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Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.
The book is available at any international bookseller such as: https://www.amazon.com/Complex-Analysis-Gruyter-Studies-Mathematics/dp/3110757699/?_encoding=UTF8&pd_rd_w=RGJOA&content-id=amzn1.sym.e4bd6ac6-9035-4a04-92a6-fc4ad60e09ad&pf_rd_p=e4bd6ac6-9035-4a04-92a6-fc4ad60e09ad&pf_rd_r=2CAMSVP0V28P95C6EQQH&pd_rd_wg=zNZx9&pd_rd_r=768b2f46-b64b-411d-8532-42cca0aa203a&ref_=pd_gw_ci_mcx_mr_hp_atf_m This is a book about the mathematical nature of our Universe.
Armed with no more than basic high school mathematics, you will be taken on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, the Theory of Relativity, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, achieving order from chaos, determining the size of the Earth with a stick in the ground, determining the age of the Solar System from meteorites, explaining how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean theorem and the symbol π, with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and the extraordinary mathematical beauty of the Universe we call home. “I first had a quick look, then I started reading it. I couldn't stop. I liked the writing style and really enjoyed the contents.” Gerard 't Hooft (Nobel Prize in Physics 1999) Amazon: www.amazon.com/Mathematical-Universe-Pythagoras-Planck-Springer/dp/3030506517/ref=sr_1_3?crid=2DM7HFCREAZGV&dchild=1&keywords=the+mathematical+universe&qid=1615231512&s=books&sprefix=the+mathemati%2Caps%2C337&sr=1-3 Prior to the 1920s it was generally thought, with a few exceptions, that our galaxy, the Milky Way, was the entire Universe. Based on the work of Henrietta Leavitt with Cepheid variables, astronomer Edwin Hubble was able to determine that the Andromeda Galaxy and others had to lie outside our own. Moreover, based on the work of Vesto Slipher, involving the redshifts of these galaxies, Hubble was able to determine that the Universe was not static, as had been previously thought, but expanding. The number of galaxies has also been expanding, with estimates varying from 100 billion to 2 trillion. While every galaxy in the Universe is interesting just by its very fact of being, the author has selected 51 of those that possess some unusual qualities that make them of some particular interest. These galaxies have complex evolutionary histories, with some having supermassive black holes at their core, others are powerful radio sources, a very few are relatively nearby and even visible to the naked eye, whereas the light from one recent discovery has been travelling for the past 13.4 billion years to show us its infancy, and from a time when the Universe was in its infancy. And in spite of the vastness of the Universe, some galaxies are colliding with others, embraced in a graceful gravitational dance. Indeed, as the Andromeda Galaxy is heading towards us, a similar fate awaits our Milky Way. When looking at a modern image of a galaxy, one is in awe at the shear wondrous nature of such a magnificent creation, with its boundless secrets that it is keeping from us, its endless possibilities for harboring alien civilizations, and we remain left with the ultimate knowledge that we are connected to its glory. Available at: http://www.morganclaypoolpublishers.com/catalog_Orig/product_info.php?products_id=1301 Amazon:www.amazon.com/Interesting-Galaxies-Universe-Concise-Physics-ebook/dp/B07HHJ12Z3/ref=sr_1_1?s=books&ie=UTF8&qid=1537841877&sr=1-1&keywords=the+most+interesting+galaxies+in+the+universe |
An orchid can grow indefinitely if properly cared for as it produces new growth as the old withers and dies. In fact, the Singapore Botanic Gardens has a thriving Tiger Orchid that was planted in 1861, and a Bulbophyllum ornatissimum, purchased at auction in 1887 is still growing at the Glasnevin National Botanical Gardens in Dublin. But they do require that the orchid grower reproduce within limits the growing conditions of their native habitat. And sometimes those conditions are of steamy South American jungles or montane rainforests of India, the highlands of New Guinea, or coastal lowlands of Brazil.
On the other hand, that is one of the features that make orchids so fascinating. Living as many people do in their own urban jungle, orchids allow us to bring some of these exotic places and their flora into our lives. Many of us will not ever visit any of the places where exotic orchids are endemic, but we can still have a sample of the place, growing in our own homes.
Orchids also represent something we have lost. Many generations of our ancestors once lived in forested regions in close quarters with Nature and for many of us that is not even a distant memory of even our grandparents. But traces of it are still in our DNA and providing homo sapiens with nature escapes and wilderness is essential for coping with modern living.
