# An Equation for the Haber Equilibrium by Gillespie L. J.

By Gillespie L. J.

Similar mathematics books

Pre-calculus Demystified (2nd Edition)

Your step by step way to getting to know precalculus

Understanding precalculus frequently opens the door to studying extra complex and sensible math matters, and will additionally aid fulfill university standards. Precalculus Demystified, moment version, is your key to getting to know this occasionally difficult subject.

This self-teaching advisor offers basic precalculus techniques first, so you'll ease into the fundamentals. You'll steadily grasp services, graphs of features, logarithms, exponents, and extra. As you move, you'll additionally triumph over issues comparable to absolute worth, nonlinear inequalities, inverses, trigonometric features, and conic sections. transparent, precise examples make it effortless to appreciate the cloth, and end-of-chapter quizzes and a last examination support make stronger key ideas.

It's a no brainer! You'll examine about:

Linear questions
Functions
Polynomial division
The rational 0 theorem
Logarithms
Matrix arithmetic
Basic trigonometry

Simple sufficient for a newbie yet not easy sufficient for a complicated scholar, Precalculus Demystified, moment variation, moment variation, is helping you grasp this crucial topic.

Il matematico curioso. Dalla geometria del calcio all'algoritmo dei tacchi a spillo

Los angeles matematica informa, in modo consapevole e inconsapevole, anche i più semplici e automatici gesti quotidiani. Avreste mai pensato che l. a. matematica ci può aiutare in line with lavorare a maglia? E che esistono numeri fortunati according to giocare al lotto, enalotto e superenalotto? E che addirittura esiste una formulation in keeping with scegliere correttamente los angeles coda al casello?

Mathematics Education and Subjectivity: Cultures and Cultural Renewal

This e-book rethinks mathematical instructing and studying with view to altering them to fulfill or withstand rising calls for. via contemplating how academics, scholars and researchers make feel in their worlds, the e-book explores how a few linguistic and socio-cultural destinations hyperlink to common conceptions of arithmetic schooling.

Strong Limit Theorems in Noncommutative L2-Spaces

The noncommutative models of primary classical effects at the nearly certain convergence in L2-spaces are mentioned: person ergodic theorems, robust legislation of huge numbers, theorems on convergence of orthogonal sequence, of martingales of powers of contractions and so on. The proofs introduce new thoughts in von Neumann algebras.

