![The Elements of Euclid for the Use of Schools and Colleges [microform]](https://cdn.kingstone.com.tw/english/images/product/9409/9781013899409m.webp "The Elements of Euclid for the Use of Schools and Colleges [microform]")
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.
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.
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.
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.
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.
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.
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.
Pattern Search Ranking and Selection Algorithms for Mixed-Variable Optimization of Stochastic Systems
A new class of algorithms is introduced and analyzed for bound and linearly constrained optimization problems with stochastic objective functions and a mixture of design variable types. The generalized pattern search (GPS) class of algorithms is extended to a new problem setting in which objective function evaluations require sampling from a model of a stochastic system. The approach combines GPS with ranking and selection (RS) statistical procedures to select new iterates. The derivative-free algorithms require only black-box simulation responses andare applicable over domains withmixedvariables (continuous, discrete numeric, and discrete categorical)to include bound and linear constraints on the continuous variables. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Additionally, specific algorithm instances are implemented that provide computational enhancements to the basic algorithm. Implementation alternatives include the use of modern RS procedures designed to provide efficientsamplingstrategies andthe use of surrogate functions that augment the search by approximating the unknown objective function with nonparametric response surfaces. In a computational evaluation, six variants of the algorithm are tested along with four competing methods on 26 standardized test problems. The numerical results validate the use of advanced implementations as a means to improve algorithm performance.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 Treatise on Plane Trigonometry, Containing an Account of Hyperbolic Functions; With Numerous Examples
"A Treatise on Plane Trigonometry, Containing an Account of Hyperbolic Functions; With Numerous Examples" is a comprehensive exploration of plane trigonometry, enriched with detailed coverage of hyperbolic functions. Written by John Casey and originally published in 1888, this treatise is designed to provide a thorough understanding of trigonometric principles and their application. The book includes numerous examples to aid comprehension and mastery of the subject matter. This classic work is an invaluable resource for students, educators, and anyone seeking a rigorous treatment of plane trigonometry and hyperbolic functions. Its enduring value lies in its clear explanations and comprehensive approach, making it a useful addition to any mathematical 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.
A Group Theoretic Tabu Search Approach to the Traveling Salesman Problem
The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, Sn, which is the set of all n! permutations on n letters whose binary operation is permutation multiplication, to describe the TSP solution space. Thus, the TSP is studied as a permutation problem rather than an integer program by applying the principles of group theory to define the tabu search move and neighborhood structure. The group theoretic concept of conjugation (an operation involving two group elements) simplifies the move definition as well as the intensification and diversification strategies. Conjugation in GTTS diversifies the search by allowing large rearrangement moves within a tour in a single move operation. Empirical results are presented along with the theoretical motivations for the research.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.
Shortest Path Problems in a Stochastic and Dynamic Environment
In this research, we consider stochastic and dynamic transportation network problems. Particularly, we develop a variety of algorithms to solve the expected shortest path problem in addition to techniques for computing the total travel time distribution along a path in the network. First, we develop an algorithm for solving an independent expected shortest path problem. Next, we incorporate the inherent dependencies along successive links in two distinct ways to find the expected shortest path. Since the dependent expected shortest path problem cannot be solved with traditional deterministic approaches, we develop a heuristic based on the K-shortest path algorithm for this dependent stochastic network problem. Additionally, transient and asymptotic versions of the problem are considered. An algorithm to compute a parametric total travel time distribution for the shortest path is presented along with stochastically shortest path measures. The work extends the current literature on such problems by considering interactions on adjacent links.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.
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.
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.
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 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.
