s rs rstr - - PowerPoint PPT Presentation
s rs rstr - - PowerPoint PPT Presentation
s rs rstr r ts s trrt t rsss
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
▼♦t✐✈❛t✐♦♥
❲❤❛t ✐s t❤❡ tr✉❡ r❛t❡ ♦❢ ♣❡rs✐st❡♥❝❡ ✐♥ s♦❝✐❛❧ st❛t✉s ht❄ ht = βht−✶ + (✶ − β)¯ h + ut , ✇❤❡r❡✿ β✿ ✐♥t❡r❣❡♥❡r❛t✐♦♥❛❧ ❡❧❛st✐❝✐t② ♦❢ h✱ ■♥❡q✉❛❧✐t② ✐♥ t❤❡ ❧♦♥❣ r✉♥✿ limt→∞ ❱❛r[ht] = σ✷
u
✶ − β✷ ❍✐❣❤ s♦❝✐❛❧ ♠♦❜✐❧✐t② ✐♥ ❢❡✇ ❣❡♥❡r❛t✐♦♥s ✐❢ β ✐s ❧♦✇✳
✷ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❚✇♦ ✐ss✉❡s
✶✮ ▼❡❛s✉r❡♠❡♥t ❡rr♦r ❜✐❛s❡s ❞♦✇♥✇❛r❞s ♣❛r❡♥t✲❝❤✐❧❞ ❝♦rr❡❧❛t✐♦♥s ▲❛t❡♥t ✈❛r✐❛❜❧❡ h ♣❡rs✐st❡♥t ❛❝r♦ss ❣❡♥❡r❛t✐♦♥s✳ ◆♦✐s✐❧② ♣r♦①✐❡❞ ❜② ♦❜s❡r✈❡❞ ♦✉t❝♦♠❡s y ✭❡✳❣✳✱ ✐♥❝♦♠❡✱ ❡❞✉❝❛t✐♦♥✱ ♦❝❝✉♣❛t✐♦♥✮✳ ▲✐t❡r❛t✉r❡✿ ♣r♦♣♦s❡s ✇❛② t♦ ❝♦rr❡❝t ❢♦r ♠❡❛s✉r❡♠❡♥t ❡rr♦r ✷✮ ❙❡❧❡❝t✐♦♥ ❜✐❛s t❤r♦✉❣❤ ♥❡♣♦t✐s♠ ❚❤✐s ♣❛♣❡r✿ ◆❡✇ ♠❡t❤♦❞ t♦ ✐❞❡♥t✐❢② ♥❡♣♦t✐s♠
✸ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❚❤✐s ♣❛♣❡r
■❞❡♥t✐❢②✐♥❣ ♥❡♣♦t✐s♠ r❡q✉✐r❡s t♦ s❡♣❛r❛t❡ s❡❧❡❝t✐♦♥ ❢r♦♠ ♠❡❛s✉r❡♠❡♥t ❡rr♦r✳ ❖✉r ♠❡t❤♦❞ r❡q✉✐r❡s✿ ❲❡❧❧ ❞❡✜♥❡❞ ✉♥✐✈❡rs❡ ♦❢ ❢❛t❤❡rs ❛♥❞ s♦♥s ✇✐t❤ ❡♥tr② r❡str✐❝t✐♦♥s ✭s❡❧❡❝t✐♦♥✮✳ → ◆❡✇ ❞❛t❛s❡t ♦♥ s❝❤♦❧❛rs ❛♥❞ ♠❡♠❜❡rs ♦❢ s❝✐❡♥t✐✜❝ ❛❝❛❞❡♠✐❡s ✐♥ ✶✶✵✵✕✶✽✵✵✳ ❖✉t❝♦♠❡ ✈❛r✐❛❜❧❡ yt ✭♥♦✐s✐❧②✮ ❝♦rr❡❧❛t❡❞ ✇✐t❤ ✉♥♦❜s❡r✈❛❜❧❡ ❤✉♠❛♥ ❝❛♣✐t❛❧✱ ht✳ → P✉❜❧✐❝❛t✐♦♥s ✐♥ ❧✐❜r❛r✐❡s t♦❞❛②✳ ❈♦✉❧❞ ❜❡ ❛♣♣❧✐❡❞ ✐♥ ♠❛♥② ♦t❤❡r ❝♦♥t❡①ts ❛s ✇❡❧❧
✹ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
■❞❡❛✿ ❙❡♣❛r❛t✐♥❣ ✏❚r✉❡✑ ❤✉♠❛♥ ❝❛♣✐t❛❧ tr❛♥s♠✐ss✐♦♥ ✈s✳ ◆❡♣♦t✐s♠