Extra info for An Equation for the Haber Equilibrium

Example text

HH< (HH% (HH@ HHH HH@ HH% HH< HH!     ❉✐❡s s✐♥❞ ❞✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥ ❡✐♥❡r ❇✐♥♦♠✐❛❧✈❡rt❡✐❧✉♥❣ ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥   ! ;\$ " %;?? H " %<%1 " %\$H\$ " %\$\$H " %%1! @ ❆❜❜✳ ✶✳✼✿ ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ♠✐t ✸ P❡r✐♦❞❡♥ ❢ür ❞✐❡ ❆❞✐❞❛s✲❆❦t✐❡ ③✉r ✒Pr♦❣♥♦s❡✏ ❞❡r ❦ü♥❢t✐❣❡♥ ❆❦t✐❡♥❦✉rs❡♥t✇✐❝❦❧✉♥❣ ▲❛✉t ✉♥s❡r❡s ▼♦❞❡❧❧s ❦❛♥♥ ❞❡r ❆❦t✐❡♥❦✉rs ❞❡r ❆❞✐❞❛s✲❆❦t✐❡ ❛♠ ✵✾✳✵✻✳✵✽ ✈✐❡r ❲❡r✲ t❡ ❛♥♥❡❤♠❡♥✿ ✺✵✱✷✶ ❜③✇✳ ✹✸✱✸✷ ♠✐t ❥❡✇❡✐❧s ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥ ✽✶ ✉♥❞ ✹✼✱✽✵ ❜③✇✳ ✹✺✱✺✵ ♠✐t ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥ ❥❡✇❡✐❧s ✸✽ ✳ ❉❡r r❡❛❧❡ ❑✉rs ❞❡r ❆❞✐❞❛s✲❆❦t✐❡ ❧❛❣ ❛♠ ✷✻✳✵✺✳✵✽ ❜❡✐ ✹✺✱✶✺✱ ❛♠ ✵✷✳✵✻✳✵✽ ❜❡✐ ✹✺✱✵✺ ✉♥❞ ❛♠ ✵✾✳✵✻✳✵✽ ❜❡✐ ✹✹✱✸✷✳ ✶✳✶✵✳ ◆❖❘▼❆▲❱❊❘❚❊■▲❯◆● ❯◆❉ ❆❑❚■❊◆❑❯❘❙❊ ✷✼ ❉❛s ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ✐st ✈❡r❣❧❡✐❝❤❜❛r ♠✐t ❞❡r ❇❡s❝❤r❡✐❜✉♥❣ ❡✐♥❡r ❆❦t✐❡♥❦✉rs✲ ❡♥t✇✐❝❦❧✉♥❣ ❞✉r❝❤ ❞❛s ❲❡r❢❡♥ ❡✐♥❡r ▼ü♥③❡ ❢ür ❥❡❞❡ ❡✐♥③❡❧♥❡ P❡r✐♦❞❡✳ ❊rs❝❤❡✐♥t ❑♦♣❢✱ st❡✐❣t ❞❡r ❆❦t✐❡♥❦✉rs ✐♥ ❞❡r ❜❡tr❡✛❡♥❞❡♥ P❡r✐♦❞❡ ❛✉❢ (  ✱ ❢ä❧❧t ❤✐♥❣❡❣❡♥ ❩❛❤❧✱ s✐♥❦t ❞❡r ❑✉rs ❛✉❢   ✳ ❉✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ❢ür ❑♦♣❢ ❜③✇✳ ❩❛❤❧ ❜❡trä❣t ❥❡  ✱ ❞❛♠✐t st❡✐❣t ❜③✇✳ s✐♥❦t ❞❡r ❆❦t✐❡♥❦✉rs ❡❜❡♥❢❛❧❧s ♠✐t ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥  ✳ ❉❛ ❞✐❡ ▼ü♥③❡ ❞❛rü❜❡r ❤✐♥❛✉s ❣❡❞ä❝❤t♥✐s❧♦s ✐st✱ tr❡t❡♥ ❩❛❤❧ ✉♥❞ ❑♦♣❢ ✐♠♠❡r ♠✐t ❞❡r✲ s❡❧❜❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ❛✉❢✱ ✉♥❛❜❤ä♥❣✐❣ ❞❛✈♦♥✱ ✇❛s ❞✐❡ ▼ü♥③❡ ❡✐♥❡♥ ❲✉r❢ ✈♦r❤❡r ❛♥③❡✐❣t❡✳ ➘❤♥❧✐❝❤ ✈❡r❤ä❧t ❡s s✐❝❤ ♠✐t ❞❡♠ ❆❦t✐❡♥❦✉rs✳ ❯♥❛❜❤ä♥❣✐❣ ❞❛✈♦♥✱ ♦❜ ❞❡r ❆❦t✐❡♥❦✉rs ✐♥ ❞❡r ✈♦r❤❡r✐❣❡♥ P❡r✐♦❞❡ st✐❡❣ ♦❞❡r s❛♥❦✱ st❡✐❣t ❜③✇✳ s✐♥❦t ❞❡r ❆❦t✐✲ ❡♥❦✉rs ✐♥ ❞❡r ❞❛r❛✉✛♦❧❣❡♥❞❡♥ P❡r✐♦❞❡ ♠✐t ❞❡rs❡❧❜❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥  ✳ ▼✐t ❞❡♠ ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ❤❛❜❡♥ ✇✐r ❡✐♥ ❡rst❡s ❡✐♥❢❛❝❤❡s ▼♦❞❡❧❧ ❦❡♥♥❡♥ ❣❡❧❡r♥t✱ ♠✐t ❞❡♠ ❡s ♠ö❣❧✐❝❤ ✐st✱ ✐♠ ❘❛❤♠❡♥ ❞❡r ❡r❧ä✉t❡rt❡♥ ▼♦❞❡❧❧❛♥♥❛❤♠❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤✲ ❦❡✐ts❛✉ss❛❣❡♥ ü❜❡r ❦ü♥❢t✐❣❡ ❆❦t✐❡♥❦✉rs❡ ③✉ tr❡✛❡♥✳ ■♠ ❘❛❤♠❡♥ ❞✐❡s❡s ▼♦❞❡❧❧s ✐st ❡s ❞❡♥♥♦❝❤ ✇✐❝❤t✐❣✱ ❞✐❡ ▼♦❞❡❧❧❛♥♥❛❤♠❡♥ ③✉ ❤✐♥t❡r❢r❛❣❡♥✳ ❑r✐t✐s❝❤ ③✉ s❡❤❡♥ ✐st ③✉♠ ❇❡✐s♣✐❡❧✱ ❞❛ss ❛✉s ❉❛t❡♥ ❞❡r ❱❡r❣❛♥❣❡♥❤❡✐t Pr♦❣♥♦s❡♥ ❢ür ❞✐❡ ❩✉❦✉♥❢t ❣❡tät✐❣t ✇❡r✲ ❞❡♥✳ ❉❛rü❜❡r ❤✐♥❛✉s ❜❧❡✐❜❡♥ ( ✉♥❞  ü❜❡r sä♠t❧✐❝❤❡ Pr♦❣♥♦s❡♥ ❦♦♥st❛♥t✱ ❞✳ ❤✳✱ ❞✐❡ ▼♦❞❡❧❧♣❛r❛♠❡t❡r s✐♥❞ st❛t✐s❝❤✳ ❉✐❡s ✐st ✐♥s♦❢❡r♥ ♣r♦❜❧❡♠❛t✐s❝❤✱ ❞❛ss ✐♥ Pr♦❣♥♦s❡♥ ü❜❡r ❡✐♥❡♥ ❧ä♥❣❡r❡♥ ❩❡✐tr❛✉♠ ♥❡✉❡ ■♥❢♦r♠❛t✐♦♥❡♥ ♥✐❝❤t ✐♥ ❞✐❡ ❇❡✇❡rt✉♥❣ ❡✐♥✢✐❡✲ ÿ❡♥✳ ❙♦ ❜❧❡✐❜❡♥ ❜❡✐s♣✐❡❧s✇❡✐s❡ ✉♥✈♦r❤❡rs❡❤❜❛r❡ ❊r❡✐❣♥✐ss❡ ✭③✳ ❇✳ ❆♥❧❡❣❡r♠❡♥t❛❧✐tät✱ ✇✐rts❝❤❛❢t❧✐❝❤❡ ➘♥❞❡r✉♥❣❡♥ ✐♥ ❞❡r ❆●✮ ✉♥❜❡rü❝❦s✐❝❤t✐❣t✳ ●❡♥❡r❡❧❧ ✇✐r❞ ❞❛s ❆❦t✐❡♥✲ ❦✉rs❣❡s❝❤❡❤❡♥ st❛r❦ ✈❡r❡✐♥❢❛❝❤t ♠♦❞❡❧❧✐❡rt✳ ❉✐❡ ❊✐❣❡♥s❝❤❛❢t ❞❡s ▼♦❞❡❧❧s✱ ❞❛ss ❞❡r ❆❦t✐❡♥❦✉rs ♥❛❝❤ ❡✐♥❡r P❡r✐♦❞❡ ♥✉r ③✇❡✐ ❲❡rt❡ ❛♥♥❡❤♠❡♥ ❦❛♥♥✱ ✐st ✉♥r❡❛❧✐st✐s❝❤✳ ✶✳✶✵ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ✉♥❞ ❆❦t✐❡♥❦✉rs❡ ✶✳✶✵✳✶ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ❉✐❡ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ st❡❧❧t ❡✐♥❡ ❣r✉♥❞❧❡❣❡♥❞❡ ❱❡rt❡✐❧✉♥❣ ❞❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐ts✲ r❡❝❤♥✉♥❣ ❞❛r✳ ❙✐❡ ✜♥❞❡t ❜❡✐ ③❛❤❧r❡✐❝❤❡♥ ♣r❛❦t✐s❝❤❡♥ Pr♦❜❧❡♠❡♥ ❆♥✇❡♥❞✉♥❣✳ ❇❡✲ tr❛❝❤t❡♥ ✇✐r ③✉♥ä❝❤st ❞✐❡ ❉❡✜♥✐t✐♦♥✳ ❉❡✜♥✐t✐♦♥ ✶✳✶✵✳✶ ✭◆♦r♠❛❧✈❡rt❡✐❧t❡ ❩✉❢❛❧❧s❣röÿ❡✮✳ ❊✐♥❡ st❡t✐❣❡ ❩✉❢❛❧❧s❣röÿ❡  ❤❡✐ÿt ♥♦r♠❛❧✈❡rt❡✐❧t ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ ❢ür ❛❧❧❡ *  ❢♦❧❣❡♥❞❡ ❉✐❝❤t❡ ❜❡s✐t③t✿   ▼❛♥ s❝❤r❡✐❜t✿    &   ✉♥❞   *      & "!

