DOCSLIB.ORG

Pdf 107.05 K

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Pdf 107.05 K ISSN: 1017-060X (Print) ISSN: 1735-8515 (Online) Special Issue of the Bulletin of the Iranian Mathematical Society in Honor of Professor Heydar Radjavi's 80th Birthday Vol. 41 (2015), No. 7, pp. 99{106 . Title: A Haar wavelets approach to Stirling's formula Author(s): M. Ahmadinia and H. Naderi Yeganeh Published by Iranian Mathematical Society http://bims.ims.ir Bull. Iranian Math. Soc. Vol. 41 (2015), No. 7, pp. 99{106 Online ISSN: 1735-8515 A HAAR WAVELETS APPROACH TO STIRLING'S FORMULA M. AHMADINIA∗ AND H. NADERI YEGANEH (Communicated by Peter Rosenthal) Dedicated to Professor Heydar Radjavi on his 80th birthday Abstract. This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences. Keywords: Haar wavelets, Parseval's identity, Stirling's formula. MSC(2010): Primary: 15-xx; Secondary: 40-xx. 1. Introduction n! Stirling's formula (lim !1 p = 1) plays an important role in statis- n nne−n 2πn tics and probability; its main use is estimating the value of n!. The first proofs of Stirling's formula were presented by de Moivre and Stirling (see [4, 8]). Es- timates of n! have been obtained via upper and lower bounds of n! by various authors (for example see [3], [5] and [6]). Some papers prove Stirling's formula by different techniques as well (for example see [2]). The present paper in- troduces a new method of proving Stirling's formula by using Haar wavelets. Although there are some proofs of Stirling's formula that are simpler than the present one, we feel that it is of interest to know that this formula can be established using Haar wavelets. The outline of the paper is as follows: In Section 2, we introduce some notation and present two lemmas related to Parseval's identity and the Haar wavelet basis. In Section 3, we present an application of the two lemmas, and in the last section we give a proof of Stirling's formula and of a lower and upper bound for n!. Article electronically published on December 31, 2015. Received: 22 November 2014, Accepted: 18 April 2015. ∗Corresponding author. ⃝c 2015 Iranian Mathematical Society 99 Haar wavelets and Stirling's formula 100 2. Preliminaries and Haar Wavelets This section introduces Haar wavelets and some related notation. The following notation is fixed throughout the paper: Z∗ := N [ f0g; (N is the set of natural numbers). The bijective function P and the surjective function Q are defined as follows: P : S ! N; P (n; k) := 2n + k; and Q : W ! Z∗;Q(r; n) := n; where S := f(n; k) 2 Z∗ × Z∗j0 ≤ k ≤ 2n − 1g; & W := f(r; n) 2 Z∗ × Z∗jr ≤ ng: Consider the following functions ( 1; 0 ≤ x < 1; ϕ(x) := 0; otherwise; and 8 > ≤ 1 <1; 0 x < 2 ; (x) := −1; 1 ≤ x < 1; :> 2 0; otherwise; and also n n n;k(x) := 2 2 (2 x − k); (n; k) 2 S: R 2 h i 1 The real Hilbert space L ([0; 1]) with inner product f; g := 0 f(x)g(x)dx, has the following orthonormal basis, which is called \the Haar wavelets basis": (2.1) fϕ(x)g [ f n;k(x) j (n; k) 2 Sg : Parseval's