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General Relativity and its Applications: Black Holes, Compact Stars and Gravitational Waves

by Paolo Pani Valeria Ferrari Leonardo Gualtieri

Containing the latest, groundbreaking discoveries in the field, this text outlines the basics of Einstein’s theory of gravity with a focus on its most important astrophysical consequences, including stellar structures, black holes and the physics of gravitational waves. Blending advanced topics - usually not found in introductory textbooks - with examples, pedagogical boxes, mathematical tools and practical applications of the theory, this textbook maximises learning opportunities and is ideal for master and graduate students in Physics and Astronomy. Key features:• Provides a self-contained and consistent treatment of the subject that does not require advanced previous knowledge of the field.• Explores the subject with a new focus on gravitational waves and astrophysical relativity, unlike current introductory textbooks.• Fully up-to-date, containing the latest developments and discoveries in the field.

General Relativity: Analytic and Symbolic Problems with Mathematica (Series in Astronomy and Astrophysics)

by Nicola Vittorio

This book provides General Relativity problems to be tackled both analytically and symbolically-numerically with the Mathematica software. In the first case, the reader is guided in setting up the appropriate solutions. In the second case, the reader is provided with very illustrative notebooks to carry out the steps necessary to solve a General Relativity problem. These include the calculation of the Christoffel symbols, Riemann, Ricci, Einstein and energy-momentum tensors, as well as the resolution of the field equations of General Relativity in different astrophysical/cosmological contexts, with and without the introduction of a cosmological constant. This study guide should be used alongside existing textbooks to provide additional learning and engagement opportunities for advanced undergraduate and graduate students in physics and astrophysics taking courses on general relativity. It may also be of interest to mathematics students interested in celestial mechanics and space sciences.A number of the Mathematica codes used in this book can be accessed online here; [INSERT URL WHEN AVAILABLE]Key Features:• Promotes the "learning by doing" approach, guiding the student in the building of the mathematical apparatus necessary to solve problems in General Relativity.• Encourages the development of analytical skills to address and solve specific and challenging problems in General Relativity.• Develops symbolic-numerical skills to address problems (often already solved analytically) so that the reader is prepared to attack even more elaborate calculations in General Relativity.

General Theory of Light Propagation and Imaging Through the Atmosphere

by T. Stewart Mckechnie

This book lays out a new, general theory of light propagation and imaging through Earth's turbulent atmosphere. Current theory is based on the - now widely doubted - assumption of Kolmogorov turbulence. The new theory is based on a generalized atmosphere, the turbulence characteristics of which can be established, as needed, from readily measurable properties of point-object, or star, images. The pessimistic resolution predictions of Kolmogorov theory led to lax optical tolerance prescriptions for large ground-based astronomical telescopes which were widely adhered to in the 1970s and 1980s. Around 1990, however, it became clear that much better resolution was actually possible, and Kolmogorov tolerance prescriptions were promptly abandoned. Most large telescopes built before 1990 have had their optics upgraded (e. g. , the UKIRT instrument) and now achieve, without adaptive optics (AO), almost an order of magnitude better resolution than before. As well as providing a more comprehensive and precise understanding of imaging through the atmosphere with large telescopes (both with and without AO), the new general theory also finds applications in the areas of laser communications and high-energy laser beam propagation.

General Theory of Light Propagation and Imaging Through the Atmosphere (Progress in Optical Science and Photonics #20)

by T. Stewart McKechnie

This 2nd edition lays out an updated version of the general theory of light propagation and imaging through Earth’s turbulent atmosphere initially developed in the late ‘70s and ‘80s, with additional applications in the areas of laser communications and high-energy laser beam propagation. New material includes a chapter providing a comprehensive mathematical tool set for precisely characterizing image formation with the anticipated Extremely Large Telescopes (ELTS), enabling a staggering range of star image shapes and sizes; existing chapters rewritten or modified so as to supplement the mathematics with clearer physical insight through written and graphical means; a history of the development of present-day understanding of light propagation and imaging through the atmosphere as represented by the general theory described. Beginning with the rudimentary, geometrical-optics based understanding of a century ago, it describes advances made in the 1960s, including the development of the ‘Kolmogorov theory,’ the deficiencies of which undermined its credibility, but not before it had done enormous damage, such as construction of a generation of underperforming ‘light bucket’ telescopes. The general theory requires no a priori turbulence assumptions. Instead, it provides means for calculating the turbulence properties directly from readily-measurable properties of star images.