HH< HH% HH@ HHH (HH@ (HH% (HH< (HH! (H1H (HH! (HH< (HH% (HH@ HHH HH@ HH% HH< HH!     ❉✐❡s s✐♥❞ ❞✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥ ❡✐♥❡r ❇✐♥♦♠✐❛❧✈❡rt❡✐❧✉♥❣ ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥   ! ;\$ " %;?? H " %<%1 " %\$H\$ " %\$\$H " %%1! @ ❆❜❜✳ ✶✳✼✿ ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ♠✐t ✸ P❡r✐♦❞❡♥ ❢ür ❞✐❡ ❆❞✐❞❛s✲❆❦t✐❡ ③✉r ✒Pr♦❣♥♦s❡✏ ❞❡r ❦ü♥❢t✐❣❡♥ ❆❦t✐❡♥❦✉rs❡♥t✇✐❝❦❧✉♥❣ ▲❛✉t ✉♥s❡r❡s ▼♦❞❡❧❧s ❦❛♥♥ ❞❡r ❆❦t✐❡♥❦✉rs ❞❡r ❆❞✐❞❛s✲❆❦t✐❡ ❛♠ ✵✾✳✵✻✳✵✽ ✈✐❡r ❲❡r✲ t❡ ❛♥♥❡❤♠❡♥✿ ✺✵✱✷✶ ❜③✇✳ ✹✸✱✸✷ ♠✐t ❥❡✇❡✐❧s ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥ ✽✶ ✉♥❞ ✹✼✱✽✵ ❜③✇✳ ✹✺✱✺✵ ♠✐t ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥ ❥❡✇❡✐❧s ✸✽ ✳ ❉❡r r❡❛❧❡ ❑✉rs ❞❡r ❆❞✐❞❛s✲❆❦t✐❡ ❧❛❣ ❛♠ ✷✻✳✵✺✳✵✽ ❜❡✐ ✹✺✱✶✺✱ ❛♠ ✵✷✳✵✻✳✵✽ ❜❡✐ ✹✺✱✵✺ ✉♥❞ ❛♠ ✵✾✳✵✻✳✵✽ ❜❡✐ ✹✹✱✸✷✳ ✶✳✶✵✳ ◆❖❘▼❆▲❱❊❘❚❊■▲❯◆● ❯◆❉ ❆❑❚■❊◆❑❯❘❙❊ ✷✼ ❉❛s ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ✐st ✈❡r❣❧❡✐❝❤❜❛r ♠✐t ❞❡r ❇❡s❝❤r❡✐❜✉♥❣ ❡✐♥❡r ❆❦t✐❡♥❦✉rs✲ ❡♥t✇✐❝❦❧✉♥❣ ❞✉r❝❤ ❞❛s ❲❡r❢❡♥ ❡✐♥❡r ▼ü♥③❡ ❢ür ❥❡❞❡ ❡✐♥③❡❧♥❡ P❡r✐♦❞❡✳ ❊rs❝❤❡✐♥t ❑♦♣❢✱ st❡✐❣t ❞❡r ❆❦t✐❡♥❦✉rs ✐♥ ❞❡r ❜❡tr❡✛❡♥❞❡♥ P❡r✐♦❞❡ ❛✉❢ (  ✱ ❢ä❧❧t ❤✐♥❣❡❣❡♥ ❩❛❤❧✱ s✐♥❦t ❞❡r ❑✉rs ❛✉❢   ✳ ❉✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ❢ür ❑♦♣❢ ❜③✇✳ ❩❛❤❧ ❜❡trä❣t ❥❡  ✱ ❞❛♠✐t st❡✐❣t ❜③✇✳ s✐♥❦t ❞❡r ❆❦t✐❡♥❦✉rs ❡❜❡♥❢❛❧❧s ♠✐t ❡✐♥❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥  ✳ ❉❛ ❞✐❡ ▼ü♥③❡ ❞❛rü❜❡r ❤✐♥❛✉s ❣❡❞ä❝❤t♥✐s❧♦s ✐st✱ tr❡t❡♥ ❩❛❤❧ ✉♥❞ ❑♦♣❢ ✐♠♠❡r ♠✐t ❞❡r✲ s❡❧❜❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ❛✉❢✱ ✉♥❛❜❤ä♥❣✐❣ ❞❛✈♦♥✱ ✇❛s ❞✐❡ ▼ü♥③❡ ❡✐♥❡♥ ❲✉r❢ ✈♦r❤❡r ❛♥③❡✐❣t❡✳ ➘❤♥❧✐❝❤ ✈❡r❤ä❧t ❡s s✐❝❤ ♠✐t ❞❡♠ ❆❦t✐❡♥❦✉rs✳ ❯♥❛❜❤ä♥❣✐❣ ❞❛✈♦♥✱ ♦❜ ❞❡r ❆❦t✐❡♥❦✉rs ✐♥ ❞❡r ✈♦r❤❡r✐❣❡♥ P❡r✐♦❞❡ st✐❡❣ ♦❞❡r s❛♥❦✱ st❡✐❣t ❜③✇✳ s✐♥❦t ❞❡r ❆❦t✐✲ ❡♥❦✉rs ✐♥ ❞❡r ❞❛r❛✉✛♦❧❣❡♥❞❡♥ P❡r✐♦❞❡ ♠✐t ❞❡rs❡❧❜❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t ✈♦♥  ✳ ▼✐t ❞❡♠ ❘❛♥❞♦♠✲❲❛❧❦✲▼♦❞❡❧❧ ❤❛❜❡♥ ✇✐r ❡✐♥ ❡rst❡s ❡✐♥❢❛❝❤❡s ▼♦❞❡❧❧ ❦❡♥♥❡♥ ❣❡❧❡r♥t✱ ♠✐t ❞❡♠ ❡s ♠ö❣❧✐❝❤ ✐st✱ ✐♠ ❘❛❤♠❡♥ ❞❡r ❡r❧ä✉t❡rt❡♥ ▼♦❞❡❧❧❛♥♥❛❤♠❡♥ ❲❛❤rs❝❤❡✐♥❧✐❝❤✲ ❦❡✐ts❛✉ss❛❣❡♥ ü❜❡r ❦ü♥❢t✐❣❡ ❆❦t✐❡♥❦✉rs❡ ③✉ tr❡✛❡♥✳ ■♠ ❘❛❤♠❡♥ ❞✐❡s❡s ▼♦❞❡❧❧s ✐st ❡s ❞❡♥♥♦❝❤ ✇✐❝❤t✐❣✱ ❞✐❡ ▼♦❞❡❧❧❛♥♥❛❤♠❡♥ ③✉ ❤✐♥t❡r❢r❛❣❡♥✳ ❑r✐t✐s❝❤ ③✉ s❡❤❡♥ ✐st ③✉♠ ❇❡✐s♣✐❡❧✱ ❞❛ss ❛✉s ❉❛t❡♥ ❞❡r ❱❡r❣❛♥❣❡♥❤❡✐t Pr♦❣♥♦s❡♥ ❢ür ❞✐❡ ❩✉❦✉♥❢t ❣❡tät✐❣t ✇❡r✲ ❞❡♥✳ ❉❛rü❜❡r ❤✐♥❛✉s ❜❧❡✐❜❡♥ ( ✉♥❞  ü❜❡r sä♠t❧✐❝❤❡ Pr♦❣♥♦s❡♥ ❦♦♥st❛♥t✱ ❞✳ ❤✳✱ ❞✐❡ ▼♦❞❡❧❧♣❛r❛♠❡t❡r s✐♥❞ st❛t✐s❝❤✳ ❉✐❡s ✐st ✐♥s♦❢❡r♥ ♣r♦❜❧❡♠❛t✐s❝❤✱ ❞❛ss ✐♥ Pr♦❣♥♦s❡♥ ü❜❡r ❡✐♥❡♥ ❧ä♥❣❡r❡♥ ❩❡✐tr❛✉♠ ♥❡✉❡ ■♥❢♦r♠❛t✐♦♥❡♥ ♥✐❝❤t ✐♥ ❞✐❡ ❇❡✇❡rt✉♥❣ ❡✐♥✢✐❡✲ ÿ❡♥✳ ❙♦ ❜❧❡✐❜❡♥ ❜❡✐s♣✐❡❧s✇❡✐s❡ ✉♥✈♦r❤❡rs❡❤❜❛r❡ ❊r❡✐❣♥✐ss❡ ✭③✳ ❇✳ ❆♥❧❡❣❡r♠❡♥t❛❧✐tät✱ ✇✐rts❝❤❛❢t❧✐❝❤❡ ➘♥❞❡r✉♥❣❡♥ ✐♥ ❞❡r ❆●✮ ✉♥❜❡rü❝❦s✐❝❤t✐❣t✳ ●❡♥❡r❡❧❧ ✇✐r❞ ❞❛s ❆❦t✐❡♥✲ ❦✉rs❣❡s❝❤❡❤❡♥ st❛r❦ ✈❡r❡✐♥❢❛❝❤t ♠♦❞❡❧❧✐❡rt✳ ❉✐❡ ❊✐❣❡♥s❝❤❛❢t ❞❡s ▼♦❞❡❧❧s✱ ❞❛ss ❞❡r ❆❦t✐❡♥❦✉rs ♥❛❝❤ ❡✐♥❡r P❡r✐♦❞❡ ♥✉r ③✇❡✐ ❲❡rt❡ ❛♥♥❡❤♠❡♥ ❦❛♥♥✱ ✐st ✉♥r❡❛❧✐st✐s❝❤✳ ✶✳✶✵ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ✉♥❞ ❆❦t✐❡♥❦✉rs❡ ✶✳✶✵✳✶ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ ❉✐❡ ◆♦r♠❛❧✈❡rt❡✐❧✉♥❣ st❡❧❧t ❡✐♥❡ ❣r✉♥❞❧❡❣❡♥❞❡ ❱❡rt❡✐❧✉♥❣ ❞❡r ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐ts✲ r❡❝❤♥✉♥❣ ❞❛r✳ ❙✐❡ ✜♥❞❡t ❜❡✐ ③❛❤❧r❡✐❝❤❡♥ ♣r❛❦t✐s❝❤❡♥ Pr♦❜❧❡♠❡♥ ❆♥✇❡♥❞✉♥❣✳ ❇❡✲ tr❛❝❤t❡♥ ✇✐r ③✉♥ä❝❤st ❞✐❡ ❉❡✜♥✐t✐♦♥✳ ❉❡✜♥✐t✐♦♥ ✶✳✶✵✳✶ ✭◆♦r♠❛❧✈❡rt❡✐❧t❡ ❩✉❢❛❧❧s❣röÿ❡✮✳ ❊✐♥❡ st❡t✐❣❡ ❩✉❢❛❧❧s❣röÿ❡  ❤❡✐ÿt ♥♦r♠❛❧✈❡rt❡✐❧t ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥ ❢ür ❛❧❧❡ *  ❢♦❧❣❡♥❞❡ ❉✐❝❤t❡ ❜❡s✐t③t✿   ▼❛♥ s❝❤r❡✐❜t✿    &   ✉♥❞   *      & "!