identity implies that X1 2Xn−1 (2.2) hf; gi = hf; ϕihg; ϕi + hf; n;kihg; n;ki; n=0 k=0 (for details see [1] and [7]). For convenience, we employ the following notation: Z Z k+1 2n f := f(x)dx: k n;k 2n 101 Ahmadinia and Naderi Yeganeh Lemma 2.1. If f and g are in L2([0; 1]), then 2Xr −1 Z Z X1 2Xn−1 r (2.3) hf; gi = 2 f g + hf; n;kihg; n;ki; k=0 r;k r;k n=r k=0 for all r 2 Z∗. Proof. This lemma is proved by induction. If r = 0, then (2.3) and (2.2) are the same. If the equation (2.3) holds for r, then (2.4) 2Xr −1 Z Z 2Xr −1 X1 2Xn−1 r hf; gi = 2 f g + hf; r;kihg; r;ki + hf; n;kihg; n;ki: k=0 r;k r;k k=0 n=r+1k=0 Let h be an arbitrary function in L2([0; 1]). Then Z Z Z (2.5) h = h + h; r;k r+1;2k r+1;2k+1 and (Z Z ) r (2.6) hh; r;ki = 2 2 h − h : r+1;2k r+1;2k+1 We can derive the following equation by using (2.5) and (2.6) in the left side of the equation: 2Xr −1 Z Z 2Xr −1 2rX+1−1Z Z r r+1 (2.7) 2 f g + hf; r;kihg; r;ki = 2 f g: k=0 r;k r;k k=0 k=0 r+1;k r+1;k Substitution of (2.7) into (2.4) yields (2.3) for r + 1. □ Lemma 2.2. If f and g are continuous functions on [0; 1] that are differentiable 0 0 on (0; 1), and if also jf (x)j < M1 and jg (x)j < M2 for all x 2 (0; 1), then the following assertions are true: jh ij M1 jh ij M2 2 (i) f; n;k < 3n +1 and g; n;k < 3n +1 ; (n; k) S; R R2 2 R 2 2 j − r j M1M2 2 (ii) r;k fg 2 r;k f r;k g < 3·23r ; (r; k) S. Proof. The mean value theorem for integrals and (2.6) imply (Z Z ) n f(c1) f(c2) h i 2 − − f; n;k = 2 f f = n +1 n +1 ; n+1;2k n+1;2k+1 2 2 2 2 2 2k 2k+1 2 2k+1 2k+2 for some c1 ( 2n+1 ; 2n+1 ) and c2 ( 2n+1 ; 2n+1 ). The mean value theorem for derivatives yields 0 − h i f (c)(c1 c2) f; n;k = n +1 ; 2 2 Haar wavelets and Stirling's formula 102 2 j − j 1 for some c (c1; c2). Note that c1 c2 < 2n . Then jf 0(c)j M jhf; ij ≤ < 1 : n;k 3n +1 3n +1 2 2 2 2 The proof of statement (i) is completed by applying a similar proof for g. To prove statement (ii), consider the following functions on [0; 1] with (r; k) 2 S arbitrary and fixed: x + k x + k f (x) := f( ); & g (x) := g( ): 1 2r 1 2r Then Z Z Z − r 1 h i − 1 h ih i fg 2 f g = r f1 ; g1 r f1 ; ϕ g1 ; ϕ r;k r;k r;k 2 2 1 n− 1 X 2X1 (2.8) = hf ; ihg ; i: 2r 1 n;l 1 n;l n=0 l=0 (The first equation is clear and the second equation is obtained from (2.2).) Since M1 and M2 are the bounds for f 0 and g0 respectively, statement (i) 2r 2r 1 1 implies M M (2.9) jhf ; ij < 1 & jhg ; ij < 2 : 1 n;k 3n +1+r 1 n;k 3n +1+r 2 2 2 2 Using (2.8) and (2.9) yields Z Z Z n X1 2X−1 r 1 M1M2 M1M2 fg − 2 f g < = : 23n+2 23r 3 · 23r r;k r;k r;k n=0 l=0 □ 3. An Application: An Infinite Product An infinite product can be obtained by applying the above two lemmas, in 1 the special case where f = 1+x and g = 1 + x. Theorem 3.1. The following equation holds: Y1 e m 2m+1 p (3.1) p e( ) 2 = π: m + 1 2 m=1 Proof. Consider the following functions on [0; 1]: 1 f(x) := ; g(x) := 1 + x: 1 + x The inner product hf; gi can be written as follows, for all r 2 Z∗: 2Xr −1 Z (3.2) hf; gi = fg; k=0 r;k 103 