41. Persönlichkeiten Von Schlesien I - O Translate this page Riesengebirge). kutta, martin, Wilhelm, (Mathematiker), * 03.11.1867in Pitschen † 25.12.1944 in Fürstenfeldbruck. L. Laband, Paul, http://www.schlesien-ahnenforschung.de/pers2.html

I J K L ... P - Z I Irgang Israel, Alexander * 11.02.1839 in Heidewald † 16.04.1922 in Berlin J Forscher, Sprachforscher und Missionar * in Herrenhut Jakubczyk, Karl * 15.10.1888 in Beuthen/OS † 08.01.1931 in Breslau Jantke, Johann Jacob Mediziner * 30.01.1687 in Brieg † 22.03.1768 in Altdorf Jantzen, Hermann Geheimer Regierungsrat, Philologe * 19.02.1874 in Breslau † 04.11.1933 in Breslau Jarczyk, Herbert Dirigent, Musiker Jary, Michael Komponist Jedin, Hubert Kirchenhistoriker † 16.07.1980 in Bonn Jung, Franz Schriftsteller † 21.01.1963 in Stuttgart Junge, Alfred K Kabus, Wilhelm * 11. 10.1818 in Rybnik † 12.04.1996 in Berlin Kalide, Erdmann Theodor Bildhauer † 23.08.1863 in Gleiwitz Schriftsteller * 07.07.1913 in Breslau Kaller, Maximilian * 10.10.1880 in Beuthen/OS Kaluza, Victor Gedichte * 10.09.1896 in Lowkowitz Kanther, Manfred Politiker * 26.05.1939 in Schweidnitz Karl II. Herzog von Oels Karsch, Anna Louisa Volksdichterin * 01.12.1722 in "Meierei Auf dem Hammer bei Schwiebus" 12.10.1791 in Berlin Kasimir I. Herzog von Oppeln Kayssler, Friedrich

42. Two Meters Below Wilhelm martin kutta (18671944) brought RK methods 1901 to a first perfection andbecame also famous for his later work in aerodynamics (jpeg files imported http://www.unige.ch/math/folks/wanner/s_c/Amsterdam.html

Two meters below sea level, what a shame! Only a solid dijk prevents these people in Amsterdam from wet feet, and the beautiful pictures of Carl Runge and Wilhelm Kutta would be seriously damaged. Here they are ... Carl David Tolmé Runge (1856-1927) initiated RK methods in 1895, is also famous for his research in complex analysis, spectroscopy, approximation theory, and other fields of applied mathematics. Wilhelm Martin Kutta (1867-1944) brought RK methods 1901 to a first perfection and became also famous for his later work in aerodynamics (jpeg files imported from the WWW pages of Tanja Van Hecke).

43. Euler Og Runge-Kutta Metoder Biografi af Carle Runge (18561927) Biografi af martin kutta (1867-1944) Metodener også kendt som Heun s metode og er simpelthen en forbedring af Eulers http://www.frhavn-gym.dk/matematik/mrunge.html

Dette er et interaktivt kursus i numerisk løsning af differentialligninger ud fra Euler's metode og Runge-Kutta metoder. Klassetrin:Højt niveau, Gymnasiet. Tag allerførst en kopi af denne side Introduktion Ved praktisk løsning af differentialligninger stilles man ofte over for et Begyndelsesværdiproblem Vi har differentialligningen med et startpunkt og skal undersøge, hvordan udviklingen er som tiden går. Det viser sig nu, at der under generelle betingelser er en entydig løsning. Augustin Cauchy (1789-1857) har som den første studeret på dette eksistens- og entydighedsproblem for differentialligninger. Linieelementer Den første angrebsvinkel til vort arbejde med problemet skal være Linieelementer Betragt f.eks. differentialligningen (¤) dy/dt = -2*t*y Vælges (t,y)=(2,½) bliver ifølge (¤) dy/dt= -2. Vi tegner nu igennem (2,½) en lille liniestykke med hældning -2 og snakker om Linieelementet (2,½,-2) Hvis vi tegner linieelementer for et utal af punkter i planen, antydes der en serie af løsningskurver. På SOS-math finder du linieelementer (slope field) og gode eksempler.