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Ailhaud J Matthaeus P Matthaeus A Mathon J Chicoyneau M Cusson P Fizes N Magnol P Saporta A Aquin LH Boulduc S Boulduc S Duverney JG Buxtorf J Buxtorf J Accorumbonus G Becker D Berger JH Bernhold JB Burman F Burman F Geuns M Bontius G Bobart J Leyser W Leyser W Leyser P Leyser P Vallisneri A Terrasson J Chartier R Duret L Goulu N Lemerre P Vauvilliers J Burnett G Burnett G Sassenus S Burnett G Cavendish W Darwin E Fuller J Bicais H Villars CLH Fontaine J Harpprecht F Helvetius J Bierling F Calvert C Cavendish W Bartholin C Bartholin C Bartholin T Calixt G Weise F Bacmeister L Bacmeister L Lindemann T Quistorp J Quistorp J Quistorp J Swantenius E Willebrand A Grape Z Habermann C Becker J Becker D Eschenbach J DeFerriere C Cassini GD Cassini GD Cassini J Cassini J Cassini J Cassini CF Cassini CF Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Bernoulli J Euler L Euler L Euler L Grynaeus S Grynaeus T Zwinger T Zwinger J Zwinger T Zwinger J Zwinger T Zwinger T Zwinger T Furstenau JH Bauhin G Bauhin JC Bauhin H Stupanus JN Faesch R Wettstein JR Wettstein JR Werenfels P Battier S Konig E Stahelin JH Ryhiner P Platter T Hopfner J Horst G Platter T Platter T Petre R Camerarius E Camerarius E Hyde E Howard C Sozzini M Mesmes J Deutsch F Flottwell C Hahn J Rast G Rast G Sanden B Sanden B Sanden H Hert J Segers J Frommann J Carrere T Accursio F Fornelius LJ Celsius MN Hydren L Aurivillius S Amaseo RQ Arntzenius H Alting H Eyssonius H Matthaeus A Mulerius N Wijnpersse D Cremer B Gorter J BernidegliAntoni F Busch J Duising B Goclenius R Hombergk zu Vach J Hunnius A Kleinschmidt J Kleinschmidt J Kornmann J Krafft J Lonicerus J Lonicerus J Matthaeus K Matthaeus K Mentzer B Molther J Nigidius P Schroder J Schroder J Vultejus J Waldschmiedt J Zaunschliffer O Bebel H Brenz J Cellius E Gmelin J Gmelin J Gmelin P Gmelin P Arnoldi J Gmelin