Consistency Results for the ROC Curves of Fused Classifiers
The U.S. Air Force is researching the fusion of multiple classifiers. Given a finite collection of classifiers one seeks a new fused classifier with improved performance. An established performance quantifier is the Receiver Operating Characteristic (ROC) curve, which allows one to view the probability of detection versus the probability of false alarm in one graph. Previous research shows that one does not have to perform tests to determine the ROC curve of this new fused classifier. If the ROC curve for each individual classifier has been determined, then formulas for the ROC curve of the fused classifier exist for certain fusion rules. This will be an enormous saving in time and money since the performance of many fused classifiers can be determined analytically. In reality only finite data is available so only an estimated ROC curve can be constructed. It has been proven that estimated ROC curves will converge to the true ROC curve in probability. This research examines if convergence is preserved when these estimated ROC curves are fused. It provides a general result for fusion rules that are governed by a Lipschitz continuous ROC fusion function and establishes a metric that can be used to prove this convergence.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Traveling Salesman Problem for Surveillance Mission Using Particle Swarm Optimization
The surveillance mission requires aircraft to fly from a starting point through defended terrain to targets and return to a safe destination (usually the starting point). The process of selecting such a flight path is known as the Mission Route Planning (MRP) Problem and is a three-dimensional, multi-criteria (fuel expenditure, time required, risk taken, priority targeting, goals met, etc.) path search. Planning aircraft routes involves an elaborate search through numerous possibilities, which can severely task the resources of the system being used to compute the routes. Operational systems can take up to a day to arrive at a solution due to the combinatoric nature of the problem. This delay is not acceptable because timeliness of obtaining surveillance information is critical in many surveillance missions. Also, the information that the software uses to solve the MRP may become invalid during computation. An effective and efficient way of solving the MRP with multiple aircraft and multiple targets is desired. One approach to funding solutions is to simplify and view the problem as a two-dimensional, minimum path problem.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Cross-Resolution Combat Model Calibration Using Bootstrap Sampling
The US Air Force uses many combat simulation models to assist them in performing combat analyses. BRAWLER is a high-resolution air-to-air combat simulation model used for engagement-level analyses of few-on-few air combat. THUNDER is a low-resolution combat simulation model used for campaign-level analyses of theater-level warfare. BRAWLER is frequently used to ensure that THUNDER air-to-air inputs are valid. This thesis describes the confederation of THUNDER and BRAWLER by clearly showing how one particular BRAWLER output, the effectiveness of a missile type, is transformed into THUNDER air-to-air input data. Since BRAWLER is a stochastic simulation model, it is necessary to replicate a number of BRAWLER simulation runs in order to obtain a sufficiently accurate estimate of the mean missile effectiveness, a number that varies for each different BRAWLER combat scenario. This thesis focuses on using two different sequential methods to determine when the minimum number of BRAWLER runs has been performed to obtain a specified relative precision. One method uses classical statistical analysis techniques, while the other uses the more modern technique of bootstrap resampling. The performance of these two methods is compared.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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.
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.
A Group Theoretic Tabu Search Approach to the Traveling Salesman Problem
The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, Sn, which is the set of all n! permutations on n letters whose binary operation is permutation multiplication, to describe the TSP solution space. Thus, the TSP is studied as a permutation problem rather than an integer program by applying the principles of group theory to define the tabu search move and neighborhood structure. The group theoretic concept of conjugation (an operation involving two group elements) simplifies the move definition as well as the intensification and diversification strategies. Conjugation in GTTS diversifies the search by allowing large rearrangement moves within a tour in a single move operation. Empirical results are presented along with the theoretical motivations for the research.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 Empirical Study of Re-Sampling Techniques as a Method for Improving Error Estimates in Split-Plot Designs
For any acquisition program, whether Department of Defense (DOD) or industry related, the primary driving factor behind the success of a program is whether or not the program remains within budget, stays on schedule and meets the defined performance requirements. If any of these three criteria are not met, the program manager may need to make challenging decisions. Typically, if the program is expected to not stay within budget or is expected to be delayed for one reason or another, the program manager will tend to limit areas of testing in order to meet these criteria. The result tends to be a reduction in the test budget and/or a shortening in the test timeline, both of which are already lean. The T and E community needs new test methodologies to test systems and gain insight on whether a system meets performance standards, within the budget and timeline constraints. In particular, both fundamental and advanced aspects of experimental design need to be adapted. The use of experiential design within DOD has continued to grow because of the needed adaptation. Many different types of experiments have been used. An experimental design that is often needed is one that involves a restricted randomization design such as a split-plot design. Split-plot designs arise when specific factors are difficult (or impossible) to vary, a frequent occurrence within the T and E community.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.
Change-Point Methods for Overdispersed Count Data
A control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the searchforand identification of the assignable cause. In this research, emphasis is placed on count processes where overdispersion has occurred. Overdispersion is common in practice and occurs when the observed variance is larger than the theoretical variance of the assumed model. Although the Poisson model is often used to model count data, the two parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data. In this research effort, maximum likelihood estimators for the time of a step change in each of the parameters of the gamma-Poisson mixture model are derived. MonteCarlo simulation is used to evaluate the rootmean square error performance of these estimators to determine their utility in estimating the change point, following a control chart signal. Results show that the estimators provide process engineers with accurate and useful estimates for the time of step change. In addition, an approach for estimating a confidence set for the process change point will be presented.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.
Change-Point Methods for Overdispersed Count Data
A control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the searchforand identification of the assignable cause. In this research, emphasis is placed on count processes where overdispersion has occurred. Overdispersion is common in practice and occurs when the observed variance is larger than the theoretical variance of the assumed model. Although the Poisson model is often used to model count data, the two parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data. In this research effort, maximum likelihood estimators for the time of a step change in each of the parameters of the gamma-Poisson mixture model are derived. MonteCarlo simulation is used to evaluate the rootmean square error performance of these estimators to determine their utility in estimating the change point, following a control chart signal. Results show that the estimators provide process engineers with accurate and useful estimates for the time of step change. In addition, an approach for estimating a confidence set for the process change point will be presented.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.
