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Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. The book contains definitions, unsolved problems, questions, theoremscorollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost primes, mobile periodicals, functions, tables, prime/square/factorial bases, generalized factorials, generalized palindromes, etc. ). ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This monograph contains discussions of hundreds of open questions, organized into 185 different topics. They represent aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In this second edition, new material has been added in addition to corrections. ... Read more

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The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers. ... Read more

Customer Reviews (2)

pankajmath
an alternate proof to show that combination coeffiecient
C(p^n,r)is divisible by p; where p a prime n & r +ve
integers.
idea first we write the expression of c(p^n,r)
& then wecan conclude from the expression that this is
divisible by p (how ?).

Different Approch to Number theory
The author develops the premise that modern number theory evolved from the ancient Greek preoccupation with two mathematical problems.Searching for the esoteric Perfect Numbers (i.e., whole numbers whose proper divisors sumto the number itself1+2+3=6) and Diophantine Equations (i.e., findingintegral solutions to certain algebraic equations, for example, z^2 = x^2 +y^2).The author calls the later Pythagorianism.The book does a good jobof showing how Fermat's Little Theorem, Euler's generalization, and thefamous Law of Quadradic Reciprocity developed out of the search forMersenne Primes, and consequently Perfect Numbers.Again, it isinteresting to see how Pythagorianism led to the development of algebraicnumbers and eventually to the solution of Fermats "Big" Theorem. Along the way the author elaborates on some of the still unresolvedconjectures within number theory.The writing can be a little"dense" at times, so that some parts require a second reading. Overall the book is enjoyable to read and you will gain some insight thatwon't be gleaned from more standard texts. ... Read more

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This volume is comprised of a series of papers dealing with some of the current unsolved problems in the field of stellar physics. It is also a celebration of the many contributions that Prof. Douglas Gough has made to this subject. Topics discussed include: stars, interiors, stars: evolution, asteroseismology, helioseismology, and fluid dynamics.

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To form an up-to-date picture of what is going on in a given area of mathematics, we usually consult a shelf of current periodicals or, to save time, the appropriate section of a reviewing journal. Thus we learn of new advances in the area, which problems have been solved, what progress has been made with others, while rarely, and then only in the context of the author's own results, do we learn which problems the author failed to solve but considers interesting. In all this, a summary of current problems has no less a place in the development of a subject than a list of achievements, though the apparent connection between the two is often deceptive. Thus, it is desirable to publish from time to time a summary of important problems with the participation of a large circle of authors. The Kourovka notebook is such a collection of unsolved problems in group theory.

The current edition is the seventh, the first having appeared in 1965. Chapter 7 is entirely new; the first six chapters are reproduced from the sixth edition with slight editorial changes. The comments on the problems have been reviewed and augmented.

Experience shows the benefits of collecting problems of interest in a given area. Of the 422 problems in the sixth edition, 151 have now been solved. ... Read more

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All papers in this proceedings volume were peer reviewed. The purview of this third conference was shifted toward biology and medicine. Among the topics covered were: the constructive role of noise in the central nervous system, neuronal networks, and sensory transduction (hearing in humans, photo- and electroreception in marine animals), encoding of information into nerve pulse trains, single molecules and noise (including single molecule detection and characterization by nanopores - molecular "Coulter counting"), concepts of noise in neurophysiology (randomness and order in brain and heart electrical activities under normal conditions and in pathology), the role of noise in genetic regulation and gene expression, biosensors, etc. ... Read more

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"Unsolved Problems on Mathematics for the 21st Century - A Tribute to Kiyoski Iséki's 80th Birthday" is a book dedicated to Dr. Kiyoshi Iséki for his contribution in the scientific, academic and public community. The book is a collection of papers written by scientists in evidence in the area of Pure and Applied Mathematics, Logic, and related issues. The book refers to some significant open problems related to Pure and Applied Mathematics, Mathematical Logic, Foundations of Mathematics, Theoretical Computer Science, correlated themes, in this century. It defines the own style of the book. ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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Noise and fluctuations are at the seat of all physical systems. The advertised scope of the conference included gravitational wave detection, quantum fluctuations, quantum Brownian motion, Brownian ratchets, stochastic resonance, biological systems, semiconductors, electronic devices, sandpile physics, optical phenomena and all types of stochastic phenomena. This solicited a wide range of papers from cosmology to biology to electronic devices. Using the study of fluctuations as the unifying theme for these diverse disciplines is a new and exciting concept. UpoN is a unique conference in that it focuses on open questions and problems, rather than answers. 90% of the solution is asking the right question. The discovery of a problem is often more profound than the discovery of a solution. In the spirit of this conference, authors were asked to (1) conclude each manuscript with a section called AConclusions and Open Questions§ and (2) ask questions to the audience at the §End.txt.Int.: of their oral presentation. An important characteristic of this conference is that refereeing of all papers was carried out to a high standard by the International Scientific Advisory Committee using a strict double-blind refereeing process. ... Read more

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This fourth edition of the conference focused mainly on noise and fluctuations at the nanometer scale in electron devices, bio-materials, and mesoscopic systems. Since the first conference, the aim of the UPoN conferences is to provide a forum for researchers working on noise and fluctuations, where they can present and discuss their scientific problems with particular attention to those which resist solutions. Topics include: Theoretical frontiers on noise and fluctuations; experimental frontiers on noise and fluctuations; enhanced and suppressed shot noise; noise and coherence; noise and chaos; constructive role of noise; noise in biological systems; noise in devices; and noise in complex systems and non-Gaussian fluctuations. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This book provides an interdisciplinary review of one of the great unsolved mysteries that has fascinated scientists for over 150 years: the origin of chirality in biomolecules.