P■❚❊▲ ✶✳ ❆❑❚■❊◆ ✭❛✮ ✭❜✮ ✭❝✮ ❆❜❜✳ ✶✳✸✿ ✭❛✮ ◆❡❣❛t✐✈ ❦♦rr❡❧✐❡rt❡✱ ✭❜✮ ✉♥❦♦rr❡❧✐❡rt❡✱ ✭❝✮ ♣♦s✐t✐✈ ❦♦rr❡❧✐❡rt❡ ❉❛t❡♥♣❛❛r❡ ❇❡✐s♣✐❡❧ ✶✳✽✳✻ ✭❑♦rr❡❧❛t✐♦♥ ③✇✐s❝❤❡♥ ❘❡♥❞✐t❡♥ ✈❡rs❝❤✐❡❞❡♥❡r ❆❦t✐❡♥✮✳ ❆❜❜✐❧❞✉♥❣ ✶✳✹ ③❡✐❣t ❞✐❡ ❘❡♥❞✐t❡♣❛❛r❡ ❣❧❡✐❝❤❡r ❩❡✐trä✉♠❡ ❞❡r ❆❧❧✐❛♥③✲❆❦t✐❡ ✉♥❞ ❞❡r ▼ü♥❝❤❡♥❡r✲ ❘ü❝❦✲❆❦t✐❡ ✈♦♠ ✵✹✳✵✻✳✵✼ ❜✐s ✶✶✳✵✻✳✵✽✳ /&8)>',)9'  -)> -  8 B-' - 8 B*(*>) HH! HH< HH% HH@ HHH (HH@ (HH% (HH< (HH! (H1H (HH! (HH< (HH% (HH@ HHH HH@ HH% HH< HH!     ❉✐❡s s✐♥❞ ❞✐❡ ❲❛❤rs❝❤❡✐♥❧✐❝❤❦❡✐t❡♥ ❡✐♥❡r ❇✐♥♦♠✐❛❧✈❡rt❡✐❧✉♥❣ ♠✐t ❞❡♥ P❛r❛♠❡t❡r♥   !