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.
Shortest Path Problems in a Stochastic and Dynamic Environment
In this research, we consider stochastic and dynamic transportation network problems. Particularly, we develop a variety of algorithms to solve the expected shortest path problem in addition to techniques for computing the total travel time distribution along a path in the network. First, we develop an algorithm for solving an independent expected shortest path problem. Next, we incorporate the inherent dependencies along successive links in two distinct ways to find the expected shortest path. Since the dependent expected shortest path problem cannot be solved with traditional deterministic approaches, we develop a heuristic based on the K-shortest path algorithm for this dependent stochastic network problem. Additionally, transient and asymptotic versions of the problem are considered. An algorithm to compute a parametric total travel time distribution for the shortest path is presented along with stochastically shortest path measures. The work extends the current literature on such problems by considering interactions on adjacent links.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A First Course in Algebra
"A First Course in Algebra," originally published in 1908, offers a comprehensive introduction to algebraic principles and problem-solving techniques. Designed for students beginning their study of algebra, this text provides a systematic approach to understanding fundamental concepts. Webster Wells, a prominent mathematics educator, presents clear explanations and numerous examples to aid comprehension. The book covers essential topics such as equations, polynomials, factoring, and radicals, laying a solid foundation for further mathematical studies. This edition retains the original content, ensuring that readers experience the timeless methods of teaching algebra that have proven effective for generations. This book is valuable for students, educators, and anyone interested in the historical development of mathematical education.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Exercises and Solutions in Probability and Statistics
The book contains hundreds of engaging, class-tested statistics exercises (and detailed solutions) that test students' understanding of the material. Many are educational in their own right--for example, baseball managers who played professional ball were often catchers; stocks that are deleted from the Dow Jones Industrial Average have generally done better than the stocks that replaced them; athletes may not get hot hands but they often get warm hands with modest improvements in their success probabilities.
Pattern Search Ranking and Selection Algorithms for Mixed-Variable Optimization of Stochastic Systems
A new class of algorithms is introduced and analyzed for bound and linearly constrained optimization problems with stochastic objective functions and a mixture of design variable types. The generalized pattern search (GPS) class of algorithms is extended to a new problem setting in which objective function evaluations require sampling from a model of a stochastic system. The approach combines GPS with ranking and selection (RS) statistical procedures to select new iterates. The derivative-free algorithms require only black-box simulation responses andare applicable over domains withmixedvariables (continuous, discrete numeric, and discrete categorical)to include bound and linear constraints on the continuous variables. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Additionally, specific algorithm instances are implemented that provide computational enhancements to the basic algorithm. Implementation alternatives include the use of modern RS procedures designed to provide efficientsamplingstrategies andthe use of surrogate functions that augment the search by approximating the unknown objective function with nonparametric response surfaces. In a computational evaluation, six variants of the algorithm are tested along with four competing methods on 26 standardized test problems. The numerical results validate the use of advanced implementations as a means to improve algorithm performance.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 Inequalities Volume 1
This is Volume 1 of the five-volume book Mathematical Inequalities, that introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
Mathematical Inequalities Volume 5
This is Volume 5 of the five-volume book Mathematical Inequalities, which introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
Scientific Research and Methodology
This textbook is designed for teaching quantitative research in the scientific, health and engineering disciplines at first-year undergraduate level, with an emphasis on statistics. It covers the research process, including asking research questions, research design, data collection, summarising data, analysis and communication. Many real journal articles are used throughout the text as examples that demonstrate the use of the techniques.Students are introduced to statistics as a method for answering questions. Descriptive research questions lead to analysis of single proportions and means. Repeated-measures research questions are answered using paired quantitative data. Relational research questions compare proportions, odds and means in different groups. Correlational research questions are studied using correlation and regression techniques.Statistical topics include numerical summary methods (such as means, odds ratios and identification of outliers), graphing (such as histograms, case-profile plots and scatterplots), confidence intervals and hypothesis testing. Emphasis is placed on understanding and concepts; while calculations are shown in simple situations, they are deferred to software when the computations become tedious and disruptive to understanding.Almost every dataset used is a real dataset, and is available online or in an associated R package SRMData. Software output is often used when calculations become onerous. The output is sufficiently generic that the book can be used in conjunction with any statistical software.