Ahmadinia and Naderi Yeganeh Lemma 2.1 and (3.2) imply that r ( ) n 2X−1 Z Z Z X1 2X−1 r (3.3) fg − 2 f g = hf; n;kihg; n;ki; k=0 r;k r;k r;k n=r k=0 The following equation is clear, by (3.3), r ( ) n X1 2X−1 Z Z Z X1 X1 2X−1 r r r (3.4) 2 fg − 2 f g = 2 hf; n;kihg; n;ki; r=0 k=0 r;k r;k r;k r=0 n=r k=0 Note that the left hand side of (3.4) is convergent by part (ii) of Lemma 2.2. Also, part (i) of Lemma 2.2 implies that the right hand side of (3.4) is absolutely convergent. Thus this series can be rearranged using the surjective function Q as follows: Q(r;n) X1 X1 2Xn−1 X1 X1 2 X−1 r h ih i r h ih i 2 f; n;k g; n;k = 2 f; Q(r;n);k g; Q(r;n);k r=0 n=r k=0 r=0 n=r k=0 X1 X 2Xi−1 t = 2 hf; i;kihg; i;ki i=0 Q(t;u)=i k=0 ! X1 Xi 2Xi−1 t = 2 hf; i;kihg; i;ki i=0 t=0 k=0 X1 2Xi−1 i+1 = (2 − 1) hf; i;kihg; i;ki: i=0 k=0 Hence, (3.4) can be written as (3.5) r ( ) r X1 2X−1 Z Z Z X1 2X−1 r r r+1 2 fg − 2 f g = (2 − 1) hf; r;kihg; r;ki: r=0 k=0 r;k r;k r;k r=0 k=0 Together, (2.2) and (3.5) yield: (3.6) hf; gi − hf; ϕihg; ϕi + A = B; where r ( ) X1 2X−1 Z Z Z A = 2r fg − 2r f g ; r=0 k=0 r;k r;k r;k and X1 2Xr −1 r+1 B = 2 hf; r;kihg; r;ki: r=0 k=0 Haar wavelets and Stirling's formula 104 Parts (ii) and (i) of Lemma 2.2 show that the series A and B are absolutely convergent.
Load more

Recommended publications
  • LOCKDOWN Maths Inspired Art No Longer an Etching but a Multi Medium Artwork A3 Size
    LOCKDOWN Maths Inspired Art No Longer an Etching but a Multi Medium Artwork A3 size Gr11 /// PMM /// Term 2 /// 2020 Term 2’s theme has been inspired by the http://www.mathart.co.za/ competition initiated by the ​ ​ education department. We want to explore the link between making art and understanding maths principles. Each learner is to find a connection between a visual composition and being able to explain this using a mathematical explanation. Patterns, tessellations, fractals, proportion and perspective are all themes one could explore in this term 2 project. I suggest learners keep their final compositions simple and clean. Simple black line work as we are producing hard ground etchings in class. Due to the lockdown situation I would like each learner to produce their final practical at home. We will stick to the same theme as you have all done much work in your SB. What I would like is a final artwork, No smaller than A3 in whatever and whichever materials you have in your space at home. Please don't forget that stationary shops including art shops are open. I understand money is tight however pens, pencils, food colouring, coffee we should be able to work with easier. You will take your final composition and produce a final artwork with your ideas and creativity around “Maths in Art”. Suggestions for paper - cardboard boxes, old cereal boxes, collaging paper together. Please explore the format of the canvas - square, rectangular, oval are all options. [Each learn has already been given a brass etching plate and therefore has the size (39com x18cm) of the final composition.
