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.
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.
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.
Statistical Methods for Image Registration and Denoising
This dissertation describes research into image processing techniques that enhance military operational and support activities. The research extends existing work on image registration by introducing a novel method that exploits local correlations to improve the performance of projection-based image registration algorithms. The dissertation also extends the bounds on image registration performance for both projection-based and full-frame image registration algorithms and extends the Barankin bound from the one-dimensional case to the problem of two-dimensional image registration. It is demonstrated that in some instances, the Cramer-Rao lower bound is an overly-optimistic predictor of image registration performance and that under some conditions, the Barankin bound is a better predictor of shift estimator performance. The research also looks at the related problem of single-frame image denoising using block-based methods. The research introduces three algorithms that operate by identifying regions of interest within a noise-corrupted image and then generating noise free estimates of the regions as averages of similar regions in the image.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.
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.
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.
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.
Statistical Methods for Image Registration and Denoising
This dissertation describes research into image processing techniques that enhance military operational and support activities. The research extends existing work on image registration by introducing a novel method that exploits local correlations to improve the performance of projection-based image registration algorithms. The dissertation also extends the bounds on image registration performance for both projection-based and full-frame image registration algorithms and extends the Barankin bound from the one-dimensional case to the problem of two-dimensional image registration. It is demonstrated that in some instances, the Cramer-Rao lower bound is an overly-optimistic predictor of image registration performance and that under some conditions, the Barankin bound is a better predictor of shift estimator performance. The research also looks at the related problem of single-frame image denoising using block-based methods. The research introduces three algorithms that operate by identifying regions of interest within a noise-corrupted image and then generating noise free estimates of the regions as averages of similar regions in the image.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.
Statistical Methods and Applications in Systems Assurance and Quality
In the era of big data and real-time monitoring, vast amounts of information are generated every second through sensors and advanced tracking systems. The information contained in the data needs to be carefully analyzed and accurate results must be delivered to the users as soon as possible. This book explores the critical role of statistics in modern technologies and applied sciences such as health, informatics, and production systems.Statistical Methods and Applications in Systems Assurance and Quality provides a comprehensive overview of statistical methods for ensuring system quality and reliability. It discusses best practices for improving the quality of manufacturing products by using proper statistical methods. The book covers the current state of statistical methods used for system quality and conveys the importance of healthcare systems and employing statistics in the detection of epidemic outbreaks.Designed for researchers, industry professionals, and academics, this reference is ideal for those working in manufacturing, healthcare, computer engineering, statistical process control, and machine learning applications. It serves as a valuable resource for anyone seeking to enhance system performance through data-driven insights.
Models Demystified
Unlock the Power of Data Science and Machine LearningIn this comprehensive guide, we delve into the world of data science, machinelearning, and AI modeling, providing readers with a robust foundation and practical skills to tackle real-world problems. From basic modeling techniques to advanced machine learning algorithms, this book covers a wide range of topics, ensuring that readers at all levels can benefit from its content. Each chapter is meticulously crafted to offer clear explanations, hands-on examples, and code snippets in both Python and R, making complex concepts accessible and actionable. Additional focus is placed on model interpretation and estimation, common data issues, modeling pitfalls to avoid, and best practices for modeling in general.
Health Metrics and the Spread of Infectious Diseases
Demonstrates how to calculate these metrics to compare the health status of different countries and explores the world of infectious diseases. Tests various machine learning tools for analyzing trends and relationships among key variables, aiming to prevent unexpected outcomes.
Advanced Engineering Mathematics with Matlab(r)
This edition continues to refine a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more practical option to align with the expectations of today's students
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.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author's motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematics New to the second edition Complete solutions to all exercises, and hints for the in-depth investigations Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties A thorough correction of typos and errors across all chapters Updates to the bibliography
The Fundamentals of Fractional Calculus
Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments and the latest research in the field of science, engineering, etc., using fractional calculus.The result of the teaching experiences of the editors and authors to engineering and science students, the volume discusses fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more.Giving a rigorous and thorough analysis of various aspects of fractional calculus, this volume helps scientific readers as well as researchers working in the area of fractional calculus to establish the key steps followed in the research methodology and concept development.
