The Methodology of Design by Geometric Code in Traditional Architecture
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Islamic Geometric Patterns Jay Bonner
Islamic Geometric Patterns Jay Bonner Islamic Geometric Patterns Their Historical Development and Traditional Methods of Construction with a chapter on the use of computer algorithms to generate Islamic geometric patterns by Craig Kaplan Jay Bonner Bonner Design Consultancy Santa Fe, New Mexico, USA With contributions by Craig Kaplan University of Waterloo Waterloo, Ontario, Canada ISBN 978-1-4419-0216-0 ISBN 978-1-4419-0217-7 (eBook) DOI 10.1007/978-1-4419-0217-7 Library of Congress Control Number: 2017936979 # Jay Bonner 2017 Chapter 4 is published with kind permission of # Craig Kaplan 2017. All Rights Reserved. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. -
Modeling Bacteria-Phage Interactions and Its Implications for Phage
CHAPTER THREE Modeling Bacteria–Phage Interactions and Its Implications for Phage Therapy Saptarshi Sinha, Rajdeep K. Grewal, Soumen Roy1 Bose Institute, Kolkata, India 1Corresponding author: e-mail address: [email protected] Contents 1. The Bacteria–Phage Interaction 104 1.1 Discovery of Bacteriophages: A Brief History 104 1.2 Lytic and Lysogenic Cycle 106 1.3 Adsorption Rate 107 1.4 Multiplicity of Infection 109 1.5 One-Step Growth Curve 110 1.6 Phage Therapy 111 1.7 Bacteria–Phage Coevolution 113 1.8 Modeling Bacteria–Phage Interactions 113 2. Mathematical Modeling 115 2.1 Differential Equations 115 2.2 Basic Model for Bacteria–Phage Interactions 117 2.3 Resource Concentration Factor 118 2.4 Phage Resistance in Bacteria 118 2.5 Bacteria–Phage Interaction Networks 120 2.6 System of ODEs 121 2.7 Recent Developments 122 3. Computer Simulations 124 3.1 Monte Carlo Simulations 124 3.2 Probability Distribution 126 3.3 Probability of Cell Division 128 3.4 Probability of Phage Adsorption 129 3.5 Latent Period and Burst Size 130 3.6 Secondary Infection and Killing 130 4. Phage Bacteria Interaction Under Spatial Limitations 132 4.1 Formation of Plaque 132 4.2 Factors Affecting Plaque Diameter 133 4.3 Modeling of Plaque Growth as a Reaction–Diffusion System 134 # Advances in Applied Microbiology, Volume 103 2018 Elsevier Inc. 103 ISSN 0065-2164 All rights reserved. https://doi.org/10.1016/bs.aambs.2018.01.005 104 Saptarshi Sinha et al. 4.4 Traveling Wave Front Solutions 135 4.5 Cellular Automata Modeling 135 4.6 SIR-Type Modeling 136 Acknowledgments 137 References 138 Abstract Bacteriophages are more abundant than any other organism on our planet. -
The Eagle 1939 (Easter)
96 THE EAGLE . THE EAGLE � I.QttQacQt 1.Q1.1.Q1 l.Q1c1tcQtcbtf.(/hf.Q1 cbt to't c.()'t '" cQt� I.Q1 eb't""" � COLLEGE AWARDS .,pt.,pt &Q'I.,pt tbtlbtc.QJcg.tQt No. 223 VOL. LI June 1939 � l.Q1 cQt cQt following awards were made on the results of the &Q'Ic.()'Ic.()'Ic.()'I&Q'I�cQtc.QJl.Q1f.(/hcQt l.Q1f.(/hcQtf.(/hl.Q1l.Q1c.()'tcQt c.()'tf.(/h l.Q1c.QJtQt�"' � THE Annual Entrance Scholarships Examination, December 1938: Major Scholarships: Read, A. H., Marlborough College, for Mathematics (Baylis Scholar- ship). Goldie, A. W., Wolverhampton Grammar School, for Mathematics. Charlesworth, G. R, Penis tone Grammar School, for Mathematics. Brough, J., Edinburgh University, for Classics. Howorth, R H., Manchester Grammar School, fo r Classics (Patchett Scholarship ). THE COMMEMORATION SERMON Freeman, E. J., King Edward VI School, Birmingham, for Classics. Crook, J. A., Dulwich College, for Classics. By THE MASTER, Sunday, 7 May 1939 Hereward, H. G., King Edward VI School, Birmingham, for Natural Sciences. T from the will of the Lady Robinson, R E., Battersea Grammar School, for History. me begin with a sentence Lapworth, H. J., King Edward VI School, Birmingham, for Modern Margaret: Languages. I "Be it remembered that it was also the last will of the said Minor Scholarships: princess to dissolve the hospital of Saint John in Cambridge Jones, R P. N., Manchester Grammar School, for Mathematics. persons, Bell, W. R G., Bradford Grammar School, for Mathematics. and to alter and to found thereof a College of secular Ferguson, J" Bishop's Stortford College, for Classics. -