44. Martin's Computing Experiences martin s Computing Experiences. during my maths degree a sputtering simulationin Algol60, using a novel self-adjusting Runge-kutta numerical integration http://www.mca-ltd.com/martin/experiences.html

Martin's Computing Experiences School DEC PDP-8/e , so interactive computing was opened up to me - albeit on an ASR-33 Teletype! As I entered the "6th form" (at age 16), the school started teaching computing, and upgraded to a " Research Machines 380Z", a Z80-based system, which had the best "software front panel" that I have (still) ever seen. Pupils were taught the ICL-CES language CESIL(mentioned here I designed and built two computers around this time: The first was based on the Z80, and had 1Kbytes of RAM, and a hardware front panel - mostly because I didn't have access to an EPROM programmer, and so had no other way to boot it! The second was a 'proper' computer, based on the 6809, and having 64KBytes of DRAM - by this time I could program a homebrew battery-backed-up pseudo PROM using my (less powerful!) BBC Micro . However, bootstrapping a usable software environment on the 6809 proved to be a much bigger task than getting the hardware running! University Going to the University of York to study Maths , I got access to big computers for the first time - they had hard disks - gosh! I also learnt my first high-level programming language - ALGOL-60 (BASIC didn't count in those days - does it now? :-). I did two computing projects during my maths degree: a sputtering simulation in Algol-60, using a novel self-adjusting

45. The Computer Journal, Volume 1, Issue 3, Pp. 118-123: Abstract. Rungekutta methods for integrating differential equations on high speed digitalcomputers. DW martin. National Physical Laboratory, Teddington, UK. http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/010118.sgm.abs.htm

Home Online Resources Table of Contents The Computer Journal, Volume 1, Issue 3, pp. 118-123: Abstract. Runge-Kutta methods for integrating differential equations on high speed digital computers DW Martin National Physical Laboratory, Teddington, UK The Runge-Kutta methods of Gill, Strachey and Boulton are discussed in respect of their accuracy, speed and storage requirements on electronic digital computers. For machines possessing a double-length accumulator alternative integration procedures are suggested which are comparable in accuracy with Gill's process and which are likely to be considerably faster. These procedures use additional storage registers to carry guarding digits of the dependent variables where the methods of Gill and Strachey achieve their accuracy by subtle algebra. Full-text in TIFF format - pp. Help with viewing full text Oxford University Press Oxford Journals

46. Thesis Martin Eckardt Translate this page Universität Erlangen Nürnberg zur Erlangung des Doktorgrades vorgelegt von MartinEckardt aus Better accuracy can be achieved with the Runge kutta algorithm. http://www.tp1.physik.uni-erlangen.de/~eckardt/thesis/thesis.html

Aspects of high-field carrier transport in AlGaAs Towards an efficient THz-emitter zur Erlangung des Doktorgrades vorgelegt von Martin Eckardt aus Erlangen Als Dissertation genehmigt von den Vorsitzender der Promotionskommission: Prof. Dr. H. Kisch Erstberichterstatter: Prof. Dr. G.H. Döhler Zweitberichterstatter: Prof. Dr. O. Pankratov Drittberichterstatter: Prof. Dr. P. Lugli Contents 1 Introduction 2 Basics 2.1 Optical Properties 2.1.2 Model of Rees ... Index Zusammenfassung Die vorliegende Arbeit ist am Lehrstuhl für Halbleiterphysik, Universität Erlangen-Nürnberg, in Zusammenarbeit mit dem Physik-Department E11, Technische Universität München, und dem Institut für Festkörperphysik, Technische Universität Wien, entstanden. Sie befasst sich mit dem Hochfeld-Ladungsträgertransport in AlGaAs mit dem Ziel der Entwicklung einer effizienten THz-Strahlungsquelle. Grundlagen Hz, Ferninfrarot) liegt einerseits oberhalb der Frequenzen, die noch bequem mit elektrisch getriebenen Quellen erreichbar sind, und andererseits unterhalb der Energien (1 THz =4 meV), die einfachen optischen Techniken zugänglich sind. Eine zur Zeit für viele Anwendungsbereiche verwendete Technik, die sog. Photomischer-Technik , benutzt die Schwebungsfrequenz zweier Laserstrahlen um periodisch Elektron-Loch-Paare in einem Halbleitermaterial zu erzeugen. Diese periodische Leitfähigkeit wird dazu benutzt, um die Spannung an angeschlossenen Antennenarmen zu modulieren und somit THz-Strahlung zu emittieren.

