Math Mammoth Grade 7 Tests and Cumulative Reviews, Canadian Version
Analysis with Mathematica(r)
A computer algebra system such as Mathematica(R) is able to do much more than just numerics: This revised text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica(R) represents domains, qualifiers and limits to implement actual proofs - a requirement to unlock the huge potential of Mathematica(R) for a variety of applications.
Probably Overthinking It
An essential guide to the ways data can improve decision making. Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which. Probably Overthinking It uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. He lays out common pitfalls--like the base rate fallacy, length-biased sampling, and Simpson's paradox--and shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world.
The Indisputable Existence of Santa Claus
In The Indisputable Existence of Santa Claus, two distinguished mathematicians explain, with humor and clarity, mathematical concepts through one very merry motif: Christmas. Lighthearted and diverting with Christmasy diagrams, sketches and graphs, equations, Markov chains, and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingsful of mathematical marvels. How do you apply game theory to select who should be on your Christmas shopping list? What equations should you use to decorate the Christmas tree? Will calculations show Santa is getting steadily thinner--shimmying up and down chimneys for a whole night--or fatter--as he munches on cookies and milk in billions of houses across the world? In their quest to provide mathematical proof for the existence of Santa, the authors take readers on a festive journey through a traditional holiday season. Every activity, from wrapping presents to playing board games to cooking the perfect turkey, is analyzed through the lens of math. Because who hasn't always wondered how to set up a mathematically perfect Secret Santa? This book belongs under your Christmas tree if you enjoy a spice of math in your eggnog.
Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3)
Multiple Integrals in Calculus
The book consists of eight chapters, each focusing on different aspects of multiple integrals and related topics in mathematical analysis.In Chapter 1, multiple integrals are defined and developed. The Jordan measure in n-dimensional unit balls is introduced, along with the definition and criteria for multiple integrals, as well as their properties. Chapter 2 delves into advanced techniques for computing multiple integrals. It introduces the Taylor formula, discusses linear maps on measurable sets, and explores the metric properties of differentiable maps. In Chapter 3, we focus on improper multiple integrals and their properties. The chapter deduces criteria for the integrability of functions of several variables and develops concepts such as improper integrals of nonnegative functions, comparison criteria, and absolute convergence. Chapter 4 investigates the Stieltjes integral and its properties. Topics covered include the differentiation of monotone functions of finite variation and the Helly principle of choice, as well as continuous functions of finite variation. Chapter 5 addresses curvilinear integrals, defining line integrals of both the first and second kinds. It also discusses the independence of line integrals from the path of integration. In Chapter 6, surface integrals of the first and second kinds are introduced. The chapter presents the Gauss-Ostrogradsky theorem and Stokes' formulas, along with advanced practical problems to practice these concepts.
Foundations of Numerical Methods and Data Analysis
This book offers a comprehensive journey into the world of numerical methods, beginning with the essential mathematical preliminaries: calculus, vectors, matrices, and programming concepts before moving into deeper areas such as error analysis, curve fitting, interpolation, and the numerical solution of ordinary and partial differential equations. Advanced chapters extend into systems of equations, finite element methods, and spectral techniques, ensuring that readers not only understand the fundamentals but also gain exposure to methods at the frontier of computational practice. A distinguishing feature of the book is the integration of theory with practice. Each concept is accompanied by carefully chosen examples, figures, and end- of-chapter exercises designed to strengthen understanding and encourage hands-on application. Historical notes and bibliographical references enrich the discussion, situating modern numerical methods in their broader intellectual context. In addition, the book pays special attention to the use of contemporary computational tools such as MATLAB, Python, and other numerical libraries, thereby bridging traditional methods with current software-driven practice. In short, it is both a textbook and a reference, meant to serve readers across different stages of their academic or professional journey. For more details, please visit https: //centralwestpublishing.com
Advanced Analytical and Numerical Methods with their Application to Industrial Problems
This book covers the models of different real-world problems that include the models using ordinary and partial differential equations and dynamical systems, uncertainty quantifications using fuzzy systems, computational methods for differential equations, modern control theory and applications, neural networks and neural computing, computational heat and mass transfer and computational fluid dynamics. It also includes various research problems on developing advanced analytical and numerical methods for solving real-world situations, with its theoretical derivations and engineering and science applications. For more details, please visit https: //centralwestpublishing.com
Evidence for Dark Numbers
This book contains several arguments for the existence of dark numbers, i.e., numbers which cannot be manipulated as individuals but only collectively. Their existence depends on the premise of actual infinity. Whether actually infinite sets exist is unknown and cannot be proven; it can only be assumed as an axiom. But if actually infinite sets exist then dark elements are unavoidable. This concept helps to explain many paradoxes of set theory like Zeno's paradox or the paradox of the binary tree or the completely scattered space of the real axis.