    [Show full text]
  • The American Mathematical Monthly
    The American Mathematical Monthly A Generalization of Wallis Product --Manuscript Draft-- Manuscript Number: Full Title: A Generalization of Wallis Product Article Type: Note Keywords: Wallis Product Corresponding Author: Mahdi Ahmadinia, Ph.D. University of Qom Qom, Qom IRAN (ISLAMIC REPUBLIC OF) Corresponding Author Secondary Information: Corresponding Author's Institution: University of Qom Corresponding Author's Secondary Institution: First Author: Mahdi Ahmadinia, Ph.D. First Author Secondary Information: Order of Authors: Mahdi Ahmadinia, Ph.D. Hamid Naderi Yeganeh, Undergraduate Student Order of Authors Secondary Information: Abstract: This note presents a generalization of Wallis' product. We prove this generalization by Stirling's formula. Then some corollaries can be obtained by this formula. Corresponding Author E-Mail: [email protected] Additional Information: Question Response 5-Character 2000 AMS/Math Reviews 00-xx Math. Classification Codes for your manuscript. The complete classification is available at http://www.ams.org/msc/. We need one Primary Code and you may enter enter additional Secondary Codes if you wish. The first code you enter will be considered your primary code. Please separate each code with a comma. We will publish your MSC code with your manuscript. Are you or your co-author eligible for the No Merten Hasse Prize? Manuscript Classifications: 0: General Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Manuscript Click hereMathematical to download Assoc. ofManuscript: America AmericanA-Generalization-of-Wallis-Product.pdf Mathematical Monthly 121:1 October 26, 2014 6:06 p.m. A-Generalization-of-Wallis-Product.tex page 1 1 2 A Generalization of Wallis Product 3 4 Mahdi Ahmadinia and Hamid Naderi Yeganeh 5 6 7 Abstract.
    [Show full text]
  • Modelling Fractals in Maxima
    МОДЕЛИРОВАНИЕ ФРАКТАЛОВ В СРЕДЕ MAXIMA часть II П.И. ТРОШИН Казанский федеральный университет Казань 2012 Оглавление ВВЕДЕНИЕ3 1 НЕПОДВИЖНЫЕ ТОЧКИ, ОРБИТЫ, БИФУРКАЦИИ5 2 ХАОТИЧЕСКАЯ ДИНАМИКА. ДЕТЕРМИНИРОВАННЫЙ ХАОС 17 3 ФРАКТАЛЬНОЕ БРОУНОВСКОЕ ДВИЖЕНИЕ 23 ПРИЛОЖЕНИЕ 38 РЕСУРСЫ ИНТЕРНЕТА 43 СПИСОК ЛИТЕРАТУРЫ 44 УКАЗАТЕЛЬ КОМАНД 47 2 ВВЕДЕНИЕ Чем абстрактнее истина, которую ты хочешь преподать, тем сильнее ты должен обольстить ею ещё и чувства. Фридрих Ницше Красоту в математике так же трудно формально определить, как и красоту в искусстве, но лю- ди, изучающие математику, обыч- но не имеют затруднений в её рас- познавании. Поль Дирак Любая формула, включенная в кни- гу, уменьшает число её покупате- лей вдвое. Стивен Хокинг астоящее пособие является продолжением части I, в которой изложены методы мо- Н делирования в системе компьютерной алгебры Maxima таких фрактальных объектов, как L-системы, системы итерированных функций, множества Мандельброта и Жюлиа, аттракторы в проблеме Кэли, а также метод нахождения фрактальной размерности. Во II части пособия излагаются методы построения паутинных и бифуркационных диаграмм, а также диаграмм орбит, построение странных аттракторов, кривых и поверх- ностей фрактального броуновского движения. Содержание этой части сфокусировано на динамических аспектах фрактальной геометрии, или на фрактальных аспектах динами- ческих систем. В качестве среды моделирования выбрана система компьютерной алгебры Maxima— свободное программное обеспечение, зарекомендовавшее себя в течение длительного вре- мени (проект зародился в 1968 году и стал открытым с 1998 года). Преимуществами этой системы являются: бесплатная лицензия, кросс- платформенность (реализация в ОС Windows, Linux, Unix, Mac OS X, BSD), открытый код (что понижает количество встроенных ошибок), поддержка языка программирования 3 4 Lisp и др.. Maxima выполняет символьные и численные вычисления, строит различные графики, обладает широким набором дополнительных программных пакетов.
