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FRACTAL REACTOR: an ALTERNATIVE NUCLEAR FUSION SYSTEM BASED on NATURE's GEOMETRY Todd Lael Siler Psi-Phi Communications, LLC 4950 S
TR0700405 13th International Conference on Emerging Nuclear Energy Systems June 03-08, 2007, İstanbul, Türkiye FRACTAL REACTOR: AN ALTERNATIVE NUCLEAR FUSION SYSTEM BASED ON NATURE'S GEOMETRY Todd Lael Siler Psi-Phi Communications, LLC 4950 S. Yosemite Street, F2-325 Greenwood Village, Colorado 80111 USA E-mai 1: [email protected] ABSTRACTS The author presents his concept of the Fractal Reactor, which explores the possibility of building a plasma fusion power reactor based on the real geometry of nature [fractals], rather than the virtual geometry that Euclid postulated around 330 BC(1); nearly every architect of our plasma fusion devices has been influenced by his three-dimensional geometry. The idealized points, lines, planes, and spheres of this classical geometry continue to be used to represent the natural world and to describe the properties of all geometrical objects, even though they neither accurately nor fully convey nature's structures and processes. (2) The Fractal Reactor concept contrasts the current containment mechanisms of both magnetic and inertial containment systems for confining and heating plasmas. All of these systems are based on Euclidean geometry and use geometrical designs that, ultimately, are inconsistent with the Non-Euclidean geometry and irregular, fractal forms of nature (j). The author explores his premise that a controlled, thermonuclear fusion energy system might be more effective if it more closely embodies the physics of a star. This exploratory concept delves into Siler's hypothesis that nature's star "fractal reactors" are composed of fractal forms and dimensions that are statistically self-similar, (4) as shown in Figures 1 & 2. -
Combinatorial Design University of Southern California Non-Parametric Computational Design Strategies
Jose Sanchez Combinatorial design University of Southern California Non-parametric computational design strategies 1 ABSTRACT This paper outlines a framework and conceptualization of combinatorial design. Combinatorial 1 Design – Year 3 – Pattern of one design is a term coined to describe non-parametric design strategies that focus on the permutation, unit in two scales. Developed by combinatorial design within a game combination and patterning of discrete units. These design strategies differ substantially from para- engine. metric design strategies as they do not operate under continuous numerical evaluations, intervals or ratios but rather finite discrete sets. The conceptualization of this term and the differences with other design strategies are portrayed by the work done in the last 3 years of research at University of Southern California under the Polyomino agenda. The work, conducted together with students, has studied the use of discrete sets and combinatorial strategies within virtual reality environments to allow for an enhanced decision making process, one in which human intuition is coupled to algo- rithmic intelligence. The work of the research unit has been sponsored and tested by the company Stratays for ongoing research on crowd-sourced design. 44 INTRODUCTION—OUTSIDE THE PARAMETRIC UMBRELLA To start, it is important that we understand that the use of the terms parametric and combinatorial that will be used in this paper will come from an architectural and design background, as the association of these terms in mathematics and statistics might have a different connotation. There are certainly lessons and a direct relation between the term ‘combinatorial’ as used in this paper and the field of combinatorics and permutations in mathematics. -
The Book Review Column1 by William Gasarch Department of Computer Science University of Maryland at College Park College Park, MD, 20742 Email: [email protected]