General and Statistical Thermodynamics (Graduate Texts in Physics)

by Raza Tahir-Kheli

This textbook provides comprehensive information on general and statistical thermodynamics. It begins with an introductory statistical mechanics course, deriving all the important formulae meticulously and explicitly, without mathematical shortcuts. In turn, the main part of the book focuses on in-depth discussions of the concepts and laws of thermodynamics, van der Waals, Kelvin and Claudius theories, ideal and real gases, thermodynamic potentials, phonons and all related aspects. To elucidate the concepts introduced and to provide practical problem-solving support, numerous carefully worked-out examples are included. The text is clearly written and punctuated with a number of interesting anecdotes. The book also provides alternative solutions to problems and second equivalent explanations of important physical concepts. This second edition has been expanded to cover the foundations of superconductivity with new chapters on Cooper pairs, the Bogoliubov transformation, and superconductivity. It is suitable as a main thermodynamics textbook for upper-undergraduate students and provides extensive coverage, allowing instructors to ‘pick and choose’ the elements that best match their class profile.

Generalized Dynamics of Soft-Matter Quasicrystals: Mathematical Models, Solutions and Applications (Springer Series in Materials Science #260)

by Tian-You Fan Wenge Yang Hui Cheng Xiao-Hong Sun

This book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.

Generalized Frequency Distributions for Environmental and Water Engineering

by Vijay P. Singh Lan Zhang

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

Generalized Statistical Thermodynamics: Thermodynamics of Probability Distributions and Stochastic Processes (Understanding Complex Systems)

by Themis Matsoukas

This book gives the definitive mathematical answer to what thermodynamics really is: a variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble, the Author imagines the ensemble of all possible probability distributions and assigns probabilities to them by selection rules that are fairly general. The calculus of the most probable distribution in the ensemble produces the entire network of mathematical relationships we recognize as thermodynamics. The first part of the book develops the theory for discrete and continuous distributions while the second part applies this thermodynamic calculus to problems in population balance theory and shows how the emergence of a giant component in aggregation, and the shattering transition in fragmentation may be treated as formal phase transitions. While the book is intended as a research monograph, the material is self-contained and the style sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in such fields as physics, chemistry, and engineering.

Generalized Wavelets and Hypergroups

by Khalifa Trimeche

Wavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now

Generation Dread: Finding Purpose In An Age Of Climate Anxiety

by Britt Wray

“Generation Dread is a vital and deeply compelling read.”—Adam McKay, award-winning writer, director, and producer (Vice, Succession, Don’t Look Up) “Read this courageous book.”—Naomi Klein, author of This Changes Everything “Wray shows finally that meaningful living is possible even in the face of that which threatens to extinguish life itself.”—Dr. Gabor Maté, author of When the Body Says No When we’re faced with record-breaking temperatures, worsening wildfires, more severe storms, and other devastating effects of climate change, feelings of anxiety and despair are normal. In Generation Dread, Britt Wray reminds us that our distress is, at its heart, a sign of our connection to and love for the world. The first step toward becoming a steward of the planet is connecting with our climate emotions—seeing them as a sign of our humanity and empathy and learning how to live with them. Britt Wray, a scientist and expert on the psychological impacts of the climate crisis, brilliantly weaves together research, insight from climate-aware therapists, and personal experience, to illuminate how we can connect with others, find purpose, and thrive in a warming, climate-unsettled world.

