Physics Now! 11-14

Author: Peter D. Riley

Publisher: Hodder Murray

ISBN: 9780719580635

Category: Education

Page: 192

View: 8517

Physics Now! is one of three Pupil's Books that cover the requirements of the National Curriculum for Science at Key Stage 3, the Common Entrance Examination at 13+ syllabus and equivalent junior science courses. Each Pupil's Book is supported by a Teacher's Resource Book that contains: the answers to the questions in the Pupil's Book, practical activities and investigations with notes for the teachers and technicians, photocopiable worksheets to support some activities, end of chapter tests with answers, two tests to be used as preparation for the end of course examinations.

The Physics of Chaos in Hamiltonian Systems

Author: George M Zaslavsky

Publisher: World Scientific

ISBN: 1908979232

Category: Science

Page: 328

View: 5609

This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools, thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincaré recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal type) symmetries. This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport properties of chaotic motion. The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.The material can also be used by graduate students. Contents:Discrete and Continuous ModelsSeparatrix ChaosThe Phase Space of ChaosNonlinearity Versus PerturbationFractals and ChaosPoincaré Recurrences and Fractal TimeChaos and Foundation of Statistical PhysicsChaos and SymmetryMore Degrees of FreedomNormal and Anomalous KineticsFractional KineticsWeak Chaos and Pseudochaos Readership: Graduate students and researchers in physics, mathematics, engineering, chemistry and biophysics. Keywords:Billiards;Separatrix Chaos;Fractal Properties;Stochastic Webs;Kinetics;Chaotic DynamicsKey Features:New sections on the islands in stochastic sea, billiards, persistent fluctuations, and log-periodicityIncludes a new chapter on weak chaos and pseudochaosUseful for graduate and undergraduate courses on the theory of chaosReviews:Reviews of the First Edition:“George Zaslavsky develops ‘fractional kinetics’ in an attempt to give a smoothed, but nondiffusive, description. This phenomenological description captures some aspects of the stickiness of islands, but I believe its mathematical justification remains elusive. Perhaps that is an excellent reason to read this book.”Nature “The book is useful for scientists who are actively working on the problems of dynamical chaos … The material can also be used as a textbook for a graduate course on new and emerging directions in Hamiltonian chaos theory.”Zentralblatt MATH

A Career in Theoretical Physics

Author: Philip W Anderson

Publisher: World Scientific

ISBN: 9814482528

Category: Science

Page: 884

View: 3885

This unique volume presents the scientific achievements of Nobel laureate Philip Anderson, spanning the many years of his career. In this new edition, the author has omitted some review papers as well as added over 15 of his research papers. As in the first edition, he provides an introduction to each paper by explaining the genesis of the papers or adding some personal history. The book provides a comprehensive overview of the author's work which include significant discoveries and pioneering contributions, such as his work on the Anderson model of magnetic impurities and the concept of localization; the study of spin glasses, the fluctuating valence problem and superexchange; his prediction of the existence of superfluidity in He3; his involvement in the discovery of the Josephson effect; his discovery of the “Higgs” mechanism in elementary particle physics; and so on. The new papers added to this edition include ”Pressure Broadening in the Microwave and Infrared Regions” — a condensation of most of the author's thesis; ”Ordering and Antiferromagnetism in Ferrites” — the best-known of the papers written by the author involving what are known as “frustrated” lattices; and ”Localized Magnetic States in Metals” — a paper mentioned in his Nobel Prize citation along with localization and superexchange; to name a few. A Career in Theoretical Physics is an essential source of reference for physicists, chemists, materials scientists and historians of science. It is also suitable reading for graduate students. Contents:Pressure Broadening in the Microwave and Infrared RegionsAbsence of Diffusion in Certain Random LatticesTheory of Dirty SuperconductorsLocalized Magnetic States in MetalsInfrared Catastrophe in Fermi Gases with Local Scattering PotentialsThe Fermi Glass: Theory and ExperimentPossible Consequences of Negative U Centers in Amorphous MaterialsLocalization ReduxSuggested Model for Prebiotic Evolution: The Use of ChaosPhysics: The Opening to Complexityand other papers Readership: Physicists, chemists and materials scientists. Keywords:Theoretical Physics;Spin Glasses;Localization;High Tc Superconductivity MagnetismKey Features:Comprehensive collection of many significant topics Philip Anderson has worked onSome of the papers included are now hard to find elsewhere, and each has been embellished with commentary on how they came to be writtenAnderson has also provided an interesting introduction setting out his philosophy of what is important in scienceFully updated to include significant new papers (around 120 more pages)