47. Computational Physics - Martin Dörr - Programm Translate this page martin Dörr. Vorlesung an der TU Berlin (FB Physik) im WS 2000/01 Wasdann mit 3-D und mehr ? - Numerik Runge-kutta Integrator (Ref. http://www.physik.tu-berlin.de/~doerr/cpprogra.htm

Wissenschaftliches Rechnen mit Anwendungen in klassischer Mechanik und Quanten-Mechanik "Computational Physics" Vorlesung an der TU Berlin (FB Physik) im WS 2000/01 Detaillierter Stichwort-Plan der Vorlesung === Version 19.9.2000 === Computer-Programme Lektion : Grundlagen Computing - Hardware : CPU; Primary, Secondary Caches; Bus; RAM; HD - Vector, Parallel Hardware; Memory and Data Handling - Software : OS (DOS, Unix, Linux); Windows, X-Win - Software : Compiler (f77, cc, c++, gpp); Interpreter (Basic, Mathematica) - Libraries (Bibliotheken) : I/O (Graphik); Mathematische Grundoperationen; (freie !) Software im Netz (Gnu, Netlib etc.) - Zahlen im Computer : IEEE Standard (Test-Programme tmach.f repres - Rundungsfehler MANTRA : Der Computer arbeitet nur mit endlicher Genauigkeit ! - Elementarste Grundlagen fortran (bzw C) (Beispiel-Programm test0.f test0.c - Strategien der Software-Entwicklung (Strukturiert, Modular, Objekte) - Benutzen des PC im PN-019/020 - 1 - PC nicht ausschalten !

48. Resultado Dos Modelos Translate this page o sistema de equações é usando o método de integração chamado de Runge-kuttaCarl David Tolmé Runge (1856-1927) e Wilhelm martin kutta (1867 - 1944 http://astro.if.ufrgs.br/evol/contorno/node5.htm

5 massas solares 25 massas solares Perda de massa População III Resultado dos Modelos e ou e terminando em , onde , onde Resultados da Seqüência Principal de Idade Zero No Physics of Shock Waves and High Temperature Hydrodynamic Phenomena , 1966, eds. W.D. Hayes e R.F. Probstein (New York: Academic Press). Naturalmente a escolha do passo de tempo, Densidade central e temperatura central para estrelas na seqüência principal de idade zero, com X=0,685 e Y=0,295. Para as estrelas de baixa massa, E F Sol a 0,9 para 3 M Sol Como para as estrelas acima de 1,2 indiano Subrahmanyan Chandrasekhar (1910-1995), Icko Iben Jr. e Gregory Laughlin, no seu artigo publicado em 1989 no Astrophysical Journal e encontraram para idade em anos. Por exemplo, para um modelo de 0,7 Evolução a partir da seqüência principal. Nas duas tabelas abaixo estão os tempos de vida em cada uma das faixas marcadas pelos números. Pontos Evolução a partir da seqüência principal para modelos de População I. Os números circundados indicam a quantia pela qual a abundâcia de lítio superficial foi reduzida, assumindo que nenhuma massa foi perdida e que o único mecanismo de mistura é a convecção. turnoff point - TOP onde anos.

49. ISTG Vol 2 - SS Gellert fem wife Germany 143 Johann kutta 20 male child Germany 144 Marie kutta 20 fem childGermany 145 Francisca kutta 19 fem child Germany 146 martin kutta 17 male http://www.immigrantships.net/v2/1800v2/gellert18770711.html

Immigrant Ships Transcribers Guild German SS Gellert Hamburg via Havre to New York July 11, 1877 DISTRICT OF NEW YORK – PORT OF NEW YORK Columns represent: Names, Age, Sex, Occupation, The country to which they severally belong, The country in which they intend to become inhabitants, Died on the voyage, Part of the vessel occupied by each passenger during the voyage. National Archives and Records Administration, Film M237, Reel 409, List 639. Transcribed by Regan Kanaley a member of the Immigrant Ships Transcribers Guild 1 October 1999 If you find an ancestor on a ship on ISTG and would like to link to your email address or home page, please submit a short paragraph about the passenger, where settled, children, etc., with the name of the ship and date of arrival, and send to the transcriber at the bottom of the manifest or to the ISTG Production Coordinator Get all your genealogy books and CDs at one convenient location: Genealogical Publishing Don't have a subscription to Ancestry.com yet? - Immigration/Emigration Databases - Search Historical Records - Census Records - Newspaper Databases ... - Complete Database Listing Website search technology courtesy of FreeFind.com