Generation Dread: Finding Purpose in an Age of Climate Crisis

by Britt Wray

FINALIST FOR THE GOVERNOR GENERAL'S LITERARY AWARDA CBC BEST CANADIAN NONFICTION BOOK OF 2022AN INDIGO TOP TEN BEST SELF-HELP BOOK OF 2022"A vital and deeply compelling read.&” —Adam McKay, award-winning writer, director and producer (Don&’t Look Up)&“Britt Wray shows that addressing global climate change begins with attending to the climate within.&” —Dr. Gabor Maté, author of The Myth of Normal"Read this courageous book.&” —Naomi KleinAn impassioned generational perspective on how to stay sane amid climate disruption.Climate and environment-related fears and anxieties are on the rise everywhere. As with any type of stress, eco-anxiety can lead to lead to burnout, avoidance, or a disturbance of daily functioning. In Generation Dread, Britt Wray seamlessly merges scientific knowledge with emotional insight to show how these intense feelings are a healthy response to the troubled state of the world. The first crucial step toward becoming an engaged steward of the planet is connecting with our climate emotions, seeing them as a sign of humanity, and learning how to live with them. We have to face and value eco-anxiety, Wray argues, before we can conquer the deeply ingrained, widespread reactions of denial and disavowal that have led humanity to this alarming period of ecological decline.It&’s not a level playing field when it comes to our vulnerability to the climate crisis, she notes, but as the situation worsens, we are all on the field—and unlocking deep stores of compassion and care is more important than ever. Weaving in insights from climate-aware therapists, critical perspectives on race and privilege in this crisis, ideas about the future of mental health innovation, and creative coping strategies, Generation Dread brilliantly illuminates how we can learn from the past, from our own emotions, and from each other to survive—and even thrive—in a changing world.

Generation Green

by Linda Sivertsen Tosh Sivertsen

We all know about the Earth's environmental crisis, but there is someone who can truly make a difference: you. If you text your friends or chat with them online, download music to your iPod, or toss bottles and papers into recycling bins, you're already more eco-savvy than you think. It's just as easy to do even more to help save the earth, and Generation Green shows you how. This book: Lays out the inside scoop on the biggest issues affecting our planet, such as global warming and overflowing landfills * Offers dozens of tips on how to shop, dress, eat, and travel the green way * Includes interviews with teens like you who are involved with fun, innovative green causes * Shows that being environmentally conscious can be a natural part of your life -- and your generation's contribution to turning things around. It doesn't matter if you can't vote or drive. Your efforts -- big or small -- will contribute to saving the planet. It's time for all of us to take action. It's time to go green!

Generation Green: The Ultimate Teen Guide to Living an Eco-Friendly Life

by Linda Sivertsen Tosh Sivertsen

We all know about the Earth's environmental crisis, but there is someone who can truly make a difference: you. If you text your friends or chat with them online, download music to your iPod, or toss bottles and papers into recycling bins, you're already more eco-savvy than you think. It's just as easy to do even more to help save the earth, and Generation Green shows you how. This book lays out the inside scoop on the biggest issues affecting our planet, such as global warming and overflowing landfills. Offers dozens of tips on how to shop, dress, eat, and travel the green way. Includes interviews with teens like you who are involved with fun, innovative green causes. Shows that being environmentally conscious can be a natural part of your life -- and your generation's contribution to turning things around. It doesn't matter if you can't vote or drive. Your efforts -- big or small -- will contribute to saving the planet. It's time for all of us to take action. It's time to go green!

Generation Us: The Challenge of Global Warming (Rapid Reads)

by Dr. Andrew J. Weaver

In clear and accessible language, Generation Us explains the phenomenon of global warming, outlines the threat it presents to future generations and offers a path toward solutions to the problem. The reality of global warming has long been accepted within the scientific community, yet it remains a hotly debated topic at the political and social level. Why is this? Is it the fact that the ultimate effects of global warming will not be felt in our lifetimes? Do we really feel no moral responsibility for future generations? Dr. Weaver, one of the world's leading experts in the field, contends that, just as humans have been responsible for creating the problem of global warming, we must also be the solution.