University Physics with Modern Physics, 2nd Edition, Bauer & Westfall, 2014

University Physics with Modern Physics

Author: Bauer & Westfall

Publisher: Bukupedia

ISBN: N.A

Category: Science

Page: 1496

View: 8041

Instructor Solutions Manual to accompany UNIVERSITY PHYSICS, Second Edition Table of Contents PART 1 MECHANICS OF POINT PARTICLES 1 Overview 1 2 Motion in a Straight Line 45 3 Motion in Two and Three Dimensions 108 4 Force 163 5 Kinetic Energy, Work, and Power 223 6 Potential Energy and Energy Conservation 255 7 Momentum and Collisions 308 PART 2 EXTENDED OBJECTS, MATTER, AND CIRCULAR MOTION 8 Systems of Particles and Extended Objects 380 9 Circular Motion 430 10 Rotation 474 11 Static Equilibrium 521 12 Gravitation 574 13 Solids and Fluids 628 PART 3 OSCILLATIONS AND WAVES 14 Oscillations 673 15 Waves 713 16 Sound 747 PART 4 THERMAL PHYSICS 17 Temperature 783 18 Heat and the First Law of Thermodynamics 806 19 Ideal Gases 835 20 The Second Law of Thermodynamics 870 PART 5 ELECTRICITY 21 Electrostatics 898 22 Electric Fields and Gauss’s Law 934 23 Electric Potential 973 24 Capacitors 1007 25 Current and Resistance 1046 26 Direct Current Circuits 1075 PART 6 MAGNETISM 27 Magnetism 1113 28 Magnetic Fields of Moving Charges 1141 29 Electromagnetic Induction 1171 30 Alternating Current Circuits 1197 31 Electromagnetic Waves 1224 PART 7 OPTICS 32 Geometric Optics 1248 33 Lenses and Optical Instruments 1270 34 Wave Optics 1304 PART 8 RELATIVITY AND QUANTUM PHYSICS 35 Relativity 1324 36 Quantum Physics 1354 37 Quantum Mechanics 1382 38 Atomic Physics 1419 39 Elementary Particle Physics 1444 40 Nuclear Physics 1464

Physik für Dummies

Author: Steven Holzner

Publisher: John Wiley & Sons

ISBN: 3527692576

Category: Science

Page: 404

View: 1375

Dieses Buch entf?hrt auch die, die damit eigentlich nichts am Hut haben, in die faszinierende Welt der Physik. Steve Holzner stellt Ihnen physikalische Ph?nomene vor und erkl?rt die dahinterstehenden Naturgesetze samt der notwendigen mathematischen Grundlagen. Egal ob Elektrizit?t, Magnetismus oder Optik, alles wird mit ausf?hrlichen Beispielen und anschaulichen Abbildungen erl?utert. Nach jedem Kapitel gibt es ?bungsaufgaben und L?sungen, mit denen man das Gelernte festigen kann.

Fractional Calculus

An Introduction for Physicists

Author: Richard Herrmann

Publisher: World Scientific

ISBN: 9814551090

Category: Science

Page: 500

View: 957

The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights. This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject. Contents:IntroductionFunctionsThe Fractional DerivativeFriction ForcesFractional CalculusThe Fractional Harmonic OscillatorWave Equations and ParityNonlocality and Memory EffectsFractional Calculus in Multidimensional Space — 2D-Image ProcessingFractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster PhysicsQuantum MechanicsThe Fractional Schrödinger Equation with the Infinite Well Potential — Numerical Results using the Riesz DerivativeUniqueness of a Fractional Derivative — the Riesz and Regularized Liouville Derivative as ExamplesFractional Spin — A Property of Particles Described with the Fractional Schrödinger EquationFactorizationSymmetriesThe Fractional Symmetric Rigid Rotorq-Deformed Lie Algebras and Fractional CalculusInfrared Spectroscopy of Diatomic Molecules Fractional Spectroscopy of HadronsMagic Numbers in Atomic NucleiMagic Numbers in Metal ClustersFractors — Fractional Tensor CalculusFractional FieldsGauge Invariance in Fractional Field TheoriesOn the Origin of SpaceOutlook Readership: Students and researchers in physics. Keywords:Mathematical Physics;Fractional Calculus;Long-Memory Kernels;Non-Local Field Theories;Fractional Quantum MechanicsKey Features:This was the first book on the market covering the full area of a physical application of fractional calculusThe book provides a skillful insight into a vividly growing research area and guides the reader from his first steps on an introductory level up to the current state of the art of a physical interpretation and application in different fieldsThis book enables the reader to participate and contribute to the development of this exciting research area by applying these methods in his own research area tooReviews:Reviews of the First Edition: “Fractional Calculus is an affordable and valuable introduction to the field that will appeal to physicists interested in scientific what-ifs.” Physics Today “… the first three chapters actually appear very helpful at the graduate level. Each chapter has a careful precis at the start. There a many analyses illustrating outcomes of fractional analyses… If this [fractional calculus] is the field of your research then this book is essential with numerous references… ” Contemporary Physics “The book has the property that derived results are directly compared with experimental findings. As a consequence, the reader is guided and encouraged to apply the fractional calculus approach in her/his research area. The reviewer strongly recommends this book for beginners as well as specialists in the fields of physics, mathematics and complex adaptive systems.” Zentralblatt MATH “A very welcome new feature in the second edition is the inclusion of exercises at the end of every chapter, with detailed solutions in the back of the book. This book is specifically aimed at physicists, although many of my colleagues outside physics have also found it useful. This is particularly true of graduate students and beginning researchers, or those new to the subject of fractional calculus.” Mark Meerschaert Dept of Statistics and Probability, Michigan State University