    [Show full text]
  • Spring Congregation 2015 May 20–22 May 25–27 the Chan Centre for the Performing Arts Dear Graduand
    spring congregation 2015 may 20–22 may 25–27 the chan centre for the performing arts Dear Graduand, Your graduation began long before this day. It began when you made the choice to study that extra hour, dedicate yourself more deeply, and strive to reach for the degree you had chosen to fully commit your life to pursuing. Many of the people that helped you arrive here today are seated beside you—friends, family, classmates— while others are thinking of you from afar. We are honoured to have given you a place to discover, inspire others and be challenged beyond what you thought was possible. We hope you know, we will always be that place for you. Yours, UBC TABLE OF CONTENTS The Graduation Journey 2 Lists of Spring 2015 Graduating Students Graduation Traditions 4 Wednesday, May 20, 2015 8:30am 27 Chancellor’s Welcome 6 11:00am 3 1 President’s Welcome 8 1:30pm 34 Musqueam Welcome 10 4:00pm 38 Honorary Degree Recipients 12 Thursday, May 21, 2015 The Board of Governors & Senate 14 8:30am 42 11:00am 46 Honoring Significant 16 1:30pm 50 Accomplishments & Contributions 4:00pm 53 Friday, May 22, 2015 Scholarships, Medals & Prizes 18 8:30am 57 11:00am 60 Schedule of Ceremonies 22 1:30pm 64 4:00pm 67 Monday, May 25, 2015 8:30am 70 11:00am 73 1:30pm 76 4:00pm 79 Tuesday, May 26, 2015 8:30am 82 11:00am 85 1:30pm 89 4:00pm 92 Wednesday, May 27, 2015 8:30am 95 11:00am 98 1:30pm 101 4:00pm 104 Acknowledgements 108 O Canada 108 Alumni Welcome 109 A General Reception will follow each Ceremony at the Flag Pole Plaza.
    [Show full text]
  • Commencement 2001-2005
    ommencement Conferring of Degrees at the Close of the 129th Academic Year Vk" Johns Hopkins University May 26, 2005 ^m 9:15 a.m. iC*5c« Graduates Seating CD c I* r r-> d S < 3 00 3 5' "C 01 3" 7T n> i 01 >< / Homewood Field 4/ Order of Seating Facing Stage (Left) Order of Seating Facing Stage (Right) Doctors of Philosophy and Doctors of Medicine -Medicine Doctors of Philosophy - Arts & Sciences Doctors of Philosophy - Advanced International Studies Doctors of Philosophy - Engineering Doctors of Philosophy, Doctors of Public Health, and Doctors of Masters and Certificates - Arts & Sciences Science - Public Health Masters and Certificates - Engineering Doctors of Philosophy and Doctors of Nursing Science - Nursing Bachelors - Engineering Doctors of Musical Arts and Artist Diplomas - Peabody Bachelors - Arts & Sciences Doctors of Education - Professional Studies in Business and Education Masters - Medicine Masters - Advanced International Studies Masters - Public Health Masters and Bachelors - Nursing Masters, Certificates, Diplomas, and Bachelors - Peabody Certificates of Advanced Graduate Study and Masters - Professional Studies in Business and Education Bachelors - Professional Studies in Business and Education Contents Order of Procession 1 Order of Events 2 Divisional Diploma Ceremonies Information 6 Johns Hopkins Society of Scholars 7 Honorary Degree Citations 11 Academic Regalia 14 Awards 16 Honor Societies 22 Student Honors 26 Candidates for Degrees 31 >--^». ^* Please note that while //// degrees are conferred, only doctoral graduates process across the stage. Though taking photos from your seats during the ceremony is not prohibited, we request that guests respect each other's comfort and enjoyment In not standing and blocking other people's views.