Compound Poisson Distributions
This book presents a comprehensive overview of compound Poisson distributions. All of the distributions listed in this book were derived, or invented, by the original authors as ""new"" statistical distributions, to fit a dataset(s) of experimental data. The properties of each newly proposed distribution were derived ab initio, sometimes with much effort by the original authors. Hence the title and motivation for this book: the primary focus here is the compound Poisson distributions themselves. We show that they are all exemplars of a common underlying formalism. General formulas (this includes both exact results and recurrences) are presented which apply to all compound Poisson distributions. In individual chapters, we apply that underlying formalism to selected compound Poisson distributions. We also derive new formulas not published in the literature. Having said the above, this book also presents a new technique for parameter estimation for a set of widely used compound Poisson distributions. The new technique is applied to several published experimental datasets, i.e. real data, not simulations. It yields equal or better fits to the data than those obtained by the original authors (in some cases, significantly better). Numerous graphs are plotted, to demonstrate the good/better fits obtained by the new technique. Hence this book contains not only pure theory, but also visually demonstrates the merits of the new formalism for fitting experimental data.
The Hidden Poetry & Music of Mathematics for Teaching Professionals
When poetry and music are interlinked with mathematics to provide phenomenal strategies to teaching mathematics. This would invite a plethora of thinking beyond classical frames to exceptional intelligent practice for teaching mathematics, including thinking outside classical frames to innovatively and creatively teach mathematics. This book is an open invite to all teaching professionals of mathematics.
Statistics for Composite Indicators
This book provides a systematic and integrated approach to construct measures of complex and multidimensional concepts called composite indicators. One of the most pressing needs of scientists and policy makers is to measure phenomena that are important to our lives in society using numbers, to observe their evolution over time, and to analyse the relationships between them in order to understand the complex reality and decide on the right actions to achieve specific goals. Many socio-economic phenomena, as well as ecological, biological and of other sciences, are multidimensional and, to be measured, require the use of statistical-mathematical techniques that facilitate their reading and use for studies and analyses. This book is a guide to the knowledge and application of statistical tools suitable for the construction of "optimal" composite indicators, i.e. indicators that provide the most accurate measure of multidimensional reality. The book is aimed at all those - statisticians, sociologists, economists, and policy makers - who wish to construct composite indicators to measure and evaluate the complex reality that surrounds us.
Unequal
An exciting "new perspective on equality and difference" (Stephon Alexander) that shows why the familiar equal sign isn't just a marker of sameness but a gateway into math's--and humanity's--most profound questions "Eugenia Cheng has opened up my mind to the wondrous world of pure mathematics in a way that I never thought was possible."―Willow Smith, singer and actress Math is famous for its equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. Much of the time it can seem like that's all mathematics is: following steps to show that what's on one side of an equation is the same as what's on the other. In Unequal, Eugenia Cheng shows that's just part of the story, and the boring part to boot. Mathematics isn't only about showing how numbers and symbols are the same. It isn't even just about numbers and symbols at all, but a world of shapes, symmetries, logical ideas, and more. And in that world, the boundary between things being equal and unequal is a gray area, or perhaps a rainbow of beautiful, vibrant, subtly nuanced color. As Unequal shows, once you go over that rainbow, almost everything can be considered equal and unequal at the same time, whether it's shapes (seen from the right perspective, a circle is the same as an ellipse), words (synonyms), or people--even numbers! It all depends on what features we care about. And it's up to us what we do about it. That's because mathematics isn't a series of rules, facts, or answers. It's an invitation to a more powerful way of thinking.
