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The Collected Mathematical Papers of James Joseph Sylvester
This is the fourth volume of "The Collected Mathematical Papers of James Joseph Sylvester," documenting the prolific output of the renowned 19th-century mathematician. James Joseph Sylvester (1814-1897) made significant contributions to algebra, number theory, geometry, and invariant theory. This collection, meticulously compiled and edited, offers a comprehensive view of his work, showcasing his innovative approaches and profound insights.Edited by H. F. Baker, this volume makes Sylvester's groundbreaking research accessible to modern mathematicians, historians of science, and anyone with an interest in the development of mathematical thought. Sylvester's papers are valuable not only for their mathematical content but also for their historical context, providing a glimpse into the mathematical landscape of the 19th century. This collection is an essential resource for understanding the evolution of modern mathematics and the enduring legacy of one of its most influential figures.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.
Ade
The ADE diagrams, shown on the cover, constitute one of the most universal and mysterious patterns in all of mathematics. John McKay's remarkable insights unveiled a connection between the 'double covers' of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognised since the late nineteenth century. The correspondence involves the ADE diagrams being interpreted in different ways: as quivers associated with the groups and as Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in algebraic geometry, string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics, it also presents standard undergraduate material from a novel perspective.
''s QUARING THE CIRCLE' A HISTORY OF THE PROBLEM'
'SQUARING THE CIRCLE' A HISTORY OF THE PROBLEM explores the long and fascinating history of one of mathematics' most enduring puzzles: the attempt to construct a square with the same area as a given circle using only a compass and straightedge. This book delves into the mathematical concepts and historical context surrounding this problem, tracing its origins in ancient Greece through centuries of failed attempts, and culminating in the eventual proof of its impossibility. E.W. Hobson provides a detailed and accessible account of the mathematical ideas underlying the problem. This book is an essential resource for anyone interested in the history of mathematics and the enduring appeal of classical geometric problems.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 Euclid...
"The Elements of Euclid" is a foundational work in geometry and mathematics, presenting a systematic development of geometric principles based on a set of axioms and postulates. This edition, while published in 1869, reflects the enduring importance of Euclid's original work, which has influenced mathematical thought for centuries. Todhunter's edition makes Euclid's "Elements" accessible to students and scholars, providing a clear and rigorous exposition of geometric concepts, including lines, circles, polygons, and solid geometry. The book's step-by-step approach and logical structure make it an invaluable resource for anyone seeking a deep understanding of Euclidean geometry.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 Note on the Integral Equation of the First Kind With a Cauchy Kernel
"A Note on the Integral Equation of the First Kind With a Cauchy Kernel" presents a rigorous mathematical exploration of integral equations. Authored by Arthur S. Peters, this work delves into the complexities of equations featuring a Cauchy kernel, offering insights valuable to mathematicians and researchers in related fields. This concise note provides a focused analysis, making it an essential reference for those studying advanced mathematical concepts and their applications.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.
Some Integral Equations Related to Abel's Equation and the Hilbert Transform
"Some Integral Equations Related to Abel's Equation and the Hilbert Transform" explores advanced mathematical concepts central to the field of integral equations. Authored by Arthur S. Peters, this work delves into the intricate relationships between Abel's equation, the Hilbert transform, and various integral equations. The book offers a rigorous treatment of these topics, providing detailed analysis and methodologies for solving complex problems. It is an invaluable resource for mathematicians, physicists, and engineers seeking a deeper understanding of these mathematical tools and their applications. This enduring work continues to be relevant for researchers and students engaged in mathematical analysis and applied mathematics.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.
Green's Function Techniques for the Solution of Time-dependant Potential Flows With a Free Surface in a Bounded Domain
This work presents Green's function techniques for solving time-dependent potential flows with a free surface in a bounded domain. It provides a detailed mathematical treatment applicable to advanced studies in fluid dynamics and engineering. The methodology allows for a rigorous analysis of complex fluid behaviors, offering insights into problems involving free surfaces and time-varying conditions.Researchers and engineers in fields such as naval architecture, hydraulic engineering, and computational fluid dynamics will find this study valuable. Its emphasis on theoretical foundations and practical applications ensures its continued relevance in addressing contemporary challenges in fluid mechanics.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.