    [Show full text]
  • Esma Newsletter February 2015
    European Society for Mathematics and the Arts Newsletter Volume 006 issue 02 February 2015 Dear All, From the correspondence received by ESMA during these last weeks, it is a pleasure to extract a few interesting information. Hamid Naderi Yeganeh (https://mathematics.culturalspot.org) <studied mathematics at the University of Qom. Winner of the gold medal at the 38th Iranian Mathematical Society's Competition (May 2014), he likes to create beautiful images from basic mathe- matical concepts.> A few numerical details of his fine aerial images, giving rise to moir´e effects, appeared on http://ams.org/mathimagery/thumbnails.php?album=40. Note that some of these images were already mathematically described by Christoph P¨oppe in Pour la Science (the French edition of Scientific American), N◦ 174, April 1992. Of course, one does not need higher mathematics to create beautiful works. In the eyes and the hands of artists, mathematical facts as basic as the Pythagorean theorem for example, are sufficient to create attractive works. Using only such standard results, Malija Belic (for instance http://geoform.net/artists/milija-belic/) show us harmonious works in the layout and the colors of the patterns. More advanced mathematics is used by <fractalist artists>, not fractal artists. In that field, our ESMA members J´er´emieBrunet et Jos Leys are well known. They have recently produced a joint work: Jos foreworded a book of fractal works made by J´er´emie. <L'art fractal, aux fronti`eres de l'imaginaire> was published by the French Editions´ Pole. In his useful foreword, Jos gives us some general ideas and tricks to create images of fractals.
    [Show full text]
  • Download Sample
    Art n Math Katherine Cook Dan Finkel Sponsors Published March, 2018 by: CoCA Center on Contemporary Art Center on Contemporary Art 114 Third Avenue South Staff: Seattle, Washington 98104 Nichole DeMent, Executive Director http://www.cocaseattle.org [email protected] Board of Directors: 206.728.1980 Sara Everett, President Copyright © 2018 Kalindi Kunis, Vice President Center on Contemporary Art Kate Vrijmoet, Chair, Secretary Eddie Reed, Treasurer ISBN 978-0-9990819-2-1 Judith Rayl, Volunteer Lead Joseph Bisacca, Director Kate Vrijmoet, Producer Tina Gonsalves, Director Archis Gore, Director Katherine Cook & Dan Finkel, Curators, Authors Travis Monroe, Director Joseph Roberts, Director, Curator Elatia Harris, Editor Robin Walker, Director Ray C. Freeman III, Publisher Artists’ images and texts used by permission. Mission Statement: All rights reserved. No part of this book may be reproduced in any manner whatsoever without CoCA Serves the Pacific Northwest as a Catalyst written permission, except in the case of brief and Forum for the Advancement, Development, quotations embodied in critical articles or reviews. and Understanding of Contemporary Art. page 2 Katherine Cook and Dan Finkel Center on Contemporary Art Art n Math Table of Contents 5 Art n Math Erik Demaine and Martin Demaine 6 What is Math? Savina Mason Suchitra Mattai 11 Equivalence Jean Mandeberg Jayadev Athreya Timea Tihanyi 21 Geometry And Topology Lun-Yi Tsai Claire B. Jones Edmund Harriss June Sekiguchi 31 Algorithms, Iteration, and Chaos Hamid Naderi Yeganeh Erik Demaine
    [Show full text]
  • Statistical Applications for Undergraduate Research Exploration
    Volume 1 April 2021 STATistical applications for undergraduate research exploration The field of statistics is the study of learning from data. Statistical learning causes you to utilize the best possible strategies to gather the information, utilize the right investigations, and adequately present the outcomes. Statistics is an urgent procedure behind how we make disclosures in science, settle on choices dependent on information, and make predictions. Statistics is an energizing field about the rush of discovery, learning, and challenging your assumptions. LIFESCI 3LL3 - Living Systems Laboratory Practicum is a lab-based statistics course that provides students with the opportunity to explore various areas of study within the Life Sciences in a small- group learning environment. Students work with large data sets and SPSS software to gain knowledge in the field of scientific research. They learn to develop research questions, run appropriate statistical tests on their data, and compose the basic requirements for a scientific manuscript. This STATure (STATistical applications for undergraduate research exploration) publication is a compilation of the final report submissions created by the students in the Winter 2021 course. Each report is unique, and tells an interesting statistical story while facilitating the formation of new learning. I hope you enjoy learning about statistics as you read these reports. Dr. Janet Pritchard (Course Creator and Instructor) Cover Art – An artistic impression of Dr. Muriel Bristol (1888-1950) who claimed to be able to tell whether the tea or the milk was added first to a cup. This lead Dr. Ronald Fisher (1890-1962) to devise the steps to test this hypothesis and eventually create the foundations for modern statistical science.