The Book Review Column1 by William Gasarch Department of Computer Science University of Maryland at College Park College Park, MD, 20742 email: [email protected] In this column we review the following books. 1. Combinatorial Designs: Constructions and Analysis by Douglas R. Stinson. Review by Gregory Taylor. A combinatorial design is a set of sets of (say) {1, . , n} that have various properties, such as that no two of them have a large intersection. For what parameters do such designs exist? This is an interesting question that touches on many branches of math for both origin and application. 2. Combinatorics of Permutations by Mikl´osB´ona. Review by Gregory Taylor. Usually permutations are viewed as a tool in combinatorics. In this book they are considered as objects worthy of study in and of themselves. 3. Enumerative Combinatorics by Charalambos A. Charalambides. Review by Sergey Ki- taev, 2008. Enumerative combinatorics is a branch of combinatorics concerned with counting objects satisfying certain criteria. This is a far reaching and deep question. 4. Geometric Algebra for Computer Science by L. Dorst, D. Fontijne, and S. Mann. Review by B. Fasy and D. Millman. How can we view Geometry in terms that a computer can understand and deal with? This book helps answer that question. 5. Privacy on the Line: The Politics of Wiretapping and Encryption by Whitfield Diffie and Susan Landau. Review by Richard Jankowski. What is the status of your privacy given current technology and law? Read this book and find out! Books I want Reviewed If you want a FREE copy of one of these books in exchange for a review, then email me at gasarchcs.umd.edu Reviews need to be in LaTeX, LaTeX2e, or Plaintext. -
Geometry, Combinatorial Designs and Cryptology Fourth Pythagorean Conference
Geometry, Combinatorial Designs and Cryptology Fourth Pythagorean Conference Sunday 30 May to Friday 4 June 2010 Index of Talks and Abstracts Main talks 1. Simeon Ball, On subsets of a finite vector space in which every subset of basis size is a basis 2. Simon Blackburn, Honeycomb arrays 3. G`abor Korchm`aros, Curves over finite fields, an approach from finite geometry 4. Cheryl Praeger, Basic pregeometries 5. Bernhard Schmidt, Finiteness of circulant weighing matrices of fixed weight 6. Douglas Stinson, Multicollision attacks on iterated hash functions Short talks 1. Mari´en Abreu, Adjacency matrices of polarity graphs and of other C4–free graphs of large size 2. Marco Buratti, Combinatorial designs via factorization of a group into subsets 3. Mike Burmester, Lightweight cryptographic mechanisms based on pseudorandom number generators 4. Philippe Cara, Loops, neardomains, nearfields and sets of permutations 5. Ilaria Cardinali, On the structure of Weyl modules for the symplectic group 6. Bill Cherowitzo, Parallelisms of quadrics 7. Jan De Beule, Large maximal partial ovoids of Q−(5, q) 8. Bart De Bruyn, On extensions of hyperplanes of dual polar spaces 1 9. Frank De Clerck, Intriguing sets of partial quadrangles 10. Alice Devillers, Symmetry properties of subdivision graphs 11. Dalibor Froncek, Decompositions of complete bipartite graphs into generalized prisms 12. Stelios Georgiou, Self-dual codes from circulant matrices 13. Robert Gilman, Cryptology of infinite groups 14. Otokar Groˇsek, The number of associative triples in a quasigroup 15. Christoph Hering, Latin squares, homologies and Euler’s conjecture 16. Leanne Holder, Bilinear star flocks of arbitrary cones 17. Robert Jajcay, On the geometry of cages 18. -
William Broadhead Professor of History Thesis Supervisor