50. Fachhochschule Wedel - Martin "Herbert" Dietze Opts Options are -r Use Runge-kutta integration -p Use primitive http://www.fh-wedel.de/~di/prakt-alt/cueb/c-ss98/ueb9/

Thema der Aufgabe [Seitenanfang] [weiter] Funktionszeiger und LCLint Aufgabenstellung [Seitenanfang] [weiter] Eine Bibliothek zur numerischen Integration Es soll eine Bibliothek erstellt werden, die Funktionen der Form double func (double) (der Name func exp oder cos ) in den Grenzen bis mit der Tafelschrittweite h numerisch integriert. typedef double (*t_func) (double); typedef double (*t_method) (t_func, double, double, double); Es sollen folgende Funktionen exportiert werden: double integrate_rk (t_func func, double x1, double x2, double h) integriert die Funktion in den Grenzen von nach mit der Tafelschrittweite h stdout oder stderr double integrate_pg (t_func func, double x1, double x2, double h) macht dasselbe wie double integrate (t_method method, t_func func, double x1, double x2, double h) ruft die Integrationsfunktion Das Testprogramm soll unter Benutzung der Funktion aus der Bibliothek die Funktionen und und h double und h angegeben. Es wurde ein nicht definierter Schalter gesetzt. LCLint Hinweise [Seitenanfang] [weiter] Hantieren mit Funktionszeigern /* definiert einen Funktionszeigertypen * mit Rueckgabewert double und einem * double-Argument */ typedef double (*t_foo) (double);

51. Prime Numbers Rungekutta method, based on the work of martin kutta(1867-1944), and the methodof successive approximations, based on the work of Emile Picard (1856-1941). http://hypatia.math.uri.edu/~kulenm/diffeqaturi/m381f00fp/theron/theronmp.html

Difference Equations and Recursive Relations Number theory index History Topics Index It is from these recursive equations that some mathematical wonders are created. We begin with plane filling curves or fractals, which are curves that fill planes without any holes. The first such curve was discovered by Guiseppe Peano in 1890. Other mathematicians who used difference equations in their work with plane filling curves include David Hilbert (1862-1943), and Niels Fabian Von Koch (1870-1924). The relevant work all three will be discussed in the following. As will the work of Emile Picard (1856-1941) and Martin Kutta (1867-1944), both of whom used recursive equations in solutions to differential equations. There are curves that fill a plane without holes. The first such curve was discovered by Guiseppe Peano in 1890 and the second by D. Hilbert (1862-1943). Calling them Peano Monster Curves, B. Mandelbrot collected a series of quotations in support of this terminology. Fractal Curves and Dimension Fractals burst into the open in early 1970s. Their breathtaking beauty captivated many a layman and a professional alike. Striking fractal images can often be

52. Literature Martin Moessner Martin Mössner 1082, Uri M. Ascher and Linda R. Petzold , Projected implicit rungekutta methodsfor differential-algebraic equations . 1272, martin Aupperle , Die Kunst http://sport1.uibk.ac.at/mm/Bib/bib.html

xx xx . xx , xx Werner Nachbauer and Elmar Kornexl and Gerald Daringer and and A. Niederkofler Einrichtung eines Messplatzes zur Technikanalyse von Skispringern an der Skisprungschnaze Bergisel and Werner Nachbauer and Kurt Schindelwig and Gerhard Innerhofer and Herwig Schretter Mechanical Properties of Snow on Ski Slopes . Abstract Book, 15th International Congress on Skiing Trauma and Skiing Safety (ICSTSS) , and , ? , pp. ? , 2004 and Werner Nachbauer and Kurt Schindelwig and Gerhard Innerhofer and Herwig Schretter Mechanical Properties of Snow on Ski Slopes . Abstract Book, 5th International Congress on Snow Engineering (ICSE) , Ed Adams and Walter Ammann and Erik Hjorth-Hansen and Harald Norem and Mike J. O'Rourke and Atsushi Sato and Jerry Johnson , Davos, Switzerland , pp. ? , 2004 and Werner Nachbauer Dehnungseigenschaften von B"andern . Department of Sport Science , University of Innsbruck, Austria , Report 2003 and Werner Nachbauer and Gerhard Innerhofer and Herwig Schretter Mechanical Properties of Snow on Ski Slopes . Poster presented at the 15th International Congress on Skiing Trauma and Skiing Safety (ICSTSS), St. Moritz / Pontresina, Switzerland , April 27th - May 2nd 2003

