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         Bernoulli Jacob:     more books (24)
  1. The Art of Conjecturing, together with Letter to a Friend on Sets in Court Tennis by Jacob Bernoulli, 2005-12-20
  2. Die Streitschriften von Jacob und Johann Bernoulli: Variationsrechnung (Gesammelten Werke der Mathematiker Und Physiker der Familie Bernoulli) (German Edition) by Jakob Bernoulli, Johann I Bernoulli, 1991-06-01
  3. Die Streitschritfen Von Jacob Und Johann Bernoulli: Variationsrechnung by Bearbeitet Von Kommentiert, Herman H. Goldstine, 1991-09
  4. Der Briefwechsel von Johann I. Bernoulli: Band 1: Der Briefwechsel mit Jacob Bernoulli, dem Marquis de l'Hôpital u.a. (German Edition) (Vol 1) by Johann I Bernoulli, 1955-01-01
  5. 1654 Births: Jacob Bernoulli, Johann Friedrich, Margrave of Brandenburg-Ansbach, Joshua Barnes, Kangxi Emperor, Michiel de Swaen
  6. Leibnizens mathematische Schriften. Abteilung 2. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 2 by Gottfried Wilhelm von Leibniz, 2010
  7. 17th-Century Swiss People: Francesco Borromini, Jacob Bernoulli, Paracelsus, Jakob Abbadie, Johann Bernoulli, Maria Sibylla Merian
  8. Leibnizens mathematische Schriften. Abteilung 1. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 1 by Gottfried Wilhelm von Leibniz, 2010
  9. People From Basel-City: Leonhard Euler, Theodor Zwinger, Jacob Bernoulli, Auguste Piccard, Matthäus Merian, Edwin Fischer, Johann Bernoulli
  10. Swiss Calvinists: Henry Dunant, Daniel Bernoulli, Jacob Bernoulli, Johann Bernoulli, Karl Barth, Philip Schaff, Nicolaus Ii Bernoulli
  11. Leibnizens mathematische Schriften. Abteilung 2. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 2 by Gottfried Wilhelm von Leibniz, 2010
  12. Swiss Scientists: Jacob Bernoulli, Emil Theodor Kocher, Kenneth Hsu, Edward Kofler, Catherine Kousmine, Alfred Métraux, Marie-Louise Von Franz
  13. 18th-Century Latin Writers: Isaac Newton, Carl Linnaeus, Leonhard Euler, Gottfried Leibniz, Daniel Bernoulli, Jacob Bernoulli, Ludvig Holberg
  14. Leibnizens mathematische Schriften. Abteilung 1. Band IV. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 4 by Gottfried Wilhelm von Leibniz, 2010

61. Antiquariat Renner - Searchengine / Suchmaschine
Translate this page Available Pages For - Verfügbare Seiten für Verkehr (Post, Eisenbahn,Fahrrad, Auto) - Transport - Land. bernoulli, jacob (50304),
http://www.antiquar-renner.com/search.mv? showcat TV

62. ESA Portal - Switzerland - Italiano - I Grandi Nomi
Translate this page La casa natale accoglieva regolarmente personaggi eminenti del mondo della matematica,quali Johann bernoulli e jacob Hermann, e ciò sviluppò la disposizione
http://www.esa.int/export/esaCP/GGGN6C0BVIC_Switzerland_it_0.html
ESA Life in Space Expanding Frontiers Improving Daily Life ... Benefits for Europe 29-Mar-2003 07:26:59 UT Contents Jakob Bernouilli (1654-1705) Johann Bernouilli (1667-1748) Daniel Bernouilli (1700-1782) Leonhard Euler (1707-1783) ... Eduard Stiefel (1909- 1978) Servizi Calendario Iscriviti Contatta ESA Ricerca All Notizie Locali Svizzera Ricerca avanzata
I grandi nomi
Alcuni scienziati svizzeri o residenti in Svizzera hanno fornito un importante contributo al progresso della ricerca o delle tecniche spaziali. Ecco la biografia di alcuni:
La famiglia Bernouilli La famiglia del droghiere Nicolaus Bernouilli (1623-1708), i cui antenati belgi e calvinisti erano riparati a Basilea dai Paesi Bassi all’arrivo del Duca d’Alba, è stata la capostipite di una dinastia di matematici. I più noti sono i figli Jacob e Johann Bernouilli, insieme al nipote Daniel, figlio di quest’ultimo.
Jakob Bernoulli