Vitruvius on Architecture: A Modem Application and Stability Analysis of Classical Structures by Ana S. Escalante Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering at the Lj Massachusetts Institute of Technology June 2013 0 2013 Ana S. Escalante. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created Signature of Author: F , 2 I- - Department of Mechanical Engineering May 28, 2013 Certified by: William Broadhead Professor of History Thesis Supervisor Accepted by: Annette Hosoi Professor of Mechanical Engineering Undergraduate Officer 1 2 Vitruvius on Architecture: A Modem Application and Stability Analysis of Classical Structures by Ana S. Escalante Submitted to the Department of Mechanical Engineering on June 7, 2013 in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Mechanical Engineering ABSTRACT Imperial Rome has left numerous legacies, the most well-known being its literature and monuments. Though many monuments, such as the Pantheon, are well-preserved, in cases where little physical evidence remains, historians can often use literary sources to inform reconstruction efforts. For more technical studies of Roman construction, technical literature is rare and the contemporary awareness of such literature even less known. When Vitruvius wrote De architectura,he did not intend for it to be a manual for instruction but rather a central source of general architectural knowledge. Directly aimed at architects, contractors, and other individuals involved in the design and construction of buildings, De architecturaprovides insight into contemporary technical knowledge. -
July 2008 CURRICULUM VITAE A. NAME: Vlastimil DLAB, F.R.S.C
July 2008 CURRICULUM VITAE A. NAME: Vlastimil DLAB, F.R.S.C. Professor Emeritus and Distinguished Research Professor B. DEGREES: R.N.Dr. Charles University 1956 (Rings of endomorphisms of abelian groups) C.Sc. Charles University 1959 (Generating systems of abelian groups) Ph.D. University of Khartoum 1962 (General algebraic dependence relations) Docent Charles University 1962 Habilitation (The Frattini subgroups of abelian groups) D.Sc. Charles University 1966 (Research in algebra, in particular, axiomatic study of general algebraic dependence structures) C. POSITIONS HELD: Assistant, Czechoslovak Academy of Science, Math. Institute, 1956. Assistant Professor, Charles University, Department of Algebra and Geometry, 1957{1959. Lecturer-Senior Lecturer, University of Khartoum, Department of Mathematics, 1959{1964. Reader, Charles University, Department of Algebra and Geometry, 1964{1965. Research Fellow-Senior Research Fellow, Australian National University, Institute of Advanced Studies, 1965{1968. Professor, Carleton University, Department of Mathematics,1968{1998. Chairman, Carleton University, Department of Mathematics, 1971{1974. Director, Ottawa-Carleton Institute of Mathematics and Statistics, 1992{1994. Chairman, Carleton University, Department of Mathematics and Statistics, 1994{ 1997. Distinguished Research Professor and Professor Emeritus, 1998{present. D. HONOURS: Diploma of Honours, Union of Czechoslovak Mathematicians, 1962. Elected Fellow of the Royal Society of Canada (Academy of Science), 1977. Japan Society for Promotion of Science Fellowship, 1981. Curriculum Vitae Vlastimil Dlab Page 2 Appointed Guest Professor, Beijing Normal University, 1988. German Research Council Senior Fellowship, 1989. Research Achievement Award, Carleton University, 1991. Professor Hospitus, Charles University, 1995. Professor Emeritus, Carleton University, 1998. Distinguished Research Professor, Carleton University, 1998. E. SCHOLARLY AND PROFESSIONAL ACTIVITIES: Member of Council and Chairman of the Research Committee of the Canadian Mathematical Society 1973{1977. -
“GOLDEN ROOT SYMMETRIES of GEOMETRIC FORMS” By
“GOLDEN ROOT SYMMETRIES OF GEOMETRIC FORMS” By: Eur Ing Panagiotis Ch. Stefanides BSc(Eng)Lon(Hons) CEng MIET MSc(Eng)Ath MΤCG SYMMETRY FESTIVAL 2006 BUDAPEST HUNGARY Published Athens 2010 - Heliotropio Stefanides Eur Ing Panagiotis Stefanides 2 Eur Ing Panagiotis Stefanides 3 GOLDEN ROOT SYMMETRIES OF GEOMETRIC FORMS” By: Eur Ing Panagiotis Ch. Stefanides BSc(Eng)Lon(Hons) CEng MIET MSc(Eng)Ath MΤCG Eur Ing Panagiotis Stefanides 4 © Copyright 2010 P. Stefanides 8, Alonion st., Kifissia, Athens, 145 62 Greece “GOLDEN ROOT SYMMETRIES OF GEOMETRIC FORMS” Published Athens 2010 - Heliotropio Stefanides Eur Ing Panagiotis Stefanides 5 To My Wife Mary, and my Daughter Natalia, for their patience and constant support, et Amorem, Qui Mundos Unit. Published Athens 2010 – Heliotropio Stefanides © Copyright 1986-2010 P. Stefanides