Mathematical Inequalities Volume 3
This is Volume 3 of the five-volume book Mathematical Inequalities, which introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
Mathematical Inequalities Volume 2
This is Volume 2 of the five-volume book Mathematical Inequalities, which introduces and develops the main types of elementary inequalities. The first three volumes are a great opportunity to look into many old and new inequalities, as well as elementary procedures for solving them: Volume 1 - Symmetric Polynomial Inequalities, Volume 2 - Symmetric Rational and Nonrational Inequalities, Volume 3 - Cyclic and Noncyclic Inequalities. As a rule, the inequalities in these volumes are increasingly ordered according to the number of variables: two, three, four, ..., n-variables. The last two volumes (Volume 4 - Extensions and Refinements of Jensen's Inequality, Volume 5 - Other Recent Methods for Creating and Solving Inequalities) present beautiful and original methods for solving inequalities, such as Half/Partial convex function method, Equal variables method, Arithmetic compensation method, Highest coefficient cancellation method, pqr method etc. The book is intended for a wide audience: advanced middle school students, high school students, college and university students, and teachers. Many problems and methods can be used as group projects for advanced high school students.
First Course in the Theory of Equations
Unlock the mysteries of algebra with "First Course in the Theory of Equations," a timeless gem that has been out of print for decades and is now beautifully restored by Alpha Editions for today's and future generations. This edition is not just a reprint it's a collector's item and a cultural treasure, inviting both casual readers and classic literature enthusiasts to delve into the world of mathematical theory. This inspiring book serves as an essential guide to understanding algebraic equations and advanced algebra concepts. It offers readers a solid foundation in equation solving techniques and mathematical problem-solving, making it an invaluable resource for students and educators alike. With clear explanations and engaging examples, it empowers readers to embrace the beauty of mathematical analysis and introductory mathematics. As you turn the pages, you ll discover the historical significance of this work, which has shaped the landscape of STEM education resources. It s an invitation to explore the elegance of equations and the thrill of discovery in the realm of mathematics. Don t miss your chance to own this restored classic that bridges the gap between past and present. Dive into "First Course in the Theory of Equations" and experience the joy of learning that transcends generations.
Proof Complexity Generators
The P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use. This is the foundational problem (the NP vs. coNP problem) of proof complexity, an area linking mathematical logic and computational complexity theory. Written by a leading expert in the field, this book presents a theory for constructing such hard tautologies. It introduces the theory step by step, starting with the historic background and a motivational problem in bounded arithmetic, before taking the reader on a tour of various vistas of the field. Finally, it formulates several research problems to highlight new avenues of research.
Differential Geometry
This book, Differential Geometry: Advanced Topics in CR and Pseudohermitian Geometry (Book I-D), is the fourth in a series of four books presenting a choice of advanced topics in Cauchy-Riemann (CR) and pseudohermitian geometry, such as Fefferman metrics, global behavior of tangential CR equations, Rossi spheres, the CR Yamabe problem on a CR manifold-with-boundary, Jacobi fields of the Tanaka-Webster connection, the theory of CR immersions versus Lorentzian geometry. The book also discusses boundary values of proper holomorphic maps of balls, Beltrami equations on Rossi spheres within the Koranyi-Reimann theory of quasiconformal mappings of CR manifolds, and pseudohermitian analogs to the Gauss-Ricci-Codazzi equations in the study of CR immersions between strictly pseudoconvex CR manifolds. The other three books of the series are: Differential Geometry: Manifolds, Bundles, Characteristic Classes (Book I-A) Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B) Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C) The four books belong to an ampler book project, "Differential Geometry, Partial Differential Equations, and Mathematical Physics", by the same authors and aim to demonstrate how certain portions of differential geometry (DG) and the theory of partial differential equations (PDEs) apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG and PDEs machinery yet do not constitute a comprehensive treatise on DG or PDEs, but rather authors' choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions--isometric, holomorphic, and CR--and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
Variational and Information Flows in Machine Learning and Optimal Transport
The Asymptotic Behavior of Porous Systems
This book presents a rigorous and comprehensive treatment of the mathematical theory and real-world applications of porous systems, with a special focus on their asymptotic behavior. It combines analytical, numerical, and computational perspectives to bridge fundamental science and engineering applications, making it relevant to mathematicians, physicists, engineers, and material scientists. It also synthesizes the mathematical foundations, modeling strategies, and engineering practices of porous media systems with asymptotic behavior as a unifying theme, which empowers the readers to model, analyze, and design next-generation porous systems across diverse disciplines.
Inverse Problems: Modelling and Simulation
This volume presents the latest theoretical and experimental advancements in the field of inverse problems in recent years. It includes outstanding research results that reflect current theoretical and numerical aspects of inverse problems and their various applications. The volume is a collection of selected contributions from nearly three hundred invited presentations at the International Conference "Inverse Problems: Modelling and Simulation" (IPMS 2024) held from May 26 to June 1, 2024, in Malta. The topics covered in this volume are closely related to emerging deterministic and stochastic models in the fields of medical imaging, biology, geophysics, radar, computer science, communication theory, signal processing, visualization, engineering, and economics. The contributions in this volume reflect a broad range of problems in the theory and applications of inverse problems that are useful for mathematicians, physicists, engineers, and researchers working with inverse problems.
