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author | Karl Berry <karl@freefriends.org> | 2017-10-22 19:51:42 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-10-22 19:51:42 +0000 |
commit | d326671c4777b4897d5ecc23008d3d53f6101fc2 (patch) | |
tree | 62679eb03b1838237e21de9b758d78e3ff3aecb1 /Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex | |
parent | b2fad8915b87bb45e4d3ffafd0f8119da45a921e (diff) |
classicthesis (22oct17)
git-svn-id: svn://tug.org/texlive/trunk@45578 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex | 32 |
1 files changed, 16 insertions, 16 deletions
diff --git a/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex b/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex index d7fdeeec58e..e9515a08000 100644 --- a/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex +++ b/Master/texmf-dist/doc/latex/classicthesis/Chapters/Chapter03.tex @@ -65,37 +65,37 @@ description of ionisation fluctuations: \begin{enumerate} \item A large number of collisions involving the loss of all or most - of the incident particle energy during the traversal of an absorber. + of the incident particle energy during the traversal of an absorber. - As the total energy transfer is composed of a multitude of small - energy losses, we can apply the central limit theorem and describe - the fluctuations by a Gaussian distribution. This case is - applicable to non-relativistic particles and is described by the - inequality $\kappa > 10 $ (\ie, when the mean energy loss in the - absorber is greater than the maximum energy transfer in a single - collision). + As the total energy transfer is composed of a multitude of small + energy losses, we can apply the central limit theorem and describe + the fluctuations by a Gaussian distribution. This case is + applicable to non-relativistic particles and is described by the + inequality $\kappa > 10 $ (\ie, when the mean energy loss in the + absorber is greater than the maximum energy transfer in a single + collision). \item Particles traversing thin counters and incident electrons under - any conditions. + any conditions. - The relevant inequalities and distributions are $ 0.01 < \kappa < 10 - $, - Vavilov distribution, and $\kappa < 0.01 $, Landau distribution. + The relevant inequalities and distributions are $ 0.01 < \kappa < 10 + $, + Vavilov distribution, and $\kappa < 0.01 $, Landau distribution. \end{enumerate} \section{Various Mathematical Examples} If $n > 2$, the identity \[ - t[u_1,\dots,u_n] = t\bigl[t[u_1,\dots,u_{n_1}], t[u_2,\dots,u_n] - \bigr] + t[u_1,\dots,u_n] = t\bigl[t[u_1,\dots,u_{n_1}], t[u_2,\dots,u_n] + \bigr] \] defines $t[u_1,\dots,u_n]$ recursively, and it can be shown that the alternative definition \[ - t[u_1,\dots,u_n] = t\bigl[t[u_1,u_2],\dots,t[u_{n-1},u_n]\bigr] + t[u_1,\dots,u_n] = t\bigl[t[u_1,u_2],\dots,t[u_{n-1},u_n]\bigr] \] -gives the same result. +gives the same result. %***************************************** %***************************************** |