    [Show full text]
  • Use of Mathematics in Art
    Areej Fatima F017-184 Everyday Science USE OF MATHEMATICS IN ART Literature Review Mathematics has been regarded as art with beauty and freedom (Morse, 1959). Consequently, its use in arts is comprehensive and is observed in diverse forms such as painting, music, dance, architecture, sculpture, and textiles (Czerniak, 1999). The use of mathematics in arts is bonded since ancient history. Evidence in history was found indicating mathematics being used yet not being acknowledged as a separate entity by the individuals using it. For instance; Leonardo da Vinci illustration of De Divina Proportione in 1509 used the golden ratio, Albrecht Durer was an engraver who used mathematics in Melencolia I, Piero Della Francesca’s use of mathematics in De Prospectiva Pingendi and other paintings (Field, 1997). These artist were familiar with mathematics and its use yet were’nt aware of it being a separate field with significant importance. Background of Islamic art used symmetries in various forms such as Mughal Jali, Muqarnas, and Persian Girih was also founded (Özdural, 2000). These findings indicated the level of mathematics surrounded in the daily lives of individuals without them knowing it. (Schattschneider, 2010), presented a semi-modern graphic artist M.C Escher who made use of geometry and tessellation with the help of H.S.M Coxeter a mathematician. MC Escher was one of the prominent findings that embraced geometrical forms and tessellations, with the help of thorough research. M.C Escher was a Dutch graphic artist who wanted to draw things with multiple perspectives which is why he experimented with maths too. Other artists with profound knowledge in mathematics also used in their work which includes: Peter Forakis (1927-2009), Charles O.
    [Show full text]
  • 3Rd National and 1St International Congress for Naval Preventive Medicine: Health, Rescue and Clinical Management on the Naval and Submarine Fleets
    See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/342674079 Infectious diseases, ship travels, marine missions, mathematics Conference Paper · January 2015 CITATIONS READS 0 6 1 author: Hamze Shahali AJA University of Medical Sciences 87 PUBLICATIONS 43 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Jet Lag in Military and Civil Aviation: A Review Study View project All content following this page was uploaded by Hamze Shahali on 04 July 2020. The user has requested enhancement of the downloaded file. Supreme Leader, Commander of Iranian Army Iranian Naval Force is a political, an international, scientific and military force. (Meetings of Naval Force Commanders with the Grand Ayatollah, Nov. 24, 2013) Abstracts 3rd National and 1st International Congress for Naval Preventive Medicine: Health, Rescue and Clinical Management on the Naval and Submarine Fleets Bandar Abbas, Iran; 16-20 January 2015 Aja University of Medical Sciences (AUMS) Hormozgan University of Medical Sciences Marine and Submarine Medicine Research Centre IN THE NAME OF GOD JOURNAL INFORMATION AIM AND SCOPE JAAM also welcomes articles in military medical education. The The “Journal of Archives in Military Medicine” (JAMM) is an editorial board of the journal appreciates novel and innovative international, peer-reviewed, open access journal that focuses on studies and offers special priority for these works. basic and clinical studies in military medicine, including etiology, CONTENT COVERAGE pathogenesis, epidemiology, diagnosis, screening, monitoring, treatment, rehabilitation and clinical practice guidelines for JAMM is a peer-review open access journal which is published a better care of military forces, veterans and their families.