Jakob Bernouilli (1654-1705)
Jakob Bernouilli nacque il 27 dicembre 1654 a Basilea, dove studiò teologia e si laureò nel 1671, ottenendo altresì un dottorato nella stessa disciplina nel 1676, dedicandosi parallelamente allo studio della matematica, contro la volontà del padre. Bernouilli fu chiamato ad occupare la cattedra di matematica all’Università di Basilea dopo aver insegnato privatamente fisica sperimentale nella stessa città a partire dal 1683 e aver pubblicato testi sulla comprimibilità dell’aria e sul punto centrale d’oscillazione, cattedra che mantenne fino alla morte nel 1705. Suo fratello Johann gli succedette fino al 1748, mentre il figlio di quest'ultimo, Daniel, ricoprì lo stesso incarico fino al 1790.

63. The Science Bookstore - Chronology
bernoulli, jacob (l) Born 12/27/1654 Died 8/16/1705, 1654 AD, bernoulli,Johann (I) Born 7/27/1667 Died 1/1/1748, 1667 AD, bernoulli
http://www.thesciencebookstore.com/chron.asp?searchstring=Bernoulli

64. Matemáticos
Translate this page B. Babbage Banach Barrow Berkeley bernoulli, Daniel bernoulli, jacob bernoulliJohan Bessel Betti Binet Bolyai Bolzano Boole Borel Brauer Brioschi Brouncker
http://mat.usal.es/Personales/JoseAngel/mates.html
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A

Abel
Adams Agnesi Arbuthnot ... Artin
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Babbage
Banach Barrow Berkeley ... Burnside C
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Caratheodory Cardan Carnot ... Cremona D
Darboux
Dedekind Dehn Delambre ... Durer d'
D'Alembert
D'Arcy-Thompson De L'Hopital De Moivre ... De Morgan E
Edgeworth
Einstein Eisenstein Euclid ... Euler F
Fejer
Fermat Fibonacci Fisher ... Frobenius G
Galileo
Galois Galton Gauss ... Gregory H Haar Hadamard Hall Halley ... Hypatia J Jacobi Jordan Julia K Kepler Killing Kirkman Klein ... Kummer L Lagrange Lambert Landau Laplace ... Lobachevsky M Maclaurin Mandelbrot Mascheroni Maupertuis ... Morse N Napier Newton Noether, Emmy Noether, Max O Oughtred P Pascal Peacock Peano Pearson ... Pythagoras Q Quetelet R Ramanujan Recorde Riccati Riemann ... Russell S Schur Schwarz Steiner Stevin ... Sylvester T Tarski Tartaglia Taylor Thales ... Turing U Ulam V Vallee-Poussin Veblen Viete Vinogradov ... Von-Neumann W Wallis Weber Wedderburn Weierstrass ... Wronski Y Yule Z Zygmund

65. ThinkQuest Library Of Entries
The spiral we are considering is named after jacob bernoulli. jacob bernoulliwas born on the 27th of December, 1654 in Basel, Switzerland
http://library.advanced.org/18222/root/story1/page4/bernoul.htm
Welcome to the ThinkQuest Internet Challenge of Entries
The web site you have requested, Wise Turtle Stories , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Wise Turtle Stories click here Back to the Previous Page The Site you have Requested ...
Wise Turtle Stories
click here to view this site
A ThinkQuest Internet Challenge 1998 Entry
Click image for the Site Languages : Site Desciption This web site will teach you about the programming language Logo, and how it's used to draw spirals, wheels, and fractals. The "philosophy" of each shape is presented along with models. Once you read about the creation of each shape you may want to try the Logo language yourself! The bibliography includes traditional and electronic sources.
Students Alexander International School of General Education
Russia Veniamin International School of General Education
Russia Anna International School of General Education
Russia Coaches Olga International School of General Education
Russia Yehuda Levinski Teachers School
Israel Donald Myers Education Center
NY, United States