On Condition Numbers and the Distance to the Nearest Ill-posed Problem
This work explores the relationship between condition numbers and the distance to the nearest ill-posed problem. It provides a rigorous mathematical analysis of condition numbers, particularly in the context of numerical stability and error analysis. The study focuses on understanding how sensitive a problem is to small changes in its input data and investigates the proximity to problems for which solutions are undefined or highly unstable. Intended for researchers and graduate students in mathematics, computer science, and engineering, "On Condition Numbers and the Distance to the Nearest Ill-posed Problem" offers valuable insights into the theoretical foundations of numerical computation and its practical implications. The concepts discussed are crucial for designing robust numerical algorithms and assessing the reliability of computational results.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.
Eigenfunction Expansions Associated With the Laplacian for Certain Domains With Infinite Boundaries
This rigorous mathematical treatment explores eigenfunction expansions associated with the Laplacian operator in domains with infinite boundaries. "Eigenfunction Expansions Associated With the Laplacian for Certain Domains With Infinite Boundaries" provides a detailed analysis of the spectral properties of the Laplacian and their applications in solving boundary value problems. It is an essential resource for researchers and graduate students in mathematics and physics working on spectral theory, partial differential equations, and related areas. The book presents advanced techniques and results, offering a valuable contribution to the understanding of mathematical analysis.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.
Using the Kth Nearest Neighbor Clustering Procedure to Determine the Number of Subpopulations
This work explores the application of the Kth Nearest Neighbor clustering procedure as a method for determining the number of subpopulations within a dataset. Authored by M. Anthony Wong and Christian Schaak, this study delves into the statistical and computational aspects of using nearest neighbor techniques to identify and delineate distinct groups within complex data. The research provides insights into the practical use of this clustering approach, offering a valuable tool for researchers and practitioners in fields requiring robust data segmentation and analysis. The methods and findings presented can aid in a more accurate understanding of population structures and facilitate informed decision-making based on data-driven insights.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.
Variable Dimension Complexes, Part II
"Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology" presents a rigorous exploration of advanced mathematical concepts at the intersection of topology and combinatorics. Authored by Robert Michael Freund of the Sloan School of Management, this work delves into the intricacies of variable dimension complexes and offers a unified perspective on several key combinatorial lemmas within the field of topology. This book is an essential resource for researchers and advanced students seeking a deeper understanding of these complex mathematical structures and their applications. It provides valuable insights and methodologies for tackling challenging problems in both theoretical and applied mathematics. 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.
On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations
This volume, "On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations," delves into the intricacies of solving time-dependent transport equations using numerical techniques. It presents a rigorous examination of various methods, offering insights into their formulation and analysis. The work is a valuable resource for researchers and practitioners interested in the mathematical and computational aspects of solving transport phenomena. The book provides a detailed treatment suitable for those seeking a deeper understanding of the subject matter.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.
Modular Invariants
"Modular Invariants" explores the mathematical theory surrounding invariants, particularly within the context of modular arithmetic and group theory. Authored by D.E. Rutherford, this work delves into the abstract algebraic structures and their applications in various mathematical and physical contexts. The book likely covers topics such as group representations, symmetric functions, and the calculation and classification of invariants under different transformations. Intended for advanced students and researchers in mathematics and physics, "Modular Invariants" offers a rigorous treatment of the subject, providing a foundation for further study in areas such as coding theory, cryptography, and theoretical physics. The enduring value of this work lies in its detailed exploration of fundamental mathematical principles and their relevance to modern scientific challenges.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.
On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations
This rigorous mathematical study, "On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations," explores advanced concepts within the field of differential equations. The work delves into the properties of invariant surfaces and the bifurcation of periodic solutions, offering a detailed analysis relevant to researchers and advanced students in mathematics and physics. Robert John Sacker's work provides valuable insights into the behavior of dynamical systems, offering a theoretical framework for understanding complex phenomena in various scientific disciplines. The concepts discussed are essential for anyone working with mathematical models of physical 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.
Robin Hood Math
How the rich and powerful use math to exploit you, and what you can do to beat them at their own game Everything we do today is recorded as data that's sold to the highest bidder. Plugging our personal data into impersonal algorithms has made government agencies more efficient and tech companies more profitable. But all this comes at a price. It's easy to feel like an insignificant number in a world of number crunchers who care more about their bottom line than your humanity. It's time to flip the equation, turning math into an empowering tool for the rest of us. Award-winning mathematician Noah Giansiracusa explains how the tech giants and financial institutions use formulas to get ahead--and how anyone can use these same formulas in their everyday life. You'll learn how to handle risk rationally, make better investments, take control of your social media, and reclaim agency over the decisions you make each day. In a society that all too often takes from the poor and gives to the rich, math can be a vital democratizing force. Robin Hood Math helps you to think for yourself, act in your own best interests, and thrive.