Another feature of orchids that make them so fascinating is that they are like no other family of flowering plants. The endless diversity of form, color, and scent of their flowers, the unusual appearance of their vegetative growth, often with pseudobulbs beneath their leaves, and of course the unusual habit of a great many orchids (about 70%) to grow in the branches of trees as epiphytes, all mark out orchids as a group of flowering plants unlike any other on Earth.
For the above reasons, many people speak of growing orchids as they would of an addiction, say to heroin. Once you have started with a single plant, that leads to two, then three, then before you know it they have taken over your house and next thing you are building a greenhouse. Or, you find yourself posting enumerable photos of orchids on Pinterest, Flickr or other image sharing websites so that you do not even have to grow orchids to become obsessed with them. Just their exotic beauty is enough for some.
This book is intended for those who have started along this long slippery slope, who know a little already about these unusual plants but now wish to go deeper into some of the technical details and also what can be learned from the fascinating ongoing orchid research.
But this is not a book about how to grow orchids. There are many fine books already on this subject. This is a book about why what you are growing is so special and why you have this persistent addiction that you cannot seem to shake. And it is also a book about sex, since orchids have mastered more techniques than are found in the Kama Sutra.
In no way can this book exhaustively cover all orchid genera and species. It is a selection only of interesting and unusual orchids and perhaps the reader’s favorite exotic orchid is not included. But many others will be, so enjoy this fascinating journey.
Available at amazon and other booksellers: Click here to order
On the other hand, that is one of the features that make orchids so fascinating. Living as many people do in their own urban jungle, orchids allow us to bring some of these exotic places and their flora into our lives. Many of us will not ever visit any of the places where exotic orchids are endemic, but we can still have a sample of the place, growing in our own homes.
Orchids also represent something we have lost. Many generations of our ancestors once lived in forested regions in close quarters with Nature and for many of us that is not even a distant memory of even our grandparents. But traces of it are still in our DNA and providing homo sapiens with nature escapes and wilderness is essential for coping with modern living.
Another feature of orchids that make them so fascinating is that they are like no other family of flowering plants. The endless diversity of form, color, and scent of their flowers, the unusual appearance of their vegetative growth, often with pseudobulbs beneath their leaves, and of course the unusual habit of a great many orchids (about 70%) to grow in the branches of trees as epiphytes, all mark out orchids as a group of flowering plants unlike any other on Earth.
For the above reasons, many people speak of growing orchids as they would of an addiction, say to heroin. Once you have started with a single plant, that leads to two, then three, then before you know it they have taken over your house and next thing you are building a greenhouse. Or, you find yourself posting enumerable photos of orchids on Pinterest, Flickr or other image sharing websites so that you do not even have to grow orchids to become obsessed with them. Just their exotic beauty is enough for some.
This book is intended for those who have started along this long slippery slope, who know a little already about these unusual plants but now wish to go deeper into some of the technical details and also what can be learned from the fascinating ongoing orchid research.
But this is not a book about how to grow orchids. There are many fine books already on this subject. This is a book about why what you are growing is so special and why you have this persistent addiction that you cannot seem to shake. And it is also a book about sex, since orchids have mastered more techniques than are found in the Kama Sutra.
In no way can this book exhaustively cover all orchid genera and species. It is a selection only of interesting and unusual orchids and perhaps the reader’s favorite exotic orchid is not included. But many others will be, so enjoy this fascinating journey.
Available at amazon and other booksellers: Click here to order
Marie Bashkirtseff was of one of the most extraordinary women of the 19th century. Her Journal (originally comprising some 20,000 hand-written pages but pared down to a few hundred for publication) was a cause célèbre after her death and continue to be an inspiration to the Women’s Movement to this day. It also inspired such writers as Anaïs Nin and Katherine Mansfield among many others.
Born into an aristocratic family in a village in Ukraine the family soon settled in France, first in Nice and later in Paris. Taught entirely by tutors at home Marie spoke multiple languages, played numerous musical instruments and longed for a singing career on the stage. An illness that affected her throat made her change course and she took up painting for which she had a latent talent. As a student at the Académie Julian in Paris she was soon exhibiting at the annual Paris Salon, the penultimate venue for artists.