66. Boys
jacob bernoulli was born December 27th, 1654. The tenth child of Nicolaus bernoulli,Johann was born on July 27th, 1667, twelve years after his brother jacob.
http://jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/Dickerson/Bernoulli/boys.html
Two Bernoulli Brothers
Nicolaus Bernoulli was a merchant in Basel, Switzerland. His family were refugees fleeing from the massacre done by the Catholics in the Netherlands. The family settled in Basel only after fleeing to Frankfurt from persecution by the Spanish rulers. Nicolaus wanted his children to study religion and medicine. Fortunately, three of his sons chose a different path in life and studied mathematics. This is the story of two of the brother's lives, Jacob and Johann, and their rivalry.
Jacob Bernoulli was born December 27th, 1654 In 1671 Jacob graduated from the University of Basel with a master's degree in philosophy and in 1676 with a licentiate in theology. Jacob studied philosophy and theology to oblige with his parents' wishes. While working on these degrees, Jacob also studied mathematics and astronomy against his parents wishes. Jacob was the first of the numerous Bernoullis to study mathematics.
After graduation, Jacob began work as a tutor in Geneva. He traveled to France, studying with the followers of Descartes for two years. Beginning in 1681, Jacob continued his travels to the Netherlands and then to England where he continued his studies with leading mathematicians and scientists.
Jacob returned to the University of Basel to teach mechanics in 1683 He turned down an appointment in the Church at this time. One year later Jacob married Judith Stupanus. Together they had a son and a daughter; neither became mathematicians.

67. Zeal.com - United States - New - Library - Sciences - Mathematics - Mathematicia
Read brief biographies of jacob, John, and Daniel bernoulli, as wellas some of the other, younger members of this family of science.
http://www.zeal.com/category/preview.jhtml?cid=540647

68. NewsScan Publishing Inc. - NewsScan Daily Archives
BENCHLEY, ROBERT. BERGMAN, INGMAR. BERLIOZ, HECTOR. BERNHARDT, SARAH. bernoulli,jacob. BERNSTEIN, LEONARD. BETHUNE, MARY MCLEOD. BETTELHEIM, BRUNO. BIKO, STEPHEN.
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69. Il Giardino Di Archimede
bernoulli, jacob - Ars coniectandi. Basilea Roma,Varesio, 1662; bernoulli, jacob - De gravitate aetheris . Amsterdam
http://www.math.unifi.it/archimede/archimede/CD_rom/elenco_CD.html
Il giardino di Archimede
Un museo per la matematica
La matematica antica su CD-rom:
una iniziativa del Giardino di Archimede per la storia della matematica
Piano dell'opera
serie I CD 1 CD 2 CD 3 CD 4 ... CD 10 serie II CD 11 CD 12 CD 13 CD numero 1
    Bernoulli, Johann - Opera. Losanna e Ginevra, Bousquet, 1747. Clairaut, Alexis Claude - Clairaut, Alexis Claude - Recherches sur les courbes a double courbure. Euler, Leonhard - Lione, Bruyset, 1795. Hermann, Jacob - Phoronomia. Amsterdam, Wetsten, 1716. Lagrange, Joseph Louis - Mecanique analytique. Parigi, Courcier, 1811. Lagrange, Joseph Louis - Theorie des fonctions analytiques. Parigi, Impr. De la Republique, 1797. Mascheroni, Lorenzo - Adnotationes ad calculum integralem Euleri. Pavia, Galeazzi, 1790. Monge, Gaspard - Geometrie descriptive. Parigi, Baudouin, 1799. Papin, Denis - Nouvelle maniere pour lever l'eau. Kassel, Estienne, 1707. Ruffini, Paolo - Teoria generale delle equazioni. Bologna, S. Tommaso, 1799. Simpson, Thomas - A treatise on Algebra. Londra, Nourse, 1745.
torna a inizio pagina CD numero 2
    Anderson, Alexander -