Tracts on Mathematical and Philosophical Subjects, Comprising Among Numerous Important Articles, The Theory of Bridges, With Several Plans of Recent Improvement; Also The Results of Numerous Experimen
This collection, "Tracts on Mathematical and Philosophical Subjects," by Charles Hutton, presents a comprehensive exploration of various scientific and engineering topics. Originally published in 1812, it offers insights into the state of mathematical and philosophical knowledge during that period. Among its numerous important articles, the book notably features 'The Theory of Bridges, ' detailing plans for recent improvements in bridge design and construction. Hutton also includes the results of numerous experiments on the force of gunpowder, offering applications to artillery and military science. This work provides a valuable resource for historians of science and engineering, as well as anyone interested in the evolution of mathematical and philosophical thought.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.
Lectures on Differential Geometry with Maple
This text is designed to update the Differential Geometry course by making it more relevant to today's students. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.
Lectures on Differential Geometry with Maple
This text is designed to update the Differential Geometry course by making it more relevant to today's students. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.
Data Analysis of Medical Studies
This book is written for the many health professionals who are regularly frustrated by elegant but ambiguous descriptions of results of data analysis. It uses articles of the New England Journal of Medicine to demonstrate how ambiguous descriptions of results of data analysis may be read, so that it is clear what they do and do not reveal. These demonstrations also show how statistics is misused.
Ade
The ADE diagrams, shown on the cover, constitute one of the most universal and mysterious patterns in all of mathematics. John McKay's remarkable insights unveiled a connection between the 'double covers' of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognised since the late nineteenth century. The correspondence involves the ADE diagrams being interpreted in different ways: as quivers associated with the groups and as Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in algebraic geometry, string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics, it also presents standard undergraduate material from a novel perspective.
Applied Engineering Mathematics
The publication of this book is motivated by the need to present the latest research & advancements in the fields of Fluid/Solid Mechanics, Nonlinear Dynamics, and Differential Equations in Applied Mathematics. This book gathers the work of leading experts, offering cutting-edge findings addressing existing challenges in the field. It covers a broad spectrum of topics, including advanced computational methods/mathematical modeling/different Mathematical methods & their applications in many scientific disciplines like predicting the nature and behavior of physical systems in engineering. These problems often require solving differential equations governing fluid flow, heat transfer, and structural deformation, often simultaneously, among other topics. Each chapter delves into specific problems, showcasing interdisciplinary approaches & demonstrating the practical impact of mathematical research on real-world issues. This book is a great resource for scholars, professionals, and researchers as it offers a comprehensive overview of cutting-edge methodologies & innovative solutions. It aims to stimulate additional investigation, promote interdisciplinary collaboration & make substantial contributions to advancing knowledge.
Information-Oriented Logic
The book introduces a new form of mathematical logic called "Information Oriented Logic" (IOL). It demonstrates that IOL is capable of solving various classical and non-classical logic problems that cannot be solved by traditional methods of logic. In this book, it is argued that two meaningful declarative sentences or symbols can make the same statement if they express the same thing or referent in different ways. The book treats a piece of information as the referent for a meaningful declarative sentence, thus inventing information-oriented logic. As a result, this book provides a comprehensive guide to this logic. Unlike traditional logic, which uses declarative sentences as the result of logical expressions, this new logic uses pieces of information. The book is intended for undergraduate and graduate students, as well as scholars applying mathematical logic to various fields such as philosophy, linguistics, ontology, information theory, computer science, etc. Additionally, it provides a new mereology in which all implications of a piece of information are its parts.
The Small Dispersion Limit of the Korteweg-deVries Equations
"The Small Dispersion Limit of the Korteweg-de Vries Equations" explores the behavior of solutions to the Korteweg-de Vries (KdV) equation as the dispersion parameter approaches zero. This limit is crucial for understanding the transition from dispersive wave phenomena to non-dispersive behavior, with applications in various fields such as fluid dynamics, plasma physics, and nonlinear optics. Authored by C. David Levermore and Peter D. Lax, this work delves into the mathematical analysis required to rigorously derive and characterize the small dispersion limit. The book provides insights into the formation of shock waves and other singular structures that arise in this limit. It is an essential resource for researchers and graduate students in applied mathematics, physics, and engineering who are interested in nonlinear wave phenomena and the asymptotic analysis of partial differential equations.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.