Artificial Intelligence in Healthcare
The two-volume set constitutes the proceedings of the Second International Conference on Artificial Intelligence in Healthcare, AIiH 2025, which took place in Cambridge, UK, in September 2025. The 60 full papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Health informatics, Personalised Healthcare, Robotics, Assisted Living Technology, Computational Medicine, Long-term Health Conditions, Maternity and Women's Health and Wellbeing.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
Classical Mechanics
Classical Mechanics is a textbook for undergraduate students majoring in Physics (or Mathematics and Physics). The book introduces the main ideas and concepts of Newtonian, Lagrangian, and Hamiltonian mechanics, including the basics of rigid body motion and relativistic dynamics, at an intermediate to advanced level. The physical prerequisites are minimal, with a short primer included in the first chapter. As to the mathematical prerequisites, only a working knowledge of linear algebra, basic multivariate calculus, and the rudiments of ordinary differential equations is expected.Features Numerous exercises and examples A focus on mathematical rigor that will appeal to Physics students wanting to specialize in theoretical physics, or Mathematics students interested in math- ematical physics Sufficient material to service either a one- or two-semester course
Modelling Order and Disorder
Modelling Order and Disorder: Integro-Differential Nonlinear Equations provides an overview of a general mathematical structure: integro-differential nonlinear equations. This mathematical structure provides a unified approach to model complex systems in social sciences, economics, biology, medicine, and other quantitative disciplines. The general aim of the book is to reflect possible organization and disorganization phenomena in the applied sciences, as well as to focus on non-local interactions.Features Applications to social, biological, and physical phenomena Suitable for researchers and post-graduate students Open questions and perspectives on future avenues of research
Master CUNY Math
CUNY(R) Math Mastery: Complete Tutorials & Practice Workbook with 300+ QuestionsYou have arrived!Here is everything you need to pass this tough test!We have helped thousands of students and we can help you! Over 200 CUNY(R) math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! CUNY(R) Math Practice Questions and Tutorials for: Numerical SkillsScientific NotationExponents and Radicals Square RootFractions, Decimals and Percent Algebra World problems with ratio and proportion One and two variable equations quadratic using different methods Translate real world problems into quadratic equa-tions and solve Advanced Algebra Trigonometry Logarithms Sequences Simple Geometry Slope of a line Linear equations from a graph Perimeter, circumference and volume Pythagorean theorem Geometric transformations CUNY(R) is a registered trademark of the City University of New York, who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Banach Algebras and Harmonic Analysis
The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. On the Banach algebra side, the reader will find idempotents and socle of a Banach algebra; closed subspaces of a Banach space, including the classical sequence spaces, which are realized as the kernel of a bounded operator; the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space; spectral synthesis properties in convolution Sobolev algebras on the real line. The harmonic analysis side includes a generalization of the famous Beurling theorem; groups with few finite-dimensional unitary representations; relations between ideals of the Figa-Talamanca Herz algebra of a locally compact group and ideals of Figa-Talamanca Herz algebra of its closed subgroup; the tame functionals on Banach algebras and in harmonic analysis; and cancellation, factorization, and isometries in algebras on a locally compact group. The book also includes four surveys written by leaders in the area of full sheaf cohomology theory for noncommutative C - algebras; one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson.
