Csaba Varga proves with sharp logic - examining numerous archeological finds - in this book that our early ancestors could write text and numbers routinely 30.000 years ago and since they never stopped doing it. He connects all writings systems, alphabets of our culture history to one proto-alphabet that did not change since those prehistoric times. Only a man could reach this goal, who can perceive as an artist, have the logic of a mathematician and is free of any political or scientific doctrines.
This book provides a modern and comprehensive presentation of a wide variety of problems arising in nonlinear analysis, game theory, engineering, mathematical physics and contact mechanics. It includes recent achievements and puts them into the context of the existing literature. The volume is organized in four parts. Part I contains fundamental mathematical results concerning convex and locally Lipschits functions. Together with the Appendices, this foundational part establishes the self-contained character of the text. As the title suggests, in the following sections, both variational and topological methods are developed based on critical and fixed point results for nonsmooth functions. The authors employ these methods to handle the exemplary problems from game theory and engineering that are investigated in Part II, respectively Part III. Part IV is devoted to applications in contact mechanics. The book will be of interest to PhD students and researchers in applied mathematics as well as specialists working in nonsmooth analysis and engineering.
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.
All languages of Eurasia and some aboriginal languages in America contain more or less remnants of the archaic, so-called "proto-nostratic" language, the first(?) one of humanity, the language of the Stone-Age, of prehistoric times. Our culture, customs and religions are the product of the archaic culture, the creator of this language. The author invites you to explore this archaic but up-to-date language. One of the most impressive recognition in the book is that "the word of the Stone Age man is a picture." Those early ancestors told pictures to each other, loudly expressed pictures.
Etymological comparison of word-samples out of different languages. "And the whole earth was of one language and of one speech". (Genesis I.11.1) Where did this language develop?, What kind of language was it? Is it still around? Supposedly we found it - what's the proof of it being the mother of all languages? - We will find the answers for all these questions by reading this book and following the author's sharp logic.
The research to find the proto-nostratic language of Eurasia lately brought more and more results. One of those discoveries is the recognition that a big part of the English vocabulary - as presented in this book - has much more similarity to the Hungarian than we thought before. These similarities are touching the basic elements of both languages. An important detail of this recognition is that we do not have to move people forth and back all over the continents to explain "takeover"- words. The common features are the legacy of an archaic root-language, once spoken by everybody in Eurasia. The recognition of so many common words could be quite useful for Hungarians learning English and vice versa.
La 4e de couverture indique : "The author introduces the reader to reasoning in law through the possilities, boundaries and traps of assuming personal responsibility and impersonal pattern adoption that have arisen in the history of human thought and in the various legal cultures. He discloses actual processes hidden by the veil of patterns followed in thinking, processes that we encounter both in our conceptual-logical quests for certainties and in the undertaking of fertilising ambiguity. When trying to identify definitions lurking behind the human construct of facts, nitons, norms, logic, and thinking, or behind the practice of giving meanings, he discovers tradition in our presuppositions, and our world-view and moral stance in our tacit agreements. Recognising the importance of the role communication plays in shaping society, he describes our existence and institutions as self-regulating processes. Since law is a wholly social venture, we not only take part in its oeuvre with our entire personality, but are also collectively responsible for its destiny. In the final analysis, anything can be qualified as 'legal' or 'non-legal' in one or another recognised sense in which law can originate, but, as a relative totality, it can only be qualified as 'more legal' or 'less legal' in any combination of the above senses. Being formed in an uninterrupted process, neither the totality nor particular pieces of law can be taken as complete or unchangeably identical with itself. Therefore law can only be identified through its motions and computable states of 'transforming into' or 'withdrawing from' the distinctive domain of the law. Thereby both society at large and its legal professionals actually contribute to -by shaping incessantly- what presents itself as ready-to-take, according to the law's official ideology. For our initation, play, role-undertaking and human responsibility lurk behind the law's formal mask in the backstage. Or, this equals to realise that all we have become subjects from mere objects, actors from mere addressees. And despite the variety of civilisational overcoasts, the entire culture of law is still exclusively inherent in us who experience it day to day. We bear it and shape it. Everything coventional in it is convenctionalised by us. It has no further existence or effect bexond this. And with its existence inherent in us, we cannot convey the responsibility to be born for it on somebody else either. It is ours in its totality so much that it cannot be torn out of our days or acts. It will thus turn into what we guard it to become. Therefore we must take care of it at all times since we are, in many ways, taking care of our own
The Author investigated 30,000 years writing-history of humanity in his previous book Signs Letters Alphabet. This book ads to his investigation everything he could find about numbers and number writing in our history. The ancient numerals: the dot, line, a line perpendicular to it (I) and a long line. Every one of these signs marked its own local value. Thus, we can write every number with different arrangements of these four signs. The reader can compare the 17,000-year-old numeral pictured on the front of this book (written on the cave's wall in Lascaux) with the 19th century signs seen on the inside of this back cover. The earliest found dot-line numeral so far is around 30,000 years old. Finds with such recordings get more numerous as we approach our time. This method was used, unchanged, in Ancient Egypt through its history, in China, by the Mayans, by the Aramaic culture in Middle East, the Eskimos and even in the salt mines of Transylvanian until the start of 20th century. Everybody did it, because there was no other kind of number-writing. We are no exception either. Our “Arabic” number-writing has a Palaeolithic origin also, except that the signs became over-ornamented in India, changing to “cifra” (adornment, ciphers), before arriving in Europe. The Palaeolithic calculator had two basic signs: dot and line. The lines could be drawn in the sand as in Egypt or even somewhere in Africa today. The dots could be pebbles, marbles, kernels or shells. The very fast calculator, with wires and beads on them is still used world wide, its name and form varies from abacus (Latin) to soroban (Japan) or from schoti Russia) to suan pan (China).
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