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Physics from Planet Earth - An Introduction to Mechanics provides a one-semester, calculus-based introduction to classical mechanics for first-year undergraduate students studying physics, chemistry, astronomy, or engineering. Developed from classroom-tested materials refined and updated for over ten years at Colgate University, the book guides students on a journey beyond standard approaches that use blocks, projectiles, and inclined planes to grander themes involving interplanetary travel, exoplanets, asteroid collisions, and dark matter.

Beginning students are often bewildered by the rapid-fire presentation of physical concepts, mathematics, and problem-solving strategies in traditional introductory textbooks. In contrast, this text:

Introduces the three conservation laws (momentum, energy, and angular momentum) as fundamental laws of nature from which secondary concepts, such as force and torque, are derived Organizes topics around the conservation laws, avoiding the typical "math overload" that confronts students at the start of standard courses Motivates and illustrates many topics through real, contemporary applications in astronomy, planetary science, and space travelAfter reviewing the basic mathematical tools needed to study mechanics, the text addresses the conservation of momentum and applications, such as gravity-assisted space travel and rocket propulsion. It next discusses Newton’s Laws and numerous space- and astronomy-based applications. The text then presents evidence for a second conservation principle, energy, which allows us to describe motion as a function of position rather than time. The book also explores the conservation of angular momentum and a variety of applications, including pulsars, orbital eccentricity, and gyroscopes. The text concludes with a discussion of dark matter, dark energy, and the ultimate fate of the universe.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

The Future of the Mind brings a topic that once belonged solely to the province of science fiction into a startling new reality. This scientific tour de force unveils the astonishing research being done in top laboratories around the world—all based on the latest advancements in neuroscience and physics—including recent experiments in telepathy, mind control, avatars, telekinesis, and recording memories and dreams. The Future of the Mind is an extraordinary, mind-boggling exploration of the frontiers of neuroscience. Dr. Kaku looks toward the day when we may achieve the ability to upload the human brain to a computer, neuron for neuron; project thoughts and emotions around the world on a brain-net; take a “smart pill” to enhance cognition; send our consciousness across the universe; and push the very limits of immortality.

Raised in Depression-era Rockaway Beach, physicist Richard Feynman was irreverent, eccentric, and childishly enthusiastic—a new kind of scientist in a field that was in its infancy. His quick mastery of quantum mechanics earned him a place at Los Alamos working on the Manhattan Project under J. Robert Oppenheimer, where the giddy young man held his own among the nation’s greatest minds. There, Feynman turned theory into practice, culminating in the Trinity test, on July 16, 1945, when the Atomic Age was born. He was only twenty-seven. And he was just getting started. In this sweeping biography, James Gleick captures the forceful personality of a great man, integrating Feynman’s work and life in a way that is accessible to laymen and fascinating for the scientists who follow in his footsteps.

From the Trade Paperback edition.

The laws of physics define every aspect of our lives and society, from human nature and relationships to geopolitical issues like financial markets, globalization, and immigration. But how can such a complex subject be understood by anyone without a quadruple-digit IQ and a pocket protector full of doctorate degrees?

The answer is here. The Quantum Rules is a different kind of physics book that will familiarize you with the important and established laws at the heart of physics by showing how the defining patterns of our lives, our behavior, and our society already follow similar rules.

Whether you struggled through science classes or already have a grounding in physics, this book can help you relate to it in a whole new way, discover new perspectives on it, and learn how to have meaningful conversations about it in a way that won’t make people’s eyes glaze over.

The Quantum Rules also does something no other book on physics can do—it will makes you laugh, and often. With an original and humorous take on the established natural laws that govern our world, Professor of Physics Kunal K. Das brings this challenging subject down to earth.

Particle physics as we know it depends on the Higgs boson: It’s the missing link between the birth of our universe—as a sea of tiny, massless particles—and the tangible world we live in today. But for more than 50 years, scientists wondered: Does it exist?

Physicist Jon Butterworth was at the frontlines of the hunt for the Higgs at CERN’s Large Hadron Collider—perhaps the most ambitious experiment in history. In Most Wanted Particle, he gives us the first inside account of that uncertain time, when an entire field hinged on a single particle, and life at the cutting edge of science meant media scrutiny, late-night pub debates, dispiriting false starts in the face of intense pressure, and countless hours at the collider itself. As Butterworth explains, our first glimpse of the elusive Higgs brings us a giant step closer to understanding the universe—and points the way to an entirely new kind of physics.

In Life’s Ratchet, physicist Peter M. Hoffmann locates the answer to this age-old question at the nanoscale. The complex molecules of our cells can rightfully be called “molecular machines,” or “nanobots”; these machines, unlike any other, work autonomously to create order out of chaos. Tiny electrical motors turn electrical voltage into motion, tiny factories custom-build other molecular machines, and mechanical machines twist, untwist, separate and package strands of DNA. The cell is like a city—an unfathomable, complex collection of molecular worker bees working together to create something greater than themselves.

