Adjoint Sensitivity Analysis of High Frequency Structures with MATLAB®

Mohamed H. Bakr

This book presents the theory of adjoint sensitivity analysis for high frequency applications through time-domain electromagnetic simulations in MATLAB®. This theory enables the efficient estimation of the sensitivities of an arbitrary response with respect to all parameters in the considered problem. These sensitivities are required in many applications including gradient-based optimization, surrogate-based modeling, statistical analysis, and yield analysis.

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Advances in Modal Logic, Volume 1

Edited by Marcus Kracht, Maarten de Rijke, Heinrich Wansing, and Michael Zakhary

Modal logic originated in philosophy as the logic of necessity and possibility. Nowadays it has reached a high level of mathematical sophistication and found many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics.
This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It offers an up-to-date perspective on the field, with contributions covering its proof theory, its applications in knowledge representation, computing and mathematics, as well as its theoretical underpinnings.
"This collection is a useful resource for anyone working in modal logic. It contains both interesting surveys and cutting-edge technical results"
--Edwin D. Mares
The Bulletin of Symbolic Logic, March 2002

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African Fractals

Modern Computing and Indigenous Design

Eglash, Ron

Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences.

Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.

Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.

Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

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After Euclid

Jesse Norman

What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In *After Euclid*, Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.

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Against Professors

Sextus Empiricus

**A suspicious mind.**

Sextus Empiricus (ca. AD 160–210), exponent of scepticism and critic of the Dogmatists, was a Greek physician and philosopher, pupil and successor of the medical sceptic Herodotus (not the historian) of Tarsus. He probably lived for years in Rome and possibly also in Alexandria and Athens. His three surviving works are *Outlines of Pyrrhonism* (three books on the practical and ethical scepticism of Pyrrho of Elis, ca. 360–275 BC, as developed later, presenting also a case against the Dogmatists); *Against the Dogmatists* (five books dealing with the Logicians, the Physicists, and the Ethicists); and *Against the Professors* (six books: Grammarians, Rhetors, Geometers, Arithmeticians, Astrologers, and Musicians). These two latter works might be called a general criticism of professors of all arts and sciences. Sextus’ work is a valuable source for the history of thought especially because of his development and formulation of former sceptic doctrines.

The Loeb Classical Library edition of Sextus Empiricus is in four volumes.

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Algebras, Diagrams and Decisions in Language, Logic and Computation

Edited by Kees Vermeulen and Ann Copestake

This exemplary volume shows how the shared interests of three different research areas can lead to significant and fruitful exchanges: six papers each very accessibly present an exciting contribution to the study and uses of algebras, diagrams, and decisions, ranging from indispensable overview papers about shared formal members to inspirational applications of formal tools to specific problems. Contributors include Pieter Adriaans, Sergei Artemov, Steven Givant, Edward Keenan, Almerindo Ojeda, Patrick Scotto di Luzio, and Edward Stabler.

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Algorithmes

Donald E. Knuth

This book is a French translation of seventeen papers by Donald Knuth on algorithms both in the field of analysis of algorithms and in the design of new algorithms. They cover fundamental concepts and techniques and numerous discrete problems such as sorting, searching, data compression, theorem-proving, and cryptography, as well as methods for controlling errors in numerical computations.

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The American and Japanese Auto Industries in Transition

Report of the Joint U.S.–Japan Automotive Study

Robert E. Cole and Taizo Yakushiji, Editors

This report was prepared for the Policy Board by the U.S. and Japanese research staffs of the Joint U.S.–Japan Automotive Study under the general direction of Professors Paul W. McCracken and Keichi Oshima, with research operations organized and coordinated by Robert E. Cole on the U.S. side, in close communication with the Taizo Yakushiji on the Japanese side. [preface]

In view of the importance of stable, long-term economic relationships between Japan and the United States, automotive issues have to be dealt with in ways consistent with the joint prosperity of both countries. Furthermore, the current economic friction has the potential to adversely affect future political relationships. Indeed, under conditions of economic stagnation, major economic issues inevitably become political issues.

With these considerations in mind, the Joint U.S.–Japan Automotive Study project was started in September 1981 to determine the conditions that will allow for the prosperous coexistence of the respective automobile industries. During this two-year study, we have identified four driving forces that will play a major role in determining the future course of the automotive industry of both countries. These are: (1) consumers’ demands and aspirations vis-à-vis automobiles; (2) flexible manufacturing systems (FMS); (3) rapidly evolving technology; and (4) the internationalization of the automotive industry. [exec. summary]

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The Applicability of Mathematics as a Philosophical Problem

Mark Steiner

This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics appears to assign the human mind a special place in the cosmos.

Mark Steiner distinguishes among the semantic problems that arise from the use of mathematics in logical deduction; the metaphysical problems that arise from the alleged gap between mathematical objects and the physical world; the descriptive problems that arise from the use of mathematics to describe nature; and the epistemological problems that arise from the use of mathematics to discover those very descriptions.

The epistemological problems lead to the thesis about the mind. It is frequently claimed that the universe is indifferent to human goals and values, and therefore, Locke and Peirce, for example, doubted science's ability to discover the laws governing the humanly unobservable. Steiner argues that, on the contrary, these laws were discovered, using manmade mathematical analogies, resulting in an anthropocentric picture of the universe as "user friendly" to human cognition--a challenge to the entrenched dogma of naturalism.