Using the Kth Nearest Neighbor Clustering Procedure to Determine the Number of Subpopulations
This work explores the application of the Kth Nearest Neighbor clustering procedure as a method for determining the number of subpopulations within a dataset. Authored by M. Anthony Wong and Christian Schaak, this study delves into the statistical and computational aspects of using nearest neighbor techniques to identify and delineate distinct groups within complex data. The research provides insights into the practical use of this clustering approach, offering a valuable tool for researchers and practitioners in fields requiring robust data segmentation and analysis. The methods and findings presented can aid in a more accurate understanding of population structures and facilitate informed decision-making based on data-driven insights.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.
On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations
This volume, "On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations," delves into the intricacies of solving time-dependent transport equations using numerical techniques. It presents a rigorous examination of various methods, offering insights into their formulation and analysis. The work is a valuable resource for researchers and practitioners interested in the mathematical and computational aspects of solving transport phenomena. The book provides a detailed treatment suitable for those seeking a deeper understanding of the subject matter.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.
Jacobi's Method is More Accurate Than QR
This study analyzes the accuracy of Jacobi's method in comparison to the QR algorithm for matrix computations. Originally published in 1988, "Jacobi's Method is More Accurate Than QR" presents a rigorous mathematical treatment demonstrating the circumstances under which Jacobi's method offers superior precision. The research contributes valuable insights to the field of numerical analysis and is useful to researchers and practitioners dealing with eigenvalue problems and matrix diagonalization.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 High School Algebra
"The High School Algebra, Part I," Volume 1, offers a comprehensive introduction to algebraic principles. Designed for secondary education, this book provides a structured approach to understanding fundamental concepts. Authored by W. J. Robertson and I. J. Birchard, this volume serves as an invaluable resource for students embarking on their algebraic journey. Originally published in 1886, this edition retains its historical context and pedagogical value, offering a glimpse into 19th-century mathematical education. "The High School Algebra" delivers clear explanations and methodical exercises suitable for classroom instruction or self-study, ensuring a solid foundation in algebra.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.
Integral Identities Involving Zonal Polynomials
"Integral Identities Involving Zonal Polynomials" presents a detailed exploration of integral identities within the context of zonal polynomials. This work delves into the mathematical intricacies of these special functions, offering a rigorous treatment suitable for advanced researchers and students in mathematics and statistics. The book focuses on establishing and analyzing various integral identities, providing a valuable resource for those working in multivariate analysis, combinatorics, and related fields. With a focus on theoretical development and mathematical precision, this book offers significant insights into the properties and applications of zonal polynomials.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.
On the Represenation of a Function by a Trigonometric Series ..
"On the Representation of a Function by a Trigonometric Series" explores the mathematical concepts surrounding the representation of functions using trigonometric series. Authored by Edward Payson Manning, this work delves into the complexities of mathematical analysis and calculus. This book offers insights into the methods and theories prevalent in the late 19th century. Mathematicians and students of mathematical history will find this book a valuable resource. It provides a detailed exploration of a key area within mathematical functions and their applications.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.
Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4
"Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4" delves into the complex mathematical principles governing sound wave propagation and directivity in the presence of a dome-shaped structure. Authored by Eleazer Bromberg, Richard Courant, K. O. Friedrichs, and J. J. Stoker, this work offers an in-depth exploration of acoustic theory. This text provides a rigorous mathematical treatment suitable for researchers, engineers, and students in acoustics, physics, and applied mathematics. It will appeal to those interested in the theoretical underpinnings of sound behavior in complex environments.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 Locally Most Powerful Rank Test for the Location Parameter of a Double Exponential Distribution
This rigorous study, "A Locally Most Powerful Rank Test for the Location Parameter of a Double Exponential Distribution," delves into the mathematical foundations of statistical testing. Eugene Laska presents a detailed analysis of a specific rank test designed to identify the location parameter within a double exponential distribution. This work is essential for statisticians and researchers seeking a deeper understanding of nonparametric methods. The book provides invaluable insights into the construction and application of powerful rank tests, making it a significant contribution to the field of statistical inference. It offers a valuable resource for those involved in theoretical and applied statistics. 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.
