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Quantumlike Chaos in Prime Number Distribution and in Turbulent Fluid Flows
 APEIRON
, 2001
"... re applied to derive the following results for the observed association between prime number distribution and quantumlike chaos. (i) Number theoretical concepts are intrinsically related to the quantitative description of dynamical systems. (ii) Continuous periodogram analyses of different set ..."
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re applied to derive the following results for the observed association between prime number distribution and quantumlike chaos. (i) Number theoretical concepts are intrinsically related to the quantitative description of dynamical systems. (ii) Continuous periodogram analyses of different sets of adjacent prime number spacing intervals show that the power spectra follow the model predicted universal inverse powerlaw form of the statistical normal distribution. The prime number distribution therefore exhibits selforganized criticality, which is a signature of quantumlike chaos. (iii) The continuum real number field contains unique structures, namely, prime numbers, which are analogous to the dominant eddies in the eddy continuum in turbulent fluid flows. Keywords: quantumlike chaos in prime numbers, fractal structure of primes, quantification of prime number distribution, prime numbers and fluid flows 1. Introduction he continuum real number field (infinite numbe
Diophantus’ 20th problem and fermat’s last theorem for n=4  Formalization of . . .
, 2005
"... We present the proof of Diophantus’ 20th problem (book VI of Diophantus’ Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the ..."
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We present the proof of Diophantus’ 20th problem (book VI of Diophantus’ Arithmetica), which consists in wondering if there exist right triangles whose sides may be measured as integers and whose surface may be a square. This problem was negatively solved by Fermat in the 17th century, who used the wonderful method (ipse dixit Fermat) of infinite descent. This method, which is, historically, the first use of induction, consists in producing smaller and smaller nonnegative integer solutions assuming that one exists; this naturally leads to a reductio ad absurdum reasoning because we are bounded by zero. We describe the formalization of this proof which has been carried out in the Coq proof assistant. Moreover, as a direct and no less historical application, we also provide the proof (by Fermat) of Fermat’s last theorem for n = 4, as well as the corresponding formalization made in Coq.
Contributions to a science of contemporary mathematics, preprint; current draft at http:// www.math.vt.edu/people/quinn
"... Abstract. This essay provides a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century, and in other sciences. Roughly, modern practice is well adapted to the structure of the subject and, within this constraint, much better ad ..."
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Abstract. This essay provides a description of modern mathematical practice, with emphasis on differences between this and practices in the nineteenth century, and in other sciences. Roughly, modern practice is well adapted to the structure of the subject and, within this constraint, much better adapted to the strengths and weaknesses of human cognition. These adaptations greatly increased the effectiveness of mathematical methods and enabled sweeping developments in the twentieth century. The subject is approached in a bottomup ‘scientific ’ way, finding patterns in concrete microlevel observations and being eventually lead by these to understanding at macro levels. The complex and intenselydisciplined technical details of modern practice are fully represented. Finding accurate commonalities that transcend technical detail is certainly a challenge, but any account that shies away from this cannot be complete. As in all sciences, the final result is complex, highly nuanced, and has many surprises. A particular objective is to provide a resource for mathematics education. Elementary education remains modeled on the mathematics of the nineteenth century and before, and outcomes have not changed much either. Modern methodologies might lead to educational gains similar to those seen in professional practice. This draft is about 90 % complete, and comments are welcome. 1.
Quantumlike Chaos in the Frequency Distributions of Bases A, C, G, T in Human Chromosome1 DNA
, 2004
"... Introduction DNA topology is of fundamental importance for a wide range of biological processes [1]. Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state fro ..."
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Introduction DNA topology is of fundamental importance for a wide range of biological processes [1]. Since the topological state of genomic DNA is of importance for its replication, recombination and transcription, there is an immediate interest to obtain information about the supercoiled state from sequence periodicities [2,3]. Identification of dominant periodicities in DNA sequence will help understand the important role of coherent structures in genome sequence organization [4,5]. Li [6] has discussed meaningful applications of spectral analyses in DNA sequence studies. Recent studies indicate that the DNA sequence of letters A, C, G and T exhibit the inverse power law form 1/f frequency spectrum where f is the frequency and a the exponent. It is possible, therefore, that the sequences have longrange order [714]. Inverse powerlaw form for power spectra of fractal spacetime fluctuations is generic to dynamical systems in nature and is identified as selforganized criticality
C. Roy Keys Inc.
"... this paper shows (Section 2) that Fibonacci series underlies fractal fluctuations on all spacetime scales ..."
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this paper shows (Section 2) that Fibonacci series underlies fractal fluctuations on all spacetime scales
The Poetics of Experience: A FirstPerson Creative and Critical Investigation of SelfExperience and the Writing of Poetry
, 2008
"... Copyright © and Moral Rights for this thesis are retained by the author and/or other copyright owners. A copy can be downloaded for personal noncommercial research or study, without prior permission or charge. This thesis cannot be reproduced or quoted extensively from without first obtaining permi ..."
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Copyright © and Moral Rights for this thesis are retained by the author and/or other copyright owners. A copy can be downloaded for personal noncommercial research or study, without prior permission or charge. This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder/s. The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", Canterbury Christ Church University,
Achievement
"... (A paper commissioned by the National Council on Education and the Disciplines (NCED) for the NCED Project on Quantitative Literacy. Do not cite or quote without permission.) Abstract: One of the many ills afflicting mathematics education is its excessively narrow focus on algebraic symbol manipulat ..."
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(A paper commissioned by the National Council on Education and the Disciplines (NCED) for the NCED Project on Quantitative Literacy. Do not cite or quote without permission.) Abstract: One of the many ills afflicting mathematics education is its excessively narrow focus on algebraic symbol manipulation to the detriment of more widely useful aspects of the mathematical sciences. The intensely vertical climb from algebra to calculus is needlessly narrow, producing more victims than successes and offering few opportunities for students to recoup from their inevitable mistakes. In this paper a proposal is made to restore balance and incentive to mathematics education in grades 612 by focusing on horizontal breadth and connectedness that offer multiple points of entry, numerous opportunities for catching up, and wide windows into the ways in which mathematical thinking pervades modern life.
Learning Goal: Students will represent and analyze mathematical patterns, relationships, and
"... functions to model and solve problems. With this learning goal in mind, Minnesota students will have the opportunity to pursue the following instructional components: • Recognize, describe, and generalize patterns and build mathematical models to make predictions. • Analyze the interaction between q ..."
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functions to model and solve problems. With this learning goal in mind, Minnesota students will have the opportunity to pursue the following instructional components: • Recognize, describe, and generalize patterns and build mathematical models to make predictions. • Analyze the interaction between quantities and/or variables to model patterns of change. • Use algebraic concepts and processes to represent and solve problems that involve variable quantities. As biology is the science of life and physics the science of energy and matter, so mathematics is
in Human Chromosome1 DNA
"... Abstract: Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse powerlaw form of the power spectra of fractal spacetime fluctuations is generic to the dynamical systems in nature and is identified as selforganized criticality. In t ..."
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Abstract: Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse powerlaw form of the power spectra of fractal spacetime fluctuations is generic to the dynamical systems in nature and is identified as selforganized criticality. In this study it is shown that the power spectra of the frequency distributions of bases A, C, G, T in the Human chromosome 1 DNA exhibit selforganized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Selforganized criticality implies that noncoding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.