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Architecture and Geometry in the Age of the Baroque

George L. Hersey

The age of the Baroque—a time when great strides were made in science and mathematics—witnessed the construction of some of the world's most magnificent buildings. What did the work of great architects such as Bernini, Blondel, Guarini, and Wren have to do with Descartes, Galileo, Kepler, Desargues, and Newton? Here, George Hersey explores the ways in which Baroque architecture, with its dramatic shapes and playful experimentation with classical forms, reflects the scientific thinking of the time. He introduces us to a concept of geometry that encompassed much more than the science we know today, one that included geometrics (number and shape games), as well as the art of geomancy, or magic and prophecy using shapes and numbers.

Hersey first concentrates on specific problems in geometry and architectural design. He then explores the affinities between musical chords and several types of architectural form. He turns to advances in optics, such as artificial lenses and magic lanterns, to show how architects incorporated light, a heavenly emanation, into their impressive domes. With ample illustrations and lucid, witty language, Hersey shows how abstract ideas were transformed into visual, tactile form—the epicycles of the cosmos, the sexual mystique surrounding the cube, and the imperfections of heavenly bodies. Some two centuries later, he finds that the geometric principles of the Baroque resonate, often unexpectedly, in the work of architects such as Frank Lloyd Wright and Le Corbusier. A discussion of these surprising links to the past rounds out this brilliant reexamination of some of the long-forgotten beliefs and practices that helped produce some of Europe's greatest masterpieces.

Hersey first concentrates on specific problems in geometry and architectural design. He then explores the affinities between musical chords and several types of architectural form. He turns to advances in optics, such as artificial lenses and magic lanterns, to show how architects incorporated light, a heavenly emanation, into their impressive domes. With ample illustrations and lucid, witty language, Hersey shows how abstract ideas were transformed into visual, tactile form—the epicycles of the cosmos, the sexual mystique surrounding the cube, and the imperfections of heavenly bodies. Some two centuries later, he finds that the geometric principles of the Baroque resonate, often unexpectedly, in the work of architects such as Frank Lloyd Wright and Le Corbusier. A discussion of these surprising links to the past rounds out this brilliant reexamination of some of the long-forgotten beliefs and practices that helped produce some of Europe's greatest masterpieces.

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Are Changing Constituencies Driving Rising Polarization in the U.S. House of Representatives?

Jesse Sussell

This report addresses two questions: first, whether the spatial distribution of the American electorate has become more geographically clustered over the last 40 years with respect to party voting and socioeconomic attributes; and second, whether this clustering process has contributed to rising polarization in the U.S. House of Representatives.

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Arithmetic

Paul Lockhart

**“Inspiring and informative…deserves to be widely read.”— Wall Street Journal**

—

Because we have ten fingers, grouping by ten seems natural, but twelve would be better for divisibility, and eight is well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.

Paul Lockhart presents arithmetic not as rote manipulation of numbers—a practical if mundane branch of knowledge best suited for filling out tax forms—but as a fascinating, sometimes surprising intellectual craft that arises from our desire to add, divide, and multiply important things. Passionate and entertaining,

“A nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education…Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting.”

—Jonathon Keats,

“What are numbers, how did they arise, why did our ancestors invent them, and how did they represent them? They are, after all, one of humankind’s most brilliant inventions, arguably having greater impact on our lives than the wheel. Lockhart recounts their fascinating story…A wonderful book.”

—Keith Devlin, author of

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Arrow Logic and Multi-Modal Logic

Edited by Maarten Marx, László Pólos, and Michael Masuch

Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program.

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Asset Prices and Monetary Policy

Edited by John Y. Campbell

Economic growth, low inflation, and financial stability are among the most important goals of policy makers, and central banks such as the Federal Reserve are key institutions for achieving these goals. In *Asset Prices and Monetary Policy*, leading scholars and practitioners probe the interaction of central banks, asset markets, and the general economy to forge a new understanding of the challenges facing policy makers as they manage an increasingly complex economic system.

The contributors examine how central bankers determine their policy prescriptions with reference to the fluctuating housing market, the balance of debt and credit, changing beliefs of investors, the level of commodity prices, and other factors. At a time when the public has never been more involved in stocks, retirement funds, and real estate investment, this insightful book will be useful to all those concerned with the current state of the economy.

The contributors examine how central bankers determine their policy prescriptions with reference to the fluctuating housing market, the balance of debt and credit, changing beliefs of investors, the level of commodity prices, and other factors. At a time when the public has never been more involved in stocks, retirement funds, and real estate investment, this insightful book will be useful to all those concerned with the current state of the economy.

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The Asymptotic Developments of Functions Defined by Maclaurin Series

By Walter B. Ford

A publication of the University of Michigan’s Science Series, The Asymptotic Developments of Functions Defined by Maclaurin Series by Walter Burton Ford is an inquiry into the problem of functions defined by Maclaurin series. Here, Ford introduces his own theorem of asymptotic developments, as well as other mathematical theorems, and applies them to mathematical problems. This book was published with the hope of stimulating further research in the field.

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Axiomatics

Mathematical Thought and High Modernism

Alma Steingart

Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics.

For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization.

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