How to Make Mathematical Candy
how to make mathematical candy Jean-Luc Thiffeault Department of Mathematics University of Wisconsin { Madison Summer Program on Dynamics of Complex Systems International Centre for Theoretical Sciences Bangalore, 3 June 2016 Supported by NSF grant CMMI-1233935 1 / 45 We can assign a growth: length multiplier per period. the taffy puller Taffy is a type of candy. Needs to be pulled: this aerates it and makes it lighter and chewier. [movie by M. D. Finn] play movie 2 / 45 the taffy puller Taffy is a type of candy. Needs to be pulled: this aerates it and makes it lighter and chewier. We can assign a growth: length multiplier per period. [movie by M. D. Finn] play movie 2 / 45 making candy cane play movie [Wired: This Is How You Craft 16,000 Candy Canes in a Day] 3 / 45 four-pronged taffy puller play movie http://www.youtube.com/watch?v=Y7tlHDsquVM [MacKay (2001); Halbert & Yorke (2014)] 4 / 45 a simple taffy puller initial -1 �1 �1�2 �1 -1 -1 -1 1�2 �1�2 �1 �2 [Remark for later: each rod moves in a ‘figure-eight’ shape.] 5 / 45 the famous mural This is the same action as in the famous mural painted at Berkeley by Thurston and Sullivan in the Fall of 1971: 6 / 45 The sequence is #folds = 1; 1; 2; 3; 5; 8; 13; 21; 34;::: What is the rule? #foldsn = #foldsn−1 + #foldsn−2 This is the famous Fibonacci sequence, Fn. number of folds [Matlab: demo1] Let's count alternating left/right folds. 7 / 45 #foldsn = #foldsn−1 + #foldsn−2 This is the famous Fibonacci sequence, Fn. -
GOLDEN and SILVER RATIOS in BARGAINING 1. Introduction There Are Five Coins on a Table to Be Divided Among Players 1 to 4. the P
GOLDEN AND SILVER RATIOS IN BARGAINING KIMMO BERG, JANOS´ FLESCH, AND FRANK THUIJSMAN Abstract. We examine a specific class of bargaining problems where the golden and silver ratios appear in a natural way. 1. Introduction There are five coins on a table to be divided among players 1 to 4. The players act in turns cyclically starting from player 1. When it is a player's turn, he has two options: to quit or to pass. If he quits he earns a coin, the next two players get two coins each and the remaining player gets nothing. For example, if player 3 quits then he gets one coin, players 4 and 1 get two coins each and player 2 gets no coins. This way the game is repeated until someone quits. If nobody ever quits then they all get nothing. Each player can randomize between the two alternatives and maximizes his expected payoff. The game is presented in the figure below, where the players' payoffs are shown as the components of the vectors. pass pass pass pass player 1 player 2 player 3 player 4 quit quit quit quit (1; 2; 2; 0) (0; 1; 2; 2) (2; 0; 1; 2) (2; 2; 0; 1) Bargaining problems have been studied extensively in game theory literature [4, 6, 7]. Our game can be seen as a barganing problem where the players cannot make their own offers but can only accept or decline the given division. Furthermore, the game is a special case of a so-called sequential quitting game which have been studied, for example, in [5, 9]. -
EVALUATION of VARIOUS FACIAL ANTHROPOMETRIC PROPORTIONS in INDIAN AMERICAN WOMEN Chakravarthy Marx Sadacharan