It was Pasteur who first initiated the search for a deterministic theory to explain the 'handedness' of biomolecules. His theory, that a 'dissimetric' force was involved, was correct in essence but he never saw the fruits of his labour. Current thinking tells us that asymmetry in the universe has its origins in the forces that unfolded after the Big Bang and, more specifically, the weak force. Being 'left handed', the weak force imprinted its signature on the evolving Universe. However, at the molecular level, the weak force does not provide a straightforward explanation of biomolecular homochirality. In fact, it is yet to be proved beyond doubt that a causal link exists at all.

Many alternative theories have been put forward, some of them resting on solid ground, but all lacking definitive experimental evidence to back them up. Some postulate that the handedness of molecules in the biosphere arose by chance but this is hard to test. Others rely on discovering life on similar planets and making comparisons with Earth. Alternative theories have emerged from a range of backgrounds including geology, biology, chemistry, physics and astronomy. Current advances in fields as diverse as space exploration, prebiotic chemistry and high-energy physics may help to provide an answer.

Important pieces of information will come from observations at the two frontiers of science: outer space and the subatomic world. Observation of distant planets, galaxies, and even actual sampling of celestial objects from beyond the solar system are projects currently underway. At the other end of the spectrum, there are experiments that study the elemental properties of matter, such as symmetry, and interactions with the fundamental forces. All these efforts will render their fruits soon.

This volume unifies all the theories of the origin of biomolecular homochirality together in one source. The various chapters focus on chance mechanisms, physical forces such as the 'weakinteraction', fluid dynamics, amplification of chirality, the organic contents of meteorites and comets and, finally, the physical view of an intrinsically asymmetric universe.

This complete, interdisciplinary review of an intriguing subject condenses a large and disparate range of contributions from journals in almost every scientific field. The various theories have been organized, interrelated and explained in a unified way. One of the book's strengths is its extensive use of graphic material to aid understanding the many subjects covered. It is fundamental, comprehensive and structured to be accessible for educational purposes.

Customer Reviews (1)

Good on the chemistry; not much about life
The reference to the molecules of life in the title of this book will, no doubt, be helpful for selling it, but, at least from the point of view of a biochemist, it is misleading. It is very much a book for people who think of "life" as the source of the materials studied by natural products chemists, but not to any significant extent as an organized system of reactions. The discussion of the properties of serine is illustrative: if one asked a biochemist to list the most interesting and important characteristics of serine its capacity to form stable non-covalent octamers in solution and in the gas phase would probably not be very prominent, but this is the property that merits five pages of discussion.

The Preface begins by recalling Pasteur's conclusion that a dissymmetric force in nature is responsible for biomolecular handedness and goes on to say that it was in essence correct, as a premonition of the weak (nuclear) force. I doubt whether I am the only person to be sceptical of any idea of accounting for biological chirality in terms of the weak force, which can explain an enantiomeric excess at thermodynamic equilibrium at 25°C of less than one part in 100 000 000 000 000 000. The weak circular polarization (less than 0.5%) of the sun's light at dawn and dusk seems equally unpromising, especially as it operates in opposite directions at the two times. However, there are chemical mechanisms that can in principle amplify extremely small enantiomeric excesses, and although the experimental data are not very promising at present it is probably in these that one needs to look for a solution. Note, incidentally, as the authors do not, that such mechanisms do not require a physical cause of the initial excess, as a statistical fluctuation could be sufficient. In other words we can see biological chirality as a frozen accident without looking for a deterministic explanation.

The title might also lead the unwary reader to expect a discussion of the origin of life, but there is very little on this. The authors appear to be attracted by the idea that organic molecules came to the earth from elsewhere in the universe, and the significant enantiomeric excess (up to 9%) of molecules identified in the Murchison meteorite perhaps supports this.

I was initially surprised at the lack of any mention of prochirality. Probably most chemists are unaware of (or are unimpressed by) the importance of prochirality in the history of biochemistry, in resolving the "puzzle" of how citrate, as a symmetrical species, could be an intermediate in the tricarboxylic acid cycle. Even if they know about prochirality many chemists would probably doubt whether it could have any relevance to the principal theme of the book. However, the ability of prochiral species to behave as if they were chiral when placed in an asymmetric environment could surely contribute to the sort of reactions postulated for amplifying small enantiomeric excesses.

I have perhaps been unduly negative in this review. Certainly, I think most biochemists will be disappointed by it, butif it is accepted on its own terms it is a competent and at times interesting summary of asymmetric influences in the physical world and their capacity to generate asymmetry in chemistry. ... Read more