J Hafenreffer M Harpprecht G Baumer J Bechtold J Hochstetter J Hoffmann D Hoffmann G Mauchart B Mogling J Mogling J Mogling J Mogling J Mogling J Osiander J Ploucquet G Pregizer J Scheinemann D Schott C Schott C Tafinger F Weiganmeier G Fomann O Gerhard J Hamberger G Hamberger G Hellfeld J Krause R Major J Posner K Sagittarius T Schelhammer C Schenck E Schmid P Schroter E Schroter J Schroter J Slevogt P Slevogt P Stock C Voit D Walch K Walch J Walch J Wedel G Wiedeburg J Wiedeburg J Voet P Voet G Albinus B Bontius G Gronovius J Heurnius J Honert T Schooten F Schooten F Schultens J Schultens A Spanheim F Vinnius A Vitriarius P Vorstius A Walaeus A Patin M Patin M Hoffmann M Rittershaus K Beuther M Lorry F Baudiss G Stryk S Crocius J Argoli A Arduino P BoscDAntic P Cusson P Michelotti F Michelotti F Michelotti F VaccaBerlinghieri F Brendel Z Alefeld J Boecler J Dasypodius P Boecler J Junius M Lorentz J Marbach J Marbach J Sebiz M Bohmer G Bohmer G Bohmer G Bohmer G Eichhorn J Gatterer J Mayer T Vogel R Volckamer J Kortholt M May J Mentzer B Mentzer B Mollenbeck A Mollenbeck A Nebel C Scheibler C Schulz J Sinold J Snell J Snell J Thom E Valentini MB Borcholten J Crell J Engelbrecht G Engelbrecht G Forster V Horneius K Kipping J Meibom H Meibom H Meibom J Meibom H Remer J Scheurl L Schmidt J Schrader C Wernsdorf J Wiedeburg C Lidbeck E Papke C Stobaeus N Stobaeus A Burman J Apinus J Baier J Baier J Bruckmann F Crell J Ehrhart B Ettmuller M Fehr J Fehr J Garmann C Gockel C Gorter J Grass S Haller A Heister L Cambout A Isenflamm H Lehmann E Linck J Mauchart J Nebel D Pohl J Preuss M Seip JP Tralles J Trommsdorff W Trumph J Valentini