Facial anthropometric proportions Rev Arg de Anat Clin; 2016, 8 (1): 10-17 ___________________________________________________________________________________________ Original Communication EVALUATION OF VARIOUS FACIAL ANTHROPOMETRIC PROPORTIONS IN INDIAN AMERICAN WOMEN Chakravarthy Marx Sadacharan Department of Anatomy, School of Medicine, American University of Antigua (AUA), Antigua, West Indies RESUMEN ABSTRACT El equililbrio y la armonía de los diferentes rasgos de The balance and harmony of various facial features la cara son esenciales para el cirujano quien debe are essential to surgeon who requires facial analysis in analizar la cara para poder planificar su tratamiento. the diagnosis and treatment planning. The evaluation La evaluación de la cara femenina se puede hacer por of female face can be made by various linear medio de medidas lineales, angulares y proporciones. measurements, angles and ratios. The aim of this El propósito de esta investigación es examinar varias study was to investigate various facial ratios in Indian proporciones faciales en las mujeres aborígenes American women and to compare them with the Indian americanas y compararlas con las normas de las and Caucasian norms. Additionally, we wanted to personas indias (de India) y las personas caucásicas. evaluate whether these values satisfy golden and Tambien queriamos saber si estas normas satisfacen silver ratios. Direct facial anthropometric measur- las proporciones de oro y de plata. Las medidas ements were made using a digital caliper in 100 Indian faciales antropometricas se tomaron utillizando un American women students (18 - 30 years) at the calibre digital en cien estudiantes aborigenes American University of Antigua (AUA), Antigua. A set americanas (18-30 años) en la Universidad Americana of facial ratios were calculated and compared with de Antigua (AUA). -
Mathematical Constants and Sequences
Mathematical Constants and Sequences a selection compiled by Stanislav Sýkora, Extra Byte, Castano Primo, Italy. Stan's Library, ISSN 2421-1230, Vol.II. First release March 31, 2008. Permalink via DOI: 10.3247/SL2Math08.001 This page is dedicated to my late math teacher Jaroslav Bayer who, back in 1955-8, kindled my passion for Mathematics. Math BOOKS | SI Units | SI Dimensions PHYSICS Constants (on a separate page) Mathematics LINKS | Stan's Library | Stan's HUB This is a constant-at-a-glance list. You can also download a PDF version for off-line use. But keep coming back, the list is growing! When a value is followed by #t, it should be a proven transcendental number (but I only did my best to find out, which need not suffice). Bold dots after a value are a link to the ••• OEIS ••• database. This website does not use any cookies, nor does it collect any information about its visitors (not even anonymous statistics). However, we decline any legal liability for typos, editing errors, and for the content of linked-to external web pages. Basic math constants Binary sequences Constants of number-theory functions More constants useful in Sciences Derived from the basic ones Combinatorial numbers, including Riemann zeta ζ(s) Planck's radiation law ... from 0 and 1 Binomial coefficients Dirichlet eta η(s) Functions sinc(z) and hsinc(z) ... from i Lah numbers Dedekind eta η(τ) Functions sinc(n,x) ... from 1 and i Stirling numbers Constants related to functions in C Ideal gas statistics ... from π Enumerations on sets Exponential exp Peak functions (spectral) .. -
The Roles of Moron Genes in the Escherichia Coli Enterobacteria Phage Phi-80