Life, Hoffman argues, emerges from the random motions of atoms filtered through the sophisticated structures of our evolved machinery. We are essentially giant assemblies of interacting nanoscale machines; machines more amazing than can be found in any science fiction novel. Incredibly, the molecular machines in our cells function without a mysterious “life force,” nor do they violate any natural laws. Scientists can now prove that life is not supernatural, and that it can be fully understood in the context of science.

Part history, part cutting-edge science, part philosophy, Life’s Ratchet takes us from ancient Greece to the laboratories of modern nanotechnology to tell the story of our quest for the machinery of life.

In this work Einstein intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general and scientific philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The theory of relativity enriched physics and astronomy during the 20th century.

(Relativity: The Special and the General Theory by Albert Einstein, 9789380914220)Physicist Dave Goldberg speeds across space, time and everything in between showing that our elegant universe—from the Higgs boson to antimatter to the most massive group of galaxies—is shaped by hidden symmetries that have driven all our recent discoveries about the universe and all the ones to come.

Why is the sky dark at night? If there is anti-matter, can there be anti-people? Why are past, present, and future our only options? Saluting the brilliant but unsung female mathematician Emmy Noether as well as other giants of physics, Goldberg answers these questions and more, exuberantly demonstrating that symmetry is the big idea—and the key to what lies ahead.

From the Trade Paperback edition.

This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.

Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

The illuminating Guide to Newton's Principia by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students.

You will follow your oxygen atoms through fire and water and from forests to your fingernails. Hydrogen atoms will wriggle into your hair and betray where you live and what you have been drinking. The carbon in your breath will become tree trunks, and the sodium in your tears will link you to long-dead oceans. The nitrogen in your muscles will help to turn the sky blue, the phosphorus in your bones will help to turn the coastal waters of North Carolina green, the calcium in your teeth will crush your food between atoms that were mined by mushrooms, and the iron in your blood will kill microbes as it once killed a star.

You will also discover that much of what death must inevitably do to your body is already happening among many of your atoms at this very moment and that, nonetheless, you and everyone else you know will always exist somewhere in the fabric of the universe.

You are not only made of atoms; you are atoms, and this book, in essence, is an atomic field guide to yourself.

“A modern voyage of discovery.” —Frank Wilczek, Nobel Laureate, author of The Lightness of Being

The Higgs boson is one of our era’s most fascinating scientific frontiers and the key to understanding why mass exists. The most recent book on the subject, The God Particle, was a bestseller. Now, Caltech physicist Sean Carroll documents the doorway that is opening—after billions of dollars and the efforts of thousands of researchers at the Large Hadron Collider in Switzerland—into the mind-boggling world of dark matter. The Particle at the End of the Universe has it all: money and politics, jealousy and self-sacrifice, history and cutting-edge physics—all grippingly told by a rising star of science writing.

"Such a richness of topics and amazing splendor of illustrations!" — Mathematics Magazine

"An inviting exposition for a literate but not highly scientific audience." — American Mathematical Monthly

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. Author Manfred Schroeder — hailed by Publishers Weekly as a modern Lewis Carroll — conveys memorable insights in the form of puns and puzzles that relate abstract mathematics to everyday experience.

Excellent entertainment for readers with a grasp of algebra and some calculus, this book forms a fine university-level introduction to fractal math. Eight pages of color images clarify the text, along with numerous black-and-white illustrations.

Kaku skillfully guides us through the latest innovations in string theory and its latest iteration, M-theory, which posits that our universe may be just one in an endless multiverse, a singular bubble floating in a sea of infinite bubble universes. If M-theory is proven correct, we may perhaps finally find answer to the question, “What happened before the big bang?” This is an exciting and unforgettable introduction into the new cutting-edge theories of physics and cosmology from one of the pre-eminent voices in the field.

From the Trade Paperback edition.

Richard Feynman, winner of the Nobel Prize in physics, thrived on outrageous adventures. Here he recounts in his inimitable voice his experience trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek; cracking the uncrackable safes guarding the most deeply held nuclear secrets; accompanying a ballet on his bongo drums; painting a naked female toreador. In short, here is Feynman's life in all its eccentric—a combustible mixture of high intelligence, unlimited curiosity, and raging chutzpah.

• It took more than an iceberg to sink the Titanic.

• The Challenger disaster was predicted.

• Unbreakable glass dinnerware had its origin in railroad lanterns.

• A football team cannot lose momentum.

• Mercury thermometers are prohibited on airplanes for a crucial reason.

• Kryptonite bicycle locks are easily broken.