70. Bernoulli Bibliography: I
IMSHENETSKII VG, 1 O funktsiyakh Yakova Bernulli i vyrazhenii raznosti mezhduodnopredel'nymi summoyu i integralom On functions of jacob bernoulli and an
http://www.mscs.dal.ca/~dilcher/berni.html
Bernoulli Bibliography
I
Back to Index Back to H On to ... J IBRAHIMOGLU I.,
),Hecettepe Bull. Natur. Sci. and Eng.
Z R [2] The value of the Dirichlet L-functions at negative integral points, Hacettepe Bull. Natur. Sci. and Eng.,
Z R [3] (C,k)-summability of the Dirichlet L-functions, Hacettepe Bull. Natur. Sci. and Eng.,
Z R IBUKIYAMA T.,
[1] On some elementary character sums, Comment. Math. Univ. St. Paul. (1998), no. 1, 7-13.
Z M IBUKIYAMA T., SAITO H.,
[1] On $L$-functions of ternary zero forms and exponential sums of Lee and Weintraub. J. Number Theory, (1994), no. 2, 252-257.
Z M [2] On zeta functions associated to symmetric matrices, I: An explicit form of zeta functions, Amer. J. Math., (1995), no. 5, 1097-1155.
Z M IBUKIYAMA T.: see also ARAKAWA T., IBUKIYAMA T., KANEKO M. ICHIMURA H.: see HACHIMORI Y., ICHIMURA H. IKEDA M.,
[1] Some inequalities for Bernoulli's polynomials and related functions, Monatsh. Math., Z M 31#2435; err.31, p.1336; R IMAI H., (1993), no. 4, 505-510. Z M R IMAOKA M.

71. UB Basel: Bernoulli-Edition
The bernoulli Family Tree. jacob I 16541705, Johann I 1667-1748, /¯¯¯¯,,.jacob HERMANN 1678-1733, Nicolaus I 1687-1759.
http://www.york.ac.uk/depts/maths/histstat/people/bernoulli_tree.htm
The Bernoulli Family Tree
Jacob I
Johann I
Jacob HERMANN
Nicolaus I
Nicolaus II
Daniel
Johann II
Johann III
Jacob II

72. Maestra
Translate this page jacob bernoulli era hermano de Johann bernoulli y tío de Daniel bernoulli. Losnúmeros de bernoulli fueron nominados por jacob bernoulli.
http://www.mat.ucm.es/deptos/am/guzman/pagjor/bern2.htm
Jacob (Jacques) Bernoulli
Jacob Bernoulli era hermano de Con su muerte su puesto en Basilea fue ocupado por su hermano Johann Bernoulli.

73. Historia Matematica Mailing List Archive: Re: [HM] Bernoulli In
Basel 1689. My quotation is from jacob bernoulli, Basiliensis, opera.Vol. and jacob bernoulli Tractatus de Seriebus Infinitis (partly) on.
http://fire1b.math.utk.edu/hypermail/historia/0028.html
Re: [HM] Bernoulli inequality
Subject: Re: [HM] Bernoulli inequality
From: Staffan Rodhe ( book@kubkou.se
Date: Wed Oct 18 2000 - 18:40:41 EDT Dear all,
In a discussion about Bernoulli inequality Heinz Lueneburg wrote:
You can find the same theorem and proof in "Tractatus de Seriebus
Infinitis" printed together with "Ars Conjectandi" 1713, eight years
after the death of Jacob Bernoulli. You can find it on page 243-244,
proposition IV.
You can find Barrow's version of the inequality in his "Lectiones
Geometricae", 1670, Chapter VII, proposition XIII, page 60. It is
nice to see that Barrow's treatment of the inequality is almost identical to Jacob Bernoulli's. Then Barrow has the priority and Bernoulli's inequality should be called Barrow's inequality (?!). of a geometric progression are greater than the corresponding terms of an arithmetic progression if the first term of both progressions are equal and the second arithmetic term is not greater than the second geometric term. The Bernoulli (Barrow) inequality is just a

74. Familie Bernoulli
Translate this page jacob bernoulli ( * 1654 in Basel , + 1705 in Basel ), jacob bernoulli, Newton,Leibniz und der Marquis de l`Hospital sandten richtige Lösungen ein.
http://www.fmi.uni-passau.de/~stifter/archiv/projekte_11/zukunft2000/bernoulli.h
Die Familie Bernoulli
Ich m öchte sie Ihnen kurz vorstellen und auf ihre wichtigsten Erkenntnisse eingehen. Jacob Bernoulli ( * 1654 in Basel , + 1705 in Basel ) - 1671 Magister der Philosophie
- 1676 Lizentiat der Theologie
- 1677 - 1680 Aufenthalt in Frankreich. Er widmet sich der Gnomontik, der Lehre der Sonnenuhren und verfasst die "Tabulae gnomonicae universalis"
- schon während des Studiums großes Interesse an der Astronomie
1681 Veröffentlichung seiner ersten wissenschaftlichen Arbeit: Anleitung zur Berechnung von Kometenbahnen
- 1681 - 82 Studienaufenthalt in den Niederlanden und in England
- 1683 hält er private Vorlesungen über Experimentalphysik
- 1685 veröffentlicht er ein erstes Problem zur Wahrscheinlichkeitsrechnung - 1687 wird er Professor für Mathematik an der Universität in Basel. Zusammen mit seinem Bruder Johann ist er ein eifriger Verfechter des Leibniz'schen Infinitesimalkalküls. Sie erkennen die Bedeutung des Rechnens mit dem " unendlich-kleinen " und wenden diese Methode bei vielen geometrischen und physikalischen Problemen an, ohne lange darüber zu philosophieren. Jacob fand unter anderem Lösungen zur stetigen Verzinsung und gab die Differentialgleichung für das Leibniz'sche Isochronenproblem an. Hierbei wurde das Wort "Integral" zum ersten Mal in unserem heutigen Sinn ( siehe Kollegstufe ) verwandt.
- 1689 - 1704 Arbeiten aus der Reihenlehre

