precision implementations in modern module-oriented FORTRAN for GFortran and Silverfrost FTN 95. The precision of many functions is up to 32 digits. New functions, especially for the scaled complementary error function (erfcx), show better performance than some standard intrinsic functions. The implementation methods are mainly rational functions, Chebyshev series and rational Chebyshev functions, series expansions and continued fractions. A menu-driven test program guides through the various error functions. The complete source code of all functions and the test program is available.
A Group Theoretic Tabu Search Methodology for Solving the Theater Distribution Vehicle Routing and Scheduling Problem
The application of Group Theory to Tabu Search is a new and exciting field of research. This dissertation applies and extends some of Colletti's (1999) seminal work in group theory and metaheuristics in order to solve the theater distribution vehicle routing and scheduling problem (TDVRSP). This research produced a robust, efficient, effective and flexible generalized theater distribution model that prescribes the routing and scheduling of multi-modal theater transportation assets to provide economically efficient time definite delivery of cargo to customers. In doing so, advances are provided in the field of group theoretic tabu search and its application to difficult combinatorial optimization problems, e.g., the multiple trip multiple services vehicle routing and scheduling problem with hubs and other defining constraints.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Number Systems
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.