Generation of Multivariate Hermite Interpolating Polynomials

by Santiago Alves Tavares

This text advances the study of approximate solutions to partial differential equations by formulating a novel approach that employs Hermite interpolating polynomials and by supplying algorithms useful in applying this approach. The book's three sections examine constrained numbers, Hermite interpolating polynomials, and selected applications. The authors outline the rules for writing the algorithms and then present them in pseudo-code. Next, they define the properties that characterize the Hermite interpolating polynomials, propose an expression and demonstrate an algorithm for generating the polynomials, and show the advantages of this new technique over the classical approach.

Genesis - In The Beginning

by Joseph Seckbach

Genesis - In The Beginning deals with the origin and diversity of Life and early biological evolution and discusses the question of where (hot or cold sources) and when the beginning of Life took place. Among the sections are chapters dealing with prebiotic chemical processes and considering self-replication of polymers in mineral habitats. One chapter is dedicated to the photobiological regime on early Earth and the emergence of Life. This volume covers the role of symmetry, information and order (homochrial biomolecules) in the beginning of Life. The models of protocells and the genetic code with gene transfer are important topics in this volume. Three chapters discuss the Panspermia hypothesis (to answer "Are we from outer Space?"). Other chapters cover the Astrobiological aspects of Life in the Universe in extraterrestrial Planets of the Solar System and deal with cometary hydrosphere (and its connection to Earth). We conclude with the history and frontiers of Astrobiogy.

Genesis of Diamonds and Associated Phases (Springer Mineralogy)

by Yuriy A. Litvin

This book presents an overview of recent advances in our understanding of the genesis of diamonds and the associated phases. It is divided into three main parts, starting with an introduction to the analysis of diamond inclusions to infer the formation processes. In turn, the second part of the book presents high-pressure experimental studies in mantle diamond-parental mineral systems with representative multicomponent boundary compositions. The experimental syngenesis phase diagrams provided reveal the physicochemical mechanisms of diamond nucleation and substantiate the mantle-carbonatite concept of the genesis of diamonds and associated phases. Lastly, the book describes the genetic classification of diamond-hosted mineral inclusions and experimentally determined RE “mineral-parental melt” partition coefficients. The physicochemical experimental evidence presented shows the driving forces behind the fractional evolution of the mantle magmas and diamond-parental melts.Given the depth and breadth of its coverage, the book offers researchers essential new insights into the ways diamonds and associated minerals and rocks are naturally created.

Genetic Engineering of Vegetable Crops (CABI Biotechnology Series)

by Pritam Kalia

Conventional plant breeding alone can no longer sustain the rising global demand for food. Genetic engineering technology makes it possible to develop new crop varieties with improved yield performance, specific quality attributes (external and internal in vegetable crops), resistance to diseases and insect pests, and environmental stresses. Genetic engineering technology for developing GM crops is complementary to genome editing and other breeding technologies. In addition to food requirements, transgenic crops have the possibility to carry edible vaccines and therapeutic proteins, to help combat human disease and malnutrition. This book reviews the importance and safety of transgenic vegetable crops and covers a wide variety of crops and different technologies. It includes: Genetic engineering in tomato, eggplant, peppers, amaranth, cauliflower, carrot, cucurbits, potato, tropical tubers and melons. Transgenic resistance to viral diseases. Embryogenic cell suspension culture. Genome editing and CRISPR/Cas9. Molecular techniques for biofortification. RNAi strategies for vegetable crop improvement. Designing futuristic vegetable crop varieties. This book is suitable for researchers in horticulture, plant science, and agricultural biotechnology as well as practitioners in vegetable breeding and seed production.