MB Valentini MB Vater C Wedel G Wepfer J Widmann J Brugmans A Huber U Schotanus H Vitringa C Voorda J Wayen J Ypey N Beauvilliers F BussyRabutin R Colbert J Riedl C Dundas R Franklin B Monro A Stewart M Canterzani S Gavinet JM Willermoz PJ Sozzini M Bignon A Cureau M Cambout A Costeo G Boivin L Garcaeus J Celsius N Balthasar J Balthasar J Battus B Bering J Colberg J Muhrbeck J Gerdes F Helwig C Lutkemann T March C Mascow G Mayer J Overkamp G Rhaw A Rhaw B Runge J Runge J Runge J Stephani M Westphal A Monro A Monro A Filelfo F Restout J Maty M Lysius H Martyn J Achard A Lauremberg W CoquebertdeMonbret C Cartheuser J Dacheroden K Hamberger G Rumpel J Rumpel J Suckow L Trommsdorff W Willemet R Abrek A Pacheco Zuniga JMF Adriani G Adriani M Akakia M Malvasia AG Hayes W Molesworth R Felibien A Warton T Molyneux W erdugo Albornoz P Cresques A Pelargus C Cocceji H Meister C Cramer J Cramer J Franck C Franck C Hensler P Kortholt C Musaus P Opitz H Dunlop W Schultingh J Tintoretto J Montesquieu C Sascerides J Langguth GA Wandal H Scavenius L Mauvillon E Brochmand H Buchwald J Dillenius J Horrebow P Hire P Hire P Kirchmaier G Fornier G Gothofred D Vogli GG Zoppio G Serres C Pryss S Wishart W Wishart W Bourdelin C Gorski J Turretin F Turretin B Blackwell T Cocchi A Doni GB Pidoux J Cardano F Ettmuller M Racine J Leveque Pouilly LJ Freitag A Freitag A Frisius G Pocquet C Fiennes JB Turgot ME Argenville AJ Ranchin E Gonzaga C Argenson M Argenson M Argenson M Lemery N Scarburgh C Torre AG Corsini F Filicaia V Bentinck W Tronchin T Maurice A Hottinger J Hottinger J Leger A Hawenreuter S Osborne T Macclesfield G Gezelius J Moreau R Moreau R Zoppio