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.
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.
Journal Of The Royal Statistical Society
This volume, "Volume 29" of the "Journal Of The Royal Statistical Society," presents a compilation of articles and discussions from the society's meetings. The journal serves as a key resource for statisticians, researchers, and anyone interested in the application of statistical methods. It covers a broad range of topics within statistical theory and its practical applications across various disciplines. A valuable historical record of statistical thought, this volume provides insight into the development of statistical practices and their impact on society.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 Study Of Matrices, Elementary Divisors, And The Classification Of Collineations
"A Study Of Matrices, Elementary Divisors, And The Classification Of Collineations" offers a rigorous exploration of advanced mathematical concepts. This book delves into the intricacies of matrix theory, providing a detailed analysis of elementary divisors and their applications. A significant portion of the work is dedicated to the classification of collineations, offering a comprehensive understanding of these transformations. Suitable for advanced students and researchers in mathematics, this text provides a thorough treatment of key algebraic topics. Frances Van Meter's work is an invaluable resource for anyone seeking a deeper understanding of matrices and their role in classifying geometric transformations.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.
Tables De La Lune
Tables De La Lune, by J. Ch. Burckhardt, presents a detailed collection of astronomical tables related to the moon's motion. This historical work provides invaluable data for astronomers, navigators, and researchers studying celestial mechanics. The tables offer precise calculations and predictions regarding the moon's position, phases, and related phenomena. A vital resource for understanding the complexities of lunar movement and its impact on various scientific 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.
A Study Of Matrices, Elementary Divisors, And The Classification Of Collineations
"A Study Of Matrices, Elementary Divisors, And The Classification Of Collineations" offers a rigorous exploration of advanced mathematical concepts. This book delves into the intricacies of matrix theory, providing a detailed analysis of elementary divisors and their applications. A significant portion of the work is dedicated to the classification of collineations, offering a comprehensive understanding of these transformations. Suitable for advanced students and researchers in mathematics, this text provides a thorough treatment of key algebraic topics. Frances Van Meter's work is an invaluable resource for anyone seeking a deeper understanding of matrices and their role in classifying geometric transformations.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 Treatise of Practical Arithmetic
"A Treatise of Practical Arithmetic" by Robert Patterson, originally published in 1819, provides a detailed exposition of arithmetical principles and their practical applications. This historical text offers insights into the methods of mathematical instruction prevalent in the early 19th century. Designed for both students and educators, the treatise covers a wide range of topics, offering a comprehensive guide to the arithmetic of its time. It remains valuable for those interested in the history of mathematics education and the evolution of arithmetical practices.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.
Tables De La Lune
Tables De La Lune, by J. Ch. Burckhardt, presents a detailed collection of astronomical tables related to the moon's motion. This historical work provides invaluable data for astronomers, navigators, and researchers studying celestial mechanics. The tables offer precise calculations and predictions regarding the moon's position, phases, and related phenomena. A vital resource for understanding the complexities of lunar movement and its impact on various scientific 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.
Practical Mathematics
"Practical Mathematics, Volume 4: Being The Essentials Of Arithmetic, Geometry, Algebra And Trigonometry" offers a comprehensive overview of fundamental mathematical principles. Designed for practical application, this volume provides readers with a solid foundation in arithmetic, geometry, algebra, and trigonometry. Claude Irwin Palmer presents mathematical concepts in a clear, accessible manner, making this book an invaluable resource for students, educators, and anyone seeking to enhance their understanding of essential mathematical skills. The book emphasizes practical application and problem-solving, ensuring that readers can confidently apply their knowledge in real-world scenarios. Whether you're a student looking to solidify your understanding or a professional seeking a refresher, this volume offers a valuable guide to mastering the essentials 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.