But it was her personality that makes Marie Bashkirtseff such an exceptional individual. At a very young age she was already exhibiting in her Journal the thoughts of a learned philosopher, wrestling with the nature of God, the position of women in society and the politics of men. On the other hand, her family life was one of constant turmoil and personal strife. Having contracted tuberculosis in early childhood she ceaselessly strove to shrug it off in her quest to achieve greatness. In the end, a great tragedy unfolds during her final days as she and her dear friend, the well-known French artist, Jules Bastien-Lepage, are both virtually dying together in one another’s arms. Marie is 25, Bastien-Lepage dies a month later age 36.
The book is somewhat unique in format. The first part of about 200 pages is a biographical section that describes Marie’s unusual and fascinating life. Then a second section, consists of a Journal excerpt (in English translation from the original French) on each left-hand page, juxtaposed with one of her outstanding works of art on the facing page. In this manner, we learn about her remarkable life and tribulations, enter her restive and brilliant mind via her Journal, as well as appreciate her exceptionally fine works as an artist.
Some Marie Bashkirtseff Quotations:
To die! My God, to die! To die without leaving anything behind me? To die like a dog, like hundreds of thousands of women whose names are barely engraved upon their tombs?
Let us love dogs; let us love only dogs. Men and cats are unworthy creatures.
Love accomplishes the miracle of mixing souls.
My relatives haven’t committed any crime except to be born stupid!
All men are scoundrels; a woman must change them as she changes her gloves.
I hide a mystery; death has touched me with its finger.
AVAILABLE now from Vernon Press at a 10% discount using code CFC33134BB0 on checkout: vernonpress.com/title?id=240#.WIPQpjk2t3k
or on Amazon: https://www.amazon.com/dp/1622731719/
or Barnes & Noble: http://www.barnesandnoble.com/w/portrait-of-young-genius-joel-l-schiff/1125364918?
Born into an aristocratic family in a village in Ukraine the family soon settled in France, first in Nice and later in Paris. Taught entirely by tutors at home Marie spoke multiple languages, played numerous musical instruments and longed for a singing career on the stage. An illness that affected her throat made her change course and she took up painting for which she had a latent talent. As a student at the Académie Julian in Paris she was soon exhibiting at the annual Paris Salon, the penultimate venue for artists.
But it was her personality that makes Marie Bashkirtseff such an exceptional individual. At a very young age she was already exhibiting in her Journal the thoughts of a learned philosopher, wrestling with the nature of God, the position of women in society and the politics of men. On the other hand, her family life was one of constant turmoil and personal strife. Having contracted tuberculosis in early childhood she ceaselessly strove to shrug it off in her quest to achieve greatness. In the end, a great tragedy unfolds during her final days as she and her dear friend, the well-known French artist, Jules Bastien-Lepage, are both virtually dying together in one another’s arms. Marie is 25, Bastien-Lepage dies a month later age 36.
The book is somewhat unique in format. The first part of about 200 pages is a biographical section that describes Marie’s unusual and fascinating life. Then a second section, consists of a Journal excerpt (in English translation from the original French) on each left-hand page, juxtaposed with one of her outstanding works of art on the facing page. In this manner, we learn about her remarkable life and tribulations, enter her restive and brilliant mind via her Journal, as well as appreciate her exceptionally fine works as an artist.
Some Marie Bashkirtseff Quotations:
To die! My God, to die! To die without leaving anything behind me? To die like a dog, like hundreds of thousands of women whose names are barely engraved upon their tombs?
Let us love dogs; let us love only dogs. Men and cats are unworthy creatures.
Love accomplishes the miracle of mixing souls.
My relatives haven’t committed any crime except to be born stupid!
All men are scoundrels; a woman must change them as she changes her gloves.
I hide a mystery; death has touched me with its finger.
AVAILABLE now from Vernon Press at a 10% discount using code CFC33134BB0 on checkout: vernonpress.com/title?id=240#.WIPQpjk2t3k
or on Amazon: https://www.amazon.com/dp/1622731719/
or Barnes & Noble: http://www.barnesandnoble.com/w/portrait-of-young-genius-joel-l-schiff/1125364918?
Dunedin-born artist Grace Joel (1865-1924) exhibited to acclaim in London and Paris, yet she and her art are relatively unknown today.
Joel excelled at portraiture and mother and child studies, and was skilled in portraying the nude. She received her artistic training in Melbourne, and lived for the mature years of her career in London, where her work appeared at the prestigious Royal Academy, as well as the Paris Salon and the Royal Scottish Academy. She also held a number of solo exhibitions in European cities. Today she is claimed by New Zealand, Australia and Britain.