Partial Differential Equations
Partial Differential Equations: Foundations and Applications offers a clear, precise, and conceptually rich introduction to one of the most fundamental areas of mathematics. Far beyond abstract formalism, partial differential equations form the language through which the laws of nature are expressed, governing phenomena in physics, engineering, and the life sciences - from heat diffusion and wave propagation to fluid motion, electromagnetism, and quantum systems.This volume is designed for undergraduate and postgraduate students in mathematics, physics, and engineering, as well as for motivated self-learners and researchers seeking a unified and reliable reference. It balances mathematical depth with conceptual clarity, integrating theory and application so that abstract methods emerge from physical motivations.This book includes: Fundamental definitions, classification, and formation of partial differential equations First-order partial differential equations: method of characteristics, Lagrange's method, Charpit's method, and applications such as transport equations and Burgers' equation Second-order partial differential equations: classification into hyperbolic, parabolic, and elliptic types, canonical forms, and associated physical models Separation of variables and Sturm-Liouville theory, with orthogonal functions and eigenfunction expansions Fourier series and Fourier transforms, convergence theorems, Parseval's identity, and applications to the heat and wave equations The heat, wave, and Laplace equations in one or more dimensions, steady-state and time-dependent solutions, and coordinate-based techniques Laplace transform methods for problems on semi-infinite domains, impulsive sources, and delta function initial conditions Each chapter is structured to develop both analytical techniques and physical insight, supported by solved examples, graded exercises, and pedagogical explanations. Special attention is given to connecting mathematical derivations with their physical interpretations, ensuring the reader gains not only procedural skill but also a comprehensive insight of the underlying principles of the subject.
A Method of Integrating the Square Roots of Quadratics
"A Method of Integrating the Square Roots of Quadratics" by Henry T. Eddy delves into a specific area of integral calculus prevalent in the late 19th century. This treatise offers a focused examination of techniques for integrating square roots of quadratic expressions, providing a detailed exploration of mathematical methods relevant to the period. Originally published in 1872, this work provides insights into the mathematical practices and challenges of the time, offering a valuable resource for those interested in the history of mathematics and the evolution of calculus. Eddy's approach gives contemporary readers a glimpse into the analytical tools employed by mathematicians of the era.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.
Differential and Integral Calculus, With Applications
"Differential and Integral Calculus, With Applications" offers a comprehensive exploration of calculus as it was understood in the late 19th century. Penned by the esteemed mathematician Sir George Greenhill, this text provides a detailed exposition of both differential and integral calculus, enriched with numerous applications to practical problems. This book is structured to guide the reader through the fundamental principles of calculus, building from basic concepts to more advanced techniques. Readers will appreciate Greenhill's rigorous approach and his commitment to clarity, making this work an invaluable resource for students and scholars alike. This edition preserves the original text's integrity, ensuring that modern readers can access the insights and methods of a bygone era 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.
A Method of Integrating the Square Roots of Quadratics
"A Method of Integrating the Square Roots of Quadratics" by Henry T. Eddy delves into a specific area of integral calculus prevalent in the late 19th century. This treatise offers a focused examination of techniques for integrating square roots of quadratic expressions, providing a detailed exploration of mathematical methods relevant to the period. Originally published in 1872, this work provides insights into the mathematical practices and challenges of the time, offering a valuable resource for those interested in the history of mathematics and the evolution of calculus. Eddy's approach gives contemporary readers a glimpse into the analytical tools employed by mathematicians of the era.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.
Lectures on the Theory of Plane Curves; Delivered to Post-graduate Students in the University of Calcutta
"Lectures on the Theory of Plane Curves" presents a detailed exploration of plane curves as delivered to post-graduate students at the University of Calcutta. Authored by Surendramohan Ganguli, these lectures offer a rigorous treatment of the subject matter, suitable for advanced students and researchers in mathematics. Originally presented in 1919, this work preserves the insights and methodologies of early 20th-century mathematical education. The content focuses on algebraic geometry and the properties of curves, providing a valuable resource for understanding the historical development of mathematical concepts. This book serves not only as a study of plane curves but also as a glimpse into the academic environment of the University of Calcutta during that era. It remains relevant for anyone interested in the foundations of geometric theories and mathematical teaching strategies.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.