Elementary Algebra. To Which Is Now Added An Appendix
"Elementary Algebra. To Which Is Now Added An Appendix" by James Hamblin Smith is a comprehensive algebra textbook designed for students seeking a solid foundation in algebraic principles. This edition includes an appendix, enhancing its value as a learning resource. The book provides a clear and methodical approach to understanding algebraic concepts, making it suitable for both classroom use and self-study. Its detailed explanations and numerous examples help to reinforce learning and build confidence in problem-solving. This textbook remains a valuable resource for anyone studying elementary 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.
The Perpetual Time Calculator, For Ascertaining The Number Of Days From Any Given Day To Any Other Within The Year
Unlock the secrets of time with "The Perpetual Time Calculator," an invaluable resource for quickly ascertaining the number of days between any two dates within the same year. This meticulously crafted reference tool offers a straightforward method for anyone needing to calculate durations, plan events, or manage schedules efficiently.Originally designed for ease of use, the calculator presents its data in a clear, accessible format, making it suitable for students, professionals, and anyone with an interest in practical mathematics and calendrical calculations. Discover the enduring utility of this timeless tool, perfect for both historical research and everyday 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.
Comparative Analysis of the Fink, Murphy, Bollman and Triangular
"Comparative Analysis of the Fink, Murphy, Bollman and Triangular" presents a rigorous examination of these mathematical models. Authored by C Shaler Smith, this work delves into the theoretical underpinnings and practical applications of each model, offering a detailed comparison of their strengths and weaknesses. This book is an essential resource for researchers, academics, and students seeking a comprehensive understanding of these mathematical concepts.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.
Tables Of Logarithms, For All Numbers From 1 To 102100
"Tables Of Logarithms, For All Numbers From 1 To 102100, And For The Sines And Tangents To Every Ten Seconds Of Each Degree In The Quadrant" is a comprehensive mathematical resource compiled by William Gardiner. This meticulously calculated volume provides logarithmic values for an extensive range of numbers, offering accuracy and detail essential for scientific, engineering, and mathematical applications. Originally published in the era of manual computation, this book stands as a testament to the dedication and precision of early mathematicians. It remains a valuable reference for historians of science, educators, and anyone with an interest in the evolution of mathematical tools and methods. Explore the enduring utility of logarithmic tables in this detailed and carefully constructed work.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.
Practical Mathematics
"Practical Mathematics, Volume 4: Being The Essentials Of Arithmetic, Geometry, Algebra And Trigonometry" offers a comprehensive overview of fundamental mathematical principles. Designed for practical application, this volume provides readers with a solid foundation in arithmetic, geometry, algebra, and trigonometry. Claude Irwin Palmer presents mathematical concepts in a clear, accessible manner, making this book an invaluable resource for students, educators, and anyone seeking to enhance their understanding of essential mathematical skills. The book emphasizes practical application and problem-solving, ensuring that readers can confidently apply their knowledge in real-world scenarios. Whether you're a student looking to solidify your understanding or a professional seeking a refresher, this volume offers a valuable guide to mastering the essentials 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.
Elements Of Spherical Trigonometry
"Elements of Spherical Trigonometry" by Augustus De Morgan is a comprehensive exploration of spherical trigonometry, designed for students and educators alike. This book provides a detailed examination of the principles and applications of trigonometry on the surface of a sphere, a crucial area of study for fields such as astronomy, navigation, and geodesy. De Morgan's clear and rigorous approach makes this text an invaluable resource for anyone seeking a solid understanding of this essential branch of mathematics.With meticulous explanations and numerous examples, this work serves as both a textbook and a reference guide. Its enduring value lies in its ability to demystify complex concepts, making it accessible to learners at various levels. Whether you are a student delving into the intricacies of spherical geometry or a professional requiring precise calculations on a spherical surface, this book offers the necessary tools and 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.