THE ROLES OF MORON GENES IN THE ESCHERICHIA COLI ENTEROBACTERIA PHAGE PHI-80 Yury V. Ivanov A Dissertation Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY December 2012 Committee: Ray A. Larsen, Advisor Craig L. Zirbel Graduate Faculty Representative Vipa Phuntumart Scott O. Rogers George S. Bullerjahn © 2012 Yury Ivanov All Rights Reserved iii ABSTRACT Ray Larsen, Advisor The TonB system couples cytoplasmic membrane-derived proton motive force energy to drive ferric siderophore transport across the outer membrane of Gram-negative bacteria. While much effort has focused on this process, how energy is harnessed to provide for transport of ligands remains unknown. Several bacterial viruses (“phage”) are known to require the TonB system to irreversibly adsorb (i.e., establish infection) in the model organism Escherichia coli. One such phage is φ80, a “cousin” of the model temperate phage λ. Determining how φ80 is using the TonB system for infection should provide novel insights to the mechanisms of TonB-dependent processes. It had long been known that recombination between λ and φ80 results in a λ-like phage for whom TonB is now required; and this recombination involved the λ J gene, which encodes the tail-spike protein required for irreversible adsorption of λ to E. coli. Thus, we suspected that a φ80 homologue of the λ J gene product was responsible for the TonB dependence of φ80. While φ80 has long served as a tool for assaying TonB activity, it has not received the scrutiny afforded λ. -
Metallic Ratios in Primitive Pythagorean Triples : Metallic Means Embedded in Pythagorean Triangles and Other Right Triangles
Journal of Advances in Mathematics Vol 20 (2021) ISSN: 2347-1921 https://rajpub.com/index.php/jam DOI: https://doi.org/10.24297/jam.v20i.9088 Metallic Ratios in Primitive Pythagorean Triples : Metallic Means embedded in Pythagorean Triangles and other Right Triangles Dr. Chetansing Rajput M.B.B.S. Nair Hospital (Mumbai University) India, Asst. Commissioner (Govt. of Maharashtra) Email: [email protected] Website: https://goldenratiorajput.com/ Lecture Link 1 : https://youtu.be/LFW1saNOp20 Lecture Link 2 : https://youtu.be/vBfVDaFnA2k Lecture Link 3 : https://youtu.be/raosniXwRhw Lecture Link 4 : https://youtu.be/74uF4sBqYjs Lecture Link 5 : https://youtu.be/Qh2B1tMl8Bk Abstract The Primitive Pythagorean Triples are found to be the purest expressions of various Metallic Ratios. Each Metallic Mean is epitomized by one particular Pythagorean Triangle. Also, the Right Angled Triangles are found to be more “Metallic” than the Pentagons, Octagons or any other (n2+4)gons. The Primitive Pythagorean Triples, not the regular polygons, are the prototypical forms of all Metallic Means. Keywords: Metallic Mean, Pythagoras Theorem, Right Triangle, Metallic Ratio Triads, Pythagorean Triples, Golden Ratio, Pascal’s Triangle, Pythagorean Triangles, Metallic Ratio A Primitive Pythagorean Triple for each Metallic Mean (훅n) : Author’s previous paper titled “Golden Ratio” cited by the Wikipedia page on “Metallic Mean” [1] & [2], among other works mentioned in the References, have already highlighted the underlying proposition that the Metallic Means -
Buggy • A12 Tunes at Concert • B6 SCITECH SPORTS PILLBOX
Researchers study neuron SDC A team defends title, Matt and Kim present new response to morphine • A5 wins Buggy • A12 tunes at concert • B6 SCITECH SPORTS PILLBOX thetartan.org @thetartan April 20, 2015 Volume 109, Issue 24 Carnegie Mellon’s student newspaper since 1906 DEBORAH CHU firmly. Junior Staffwriter Casalegno described this occasion as “momentous,” This year’s Midway Open- drawing parallels between ing Ceremony for Spring Car- the all-encompassing essence nival paid a bittersweet fare- of Spring Carnival and the in- well to its longstanding place terdisciplinary