Learning LibGDX Game Development - Second Edition

Author: Suryakumar Balakrishnan Nair,Andreas Oehlke

Publisher: Packt Publishing Ltd

ISBN: 1783554789

Category: Computers

Page: 478

View: 2769

This book is aimed at indie and existing game developers as well as those who want to get started with game development using LibGDX. Basic knowledge of Java programming and game development is required.

Introduction to the Electronic Properties of Materials, 2nd Edition

Author: David C. Jiles

Publisher: CRC Press

ISBN: 9780748760428

Category: Technology & Engineering

Page: 448

View: 637

Electronic materials provide the basis for many high tech industries that have changed rapidly in recent years. In this fully revised and updated second edition, the author discusses the range of available materials and their technological applications. Introduction to the Electronic Properties of Materials, 2nd Edition presents the principles of the behavior of electrons in materials and develops a basic understanding with minimal technical detail. Broadly based, it touches on all of the key issues in the field and offers a multidisciplinary approach spanning physics, electrical engineering, and materials science. It provides an understanding of the behavior of electrons within materials, how electrons determine the magnetic thermal, optical and electrical properties of materials, and how electronic properties are controlled for use in technological applications. Although some mathematics is essential in this area, the mathematics that is used is easy to follow and kept to an appropriate level for the reader. An excellent introductory text for undergraduate students, this book is a broad introduction to the topic and provides a careful balance of information that will be appropriate for physicists, materials scientists, and electrical engineers.

IUTAM Symposium on Computational Physics and New Perspectives in Turbulence

Proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, Nagoya University, Nagoya, Japan, September, 11-14, 2006

Author: Yukio Kaneda

Publisher: Springer Science & Business Media

ISBN: 9781402064722

Category: Science

Page: 450

View: 594

This volume contains the proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, held at Nagoya University, Nagoya, Japan, in September 2006. With special emphasis given to fundamental aspects of the physics of turbulence, coverage includes experimental approaches to fundamental problems in turbulence, turbulence modeling and numerical methods, and geophysical and astrophysical turbulence.

Biology Now! 11-14 Pupil's Book

Author: Peter D. Riley

Publisher: Hodder Murray

ISBN: 9780719580604

Category: Education

Page: 240

View: 8083

Biology Now! 11-14 is one of three Pupil's Books that cover the requirements of the National Curriculum for science at Key Stage 3, the Common Entrance Examination at 13+ syllabus and equivalent junior science courses. Based on Biology Now! 11-14, the clear text and colourful illustrations and photographs fully explain the concepts and encourage background reading. Boxed sections are used to show how scientific ideas have developed and how they are applied in today's world. Throughout there are numerous questions that test a range of skills including comprehension, application, analysis and evaluation. These may be used as a basis for classwork or homework. There are also 'For discussion' sections to encourage group discussion. In this second edition the Chapters have been reorganised to reflect the QCA Scheme of Work. There is also additional information on types of tissue, parental care in different organisms, daily adaptations in plants and animals and a new chapter on Plants for Food. Each book has a glossary and is supported by a Teacher's Resource Book that contains details of practical work.