A Course of Mathematics
A Course of Mathematics, designed for the use of officers and cadets at the Royal Military College, presents a comprehensive two-volume exploration of essential mathematical principles. Authored by Isaac Dalby, this meticulously structured course provides a solid foundation in mathematics, tailored for military applications. From fundamental concepts to advanced techniques, the volumes cover a wide range of topics, including algebra, geometry, trigonometry, and calculus. This historic text offers a unique glimpse into the mathematical education provided to military personnel in the 19th century. Its detailed explanations and practical examples make it a valuable resource for anyone interested in the history of mathematics education or the application of mathematical principles in military contexts. "A Course of Mathematics" remains a testament to the importance of mathematical proficiency in military training and strategic thinking.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.
Archiv Der Mathematik Und Physik
Archiv Der Mathematik Und Physik, Volume 23 presents a comprehensive collection of articles and discussions from the Berliner Mathematische Gesellschaft. This volume offers valuable insights into the mathematical and physical sciences as understood and developed during the period it was published. Featuring contributions from leading scholars and researchers of the time, the book covers a wide range of topics, reflecting the state-of-the-art in mathematical theories and physical experiments. Readers interested in the history of science, particularly the evolution of mathematical and physical thought, will find this volume an essential resource. The detailed expositions and rigorous analyses make "Archiv Der Mathematik Und Physik" a significant historical document, preserving the intellectual landscape of its era and showcasing the foundations upon which modern science was built.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.
Recent Developments in Spectral and Approximation Theory
The Messenger Of Mathematics
"The Messenger of Mathematics, Volume 20" is a historical record of mathematical thought and discovery. Authored by James Whitbread Lee Glaisher, this volume presents a collection of articles and notes on various mathematical topics. It offers a glimpse into the mathematical landscape of the late 19th century.This compilation is valuable for historians of science, mathematicians, and anyone interested in the evolution of mathematical ideas. The articles cover a range of subjects, reflecting the diverse interests and ongoing research within the mathematical community of the time.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.
The American Mathematical Monthly
Explore the rich history and contemporary developments in mathematics with "The American Mathematical Monthly, Volume 25." This official journal of the Mathematical Association of America offers a diverse collection of articles, discussions, and problems that cater to a wide audience, from students to seasoned mathematicians. Published by the Mathematical Association of America, this volume continues the journal's tradition of providing accessible and insightful content. Delve into thought-provoking essays, innovative solutions, and historical perspectives that highlight the beauty and complexity of mathematics. Whether you are an educator looking for fresh material or a mathematics enthusiast eager to expand your knowledge, "The American Mathematical Monthly" provides valuable insights and fosters a deeper appreciation for the mathematical sciences.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.
Practical Mathematics Part Iv
"Practical Mathematics Part IV: Trigonometry and Logarithms" offers a comprehensive exploration of these essential mathematical concepts. Designed for practical application, this book provides clear explanations and numerous examples to aid understanding. Beginning with the fundamentals of trigonometry, it progresses through trigonometric functions, identities, and their applications in solving real-world problems. The section on logarithms covers their properties, computations, and uses in various fields. This book is a valuable resource for students, engineers, and anyone seeking a solid foundation in trigonometry and logarithms.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 Messenger Of Mathematics
"The Messenger of Mathematics, Volume 20" is a historical record of mathematical thought and discovery. Authored by James Whitbread Lee Glaisher, this volume presents a collection of articles and notes on various mathematical topics. It offers a glimpse into the mathematical landscape of the late 19th century.This compilation is valuable for historians of science, mathematicians, and anyone interested in the evolution of mathematical ideas. The articles cover a range of subjects, reflecting the diverse interests and ongoing research within the mathematical community of the time.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.