G Marchetti P Percy H Pietre S Rechenberg A Mercklin G Douglas J Gadolin J Aepinus F Vater C Mayer T Mikan JG Barzizza G Mortimer J Pohl J Planta A Cravetta A Trommsdorff W Charteris H George ? Nymannus H DegliOddi O Patin G Riolan J Vaillant JF Wormius O Wormius W Wormius W Dreier C GallaratiLomeno A Tibbon J Tibbon S Robartes J Abigdor A Borgognoni U Aiton W Sebiz M Sebiz J Koch U Pantaleon H Ribiers E Broussonnet F Chastelain J Ranchin E Maynier G Sprat T Yorke P Yorke C De la Gardie MG Trevor T Wren C Wollaston F Wollaston F Willett R Arsendo R
b = ✵.✺✵✽∗∗∗ ✭s✳❡✳ ✵✳✵✷✹✮
- ● ●●●
- ●
- ●
- Sons' log publications
Fathers' log publications
KS = ✵.✶✵✸∗∗∗ ✭♣✲✈❛❧✳ ✵✳✵✵✵✮
✺ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
Pr❡✈✐❡✇ ♦❢ t❤❡ ❘❡s✉❧ts
❲❡ ✜♥❞ ❡✈✐❞❡♥❝❡ ✐♥ ❢❛✈♦r ♦❢ t❤❡ ❡①✐st❡♥❝❡ ♦❢ ♥❡♣♦t✐s♠✳ ≈ ✶✺% s❝❤♦❧❛rs✬ s♦♥s ❛r❡ s❝❤♦❧❛rs t❤❡♠s❡❧✈❡s t❤❛♥❦s t♦ ♥❡♣♦t✐s♠✳ ▲♦ss ♦❢ s❝✐❡♥t✐✜❝ ♦✉t♣✉t ❜❡❝❛✉s❡ ♦❢ ♥❡♣♦t✐s♠ ≈ ✶✼✪ ❚❤❡ tr✉❡ r❛t❡ ♦❢ tr❛♥s♠✐ss✐♦♥ ♦❢ ❤✉♠❛♥ ❝❛♣✐t❛❧ r❡♠❛✐♥s ❤✐❣❤ ✭β ≈ ✵.✻✮✱
✻ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❉❛t❛❜❛s❡
❉❛t❛❜❛s❡ ❜✉✐❧t ❢r♦♠ ❜♦♦❦s ❛♥❞ ❝❛t❛❧♦❣✉❡s ♦❢ ✉♥✐✈❡rs✐t✐❡s ❛♥❞ ❛❝❛❞❡♠✐❡s✳ ▼❛t❝❤❡❞ ✇✐t❤ ❜✐♦❣r❛♣❤✐❝❛❧ ❞✐❝t✐♦♥❛r✐❡s✳ ❈♦✈❡r❛❣❡✿ ♣r❡✲✐♥❞✉str✐❛❧ ❊✉r♦♣❡ ✭< ✶✽✵✵✮✳ ✶✵✻✽ ❢❛t❤❡r✲s♦♥ ♣❛✐rs ✐♥ ✶✶✷ ✐♥st✐t✉t✐♦♥s✳ ❙❝❤♦❧❛r✬s ♣✉❜❧✐❝❛t✐♦♥s ✭❧✐❜r❛r② ❤♦❧❞✐♥❣s ✐♥ ❲♦r❧❞❝❛t✮✳
✼ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❈♦✈❡r❡❞ ✐♥st✐t✉t✐♦♥s✿ t♦♣ ✶✺
■♥st✐t✉t✐♦♥ ❈♥tr② ❉❛t❡s ◆❜✳ ▼❛✐♥ ❙♦✉r❝❡ ❯♥✐✈❡rs✐t② ♦❢ ❇♦❧♦❣♥❛ ■❚❆ ✶✵✽✽ ✶✺✻ ▼❛③③❡tt✐ ✭✶✽✹✼✮ ❘♦②❛❧ ❙♦❝✐❡t② ♦❢ ▲♦♥❞♦♥
- ❇❘