nature of the on the Morewood Gardens future Tepper Quadrangle. parking lot. It touched on the The Quadrangle is scheduled new Tepper Quadrangle that to be built on the Morewood would take its place, and re- gardens parking lot, making minded us of the philanthro- this occasion also a hand-off. py aspect of Carnival. True “[The Tepper Quadrangle] to Carnegie Mellon tradition, is a new chapter in our cam- the air echoed with the sound pus history that will bring to- of bagpipes as Carnival offi- gether the whole of our cam- cially kicked off. pus … where collaboration People huddled inside will reign,” Casalegno said. the large Alumni Association “It will be a place where inno- Tent on the Morewood Gar- vation will thrive.” dens parking lot while rain As for Midway’s new home drizzled outside. Dean of Stu- on the CFA lawn, Casalegno dent Affairs Gina Casalegno points out that it would be joked that despite last year’s closer to other Carnival ac- announcement that Midway tivities such as Sweepstakes, would not take place at the more commonly known as Morewood Gardens park- Buggy. -
Exploitation Du Potentiel Des Bactériophages Dans Le Traitement Des Surfaces En Contact Avec L’Eau, Contaminées Par Un Biofilm De P
Exploitation du potentiel des bactériophages dans le traitement des surfaces en contact avec l’eau, contaminées par un biofilm de P. aeruginosa Vanessa Magin To cite this version: Vanessa Magin. Exploitation du potentiel des bactériophages dans le traitement des surfaces en contact avec l’eau, contaminées par un biofilm de P. aeruginosa. Ingénierie de l’environnement. Ecole nationale supérieure Mines-Télécom Atlantique, 2019. Français. NNT : 2019IMTA0146. tel-02391184 HAL Id: tel-02391184 https://tel.archives-ouvertes.fr/tel-02391184 Submitted on 3 Dec 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. • THESE DE DOCTORAT DE L’ÉCOLE NATIONALE SUPERIEURE MINES-TELECOM ATLANTIQUE BRETAGNE PAYS DE LA LOIRE - IMT ATLANTIQUE COMUE UNIVERSITE BRETAGNE LOIRE ECOLE DOCTORALE N° 602 Sciences pour l'Ingénieur Spécialité : Génie des Procédés et Bioprocédés Par Vanessa MAGIN Par Vanessa MAGIN Exploration du potentiel des bactériophages dans le traitement des surfaces en contact avec l’eau, contaminées par un biofilm de P.aeruginosa Thèse présentée et soutenue -
Dynamics of Units and Packing Constants of Ideals
Perspectives • Continued Fractions in Q(√D) Dynamics of units and • The Diophantine semigroup packing constants of ideals • Geodesics in SL2(R)/SL2(Z) • (Classical) Arithmetic Chaos • Well-packed ideals Curtis T McMullen 1 Harvard University • Dynamics of units on P (Z/f) • Link Littlewood & Zaremba conjectures Continued Fractions Diophantine numbers Q. How to test if a real number x is in Q? x = [a , a , a , a , ...] = a + 1 0 1 2 3 0 a + 1 Q. How to test if a real number x is in Q(√D)? 1 a2 + 1 a3 + ... 1 x = [a0, a 1, a 2, a 3, ...] = a0 + a1 + 1 a2 + 1 BN = {x real : ai ≤N} a3 + ... BN-Q is a Cantor set of dim→1 as N→∞. A. x is in Q(√D) iff ai’s repeat. Conjecture: x algebraic and Diophantine iff x is rational or quadratic Diophantine sets in [0,1] Examples BN = {x : ai ≤N} γ = golden ratio = (1+√5)/2 = [1,1,1,1....] = [1] σ = silver ratio = 1+√2 = [2] [1,2,2,2] (√30) B2 [1,2] Q(√3) Q [1,2,2] Q(√85) [1,1,1,2] Q(√6) [1,1,2] Q(√10) [1,1,2,2] Q(√221) B4 Question: Does Q(√5) contain infinitely many periodic continued fractions with ai ≤ M? Thin group perspective Theorem Every real quadratic field contains infinitely GN = Diophantine semigroup in SL2(Z) many uniformly bounded, periodic continued fractions. generated by Wilson, Woods (1978) 01 01 01 ( 11) , ( 12) ,...( 1 N ) . Example: [1,4,2,3], [1,1,4,2,1,3], [1,1,1,4,2,1,1,3]..