Eur Ing Panagiotis Stefanides 6 ACKNOWLEDGEMENTS I thank all those colleagues, fellow engineers friends, parental family and relations, who assisted me in any way, together with their valued suggestions, for this work to be presented to the SYMMETRY FESTIVAL 2006, BUDAPEST HUNGARY, where my special thanks goes to the Chairman of this International Conference, Professor György Darvas, who invited me, and gave me the chance for my ideas to be disseminated internationally, and also I thank Painter Takis Parlavantzas, member of the Hellenic Society of Ekastic Arts, for inviting me to present a paper at the “Arts Symposium” in Xanthe [Demokriteio University -22-24 Nov 1991] under the title “Geometric Concepts in Plato, Related to Art”. Similarly I thank the Hellenic Mathematical Society for giving me the floor [2-4 Mar. 1989] to present my novel paper “The Most Beautiful Triangle- Plato’s Timaeus” at the conference “ History and Philosophy of Classical Greek Mathematics”[ Professor Vassilis Karasmanis] and also the Hellenic Physicists’ Society,[ Mrs D. -
Modules Over Semisymmetric Quasigroups
Modules over semisymmetric quasigroups Alex W. Nowak Abstract. The class of semisymmetric quasigroups is determined by the iden- tity (yx)y = x. We prove that the universal multiplication group of a semisym- metric quasigroup Q is free over its underlying set and then specify the point- stabilizers of an action of this free group on Q. A theorem of Smith indicates that Beck modules over semisymmetric quasigroups are equivalent to modules over a quotient of the integral group algebra of this stabilizer. Implementing our description of the quotient ring, we provide some examples of semisym- metric quasigroup extensions. Along the way, we provide an exposition of the quasigroup module theory in more general settings. 1. Introduction A quasigroup (Q, ·, /, \) is a set Q equipped with three binary operations: · denoting multiplication, / right division, and \ left division; these operations satisfy the identities (IL) y\(y · x)= x; (IR) x = (x · y)/y; (SL) y · (y\x)= x; (SR) x = (x/y) · y. Whenever possible, we convey multiplication of quasigroup elements by concatena- tion. As a class of algebras defined by identities, quasigroups constitute a variety (in the universal-algebraic sense), denoted by Q. Moreover, we have a category of quasigroups (also denoted Q), the morphisms of which are quasigroup homomor- phisms respecting the three operations. arXiv:1908.06364v1 [math.RA] 18 Aug 2019 If (G, ·) is a group, then defining x/y := x · y−1 and x\y := x−1 · y furnishes a quasigroup (G, ·, /, \). That is, all groups are quasigroups, and because of this fact, constructions in the representation theory of quasigroups often take their cue from familiar counterparts in group theory. -
New and Forthcoming Books in 2020 Now Available on Worldscinet
View this flyer online at http://bit.ly/ws-newmathematics2020 New and Forthcoming books in 2020 Now available on WorldSciNet Essential Textbooks in Physics How to Derive a Formula Volume 1: Basic Analytical Skills and Methods for Physical Scientists by Alexei A Kornyshev & Dominic O’Lee (Imperial College London, UK) “In this book, the authors teach the art of physical applied mathematics at the advanced undergraduate level. In contrast to traditional mathematics books, formal derivations and theorems are replaced by worked examples with intuitive solutions and approximations, given some familiarity with physics and chemistry. In this way, the book covers an Fundamental Concepts in A Course in Game Theory ambitious range of topics, such as vector calculus, differential and integral equations, Modern Analysis by Thomas S Ferguson (University of California, Los Angeles, USA) linear algebra, probability and statistics, An Introduction to Nonlinear Analysis functions of complex variables, scaling and 2nd Edition This book presents various mathematical models dimensional analysis. Systematic methods by Vagn Lundsgaard Hansen of games and study the phenomena that arise. of asymptotic approximation are presented (Technical University of Denmark, Denmark) In some cases, we will be able to suggest in simple, practical terms, showing the With: Poul G Hjorth what courses of action should be taken by the value of analyzing ‘limiting cases’. Unlike players. In others, we hope simply to be able to most science or engineering textbooks, the In this book, students from both pure and understand what is happening in order to make physical examples span an equally broad applied subjects are offered an opportunity to better predictions about the future. -