Multiple Extension Algebraic Number Fields
Multiple Extension Algebraic Number Fields explores advanced topics in algebraic number theory, focusing on field extensions. This work by Chung-jen Ho delves into the complexities of number fields and their extensions, offering a rigorous mathematical treatment suitable for researchers and graduate students in mathematics. The book provides detailed analysis and proofs related to the structure and properties of these fields, making it a valuable resource for those studying advanced algebra and number theory.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.
Variable Dimension Complexes, Part II
"Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology" presents a rigorous exploration of advanced mathematical concepts at the intersection of topology and combinatorics. Authored by Robert Michael Freund of the Sloan School of Management, this work delves into the intricacies of variable dimension complexes and offers a unified perspective on several key combinatorial lemmas within the field of topology. This book is an essential resource for researchers and advanced students seeking a deeper understanding of these complex mathematical structures and their applications. It provides valuable insights and methodologies for tackling challenging problems in both theoretical and applied mathematics. 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.
On the Represenation of a Function by a Trigonometric Series ..
"On the Representation of a Function by a Trigonometric Series" explores the mathematical concepts surrounding the representation of functions using trigonometric series. Authored by Edward Payson Manning, this work delves into the complexities of mathematical analysis and calculus. This book offers insights into the methods and theories prevalent in the late 19th century. Mathematicians and students of mathematical history will find this book a valuable resource. It provides a detailed exploration of a key area within mathematical functions and their applications.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 Exercise Book in Algebra
An Exercise Book in Algebra, by Matthew S. McCurdy, is a comprehensive collection of algebraic problems and exercises designed to reinforce fundamental concepts. Originally published in 1904, this book serves as a valuable resource for students seeking to solidify their understanding of algebra through practice. It offers a wide range of exercises covering various topics, from basic equations to more advanced concepts. This book provides ample opportunity for students to hone their skills and develop a deeper understanding of algebraic principles. Suitable for classroom use or self-study, "An Exercise Book in Algebra" remains a relevant and practical guide for anyone looking to master this essential branch of mathematics.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.
Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4
"Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4" delves into the complex mathematical principles governing sound wave propagation and directivity in the presence of a dome-shaped structure. Authored by Eleazer Bromberg, Richard Courant, K. O. Friedrichs, and J. J. Stoker, this work offers an in-depth exploration of acoustic theory. This text provides a rigorous mathematical treatment suitable for researchers, engineers, and students in acoustics, physics, and applied mathematics. It will appeal to those interested in the theoretical underpinnings of sound behavior in complex environments.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.
Algebra; an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges
"Algebra; an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges" by George Crystal is a comprehensive algebra textbook originally published in 1888. Designed for advanced secondary students and college undergraduates, this book offers a rigorous and thorough exploration of algebraic principles. Its detailed explanations and numerous examples make it an invaluable resource for students seeking a solid foundation in algebra. This edition retains the original content, ensuring that readers can benefit from Crystal's clear and systematic approach to the subject, making it a valuable addition to any mathematics library.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.
First Lessons in Algebra
"First Lessons in Algebra" by Ebenezer Bailey, originally published in 1841, provides a foundational introduction to the principles of algebra. Designed for students encountering algebraic concepts for the first time, this classic text offers a structured approach to learning, emphasizing clear explanations and practical exercises. Bailey's method focuses on building a strong understanding of basic operations and equations, making it an invaluable resource for both students and educators. Though written in the 19th century, the core concepts remain relevant, offering insights into historical teaching methods and the enduring principles of mathematical education. A valuable addition to any mathematics education collection.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 Hybrid Approach to Discrete Mathematical Programming
"A Hybrid Approach to Discrete Mathematical Programming" presents a detailed exploration of methods for solving optimization problems where the variables are restricted to discrete values. This book, authored by Roy Earl Marsten and Thomas L. Morin, delves into the intricacies of combining various techniques to tackle complex mathematical programming challenges. It offers insights into modeling real-world scenarios using discrete variables and designing efficient algorithms to find optimal or near-optimal solutions. This text is valuable for researchers and practitioners in operations research, computer science, and engineering, providing a comprehensive overview of hybrid approaches in discrete optimization.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.
Integral Identities Involving Zonal Polynomials
"Integral Identities Involving Zonal Polynomials" presents a detailed exploration of integral identities within the context of zonal polynomials. This work delves into the mathematical intricacies of these special functions, offering a rigorous treatment suitable for advanced researchers and students in mathematics and statistics. The book focuses on establishing and analyzing various integral identities, providing a valuable resource for those working in multivariate analysis, combinatorics, and related fields. With a focus on theoretical development and mathematical precision, this book offers significant insights into the properties and applications of zonal polynomials.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.