Essays in Classical Number Theory
Offering a comprehensive introduction to number theory, this is the ideal book both for those who want to learn the subject seriously and independently, or for those already working in number theory who want to deepen their expertise. Readers will be treated to a rich experience, developing the key theoretical ideas while explicitly solving arithmetic problems, with the historical background of analytic and algebraic number theory woven throughout. Topics include methods of solving binomial congruences, a clear account of the quantum factorization of integers, and methods of explicitly representing integers by quadratic forms over integers. In the later parts of the book, the author provides a thorough approach towards composition and genera of quadratic forms, as well as the essentials for detecting bounded gaps between prime numbers that occur infinitely often.
Trigonometric Transforms for Image Reconstruction
This dissertation demonstrates how the symmetric convolution-multiplication property of discrete trigonometric transforms can be applied to traditional problems in image reconstruction with slightly better performance than Fourier techniques and increased savings in computational complexity for symmetric point spread functions. The fact that the discrete Fourier transform diagonalizes a circulant matrix provides an alternate way to derive the symmetric convolutionmultiplication property for discrete trigonometric transforms. Derived in this manner, the symmetric convolution-multiplication property extends easily to multiple dimensions and generalizes to multidimensional asymmetric sequences. The symmetric convolution-multiplication property allows for linear filtering of degraded images via point-by-point multiplication in the transform domain of trigonometric transforms. Specifically in the transform domain of a type-II discrete cosine transform, there is an asymptotically optimum energy compaction about the lowfrequency indices of highly correlated images which has advantages in reconstructing images with high-frequency noise. The symmetric convolution-multiplication property allows for wellapproximated scalar representations in the trigonometric transform domain for linear reconstruction filters such as the Wiener filter. An analysis of the scalar Wiener filter's improved meansquared error performance in the trigonometric transform domain is given.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Nonlinear Regression Methods for Estimation
Regression techniques are developed for batch estimation and applied to three specific areas, namely, ballistic trajectory launch point estimation, adaptive flight control, and radio-frequency target triangulation. Specifically, linear regression with an intercept is considered in detail. An augmentation formulation is developed. Extensions of theory are applied to nonlinear regression as well. The intercept parameter estimate within the linear regression is used to identify the e ects of trim change that are associated with the occurrence of a control surface failure. These estimates are used to adjust the inner loop control gains via a feed-forward command, hence providing an automatic recon gurable retrim of an aircraft. The regression algorithms are used to consider reduced information applications, such as initial position target determination from bearings-only measurement data. In total, this dissertation develops algorithms for batch processes that broaden the envelope of successful estimation within the three aforementioned application areas. Additionally, the developed batch algorithms do not adversely impact the estimation ability in cases that are already estimated successfully by conventional approaches.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.
Entire Blow-Up Solutions of Semilinear Elliptic Equations and Systems
We examine two problems concerning semilinear elliptic equations. We also give alternative conditions that ensure existence of nonnegative radial solutions blowing up at infinity. Similarly, for systems, we provide conditions on p, q, f and g that guarantee existence of nonnegative solutions on the entire space. In this case, the main requirement for f and g will be closely related to a growth requirement known as the Keller-Osserman condition. Further, we demonstrate the existence of solutions blowing up at infinity and describe a setof initial conditionsthat would generate such solutions. Lastly, we examine several specific equations and systems numerically to graphically demonstrate the results of our analysis.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Primer on Semiconvex Functions in General Potential Theories
This book examines the symbiotic interplay between fully nonlinear elliptic partial differential equations and general potential theories of second order. Starting with a self-contained presentation of the classical theory of first and second order differentiability properties of convex functions, it collects a wealth of results on how to treat second order differentiability in a pointwise manner for merely semicontinuous functions. The exposition features an analysis of upper contact jets for semiconvex functions, a proof of the equivalence of two crucial, independently developed lemmas of Jensen (on the viscosity theory of PDEs) and Slodkowski (on pluripotential theory), and a detailed description of the semiconvex approximation of upper semicontinuous functions. The foundations of general potential theories are covered, with a review of monotonicity and duality, and the basic tools in the viscosity theory of generalized subharmonics, culminating in an account of the monotonicity-duality method for proving comparison principles. The final section shows that the notion of semiconvexity extends naturally to manifolds. A complete treatment of important background results, such as Alexandrov's theorem and a Lipschitz version of Sard's lemma, is provided in two appendices. The book is aimed at a wide audience, including professional mathematicians working in fully nonlinear PDEs, as well as master's and doctoral students with an interest in mathematical analysis.
