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The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices.

One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Readership

Graduate students and researchers interested in algebraic geometry, number theory, and algebraic groups.

Cover 1
Title page 4
Contents 6
Preface 8
- Acknowledgments 11
Introduction 12
- 0.1. Outline of the theory 12
- 0.2. Comparison with other theories 33
Chapter 1. Algebraic background 38
- 1.1. Algebra 38
- 1.2. Algebraic geometry 43
- 1.3. Superalgebra 44
Chapter 2. Classical differential geometry revisited 50
- 2.1. Connections in principal bundles and curvature 50
- 2.2. Lie algebra and classical groups 64
- 2.3. Involutions and symmetric spaces 69
- 2.4. Logarithmic derivative and differential Galois groups 74
- 2.5. Chern connections: the symmetric/anti-symmetric case 75
- 2.6. Chern connections: the hermitian case 81
- 2.7. Levi-Cività connection and Fedosov connection 83
- 2.8. Locally symmetric connections 89
- 2.9. Ehresmann connections attached to inner involutions 90
- 2.10. Connections in vector bundles 91
- 2.11. Lax connections 93
- 2.12. Hamiltonian connections 96
- 2.13. Cartan connection 103
- 2.14. Weierstrass and Riccati connections 105
- 2.15. Differential groups: Cassidy and Painlevé 106
Chapter 3. Arithmetic differential geometry: generalities 110
- 3.1. Global connections and their curvature 110
- 3.2. Adelic connections 123
- 3.3. Semiglobal connections and their curvature; Galois connections 126
- 3.4. Curvature via analytic continuation between primes 130
- 3.5. Curvature via algebraization by correspondences 136
- 3.6. Arithmetic jet spaces and the Cartan connection 149
- 3.7. Arithmetic Lie algebras and arithmetic logarithmic derivative 158
- 3.8. Compatibility with translations and involutions 163
- 3.9. Arithmetic Lie brackets and exponential 170
- 3.10. Hamiltonian formalism and Painlevé 172
- ...

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Foundations of Arithmetic Differential Geometry

یاهو مارکت شنبه 25 آذر 1396 ساعت 21:51

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Applied Linguistics in the Middle East and North Africa: Current Practices and Future Directions

This volume offers a comprehensive and up-to-date overview of applied research efforts in the Middle East and North Africa (MENA). This region has not received due attention in the literature and this publication provides a much-needed contribution to the existing body of knowledge. The editor recruited a number of renowned scholars who either work in the MENA countries or have experience doing research in this region to contribute to this project. The selection of chapters ensured representation of applied linguistics efforts in North Africa, the Levant, and the Gulf. The book looks into language research within social and educational MENA contexts. The final part of the book provides a forward-looking perspective about applied linguistics research and practices in the Middle East and North Africa. The book is primarily written for those interested in applied linguistics, particularly researchers, graduate students, and language professionals in the MNEA region.

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Applied Linguistics in the Middle East and North Africa: Current Practices and Future Directions

یاهو مارکت شنبه 25 آذر 1396 ساعت 21:51

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Heinemann chemistry 2

This Combo Pack contains the Student Book and access to Reader+ for Heinemann Chemistry 2, 5th Edition.

Reader+ gives you access to the eBook version of your Student Book as well as bonus multimedia assets. It’s built to work online and offline, making content easily available anytime, anywhere, in every school. It works on PC and Mac, Android and iOS.

Learners can quickly navigate through their eBooks, read them, take notes and save bookmarks. Reader+ integrates multimedia (audio/video) and interactive activities that enhance and extend the reading experience.

**Note: when you order any Student Book that includes access to the eBook, the access code may be referred to as "eBook 3.0" instead of Reader+. If you activate this code now you will receive access to eBook 3.0 for the remainder of 2017. From January 2018 your account will be switched over to the corresponding Reader+ product.

The market-leading and well known Heinemann Chemistry has been updated to fully match the 2016-2020 VCE Chemistry Study Design. Weve vastly improved this series while still retaining the style and approach that teachers love.

Unit 3: How can chemical processes be designed to optimise efficiency?
Area of study 1: What are the options for energy production?
Chapter 1: Fuels
Types of fuels
Fossil fuels and biofuels
Petro diesel and biodiesel
Chapter 2: Energy from fuels
Exothermic and endothermic reactions
Thermochemical equations and energy profile diagrams
Energy from combustion
Determining the heat of combustion of fuels
Chapter 3: Combustion of fuels
Introducing gases
Universal gas equation
Calculations involving combustion of fuels - Part 1
Calculations involving combustion of fuels - Part 1
Calculations involving energy changes
Chapter 4: Redox reactions
Oxidation and reduction
Oxidation numbers
Writing complex redox equations
Chapter 5: Galvanic cells as a source of energy
Galvanic cells
The electrochemical series
Predicting direct redox reactions
Everyday sources of power
Chapter 6: Fuel cells as a source of energy
Fuel cells
Area of study 2: How can the yield of a chemical product be optimised?
Chapter 7: Rate of chemical reactions
Investigating the rate of chemical reactions
Collision theory
Collision theory and reaction rate
Catalysts
Chapter 8: Equilibrium
Dynamic equilibrium
The equilibrium law
Working with equilibrium constants
Calculations involving equilibrium
Le Chateliers principle
Further applications of Le Chateliers principle
Optimising the yield of industrial processes
Chapter 9: Production of chemicals by electrolysis
Electrolytic cells
Commercial electrolytic cells
Faradays laws
Unit 4: How are organic compounds categorised, analysed and used?
Area of Study 1: How can the diversity of carbon compounds be explained and categorised?
Chapter 10: Structure and nomenclature of organic compounds
Carbon compounds and structural isomers
Stereoisomers
The simplest hydrocarbons
Functional groups - Part 1
Functional groups - Part 2
IUPAC nomenclature
Chapter 11: Properties and reactions of organic compounds
Boiling points and solubility of organic compounds
Viscosity and flashpoints of organic compounds
Chemical properties of alkanes, halo alkanes and alkenes
Reactions of alcohols, carboxylic acids and esters
Reaction pathways
Yield and the chemical industry
Chapter 12: Analysis of organic compounds using spectroscopic techniques
Infrared spectroscopy
Nuclear magnetic resonance spectroscopy
Mass spectroscopy
Determination of molecular structure using spectroscopy
Chapter 13: Analysis of organic compounds using chromatography
Principles of chromatography
High performance liquid chromatography
Chapter 14: Analysis of organic compounds using volumetric analysis
Principles of volumetric analysis
Acid base titrations
Redox titrations
Area of Study 2: What is the chemistry of food?
Chapter 15: Structure and bonding in food molecules
Amino acids
The formation of proteins
The primary and secondary structures of proteins
The tertiary structure of proteins
Fats and oils
Carbohydrates
Vitamins
Chapter 16: Metabolism of food in the human body
Metabolism of food in the human body
Action of enzymes
Enzymes - dependence of pH and temperature
Hydrolysis of carbohydrates
Hydrolysis of fats and oils
Chapter 17: The energy content of food
Food - an energy source
Calorimetry - determining the energy content of food
Calibration of calorimeters

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Heinemann chemistry 2

یاهو مارکت شنبه 25 آذر 1396 ساعت 21:50

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