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The study of bialgebraic structures started very recently. Till date there are no books solely dealing with bistructures. The study of bigroups was carried out in 1994-1996. Further research on bigroups and fuzzy bigroups was published in 1998. In the year 1999, bivector spaces was introduced. In 2001, concept of free De Morgan bisemigroups and bisemilattices was studied. It is said by Zoltan Esik that these bialgebraic structures like bigroupoids, bisemigroups, binear rings help in the construction of finite machines or finite automaton and semi automaton. The notion of non-associative bialgebraic structures was first introduced in the year 2002. The concept of bialgebraic structures which we define and study are slightly different from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebraic structures using category theory or linear logic....

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A collection of papers concerning Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

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This document will describe the current status on the search for factors of Smaranda.che consecutive numbers and their reverse. A complete list up to index 200 will be given, with all known factors. Smarandache numbers are the concatenation of the natural numbers from one up to the given index, and reverse Smaranda.che numbers are the concatenation of the natural numbers from the given index dO\vIJ. to 1....

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A collection of papers concerning smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

Description Details
A collection of papers concerning Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

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As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of intrinsic imperfection where a typical and single value does not exist), incomplete knowledge (ignorance of the totality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures).”...

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In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full of indeterminacy; it interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential system, may be false in another, and vice versa; attempts to make peace in the war of ideas, and to make w...

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Papers concerning any of the Smarandache type functions, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, conjectures, open problems, neutrosophic logic/set/probability, etc. have been selected for this volume. The...

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Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe} quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or Gennan....

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The creation of a book is an act that requires several preconditions. I) An interesting and worthwhile subject; 2) A fair, yet demanding editor.; 3) Someone willing to put the words on paper. Given the existence of these three items, the leap to making the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As such, it is hoped that you get as much out of this book as the author did in writing it. While all books are a collective work, the responsibility for any errors ultimately falls to the author, and this is no exception....

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As one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft spot in their hearts for the "purity" of the integers. When "Fermat's Last Theorem" was finally proven after centuries of effort, the result was discussed on many major news shows in the US. Brief comments also appeared in the major weekly news magazines....

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As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classical logic, but as you will see in the book, there are two intermediate steps between them. Neutrosophic logic is yet another idea generated by Florentin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to quantum me...

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For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer examination. "The speed of light relative to what?" I often asked anyone who would listen. The common response was, "Light needs no specification of that kind; its speed is the same no matter who measures it." "That's true." I would respond; "That's just the second postulate of special relativity which is not in doubt; but that postulate applies to light, and we're talking about rocketships here." However it seemed that no one understood what I was saying. By referring to the universal constant c= 299.792 458 megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of discussion even when it is not. The careful reader will know not to immediately think "light" when he hears or reads "the speed of light." But it is better to have a neutral name for that universal constant. It has been called the Lorentz speed; Ignaz...

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One's reach should exceed one's grasp. Thus we reach for Alpha Centauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or under any plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase one has a high probability of success, given the required propulsion system; the chances of phase two working will be indicated by results obtained from phase one. A fundamental problem is the one of propulsion. It is important to the working of this plan, a highly optimistic one, that the engine be capable of a sustained acceleration of ¼ G in phase one and 1G in phase two. (1G = 9.80665 m/s2) Such an engine is within the reach of present ideas....

Table of Contents Details
Prefaces. 6 -- Ch.1. Introduction . 11 -- Ch.2. The Human Barrier. 14 -- Ch.3. An Overview. 18 -- Ch.4. Acceleration Due to Light Pressure. 21 -- Ch.5. Light Sailing is Not All There Is. 27 -- Ch.6. Einstein's Light Barrier. 32 -- Ch.7. The Phase One Experiment: The First Starship. 37 -- Ch.8. The Phase Two Experiment: Alpha Centauri or Bust!. 45 -- Ch.9. Voyage to the Center of the Galaxy. 50 -- Ch.10. An Hypothesis: There is no Speed Barrier in the Universe. 52 --...