One possible reason why Joel's work has not remained visible is that few details of he personal life survive. Only three letters have been found, and they reveal little of the person who wrote them. Undaunted, the author has pulled together from the words of her contemporaries, various newspaper accounts, scraps in other historical archives and close study of her extant paintings a portrayal of this talented woman that is as intimate and engaging as her work. He also sets Grace Joel and her work in the times in which she lived, and the artistic communities of which she was apart in the Belle Epoque.
Joel excelled at portraiture and mother and child studies, and was skilled in portraying the nude. She received her artistic training in Melbourne, and lived for the mature years of her career in London, where her work appeared at the prestigious Royal Academy, as well as the Paris Salon and the Royal Scottish Academy. She also held a number of solo exhibitions in European cities. Today she is claimed by New Zealand, Australia and Britain.
One possible reason why Joel's work has not remained visible is that few details of he personal life survive. Only three letters have been found, and they reveal little of the person who wrote them. Undaunted, the author has pulled together from the words of her contemporaries, various newspaper accounts, scraps in other historical archives and close study of her extant paintings a portrayal of this talented woman that is as intimate and engaging as her work. He also sets Grace Joel and her work in the times in which she lived, and the artistic communities of which she was apart in the Belle Epoque.
This is an accessible and multidisciplinary introduction to cellular automata. As the applicability of cellular automata broadens and technology advances, there is a need for a concise, yet thorough, resource that lays the foundation of key cellularautomata rules and applications. In recent years, Stephen Wolfram's A New Kind of Science has brought the modeling power that lies in cellular automata to the attentionof the scientific world, and now, Cellular Automata: A Discrete View of the World presents all the depth, analysis, and applicability of the classic Wolfram text in a straightforward, introductory manner. This book offers an introduction to cellular automata as a constructive method for modeling complex systems where patterns of self-organization arising from simple rules are revealed in phenomena that exist across a wide array of subject areas, including mathematics, physics, economics, and the social sciences. The book begins with a preliminary introduction to cellular automata, including a brief history of the topic along with coverage of sub-topics such as randomness, dimension, information, entropy, and fractals. The author then provides a complete discussion of dynamical systems and chaos due to their close connection with cellular automata and includes chapters that focus exclusively on one- and two-dimensional cellular automata. The next and most fascinating area of discussion is the application of these types of cellular automata in order to understand the complex behavior that occurs in natural phenomena. Finally, the continually evolving topic of complexity is discussed with a focus on how to properly define, identify, and marvel at its manifestations in various environments. The author's focus on the most important principles of cellular automata, combined with his ability to present complex material in an easy-to-follow style, makes this book a very approachable and inclusive source for understanding the concepts and applications of cellular automata. The highly visual nature of the subject is accented with over 200 illustrations, including an eight-page color insert, which provide vivid representations of the cellular automata under discussion. Readers also have the opportunity to follow and understand the models depicted throughout the text and create their own cellular automata using Java applets and simple computer code, which are available via the book's FTP site. This book serves as a valuable resource for undergraduate and graduate students in the physical, biological, and social sciences and may also be of interest to any reader with a scientific or basic mathematical background.
The Laplace transform is a wonderful tool for solving ordinary and partial differential equations and has enjoyed much success in this realm. With its success, however, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. Even proofs of theorems often lack rigor, and dubious mathematical practices are not uncommon in the literature for students. In the present text, I have tried to bring to the subject a certain amount of mathematical correctness and make it accessible to un dergraduates. Th this end, this text addresses a number of issues that are rarely considered. For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, why is it justified to take the Laplace transform of both sides of the equation (Theorem A. 6)? Or, in many proofs it is required to take the limit inside an integral. This is always fraught with danger, especially with an improper integral, and not always justified. I have given complete details (sometimes in the Appendix) whenever this procedure is required. IX X Preface Furthermore, it is sometimes desirable to take the Laplace trans form of an infinite series term by term. Again it is shown that this cannot always be done, and specific sufficient conditions are established to justify this operation.
This is the first book devoted solely to the subject of normal families of analytic and meromorphic functions since the 1927 treatise of Paul Montel. A considerable body of research has evolved since then, and this text provides a comprehensive treatment of the entire theory. Since its inception early this century, the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter which has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Numerous applications of the normal family theory are discussed, particularly those found in the study of extremal problems, normal functions, harmonic functions, discontinuous groups, and complex dynamical systems. Only a basic knowledge of complex analysis and topology is assumed. All other necessary material for the study of the subject is included in the first chapter. The scope of the book ranges from advanced undergraduate to research level.