Genetic Engineering, Biofertilisation, Soil Quality and Organic Farming

by Eric Lichtfouse

Sustainable agriculture is a rapidly growing field aiming at producing food and energy in a sustainable way for humans and their children. Sustainable agriculture is a discipline that addresses current issues such as climate change, increasing food and fuel prices, poor-nation starvation, rich-nation obesity, water pollution, soil erosion, fertility loss, pest control, and biodiversity depletion. Novel, environmentally-friendly solutions are proposed based on integrated knowledge from sciences as diverse as agronomy, soil science, molecular biology, chemistry, toxicology, ecology, economy, and social sciences. Indeed, sustainable agriculture decipher mechanisms of processes that occur from the molecular level to the farming system to the global level at time scales ranging from seconds to centuries. For that, scientists use the system approach that involves studying components and interactions of a whole system to address scientific, economic and social issues. In that respect, sustainable agriculture is not a classical, narrow science. Instead of solving problems using the classical painkiller approach that treats only negative impacts, sustainable agriculture treats problem sources. Because most actual society issues are now intertwined, global, and fast-developing, sustainable agriculture will bring solutions to build a safer world. This book series gathers review articles that analyze current agricultural issues and knowledge, then propose alternative solutions. It will therefore help all scientists, decision-makers, professors, farmers and politicians who wish to build a safe agriculture, energy and food system for future generations.

Genetic Manipulation in Plants for Mitigation of Climate Change

by Om Parkash Dhankher Pawan Kumar Jaiwal Rana Pratap Singh

This book presents a detailed overview and critical evaluation of the state of the art and latest approaches in genetic manipulation studies on plants to mitigate the impact of climate change on growth and productivity. Each chapter has been written by experts in plant-stress biology and highlights the involvement of a variety of genes/pathways and their regulation in abiotic stress, recent advances in molecular breeding (identification of tightly liked markers, QTLs/genes), transgenesis (introduction of exogenous genes or changing the expression of endogenous stress- responsive genes) and genomics approaches that have made it easier to identify and isolate several key genes involved in abiotic stress such as drought, water lodging/flooding, extreme temperatures, salinity and heavy-metal toxicity. Food and nutritional security has emerged as a major global challenge due to expanding populations, and cultivated areas becoming less productive as a result of extreme climatic changes adversely affecting the quantity and quality of plants. Hence, there is an urgent need to develop crop varieties resilient to abiotic stress to ensure food security and combat increased input costs, low yields and the marginalization of land. The role of GM crops in poverty alleviation, nutrition and health in developing countries and their feasibility in times of climate change are also discussed. Recent advances in gene technologies have shown t he potential for faster, more targeted crop improvements by transferring genes across the sexual barriers. The book is a valuable resource for scientists, researchers, students, planners and industrialists working in the area of biotechnology, plant agriculture, agronomy, horticulture, plant physiology, molecular biology, plant sciences and environmental sciences.

Genetically Engineered Crops: Experiences and Prospects

by Engineering Medicine National Academies of Sciences

Genetically engineered (GE) crops were first introduced commercially in the 1990s. After two decades of production, some groups and individuals remain critical of the technology based on their concerns about possible adverse effects on human health, the environment, and ethical considerations. At the same time, others are concerned that the technology is not reaching its potential to improve human health and the environment because of stringent regulations and reduced public funding to develop products offering more benefits to society. While the debate about these and other questions related to the genetic engineering techniques of the first 20 years goes on, emerging genetic-engineering technologies are adding new complexities to the conversation. Genetically Engineered Crops builds on previous related Academies reports published between 1987 and 2010 by undertaking a retrospective examination of the purported positive and adverse effects of GE crops and to anticipate what emerging genetic-engineering technologies hold for the future. This report indicates where there are uncertainties about the economic, agronomic, health, safety, or other impacts of GE crops and food, and makes recommendations to fill gaps in safety assessments, increase regulatory clarity, and improve innovations in and access to GE technology.