75. OPE-MAT - Historique
Translate this page János Brisson, Barnabé Berkeley, George Bolza, Oskar Brocard, Henri Bernays,Paul Bolzano, Bernhard Broglie, Louis de bernoulli, jacob Bombelli, Rafael
http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm
A
Abel
, Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali
B
Babbage
, Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl

76. Bernoulli
to physics; his son, Johann bernoulli, 17461807, who was astronomer royal at Berlinand also studied mathematics and geography; and jacob bernoulli, 1759-89
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    Bernoulli name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, 1654-1705, became professor at Basel in 1687. One of the chief developers both of the ordinary calculus and of the calculus of variations , he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the coefficients of the exponential series expansion of x e ). He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, Johannis Bernoulli opera omnia. His son, Daniel Bernoulli, 1700-1782, was a mathematician, physicist, and physician and has often been called the first mathematical physicist. He received his doctorate in medicine but became professor of mathematics at the St. Petersburg Academy in 1725. He was professor of anatomy and botany at Basel from 1733, later becoming professor of natural philosophy (physics). His greatest work was his Hydrodynamica (1738), which included the principle now known as
  • 77. CAC-NET/FoCM-NET: Help File
    being returned to you. Ambiguous key try one of the following bernoulli,daniel = cac.dbernoulli bernoulli, jacob = cac.jbernoulli;
    http://www.cs.columbia.edu/cacnet/help.html
    The CAC-NET/FoCM-NET Help File
    This version of the CAC-NET/FoCM-NET help file has been modified somewhat to make it more Web-aware. If you wish, you can see the (original) text version. Welcome to CAC-NET/FoCM-NET, an electronic conferencing system for researchers in Continuous Algorithms and Complexity and in Foundations of Computational Mathematics . It is based on NA-NET, a successful system that has been used by numerical analysts over the past few years. Credits: The CAC-NET/FoCM-NET software is a slight modification of that used by NA-NET. The NA-NET was originated at Stanford University by Gene Golub. Their software was written by Mark Kent (Stanford) and Bill Rosener (Tenessee). The Oak Ridge NA-NET operation is run under the direction of Jack Dongarra, who has graciously allowed me to use the NA-NET software, help files, etc., which I have modified to suit our own needs. MOTIVATION: This mail facility was created to allow researchers in Continuous Algorithms and Complexity (CAC) and in Foundations of Computational Mathematics (FoCM) an easy method of communicating with one another. The main advantage of the CAC-NET/FoCM-NET is uniformity of addressing. All mail is addressed to the Internet host "cs.columbia.edu" at Columbia University. Hence, members of the CAC-NET/FoCM-NET do not need to remember complicated addresses or even where a member is currently located. As long as moving members change their e-mail address in the CAC-NET/FoCM-NET (see feature 5 below) everything works smoothly.