Introduction to Nuclear and Particle Physics

Author: A Das,T Ferbel

Publisher: World Scientific

ISBN: 9814483338

Category: Nuclear physics

Page: 416

View: 8452

' The original edition of Introduction to Nuclear and Particle Physics was used with great success for single-semester courses on nuclear and particle physics offered by American and Canadian universities at the undergraduate level. It was also translated into German, and used overseas. Being less formal but well-written, this book is a good vehicle for learning the more intuitive rather than formal aspects of the subject. It is therefore of value to scientists with a minimal background in quantum mechanics, but is sufficiently substantive to have been recommended for graduate students interested in the fields covered in the text. In the second edition, the material begins with an exceptionally clear development of Rutherford scattering and, in the four following chapters, discusses sundry phenomenological issues concerning nuclear properties and structure, and general applications of radioactivity and of the nuclear force. This is followed by two chapters dealing with interactions of particles in matter, and how these characteristics are used to detect and identify such particles. A chapter on accelerators rounds out the experimental aspects of the field. The final seven chapters deal with elementary-particle phenomena, both before and after the realization of the Standard Model. This is interspersed with discussion of symmetries in classical physics and in the quantum domain, bringing into full focus the issues concerning CP violation, isotopic spin, and other symmetries. The final three chapters are devoted to the Standard Model and to possibly new physics beyond it, emphasizing unification of forces, supersymmetry, and other exciting areas of current research. The book contains several appendices on related subjects, such as special relativity, the nature of symmetry groups, etc. There are also many examples and problems in the text that are of value in gauging the reader's understanding of the material. Contents:Rutherford ScatteringNuclear PhenomenologyNuclear ModelsNuclear RadiationApplications of Nuclear PhysicsEnergy Deposition in MediaParticle DetectionAcceleratorsProperties and Interactions of Elementary ParticlesSymmetriesDiscrete TransformationsNeutral Kaons, Oscillations, and CP ViolationFormulation of the Standard ModelStandard Model and Confrontation with DataBeyond the Standard Model Readership: Advanced undergraduates and researchers in nuclear and particle physics. Keywords:Rutherford Scattering;Nuclear Properties;Nuclear Structure;Elementary Particles;Sub-Structure of Particles;Particle Detectors;Interactions in Matter;The Standard Model;Symmetries of Nature;Theories of Nuclear and Particle Structure;Radioactivity;SupersymmetryReviews: “The book by Das and Ferbel is particularly suited as a basis for a one-semester course on both subjects since it contains a very concise introduction to those topics and I like very much the outline and contents of this book.” Kay Konigsmann Universität Freiburg, Germany “The book provides an introduction to the subject very well suited for the introductory course for physics majors. Presentation is very clear and nicely balances the issues of nuclear and particle physics, exposes both theoretical ideas and modern experimental methods. Presentation is also very economic and one can cover most of the book in a one-semester course. In the second edition, the authors updated the contents to reflect the very recent developments in the theory and experiment. They managed to do it without substantial increase of the size of the book. I used the first edition several times to teach the course ‘Introduction to Subatomic Physics’ and I am looking forward to use this new edition to teach the course next year.” Professor Mark Strikman Pennsylvania State University, USA “This book can be recommended to those who find elementary particle physics of absorbing interest.” Contemporary Physics '

Die Ordnung der Zeit

Author: Carlo Rovelli

Publisher: Rowohlt Verlag GmbH

ISBN: 3644000751

Category: Science

Page: 192

View: 835

Leben wir in der Zeit oder lebt die Zeit vielleicht nur in uns? Alle theoretischen Physiker von Weltrang, die den großen und kleinen Kräften des Universums nachspüren, beschäftigen sich immer wieder mit der entscheidenden Frage, was Zeit ist. Wenn ihre großen Modelle die Zeit zur Erklärung des Elementaren nicht mehr brauchen, wie kommt es dann, dass sie für unser Leben so wichtig ist? Geht es wirklich ohne sie? Carlo Rovelli gibt in diesem Buch überraschende Antworten. Er nimmt uns mit auf eine Reise durch unsere Vorstellungen der von der Zeit und spürt ihren Regeln und Rätseln nach. Ein großes, packend geschriebenes Lese-Abenteuer, ein würdiger Nachfolger des Welt-Bestsellers "Sieben kurze Lektionen über Physik".