53. Martin J. Gander 12. Download the Maple demo for the explicit Runge kutta methods of order InstructorsMartin Gander, mgander@math.mcgill.ca, office in Burnside Hall, Room 1114 http://www.math.mcgill.ca/mgander/189-261.php

Martin J. Gander Dept. of Mathematics and Statistics McGill University Montreal, QC, H3A 2K6 mgander@math.mcgill.ca Home Research Teaching ... Personal :: Differential Equations (MATH 261), winter 2004 This course is an introduction to ordinary differential equations. It uses as a textbook Boyce and DiPrima , Elementary Differential Equations and Boundary Value Problems, 6th edition, and treats chapters 1-9: historical background and terminology, existence and uniqueness, first order differential equations, modeling and applications, numerical methods, second and higher order differential equations, Laplace transforms, linear systems of differential equations and series solutions of second order linear equations. Announcements: Review sessions for the final will be held this week in McConnell Engineering room 304: Wednesday April 21: Mohammad Khalil: 2pm-4pm Thursday April 22: Steve Cohen: 2pm-4pm Friday April 23: Camille Belanger: 9:30am-11:30am Download the Maple examples for the higher order ODEs in postscript or pdf format.

54. Martin J. Gander martin J. Gander Dept. 2002) A graduate course in numerical methods for ordinaryand partial differential equations, including Rungekutta, Linear Multistep http://www.math.mcgill.ca/mgander/teaching.php

Martin J. Gander Dept. of Mathematics and Statistics McGill University Montreal, QC, H3A 2K6 mgander@math.mcgill.ca Home Research Teaching ... Personal CSE at McGill New degree program in Computational Science and Engineering Seminars McGill: CSE Applied Mathematics Genève: Analyse numérique :: Teaching Interests My teaching interests are both in Mathematics and Computer Science: in addition to undergraduate courses in both areas, I am interested and qualified to teach at the graduate level Scientific Computing, Numerical Differential Equations, Matrix Computations, Differential Equations, Parallel Computing, Numerical Dynamical Systems, Algorithms and Data Structures and Object Oriented Programing. :: Courses I teach this year at McGill Ordinary Differential Equations (MATH 325, fall): Introduction to ordinary differential equations: first and second order equations, linear equations, series solutions, Frobenius method, Laplace transforms and applications. Differential Equations (MATH 261, winter): Introduction to differential equations: first order and linear second order equations, higher order equations, solution by series, Laplace transform and simple numerical methods.

55. Kiehl, Martin : Partitioning In... Author(s) Kiehl, martin Title Partitioning in Reaction Kinetics analysis, Ordinarydifferential equations, Multistep, Rungekutta and extrapolation methods http://www-lit.ma.tum.de/veroeff/html/969.34005.html

Kiehl, Martin : Partitioning in... Author(s) Kiehl, Martin Title Partitioning in Reaction Kinetics Electronic source [gzipped ps-file] [ps-file] Published in Keil et. al.: Scientific Computing in Chemical Engineering, Springer, p. 122-128 Mathematics Subject Classification 34A65 [ Ordinary differential equations, General theory, Stiff equations] 65L05 [ Numerical analysis, Ordinary differential equations, Initial value problems] 65L06 [ Numerical analysis, Ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods] Abstract Abstract can be found under http://www-home.ma.tum.de/~kiehl/PRK.ps Keywords reaction kinetics; initial-value problems; partitioned Euler method Language English Publication time Notes complete list of publications Kommentare, Fragen oder Anregungen bitte per e-mail an kaplan@ma.tum.de Michael Kaplan , 12 Feb 04 (09:59)