Graph Neural Networks: Essentials and Use Cases
This book explains the technologies and tools that underpin GNNs, offering a clear and practical guide to their industrial applications and use cases. AI engineers, data scientists, and researchers in AI and graph theory will find detailed insights into the latest trends and innovations driving this dynamic field. With practical chapters demonstrating how GNNs are reshaping various industry verticals--and how they complement advances in generative, agentic, and physical AI--this book is an essential resource for understanding and leveraging their potential. The neural network paradigm has surged in popularity for its ability to uncover hidden patterns within vast datasets. This transformative technology has spurred global innovations, particularly through the evolution of deep neural networks (DNNs). Convolutional neural networks (CNNs) have revolutionized computer vision, while recurrent neural networks (RNNs) and their advanced variants have automated natural language processing tasks such as speech recognition, translation, and content generation. Traditional DNNs primarily handle Euclidean data, yet many real-world problems involve non-Euclidean data--complex relationships and interactions naturally represented as graphs. This challenge has driven the rise of graph neural networks (GNNs), an approach that extends deep learning into new domains. GNNs are powerful models designed to work with graph-structured data, where nodes represent individual data points and edges denote the relationships between them. Several variants have emerged: Graph Convolutional Networks (GCNs): These networks learn from a node's local neighborhood by aggregating information from adjacent nodes, updating the node's representation in the process. Graph Attentional Networks (GATs): By incorporating attention mechanisms, GATs focus on the most relevant neighbors during aggregation, enhancing model performance. Graph Recurrent Networks (GRNs): These networks combine principles from RNNs with graph structures to capture dynamic relationships within the data. GNNs are applied in a variety of advanced use cases, including node classification, link prediction, graph clustering, anomaly detection, recommendation systems, and also in natural language processing and computer vision. They help forecast traffic patterns, analyze molecular structures, verify programs, predict social influence, model electronic health records, and map brain networks.
The American Mathematical Monthly
Explore the rich history and contemporary developments in mathematics with "The American Mathematical Monthly, Volume 25." This official journal of the Mathematical Association of America offers a diverse collection of articles, discussions, and problems that cater to a wide audience, from students to seasoned mathematicians. Published by the Mathematical Association of America, this volume continues the journal's tradition of providing accessible and insightful content. Delve into thought-provoking essays, innovative solutions, and historical perspectives that highlight the beauty and complexity of mathematics. Whether you are an educator looking for fresh material or a mathematics enthusiast eager to expand your knowledge, "The American Mathematical Monthly" provides valuable insights and fosters a deeper appreciation for the mathematical sciences.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 Arthur Cayley
This is Volume 2 of the collected mathematical papers of Arthur Cayley, a prominent 19th-century British mathematician. Cayley's work spanned numerous areas of mathematics, making significant contributions to algebra, geometry, and number theory. This volume contains a selection of his papers, offering insights into the mathematical landscape of his time.Researchers and students of mathematics will find this collection a valuable resource for understanding the historical development of mathematical thought. Cayley's rigorous approach and innovative ideas continue to resonate with mathematicians today, making "The Collected Mathematical Papers" a timeless contribution 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 Arthur Cayley
This is Volume 2 of the collected mathematical papers of Arthur Cayley, a prominent 19th-century British mathematician. Cayley's work spanned numerous areas of mathematics, making significant contributions to algebra, geometry, and number theory. This volume contains a selection of his papers, offering insights into the mathematical landscape of his time.Researchers and students of mathematics will find this collection a valuable resource for understanding the historical development of mathematical thought. Cayley's rigorous approach and innovative ideas continue to resonate with mathematicians today, making "The Collected Mathematical Papers" a timeless contribution 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.
Computational Statistics - Predicting the Future from Sample Data
How can we uncover hidden patterns in noisy, complex data? How can we make reliable predictions in an unpredictable world? And how can the combination of statistical theory, data from diverse sources, and increased computing power help us predict the future? In this age of data, and especially big data, computational statistics has become central to scientific discovery and decision-making. Therefore, this book explores the growing role of computational methods in statistical analysis, highlighting how we can transform sample data into meaningful predictions across various disciplines and domains. This volume brings together five chapters, each of which addresses a unique aspect of modern computational statistics and is ideal for statisticians, data scientists, university professors, graduate students, and researchers who seek to deepen their knowledge of computational statistics and its impact on the real world.
