Distribution of Sequences: A Theory
doc. RNDr. Oto Strauch, DrSc.
Abstract: In this book we develop the theory of distribution of sequences which we shall identify it with the theory of distribution functions of sequences.
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VEDA - Publishing House of the Slovak Academy of Sciences has issued the book
Credo of a mathematician about music and a little bit also about philosophy (in Slovak)
by J. Haluška (research fellow of MI SAS).
Additional information on the book (contents, foreword, order information) is available at the author's website.
A book by Peter Lang - Europaeischer Verlag der Wissenshaften, authors: Oto Strauch / Štefan Porubský
Distribution of Sequences: A Sampler
"This is the first monograph aiming in a systematized description of a variety of aspects of the distribution properties of one-dimensional or multi-dimensional sequences. The heart of the book is formed by more than 500 items of sequences, for instance those involving logarithmic functions, trigonometric functions, polynomials, sum-of-digits functions, integer part functions, number-theoretic functions, primes, normal numbers, the van der Corput sequence, pseudorandom number generators, etc. Properties of sequences like low discrepancy sequences, good lattice points, nets, lattice rules, completely uniformly distributed sequences, block sequences, circle sequences, etc. are also covered. The reader finds after a complete mathematical description of the sequences characterizations of their currently known distribution properties (in terms of distribution functions, or various types of discrepancy, diaphony, dispersion, etc.) together with comments documenting the history, development, open problems (if exist) and the relevant literature for each of the referred to sequences. The cummulative updated bibliography at the end of the book contains more than 1000 items. The book can be useful not only to advanced students and mathematicians working in the area but also for those wanting to delve deeper into the many facets of the uniform distribution of sequences and in applications of quasi-Monte Carlo methods."
Published in conjunction with VEDA, publishing house of the Slovak Academy of Sciences.
A book by Marcel Dekker - Ister Sciences, author J. Haluška, titled
The Mathematical Theory of Tone Systems
Containing over 200 chapter examples of past and prevalent tone systems-and an appendix with hundreds more- The Mathematical Theory of Tone Systems views classical harmonic analysis vis-a-vis uncertainty-based information theory…covers dissonance functions, fuzziness, and relatedness within tone systems…explores wavelets and nonspecificity, as well as pitch granulation and ambiguity…discusses measurements for equal temperaments along with algebraic representations of harmonic structures…identifies acoustics algorithms, facets of meantone systems, and the anatomy of the Pythagorean whole tone…provides a formalization of well tempered tone systems…regards Pythagorean systems of India and China, African free tuning, Indonesian gamelan, Pacific Ocean tuning, and Western system trends…and considers Petzval tone systems and Huygens-Fokker tuning, tetrachords, the Euler space, and commas.
JÁN HALUŠKA is a senior research fellow at the Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovak Republic. The author of number mathematical publications and a frequent presenter at international conferences, he is also the editor of the journal Tatra Mountains Mathematical Publications. Dr. Haluška was honored with the Prize of the Slovak Academy of Sciences (1999) for a collection of papers on tone systems. His musical background includes ten years' experience as a practicing organist and pipe organ tuner. Dr. Haluška received the M.S. degree (1978) from Odessa State University, Ukraine, the RNDr. degree (1986) from Comenius University, Bratislava, Slovak Republic, and the Ph.D. degree (1991) from the Mathematical Institute of the Slovak Academy of Sciences.
Published in conjunction with Ister Science Ltd.
Distribution for the Slovak and Czech Republic:
Ister Science, Staromestska 6, 811 03 Bratislava, Slovakia
A book by Kluwer Academic Publishers with title
New Trends in Quantum Structures
was published. Authors A. Dvurečenskij and S. Pulmannová are SAS employees.
This monograph deals with the latest results concerning different types of quantum structures. This is an interdisciplinary realm joining mathematics, logic and fuzzy reasoning with mathematical foundations of quantum mechanics, and it indicates many ways of their applications.
The book consists of seven chapters. The first four chapters are devoted to difference posets and effect algebras; MV-algebras and quantum MV-algebras, and their quotients; and to tensor product of difference posets. Chapter 5 and 6 discuss BCK-algebras with their applications. Chapter 7 addresses Loomis-Sikorski-type theorems for MV-algebras and BCK-algebras. Throughout the book, important facts and concepts are illustrated by exercises.
This book will be of interest to mathematicians, physicists, logicians, philosophers, quantum computer experts, and students interested in mathematical foundations of quantum mechanics, as well as in non- communicative measure theory, orthomodular lattices, MV-algebras, effect algebras, Hilbert space quantum mechanics, and fuzzy sets ideas.
Distributor for Slovak Republic and Czech Republic,
Ister Science Ltd.,
811 03 Bratislava,
In all other countries, sold and distributed by
Kluwer Academic Publishers,
P. O. Box 322, 3300 AH Dordrecht, The Netherlands.