Genetically Engineered Organisms: Assessing Environmental and Human Health Effects

by Deborah K. Letourneau Beth Elpern Burrows

Genetic engineering suggests new avenues for constructing useful products, but it also poses hazards to the health of the environment and the public. Delineating those hazards is complicated, difficult, and important at every level of risk assessment and risk management decision-making. Risk assessment and risk management may be further complicated

Genetically Modified Crops and Food Security: Commercial, Ethical and Health Considerations (Earthscan Food and Agriculture)

by Vishal Sharma Jasmeet Kour Imtiyaz Khanday

This book reviews a wide-range of genetically modified (GM) crops to understand how they are produced, the impacts on the agricultural industry, and their potential for improving food security. The production of GM crops has now become an invaluable asset in the agricultural toolbox. With a significant portion of the world suffering from hunger and poverty, this book examines how food security can be achieved through GM crops. A wide variety of crops are examined, from the earliest developments of GM tomatoes and potatoes to recent interest in the development of low-cost, high yielding biofuels, such as microalgae. Chapters also discuss the role of GM crops in pest management and the consequential reduction in the use of insecticides. Overall, this book provides an important synthesis of GM crops from their commercial value to the agricultural industry, as well as their potential for improving food security. This book will be of great interest to students and scholars of agricultural engineering, crop science, food biotechology, food security, and those interested in food and agriculture and sustainable development more broadly.

Genetically Modified Pest-protected Plants: Science And Regulation

by National Research Council

This book explores the risks and benefits of crops that are genetically modified for pest resistance, the urgency of establishing an appropriate regulatory framework for these products, and the importance of public understanding of the issues.The committee critically reviews federal policies toward transgenic products, the 1986 coordinated framework among the key federal agencies in the field, and rules proposed by the Environmental Protection Agency for regulation of plant pesticides. This book provides detailed analyses of: Mechanisms and results of genetic engineering compared to conventional breeding for pest resistance. Review of scientific issues associated with transgenic pest-protected plants, such as allergenicity, impact on nontarget plants, evolution of the pest species, and other concerns. Overview of regulatory framework and its use of scientific information with suggestions for improvements.

Genetics of Salt Tolerance in Plants: A Central Dogma Perspective and Strategies for Enhancement

by Kehinde A. Adeboye Victor J. Bamisaye Farwa Basit Usman Rabi’u Bello Javaid Akhter Bhat Jamindar Buddiga Utpal Das Balasundari Dharbaranyam Xianzhong Feng M. Gayathri Abubakar Mohammad Gumi Md Sazzad Hossain Emmanuel O. Idehen Krishnananda P. Ingle Nancy McMulkin Mushtaq Ahmad Najar Oyeboade A. Oyetunde Kapil Patil Britta Pitann Shiva Sai Prasad Fergie Ann Quilloy Md Zillur Rahman J. R. Rajeshwar P. W. Ramteke Hamza Ramzan Vincent Pamugas Reyes Kausalya Sakthivel Palanisamy Senthilmurugan Usama Sheraz Sajid Shokat Pradeep Kumar Shukla Atul Singh Gayatri Venkataraman Mst Ishrat Zahan

Gene expression in cells follows a prescribed pathway that conforms to the Central Dogma; where the genetic information stored in DNA is transcribed into RNA and then expressed into proteins, which influences most plant traits. Plant salt tolerance research is directed towards identifying nucleotide variants that could contribute to tolerant phenotypes. This book comprehensively presents the current state of knowledge on plant salt tolerance through meticulous analysis of the processes operating across the Central Dogma. It provides a detailed account of modulation of gene expression through genome editing systems to achieve crop improvement against salt stress. It also provides state-of-the-art information on advances in breeding technologies of genome selection and accelerated de novo domestication for rapidly improving the salt tolerance of plants for global food security. This book: 1.Provides a comprehensive coverage of plant salt tolerance mechanisms. 2.Spotlights various factors functioning along the Central Dogma pathway and their regulation in response to salinity. 3.Examines how these factors function to protect the plants from high salinity. 4.Highlights advances in cutting-edge breeding technologies for improving salt tolerance. The book will be of particular value to students and researchers of plant genetics, molecular biology and physiology and those with an interest in salinity and salt tolerance.

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