“Things fall apart” is more than a poetic insight—it is a fundamental property of the physical world. Why Things Break explores the fascinating question of what holds things together (for a while), what breaks them apart, and why the answers have a direct bearing on our everyday lives.

When Mark Eberhart was growing up in the 1960s, he learned that splitting an atom leads to a terrible explosion—which prompted him to worry that when he cut into a stick of butter, he would inadvertently unleash a nuclear cataclysm. Years later, as a chemistry professor, he remembered this childhood fear when he began to ponder the fact that we know more about how to split an atom than we do about how a pane of glass breaks.

In Why Things Break, Eberhart leads us on a remarkable and entertaining exploration of all the cracks, clefts, fissures, and faults examined in the field of materials science and the many astonishing discoveries that have been made about everything from the explosion of the space shuttle Challenger to the crashing of your hard drive. Understanding why things break is crucial to modern life on every level, from personal safety to macroeconomics, but as Eberhart reveals here, it is also an area of cutting-edge science that is as provocative as it is illuminating.

From the Hardcover edition.

"Vivid . . . impressive. . . . Splendidly informative."—The New York Times

"Succeeds spectacularly."—Science

"A tour de force."—Salon

Already internationally acclaimed for his elegant, lucid writing on the most challenging notions in modern physics, Sean Carroll is emerging as one of the greatest humanist thinkers of his generation as he brings his extraordinary intellect to bear not only on Higgs bosons and extra dimensions but now also on our deepest personal questions: Where are we? Who are we? Are our emotions, our beliefs, and our hopes and dreams ultimately meaningless out there in the void? Do human purpose and meaning fit into a scientific worldview?

In short chapters filled with intriguing historical anecdotes, personal asides, and rigorous exposition, readers learn the difference between how the world works at the quantum level, the cosmic level, and the human level—and then how each connects to the other. Carroll's presentation of the principles that have guided the scientific revolution from Darwin and Einstein to the origins of life, consciousness, and the universe is dazzlingly unique.

Carroll shows how an avalanche of discoveries in the past few hundred years has changed our world and what really matters to us. Our lives are dwarfed like never before by the immensity of space and time, but they are redeemed by our capacity to comprehend it and give it meaning.

The Big Picture is an unprecedented scientific worldview, a tour de force that will sit on shelves alongside the works of Stephen Hawking, Carl Sagan, Daniel Dennett, and E. O. Wilson for years to come.

It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived.

As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

A comprehensive and comprehensible introduction to the subject, this book is ideal for undergraduates in computer science, physicists, communications engineers, workers involved in artificial intelligence, biologists, psychologists, and physiologists.

Since the first edition only five years ago, the simulation world has changed significantly -- current techniques have matured and new ones have appeared. This new edition deals with these new developments; in particular, there are sections on:

· Transition path sampling and diffusive barrier crossing to simulaterare events

· Dissipative particle dynamic as a course-grained simulation technique

· Novel schemes to compute the long-ranged forces

· Hamiltonian and non-Hamiltonian dynamics in the context constant-temperature and constant-pressure molecular dynamics simulations

· Multiple-time step algorithms as an alternative for constraints

· Defects in solids

· The pruned-enriched Rosenbluth sampling, recoil-growth, and concerted rotations for complex molecules

· Parallel tempering for glassy Hamiltonians

Examples are included that highlight current applications and the codes of case studies are available on the World Wide Web. Several new examples have been added since the first edition to illustrate recent applications. Questions are included in this new edition. No prior knowledge of computer simulation is assumed.

For more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.”

Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions.

Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes.

“For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.

Three millennia ago, the Greek philosopher Zeno constructed a series of logical paradoxes to prove that motion is impossible. Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno?s Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs?but through it all, the paradox of motion remains.

- Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis.

This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.

- Fully searchable CD that puts information at your

fingertips included with text

- Most up to date listing of integrals, series and

products

- Provides accuracy and efficiency in work

assumes only basic mathematical knowledge on the part of the reader and includes more than 100 discussion questions and some 70 problems, with solutions as well as further supplementary material available free to lecturers from the Wiley-VCH website.

As computer chips continue to shrink in size, scientists anticipate the end of the road: A computer in which each switch is comprised of a single atom. Such a device would operate under a different set of physical laws: The laws of quantum mechanics. Johnson gently leads the curious outsider through the surprisingly simple ideas needed to understand this dream, discussing the current state of the revolution, and ultimately assessing the awesome power these machines could have to change our world.

From the Trade Paperback edition.

The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book.

Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

Part one provides an introduction to quantum information processing using diamond, as well as its principles and fabrication techniques. Part two outlines experimental demonstrations of quantum information processing using diamond, and the emerging applications of diamond for quantum information science. It contains chapters on quantum key distribution, quantum microscopy, the hybridization of quantum systems, and building quantum optical devices. Part three outlines promising directions and future trends in diamond technologies for quantum information processing and sensing.