    [Show full text]
  • Download the 35Th Fajr International Film Festival Catalogue
    264 In the Name of God Download PDF version of FIFF Festival Catalogue Signs Asian premiere A.P. International premiere Int.p. National premiere N.P. How to use the app World premiere W.P. get.winkere.com Regional premiere R.P. Middle East premiere ME.P Question & Answer Q&A 3 2 1 Original Voice OV Director Of Photography DOP Catalogue of 35th Fajr International Film Festival Tehran, 21st-28th. April. 2017 Supervisor: Kayvan Kassirian Editor-in-chief: Somayeh Alipour With Special Thanks to Amir Esfandiari, Iraj Taghipour, Kamyar Mohs- enin, Ali Eftekhari, Raha Pourghassem English to Persian Translator: Lida Sadrololamayi, Hafez Rouhani, Farzad Mozafari, Ghodratollah Shafiee Persian to English Translator: Ghanbar Naderi, Ahmad Khouzani, Hos- sein Bouye Editor: Masoumeh Alipour Art Manager: Hamidreza Baydaghi Graphics: Afshin Ziaeeian Alipour, Leili Eskandarpour Print Supervisor: Mehrdad Haji Hassani Printing: Senobar The Official apps of FIFF Message of Head of Iranian Cinema Organization 4 Message of the Festival Director 5 About 34th Fajr Film Festival 7 Rules and Regulations of 35th Fajr Festival 11 Juries 15 International Competition 27 Panorama of Films from Asian and Islamic Countries 73 Festival of Festivals 119 Docs in Focus 135 Special Screenings 149 Classics Preserved 177 Korean Cinema 189 Baltic Cinema 197 Shadows of Horror 205 Broken Olive Trees 213 Enviromental Films 225 Interfaith Competition Nominees 227 Here is the Friend’s Home 229 Workshops 239 Organization 255 Index 261 Message of Head Iranian Cinema Organization Deputy Minister of Culture and Islamic Guidance and Head of Iranian Cinema Organization 4 Mohammad Mehdi Heydarian has sent the followin message to the organizers of this year’s Fajr International Film Festival.
    [Show full text]
  • Maren Oates, Schack Art Center, (425) 259-5050 X25 Or [email protected]
    FOR IMMEDIATE RELEASE For Media Inquiries & Images: Maren Oates, Schack Art Center, (425) 259-5050 x25 or [email protected] Schack Exhibit Explores Where Art Intersects Math Everett, WA (April 9, 2018) - While math and art may seem like disciplines far apart, the Schack's upcoming exhibit helps demonstrate how mathematics has influenced art for centuries. The Intersection of Art + Math, presented in partnership with Art ꓵ Math by Seattle's Center on Contemporary Art (CoCA), offers a fresh perspective on how artists utilize math concepts and theories in the creation of their work. Co-curators and mathematician educators, Katherine Cook and Dr. Dan Finkel are clear, "If anyone ever doubted that the questions and processes of mathematics were inherently linked to aesthetic experience, let the artworks in this show be evidence to the contrary." A diverse selection of media will be featured in the exhibit from artists and mathematicians including sculpture and oil paint, to textile and metalwork. Mathematician artists include Jayadev Athreya, Katherine Cook, Erik and Martin Demaine, Edmund Harriss, and Hamid Naderi Yeganeh. Visual artists who use mathematical principles in their practices include Paul Vexler, Suze Woolf, Caryl Bryer Fallert-Gentry, Amber Barney-Nivon, Rachel Holloway, Claire B. Jones, George Legrady, Jean Mandeberg, Savina Mason, Suchitra Mattai, June Sekiguchi, TimeaTihanyi/Sliprabbit, Lun Yi Tsai, and Ilana Zweschi. The mezzanine gallery will also feature a new installation and mural created on-site by artist Harold Hollingsworth. Hollingsworth's artwork is characterized by colorful eruptions, rich surfaces, and rhythmic playfulness. He is best known for his work with familiar imagery such as old road sign graphics, as well as vintage and modern fonts.
    [Show full text]