    78. CAC-NET/FoCM-NET: Easy Email
    Ambiguous key try one of the following bernoulli, daniel= cac.dbernoulli bernoulli, jacob = cac.jbernoulli
    http://www.cs.columbia.edu/cacnet/ez-email.html
    Easy Email
    The mail facility was created to allow researchers in Continuous Algorithms and Complexity (CAC) and in Foundations of Computational Mathematics (FoCM) an easy method of communicating with one another. The main advantage of the CAC-NET/FoCM-NET is uniformity of addressing. All mail is addressed to the Internet host cs.columbia.edu at Columbia University. Hence, members of the CAC-NET/FoCM-NET do not need to remember complicated addresses or even where a member is currently located. As long as moving members change their e-mail address in the CAC-NET/FoCM-NET everything works smoothly. Examples: For example, to mail to Art Werschulz, you would send mail to cac.werschulz@cs.columbia.edu or to focm.werschulz@cs.columbia.edu Mail sent to a nonexistent CAC-NET/FoCM-NET name (e.g., cac.abcde@cs.columbia.edu ) will result in the following message being returned to you. - CAC-NET/FoCM-NET key not found. Message returned. . . . - Mail sent to a non-unique cac-net name (e.g., cac.bernoulli@cs.columbia.edu

    79. Jacob Bernoulli
    Urodzil sie w Bazylei; rodzina Bernoullich przywedrowala z Holandiido Szwajcarii w XVI wieku. Znaczny wplyw na rozwój nauki
    http://www.mat.uni.torun.pl/~cichy/Jacob Bernoulli.htm
    Urodzi³ siê w Bazylei; rodzina Bernoullich przywêdrowa³a z Holandii do Szwajcarii w XVI wieku. Znaczny wp³yw na rozwój nauki w Bazylei mia³ wówczas patrycjat kupiecki, do którego zalicza³a siê równie¿ rodzina Bernoullich. Jakub z woli ojca studiowa³ teologiê, ale interesowa³a go równie¿ matematyka, której poœwiêca³ wiele czasu. Matematyczne wykszta³cenie uzupe³ni³ w Holandii, Anglii i Francji. Po powrocie z podró¿y bez reszty zaj¹³ siê studiowaniem matematyki i astronomii. Dwie og³oszone prace z astronomii nie przynios³y mu oczekiwanego rozg³osu. Rok 1687 by³ szczególnie wa¿ny dla Jakuba, w roku tym bowiem obj¹³ katedrê matematyki na uniwersytecie w Bazylei i rozpocz¹³ owocn¹ korespondencjê z Leibnizem. Wa¿n¹ czêœci¹ analizy matematycznej jest rachunek wariacyjny (tak¹ nazwê nosz¹ metody wyznaczania najmniejszych i najwiêszych wartoœci funkcjona³ów, tj. funkcji, których argumentem s¹ funkcje albo uk³ady funkcji, a wartoœciami liczby rzeczywiste). Powszechnie s³usznie uznaje siê, ¿e twórc¹ rachunku wariacyjnego by³ Euler. Mimo to du¿ym krokiem naprzód w rozwoju rachunku wariacyjnego (pasjonowa³ on uczonych ju¿ w staro¿ytnoœci) by³o rozwi¹zanie przez Jakuba postawionego przez jego brata Jana w roku 1696 zadania o brachistochronie. Stanowi³o ono pierwsz¹ próbê zastosowania rachunku ró¿niczkowego do rozwi¹zywania zadañ wariacyjnych. Ponadto interesowa³y go krzywe specjalne; do ich badania u¿ywa³ tak¿e wspó³rzêdnych biegunowych. Najbardziej zajmowa³a go spirala logarytmiczna; odkry³ jej ciekawe w³asnoœci. Jest ona wyryta na jego grobie (takie by³o jego ¿yczenie) i zaopatrzona napisem: "Tak samo powstajê, choæ siê zmieniam". Uczony ten du¿e zas³ugi po³o¿y³ tak¿e w teorii szeregów. Jego publikacje z okresu 1689-1704 stanowi³y pierwszy przewodnik w tej dziedzinie matematyki. Drug¹ dziedzin¹ matematyki, obok rachunku ró¿niczkowego, w której zapisa³ siê trwale, jest rachunek prawdopodobieñstwa. Dla jej potrzeb rozwin¹³ analizê kombinatoryczn¹. Podstawowym dorobkiem jego w tej dziedzinie by³ dowód twierdzenia zwanego "prawem wielkich liczb", które obecnie znane jest jako twierdzenie Benoulliego.

    80. B Index
    Benedetti, Giovanni (211) Bergman, Stefan (311*) Berkeley, George (239*) Bernays,Paul Isaac (772*) bernoulli, Daniel (2341*) bernoulli, jacob (1913*) bernoulli
    http://www.math.hcmuns.edu.vn/~algebra/history/history/Indexes/B.html

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