A Mathematician's Lament
A Mathematician’s Lament by Paul Lockhart musician wakes from a terrible nightmare. In his dream he finds himself in a society where A music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer. Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school. As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. -
Forgotten Mathematician Henry Lowig (1904–1995)
Forgotten mathematician Henry Lowig (1904–1995) Martina Bečvářová Life story of Heinrich Löwig – Jindřich Löwig – Henry Lowig In: Martina Bečvářová (author); Jindřich Bečvář (author); Vlastimil Dlab (author); Antonín Slavík (author): Forgotten mathematician Henry Lowig (1904–1995). (English). Praha: MATFYZPRESS, Vydavatelství Matematicko-fyzikální fakulty v Praze, 2012. pp. 17–[74]. Persistent URL: http://dml.cz/dmlcz/402297 Terms of use: © Matfyzpress © Bečvářová, Martina © Bečvář, Jindřich © Dlab, Vlastimil © Slavík, Antonín Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 17 LIFE STORY Heinrich Löwig – Jindřich Löwig – Henry Lowig Do not hold our nation’s name sacred, This land in which we live. Our true homeland is only in our hearts, Where it cannot be struck or stolen. Ján Kollár (1793–1852) This chapter describes the difficult life experiences and mathematical work of Henry Lowig (1904–1995), a long forgotten mathematician who came from the Czech lands and whose life story paralleled the evolution of the Czech nation during the 20th century. Henry Lowig initially devoted his time to differential and functional equations, linear algebra and functional analysis; later he primarily focused on modern algebra, specifically, lattice theory. He published over 20 articles and 40 reviews on these topics. However he never wrote any textbooks or monographs, he has no disciples or followers in the Czech Republic, and his professional work was written only in German and English. -
BIRS 2010 Scientific Report
Banff International Research Station for Mathematical Innovation and Discovery 2010 Scientific Report 5-Day Workshops 2010 Jan 10 Jan 15 Mathematics and Physics of Polymer Entanglement Jan 17 Jan 22 Multi-Scale Stochastic Modeling of Cell Dynamics Jan 24 Jan 29 Sparse Random Structures: Analysis and Computation Jan 31 Feb 5 Theory and Applications of Matrices Described by Patterns Jan 31 Feb 5 Branching Random Walks and Searching in Trees Feb 7 Feb 12 Small-scale Hydrodynamics: Microfluidics and Thin Films Feb 14 Feb 19 Convex Algebraic Geometry Feb 21 Feb 26 Some Mathematical Problems of Material Science Feb 28 Mar 5 Randomization, Relaxation and Complexity Mar 7 Mar 12 Quasi-Isometric Rigidity in Low-Dimensional Topology Mar 7 Mar 12 (0,2) Mirror Symmetry and Heterotic Gromov-Witten Invariants Mar 14 Mar 19 Geometric Scattering Theory and Applications Mar 21 Mar 26 Deterministic and Stochastic Front Propagation Mar 28 Apr 2 Volume Inequalities Apr 4 Apr 9 Coordinated Mathematical Modeling of Internal Waves Apr 11 Apr 16 Generalized Complex and Holomorphic Poisson Geometry Apr 18 Apr 23 Optimal Transportation and Applications Apr 25 Apr 30 Character Varieties in the Geometry and Topology of Low-Dimensional Manifolds May 2 May 7 Functional Data Analysis: Future Directions May 2 May 7 Creative Writing in Mathematics and Science May 9 May 14 Nonlinear Diffusions and Entropy Dissipation: From Geometry to Biology May 16 May 21 Inverse Transport Theory and Tomography May 23 May 28 Self-assembly of Block Copolymers: Theoretical Models and Mathematical