Recent Progress Numeric Analy Nonlinear Dispersive Equation
This book presents an overview of recent advances in the numerical analysis of nonlinear dispersive partial differential equations (PDEs) -- including the nonlinear Schr繹dinger equation, the Korteweg-de Vries (KdV) equation, and the nonlinear Klein-Gordon equation. These fundamental models are central to mathematical physics and computational PDE theory, and their analysis, both individually and through asymptotic relationships, has become an active and evolving area of research.Recent progress includes the extension of harmonic analysis tools, such as Strichartz estimates and Bourgain spaces, into discrete settings. These innovations have improved the accuracy and flexibility of numerical methods, especially by relaxing regularity assumptions on initial data, potentials, and nonlinearities. Additionally, enhanced long-time numerical estimates now support simulations over substantially longer time intervals, expanding the practical reach of computational models.The analytical breakthroughs that underpin these developments trace back to the seminal work by Jean Bourgain in the 1990s, which introduced powerful techniques for studying dispersive PDEs. Adapting these continuous tools to discrete frameworks has proven both challenging and rewarding, offering new insights into the interface between numerical computation and theoretical analysis.Aimed at graduate students, researchers, and practitioners in numerical analysis, applied mathematics, and computational physics, this volume provides a clear entry point into cutting-edge research, supported by a rich bibliography for further exploration.
Communicating the Quantum Way
The book consists of scientific essays dedicated to A S Holevo on the occasion of his 80th birthday, written by prominent researchers in theoretical-mathematical physics. It is a snapshot of contemporary research at the frontier of quantum information science, work that builds on Holevo's pioneering contributions during the decades of his distinguished career.While a portion of the book are the 15 articles published in a special issue of IJQI, the book contains additional material such as a summary of Holevo's scientific life, with comments on research directions not covered in the 15 articles, and the list of his publications.
Algebra Refresher Workbook for Adults Returning to School
Struggling to remember the algebra you haven't touched since high school-just when that placement test is around the corner?Do you dread being the oldest student in class-only to freeze when the instructor writes 2x + 3 = 9 on the board?⭐️ 1st BONUS: 1-PAGE SCIENTIFIC CALCULATOR GUIDE⭐️ 2nd BONUS: FORMULA SHEET FOR BOOK⭐️ 3rd BONUS: WE'LL SOLVE A PROBLEM FOR YOUIf so, Algebra Refresher Workbook for Adults Returning to School is the reboot every busy learner needs. Drawing on a decade as an engineer and more than 10 years tutoring adult students, Hadden Mendoshek has distilled the most essential algebra skills into a 30-day, 30-worksheet program that fits into coffee breaks-not semesters.Inside this workbook, readers will discover: A complete 30-day road map that guides learners from integers to linear equations without guesswork.300 carefully sequenced problems-each spaced for comfortable, uncluttered work.Step-by-step walkthroughs that model exactly how to solve every type of question.Guided examples that act as an on-page tutor before the learner tries solo practice.Progressively tougher drills that build confidence one small victory at a time.Real-world applications showing how solving for x saves money, time, and stress.Handy reference sheets for formulas, properties, and number rules.Answer key for every problem.Visual aids and graphs for learners who absorb information best through images.....