✶✻✻✵ ✻✺ ✇✇✇✳r♦②❛❧s♦❝✐❡t②✳♦r❣✴ ❯♥✐✈❡rs✐t② ♦❢ ❆✈✐❣♥♦♥ ❋❘❆ ✶✸✵✸ ✶✼✾✸ ✺✽ ▲❛✈❛❧ ✭✶✽✽✾✮✱ ▲❛✈❛❧ ✭✶✽✽✾✮✱ ❚❡✉❧❡ ✭✶✽✽✼✮ ❋♦✉r♥✐❡r ✭✶✽✾✷✮✱ ❇❛r❥❛✈❡❧ ✭✶✽✹✶✮✱ ❉✉❤❛♠❡❧ ✭✶✽✾✺✮ ❯♥✐✈❡rs✐t② ♦❢ ❚ü❜✐♥❣❡♥ ❉❊❯ ✶✹✼✻ ✹✷ ❈♦♥r❛❞ ✭✶✾✻✵✮ ▲❡♦♣♦❧❞✐♥❛ ❉❊❯ ✶✻✺✷ ✸✼ ✇✇✇✳❧❡♦♣♦❧❞✐♥❛✳♦r❣✴ ❯♥✐✈❡rs✐t② ♦❢ ❇❛s❡❧ ❈❍❊ ✶✹✻✵ ✸✷ ❍❡r③♦❣ ✭✶✼✽✵✮ ✫ ❘❡♣✳ ❆❝❛❞✳ ●❡r♠✳ ❯♥✐✈❡rs✐t② ♦❢ ▼♦♥t♣❡❧❧✐❡r ❋❘❆ ✶✷✽✾ ✶✼✾✸ ✸✵ ❉✉❧✐❡✉ ✭✶✾✼✺✱ ✶✾✼✾✱ ✶✾✽✸✮ ❯♥✐✈❡rs✐t② ♦❢ P❛❞♦✈❛ ■❚❆ ✶✷✷✷ ✷✼ P❡s❡♥t✐ ✭✶✾✽✹✮✱ ❋❛❝❝✐♦❧❛t✐ ✭✶✼✺✼✮ ❯♥✐✈❡rs✐t② ♦❢ ❏❡♥❛ ❉❊❯ ✶✺✺✽ ✷✼
- ü♥t❤❡r ✭✶✽✺✽✮
❯♥✐✈❡rs✐t② ♦❢ P❛✈✐❛ ■❚❆ ✶✸✻✶ ✷✼ ❘❛❣❣✐ ✭✶✽✼✾✮ ❯♥✐✈❡rs✐t② ♦❢ ▼❛r❜✉r❣ ❉❊❯ ✶✺✷✼ ✷✹
- ✉♥❞❧❛❝❤ ✭✶✾✷✼✮
❯♥✐✈❡rs✐t② ♦❢ ●r❡✐❢s✇❛❧❞ ❉❊❯ ✶✹✺✻ ✷✹ ❆❧❧❣❡♠❡✐♥❡ ❉❡✉ts❝❤❡ ❇✐♦❣r❛♣❤✐❡ ❯♥✐✈❡rs✐t② ♦❢ ●✐❡ss❡♥ ❉❊❯ ✶✻✵✼ ✷✸ ❍❛✉♣t ✭✶✾✵✼✮ ❯♥✐✈❡rs✐t② ♦❢ ❍❡❧♠st❡❞t ❉❊❯ ✶✺✼✺ ✶✽✵✾ ✷✵ ✇✇✇✳✉♥✐✲❤❡❧♠st❡❞t✳❤❛❜✳❞❡✴ ❯♥✐✈❡rs✐t② ♦❢ P❛r✐s ❋❘❆ ✶✷✵✵ ✶✼✾✸ ✶✽ ❍❡r③♦❣ ✭✶✼✽✵✮✱ ❆♥t♦♥❡tt✐ ✭✷✵✶✸✮
✽ ✴ ✶✻
0km 300km 600km
N
cases
1 5 25 50 100 150
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
◗✉❛❧✐t❛t✐✈❡ ❡✈✐❞❡♥❝❡
◆❡♣♦t✐s♠ ❆❢t❡r s✐①t② ②❡❛rs ♦❢ t❡❛❝❤✐♥❣ ❝❛♥♦♥ ❧❛✇ ✐♥ ❙❛❧❛♠❛♥❝❛✱ ❏✉❛♥ ❆❧❢♦♥s♦ ❇❡♥❛✈❡♥t❡ ✭✲✶✹✼✽✮ r❡t✐r❡❞ ✐♥ ✶✹✻✸✳ ❍❡ r❡t❛✐♥❡❞ ❤✐s ❝❤❛✐r ❛♥❞ ❤✐s ❧❡❝t✉r❡s ✇❡r❡ t❛✉❣❤t ❜② s✉❜st✐t✉t❡s✱ ✐♥❝❧✉❞✐♥❣ ❤✐s s♦♥ ❉✐❡❣♦ ❆❧❢♦♥s♦ ❞❡ ❇❡♥❛✈❡♥t❡ ✭❝✳ ✶✹✸✵✲✶✺✶✷✮✳ ❋✐♥❛❧❧②✱ ♦♥ ◆♦✈❡♠❜❡r ✶✾✱ ✶✹✼✼✱ ❇❡♥❛✈❡♥t❡ r❡s✐❣♥❡❞ t♦ ❤✐s ❝❤❛✐r ♦♥ t❤❡ ❝♦♥❞✐t✐♦♥ t❤❛t ❤✐s s♦♥ ✇❛s ✜r♠❧② ❛♣♣♦✐♥t❡❞ t♦ ✐t✳ ✭s♦✉r❝❡✿ ❉✐❝❝✐♦♥❛r✐♦ ❇✐♦❣rá✜❝♦ ❊s♣❛ñ♦❧✮ ❍✉♠❛♥ ❝❛♣✐t❛❧ tr❛♥s♠✐ss✐♦♥ ❆❜♦✉t ❏❡❛♥ ❇❛✉❤✐♥ ✭✶✺✹✶✲✶✻✶✸✱ ♣r♦❢❡ss♦r ✐♥ ❇❛s❡❧✮✿ ❍✐s ❢❛t❤❡r✱ ❏❡❛♥ ❇❛✉❤✐♥ ✭✶✺✶✶✲✶✺✽✷✱ ♣r♦❢❡ss♦r ♦❢ ♠❡❞✐❝✐♥❡ ✐♥ ❇❛s❡❧✮✱ ✇❛s ❤✐s ✜rst ♠❛st❡r ✐♥ t❤❡ st✉❞② ♦❢ ♠❡❞✐❝✐♥❡ ❛♥❞ ♦❢ ❛❧❧ t❤❡ ✉♥❞❡r❧②✐♥❣ s❝✐❡♥❝❡s✳ ✭s♦✉r❝❡✿ ▼✐❝❤❛✉❞✱ ❜✐♦❣r❛♣❤✐❡ ✉♥✐✈❡rs❡❧❧❡✱ ✶✽✶✶✮
✶✵ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❙tr✉❝t✉r❛❧ ♠♦❞❡❧
❙❡t ♦❢ ❛❧❧ ❧✐♥❡❛❣❡s✿ I ❋❛t❤❡r✬s ❤✉♠❛♥ ❝❛♣✐t❛❧ ✭✉♥♦❜s❡r✈❡❞✮✿ ht−✶ ∼ N(µh, σ✷
h).