56. Index Of /veroeff/html martin Ada 010.65005 010.65003.html Bornemann, Folkmar Runge-kutta Methods http://www-lit.ma.tum.de/veroeff/html/

Zentrum Mathematik der Bibliographic data Here you'll find the bibliographic data of publications in our department. If you want to search a specific entry, you should use our harvest broker form for all reports of the department. Please direct your comments or questions by e-mail to M. Kaplan Name Description Parent Directory ... 029.94009.html Alpers, Andreas; Gritzmann, Peter; Thorens, Lion> 019.60005.html Asmussen, Soeren; Kalashnikov, Vladimir; Kluppel> 980.60005.html Asmussen, Soeren; Kluppelberg, Claudia; Sigman, > 970.05010.html Babel Luitpold : Traversing and... 960.68018.html Babel, L.; Baumann, S.; Lüdecke, M.; Tinhofer, G> 960.68019.html Babel, L.; Chuvaeva, I.V.; Klin, M.; Pasechnik, > 940.08005.html Babel, Luitpold : Computational Aspects... 020.05003.html Babel, Luitpold : Computing Coherent... 990.05001.html Babel, Luitpold : On Graphs... 980.05015.html Babel, Luitpold : On the... 980.05018.html Babel, Luitpold : Recognizing the... 960.68008.html

57. Ingenta: Article Summary -- High Order Runge-Kutta-Nystrom Codes For The Integra kuttaNystrom codes for the integration of oscillatory problems Applied NumericalMathematics January 2004, vol. 48, no. 1, pp. 13-25(13) Garcia A.1; martin P http://www.ingenta.com/isis/searching/ExpandTOC/ingenta?issue=pubinfobike://els/

58. Martin Lillieroth Smakprov Teslatrasslet känt. Det var en anledning att använda Rungekutta 4 (RK4), för lösningav differentialekvationssystemet, i stället för ode45. http://www.f.kth.se/~martinli/tesla.php

59. Seznam Osob Podle Jména: Ku Kuscer, Ivan, (19181979), fyzik. Kutcher, Ashton, (narozený 1978),herec; kutta, martin Wilhelm, (1867-1944), matematik; Kuttner http://wikipedia.infostar.cz/l/li/list_of_people_by_name__ku.html

švodn­ str¡nka Tato str¡nka v origin¡le Seznam osob podle jm©na: Ku Seznam osob podle jm©na B C D ... J K L M N O ... Ka - Kb - Kc - Kd - Ke - Kf - Kg - Kh Ki Kj - Kk - Kl - Km - Kn Ko - Kp - Kq - Kr - Ks - Kt - Ku - Kv - Kw - Kx - Ky - Kz Kubasov, Valeri , (narozen½ 1935), astronaut Rusa Kublai Khan , (1215-1294), mongolsk½ c­sař Kubrick, Stanley , (1928-1999), americk½ filmov½ režis©r Kucan, Milan , (narozen½ 1941), prezident Slovinska Kucera, Jan, (narozen½ 1928), autor Kucey, Robert N , (narozen½ 1940), kanadsk½ romanopisec, spisovatel Kudrow, Lisa , (narozen½ 1963), americk¡ herečka Kuehn, Dieter, (narozen½ 1935), vypravěč, dramatik a esejista Kuehn, Heinz, (1912-1992), politik Kuenneke, Eduard, (1885-1953), skladatel Kuerti, Anton, pianista Kuhar, Lovro, (1893-1950), autor. Kuhn, Thomas filozof věda Kuhn, Thomas Samuel , (1922-1996), spisovatel a filozof Kuiper, Gerard , (1905-1973), astronom Kujau, Konrad , (1938-2000), Němec plagi¡tor Hitler den­ky Kujo Yoritsugu Japonec shogun Kujo Yoritsune ... Kukeiha, klub , skladatel Kulik, Ilia, (narozen½ 1977)

60. ChadFowler.com martin/essays/burkequote.html 1 /a , a href= http//www.tartarus.org/~martin/essays/burkequote2 Letme teach you a sentence blockquote Tu paagal kutta hai. http://www.chadfowler.com/index.cgi/Computing/BadMenCombine.html?rss

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 3     41-60 of 91    Back | 1  | 2  | 3  | 4  | 5  | Next 20