Quantum Information Processing with Diamond is a key reference for R&D managers in industrial sectors such as conventional electronics, communication engineering, computer science, biotechnology, quantum optics, quantum mechanics, quantum computing, quantum cryptology, and nanotechnology, as well as academics in physics, chemistry, biology, and engineering.

Brings together the topics of diamond and quantum information processingLooks at applications such as quantum computing, neural circuits, and in vivo monitoring of processes at the molecular scaleStarting with the recent development of modeling of solvation effect using the Polarizable Continuum Model (PCM) at the Coupled-Cluster level and the effects of extreme pressure on the molecular properties within the PCM framework, this volume focuses on the association/dissociation of ion pairs in binary solvent mixtures, application of graph theory to determine the all possible structures and temperature-dependent distribution of water cluster, generalized-ensemble algorithms for the complex molecular simulation, QM/MD based investigation of formation of different nanostructures under nonequilibrium conditions, quantum mechanical study of chemical reactivity of carbon nanotube, covalent functionalization of single walled-carbon nanotube, designing of functional materials, importance of long-range dispersion interaction to study nanomaterials, recent advances in QSPR/QSAR analysis of nitrocompounds, prediction of physico-chemical properties of energetic materials, electronic structure and properties of 3d transition metal dimers, the s-bond activation reactions by transition metal complexes, theoretical modeling of environmental mercury depletion reaction, organolithium chemistry and computational modeling of low-energy electron induced DNA damage.

Practical Aspects of Computational Chemistry II: An Overview of the Last Two Decades and Current Trends is aimed at theoretical and computational chemists, physical chemists, materials scientists, and particularly those who are eager to apply computational chemistry methods to problems of chemical and physical importance. This book provides valuable information to undergraduate, graduate, and PhD students as well as to established researchers.

Practical Aspects of Computational Chemistry II: An Overview of the Last Two Decades and Current Trends is aimed at theoretical and computational chemists, physical chemists, materials scientists, and particularly those who are eager to apply computational chemistry methods to problems of chemical and physical importance. This book provides valuable information to undergraduate, graduate, and PhD students as well as to established researchers.

This volume poses (and answers) important questions of interest to the computational chemistry community and beyond. What is the historical background of the “Structural Chemistry”? Is there any way to avoid the problem of intruder state in the multi-reference formulation? What is the recent progress on multi-reference coupled cluster theory? Starting with a historical account of structural chemistry, the book focuses on the recent advances made in promising theories such as many body Brillouin-Wigner theory, multireference state-specific coupled cluster theory, relativistic effect in chemistry, linear and nonlinear optical properties of molecules, solution to Kohn-Sham problem, electronic structure of solid state materials, development of model core potential, quantum Monte Carlo method, nano and molecular electronics, dynamics of photodimerization and excited states, intermolecular interactions, hydrogen bonding and non-hydrogen bonding interactions, conformational flexibility, metal cations in zeolite catalyst and interaction of nucleic acid bases with minerals.

Practical Aspects of Computational Chemistry I: An Overview of the Last Two Decades and Current Trends is aimed at theoretical and computational chemists, physical chemists, materials scientists, and particularly those who are eager to apply computational chemistry methods to problem of chemical and physical importance. This book will provide valuable information to undergraduate, graduate, and PhD students as well as to established researchers.

This book will be mandatory reading for anyone working on the foundations of modern devices such as free electron lasers, plasma accelerators, synchroton sources and other modern sources of bright, coherent radiation with high spectral density.

Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure.

The book is arranged in four sections, devoted to realizing the universal principle force equals curvature:

Part I: The Euclidean Manifold as a Paradigm

Part II: Ariadne's Thread in Gauge Theory

Part III: Einstein's Theory of Special Relativity

Part IV: Ariadne's Thread in Cohomology

For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum.

Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

The book begins by introducing the reader to symbolic computation and how it can be applied to solve a broad range of practical problems. Chapters cover topics that include: infinite series; complex numbers and functions; vectors and matrices; vector analysis; tensor analysis; ordinary differential equations; general vector spaces; Fourier series; partial differential equations; complex variable theory; and probability and statistics. Each important concept is clarified to students through the use of a simple example and often an illustration.

This book is an ideal reference for upper level undergraduates in physical chemistry, physics, engineering, and advanced/applied mathematics courses. It will also appeal to graduate physicists, engineers and related specialties seeking to address practical problems in physical science.

Clarifies each important concept to students through the use of a simple example and often an illustrationProvides quick-reference for students through multiple appendices, including an overview of terms in most commonly used applications (Mathematica, Maple)Shows how symbolic computing enables solving a broad range of practical problems

In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.