❈❤✐❧❞r❡♥✬s ❤✉♠❛♥ ❝❛♣✐t❛❧✭✉♥♦❜s❡r✈❡❞✮✿ ht = βht−✶ + ut, ❙❡t P ♦❢ s❝❤♦❧❛r ❧✐♥❡❛❣❡s✿ P = {i | ht−✶ > ✵, ht > −ν} ⊂ I P✉❜❧✐❝❛t✐♦♥s ♦❢ ❢❛t❤❡rs✿ yt−✶ = max(π, ht−✶ + ε) P✉❜❧✐❝❛t✐♦♥s ♦❢ s♦♥s✿ yt = max(π, ht + ǫ)
✶✶ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❊st✐♠❛t✐♦♥ ❜② s✐♠✉❧❛t❡❞ ♠❡t❤♦❞ ♦❢ ♠♦♠❡♥ts
♣❛r❛♠❡t❡r ❡st✐♠❛t✐♦♥ β ✵✳✺✼✹ ✭✵✳✵✺✶✮ µh ✷✳✺✷✻ ✭✵✳✺✸✺✮ σh ✸✳✸✼✷ ✭✵✳✷✹✺✮ σe ✵✳✸✼✻ ✭✵✳✶✶✶✮ π ✷✳✷✸✸ ✭✵✳✶✽✾✮ ν ✺✳✼✹✶ ✭✶✳✺✶✸✮
✶✷ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
■♠♣♦rt❛♥❝❡ ♦❢ ◆❡♣♦t✐s♠✿ s✐♠✉❧❛t✐♦♥
❙✐♠✉❧❛t❡ ♠♦❞❡❧ ✇✐t❤ ν = ✵ ❛❧❧♦✇s t♦ ❛ss❡ss t❤❡ s✐③❡ ♦❢ ♥❡♣♦t✐s♠✿ s = ✶✹.✹%✱ s ✐s t❤❡ % ♦❢ s❝❤♦❧❛rs✬ s♦♥s ✇♦✉❧❞ ♥♦t ❜❡ s❝❤♦❧❛rs t❤❡♠s❡❧✈❡s✳ ❘❡♣❧❛❝❡ ♥❡♣♦t✐❝ s❝❤♦❧❛rs ✇✐t❤ ❛✈❡r❛❣❡ s❝❤♦❧❛r✿ ■♥❝r❡❛s❡ ✐♥ ♠❡❛♥ ♣✉❜❧✐❝❛t✐♦♥s ❜② ✶✻✳✽✪
✶✸ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❍❡t❡r♦❣❡♥❡✐t② ♦❢ ◆❡♣♦t✐s♠ s ❜② ❋✐❡❧❞
Theology Law Medecine Arts & Sciences
N = 288, s = 20% N = 323, s = 17% N = 165, s = 12%
Source: les cinq facult´ es, livre des privil` eges de l’universit´ e de Louvain, c. 1450
N = 136, s = 5%
✶✹ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❍❡t❡r♦❣❡♥❡✐t② ♦❢ ◆❡♣♦t✐s♠ s ❜② ❘❡❧✐❣✐♦♥
Protestant institutions: Catholic institutions:
N = 344, s = 27%
(after 1527)
N = 515, s = 3%
Source: Emile Delper´ ee (1878)
✶✺ ✴ ✶✻
■♥tr♦❞✉❝t✐♦♥ ❉❛t❛ ❙tr✉❝t✉r❛❧ ❡st✐♠❛t✐♦♥
❍❡t❡r♦❣❡♥❡✐t② ♦❢ ◆❡♣♦t✐s♠ s ❜② ❛❣❡ ❛t ❛♣♣♦✐♥t♠❡♥t
❆♣♣♦✐♥t❡❞ ❜❡❢♦r❡ ❞❡❛t❤ ♦❢ ❢❛t❤❡r✿ N = ✹✸✸✱ s = ✶✺% ❆♣♣♦✐♥t❡❞ ❛❢t❡r ❞❡❛t❤ ♦❢ ❢❛t❤❡r✿ N = ✹✺✹✱ s = ✽% T HE END
✶✻ ✴ ✶✻