Two-Stage Stochastic Linear Programming With Recourse
The LP recourse problem applies to two-stage optimization problems where uncertainty in resource availability of the second stage hinders informed decision making. The recourse function affords a way to compensate "later" for an error in prediction "now." The literature provides a rich body of work on the optimization of such problems, but little research has been accomplished regarding the characterization of the surface in the local region of optimality, in particular sensitivity analysis. A decision maker faced with considerations other than the modeled objective function must be presented with a way to estimate the impact of operating at non-optimal decision variable values. This work develops and demonstrates a technique for characterizing the surface using response surface methodology. Specifically, the flexibility and utility of RSM techniques applied to this class of problems is demonstrated, and a methodology for characterizing the surface in the local region using a low-order polynomial 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.
A New Sequential Goodness-of-Fit Test for a Family of Two Parameter
The objective of this research is to develop a new goodness-of-fit test for the gamma distribution. The gamma distribution is widely used for reliability and failure time estimations in the real world. Several methods to measure the fit of data to a hypothesized distribution are commonly used such as the chi-squared test, and Anderson-Darling test. The most important aspect of these tests is how well the results reflect the distribution family. This research will use the sequential test with skewness and Q-statistic as test statistics for fitting a gamma distribution. The main idea of a sequential test is that the power of test will be greater than the power of the individual tests. The critical values and significance levels will be created using Monte Carlo simulation. Various power studies against different alternative distributions will be compared to validate the power of the sequential 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.
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.
A Recommendation of Statistical Analysis for Test and Evaluation
This research was intended to provide a consistent analytical approach to test and evaluation procedures for AFOTEC. Particularly, this thesis had a two-pronged focus. The first was a provision of guidance that consisted of a review of key terms and essential steps necessary to achieve sound and accurate system analysis. The second was an upgrade of COBRA software that assists analysts in accomplishing accurate analysis. The analysis and reporting procedure guidance was drawn from an extensive literature review of hypothesis testing and statistical methods used to measure and make inferences about sample parameters. AFOTEC test and evaluation guidelines were also reviewed, specifically the guidance of how test teams should rate measures of performance. The literature review of hypothesis testing and statistical methods were also used to improve COBRA. Finally, a thorough literature review of reliability, key statistical distributions, and confidence bounds were instrumental in COBRA's upgrade. The recommended analysis and reporting procedures were a key result of this research effort. The implementation of the recommended analysis and reporting procedures along with using COBRA as an aid will help to ensure AFOTEC is able to consistently and accurately evaluate the effectiveness and suitability of a system.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.
Parameter Estimation of the Mixed Generalized Gamma Distribution Using Maximum Likelihood Estimation and Minimum Distance Estimation
This research studied parameter estimation of the special cases of the Mixed Generalized Gamma Distribution and built upon them until the full nine-parameter distribution was being estimated. First, special cases of a single Generalized Gamma Distribution were estimated. Next, mixtures of Exponential distributions with both known and unknown location parameters were estimated. Next, mixtures of Weibull distributions with both known and unknown location parameters were estimated. Lastly, the full nine-parameter Mixed Generalized Gamma Distribution was estimated.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.
Statistical Removal of Shadow for Applications to Gait Recognition
The purpose of this thesis is to mathematically remove the shadow of an individual on video. The removal of the shadow will aid in the rendering of higher quality binary silhouettes than previously allowed. These silhouettes will allow researchers studying gait recognition to work with silhouettes unhindered by unrelated data. The thesis begins with the analysis of videos of solid colored backgrounds. A formulation of the effect of shadow on specified colors will aid in the derivation of a hypothesis test to remove an individual's shadow. Video of an individual walking normally, perpendicular to the camera will be utilized to test the algorithm. First, the algorithm replaces shaded pixels, pixel values determined to be shadows, with corresponding pixels of an average background. A hypothesis test will be employed to determine if a pixel value is a shaded pixel. The rejection region for the hypothesis test will be determined from the pixel values of the frames containing a subject. Once the shaded pixels are replaced, the resulting frames will then be run through a background subtraction algorithm and filtered, resulting in a series of binary silhouettes. Researchers can then utilize the series of binary silhouettes to accomplish a gait recognition algorithm.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.