Superstrings and Other Things

A Guide to Physics, Second Edition

Author: Carlos I. Calle

Publisher: CRC Press

ISBN: 1439810745

Category: Science

Page: 567

View: 5269

A research scientist at NASA working on planetary exploration, Carlos Calle has the opportunity to ponder what seems imponderable, but while that might make Dr. Calle unusual, what makes him truly special is his ability to translate the algebraic formulas and calculus-based logic into concepts that can be appreciated and held in awe by those in possession of tools no more sophisticated than curiosity and imagination. Superstrings and Other Things: A Guide to Physics, Second Edition continues to take the interested on a uniquely accessible journey through physics. This guide explains the basic concepts of motion, energy, and gravity, right up through the latest theories about the structure of matter, the origin of the universe, and the beginning of time. Fully illustrated throughout, the book explores major discoveries and the scientists behind them, from Galileo, Newton, and Einstein, to Feynman and Hawking. Numerous examples of physics in everyday situations are provided and made tangible. When Dr. Calle wrote the first edition of this bestseller, even he would have been surprised by the newest development in String Theory, the far reaching M-Theory. In addition to details about M-Theory, he adds a number of other surprises and updated material for this edition. Not only will you be rewarded with a basic understanding of the fundamental concepts of physics, but you will also come to have the chance to stand on the very edge of the breathtaking frontiers of physics today. Offers non-science students and others access to the highest peaks of physics Supports a truly conceptual approach to teaching physics without advanced math Emphasizes concepts and ideas rather than equations Provides up-to-date coverage of modern physics Showcases modern applications of physics in our everyday world Builds interest with landmark discoveries and recent breakthroughs Ties ideas to history with several biographical sketches Includes clear illustrations and beautiful photographs in a four page insert Provides a wealth of conceptual and numerical problems Now includes a Solutions Manual with qualifying course adoptions Carlos I. Calle is a senior research physicist at NASA Kennedy Space Center and the founder and director of NASA’s Electrostatics and Surface Physics Laboratory. He is the recipient of numerous NASA awards for exceptional contributions to the space program and outstanding support of the Space Shuttle Program. With his laboratory staff, he has developed technologies for NASA’s lunar and Martian exploration programs and has also developed new testing techniques for several Space Shuttle systems. As a professor of physics during the early part of his career, he taught the whole range of college physics courses. He has published over 150 scientific papers and other popular books on physics.

Introductory Solid State Physics, Second Edition

Author: H.P. Meyers,H.P. Myers

Publisher: CRC Press

ISBN: 1420075020

Category: Science

Page: 536

View: 500

Assuming an elementary knowledge of quantum and statistical physics, this book provides a comprehensive guide to principal physical properties of condensed matter, as well as the underlying theory necessary for a proper understanding of their origins. The subject matter covers the principal features of condensed matter physics, but with particular accent on the properties of metal alloys. Relevance to technical applications is recognized.

Practical Radiotherapy

Physics and Equipment

Author: Pam Cherry,Angela Duxbury

Publisher: John Wiley & Sons

ISBN: 1444316184

Category: Medical

Page: 304

View: 1000

Practical Radiotherapy introduces the reader to the physics and equipment that is central to radiotherapy practice. The early section of the book deals with the essential physics and mathematics of radiation beams with chapters on atomic and applied laws of physics, X-ray production, radiation dosimetry and X-ray interactions with matter. Each of the key pieces of radiotherapy department equipment is described in detail and further sections embrace all aspects of the therapeutic radiographer’s work including: imaging systems, verification and immobilisation, legislation, radionuclide imaging and brachytherapy. Based on the most up-to-date scientific information in radiotherapy, Pracatical Radiotherapy is written by an experienced team of practitioners and teachers who present a difficult and dry subject in a reader-friendly manner, covering all of the required core information. This second edition has been extensively revised and is fully up to date with key developments in equipment and practice, namely: stereotacic radiosurgery, CT SIM and SIM CT, portal imaging, MLC and HDR brachytherapy. Features • Covers the required core information in a single volume • Reader-friendly style and format • Self-assessment and further reading at the end of each chapter • All of the contributors are well known teachers in the field

Simplicius: On Aristotle Physics 5

Author: J.O. Urmson

Publisher: A&C Black

ISBN: 147250187X

Category: Philosophy

Page: 199

View: 6831

Simplicius, the greatest surviving ancient authority on Aristotle's Physics , lived in the sixth century A. D. He produced detailed commentaries on several of Aristotle's works. Those on the Physics, which alone come to over 1,300 pages in the original Greek, preserve a centuries-old tradition of ancient scholarship on Aristotle. In Physics Book 5 Aristotle lays down some of the principles of his dynamics and theory of change. What does not count as change: change of relation? The flux of time? There is no change of change, yet acceleration is recognised. Aristotle defines 'continuous', 'contact' and 'next', and uses these definitions in discussing when we can claim that the same change or event is still going on. This volume is complemented by David Konstan's translation of Simplicius' commentary on Physics Book 6, which has already appeared in this series. It is Book 6 that gives spatial application to the terms defined in Book 5, and uses them to mount a celebrated attack on atomism. Simplicius' commentaries enrich our understanding of the Physics and of its interpretation in the ancient world.

Groups, Representations and Physics

Author: H.F Jones

Publisher: CRC Press

ISBN: 9781420050295

Category: Mathematics

Page: 340

View: 6636

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.