%% %% This is file `formula.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% formula.dtx (with options: `formula') %% %% Copyleft 1997 Andreas Tille %% %% Usage without any waranty %% \csname @ifundefined\endcsname{formuladef}{}{\endinput} \NeedsTeXFormat{LaTeX2e}[1997/12/01] \ProvidesPackage{formula} \RequirePackage{amsfonts} \RequirePackage{amstext} \RequirePackage{textcomp}[1998/03/05 v1.9n] \RequirePackage{xspace} \def\formuladef#1 #2 #3 #4{% \globaldefs=1% \expandafter\newcommand\expandafter{\csname#1\endcsname} {\relax\ensuremath{#2}\xspace}% \expandafter\newcommand\expandafter{\csname#1doc\endcsname} {\csname#1\endcsname & #3\\}% \expandafter\newcommand\expandafter{\csname#1art\endcsname} {#4\xspace}% der Artikel \expandafter\newcommand\expandafter{\csname#1txt\endcsname} {#3\xspace}% der beschreibende Text \expandafter\newcommand\expandafter{\csname#1my\endcsname} {{\tt\char92#1} & \csname#1doc\endcsname} \globaldefs=0}% \def\formulaarg#1 #2 #3 #4 #5{% \globaldefs=1% \expandafter\newcommand\expandafter{\csname#1\endcsname}[1]% {\relax\ensuremath{#2{##1}}\xspace}% \expandafter\newcommand\expandafter{\csname#1doc\endcsname}% {\csname#1\endcsname{#5} & #3\\}% \expandafter\newcommand\expandafter{\csname#1art\endcsname}% {#4}% der Artikel \expandafter\newcommand\expandafter{\csname#1txt\endcsname}% {#3}% der beschreibende Text \expandafter\newcommand\expandafter{\csname#1my\endcsname}% {{\tt\char92#1\{}{\em #5}{\tt \}} & \csname#1doc\endcsname} \globaldefs=0}% \def\formulamit#1 #2 #3 #4 #5 #6{% \globaldefs=1% \expandafter\newcommand\expandafter{\csname#1\endcsname}[1]% {\relax\ensuremath{#2{##1}#3}\xspace}% \expandafter\newcommand\expandafter{\csname#1doc\endcsname} {\csname#1\endcsname{#6} & #4\\}% \expandafter\newcommand\expandafter{\csname#1art\endcsname} {#5}% der Artikel \expandafter\newcommand\expandafter{\csname#1txt\endcsname} {#4}% der beschreibende Text \expandafter\newcommand\expandafter{\csname#1my\endcsname}% {{\tt\char92#1\{}{\em #6}{\tt \}} & \csname#1doc\endcsname} \globaldefs=0}% \def\formuladiff#1 #2 #3 #4 #5 #6{% \globaldefs=1% \expandafter\newcommand\expandafter{\csname#1\endcsname}[1]% {\relax\ensuremath{\frac{#2^{##1}#3}{#2#4^{##1}}}\xspace}% \expandafter\newcommand\expandafter{\csname#1doc\endcsname}% {\csname#1\endcsname{n} & #5\\}% \expandafter\newcommand\expandafter{\csname#1art\endcsname}% {#6}% der Artikel \expandafter\newcommand\expandafter{\csname#1txt\endcsname}% {#5}% der beschreibende Text \expandafter\newcommand\expandafter{\csname#1my\endcsname}% {{\tt\char92#1\{}{\em n}{\tt \}} & \csname#1doc\endcsname} \globaldefs=0}% \newcommand{\eorg}[2]{% \expandafter\ifx\csname l@german\endcsname\relax #1% \else \ifnum\csname l@german\endcsname=\language #2% \else #1\fi\fi} \newif\ifpredefinition \predefinitiontrue \newcommand{\NoPreDefinition}{\predefinitionfalse} \DeclareOption{nopredefinition}{\NoPreDefinition} \ProcessOptions \ifpredefinition \formuladef MA {\text{\bf A}} {\eorg{m}{M}atrix A} {\eorg{the}{die}} \formuladef Cmess {\text{C}_m} {\eorg{linear capacitor for measurement} {linearer Me\ss{}kondensator}} {} \formuladef Cnl {C_{nl}} {\eorg{nonlinear capacity of the sample} {nichtlineare Kapazit\"at der Probe}} {\eorg{the}{die}} \formulaarg Cr {\mathbb{C}^} {\eorg{set of r times continuous differentiable functions} {Menge der r-mal stetig differenzierbaren Funktionen}} {} {r} \formuladef dPR {d} {\eorg{d}{D}imension \eorg{of phase space}{des Phasenraums}} {die} \formuladef DV {D} {dielektrische Verschiebung} {die} \formuladef Det {\text{det}} {Determinante einer Matrix} {die} \formuladef Dx {\text{\bf D}_x} {Jakobimatrix} {die} \formuladef EF {E} {elektrische Feldst\"arke} {die} \formuladef EC {E_C} {Koerzitivfeldst\"arke} {die} \formuladef ECnl {E_{\Cnl}} {elektrische Feldst\"arke \"uber der Probe} {die} \formuladef dynSys {\vec{f}(\vec{x},\vp)} {beliebiges dynamisches System} {ein} \formulamit Effi {f_} {(\cdot,\cdot)} {} {} {i} \formuladef falles {\Effi{1}, \Effi{2}, \cdots} {Komponenten des beliebigen dynamischen Systems} {} \formuladef F {\text{F}} {Probenfl\"ache} {die} \formuladef Fouri {\mathcal{F}} {Fouriertransformation} {die} \formuladef Fourin {\text{F}_{i,n}} {$n$-te Fourierkomponente von \Effi{i}} {die} \formuladef FOp {\Fouri_{n}} {Operator f\"ur die $n$-te Fourierkomponente} {der} \formuladef FB {\text{f}} {Brennweite} {die} \formuladef freq {f} {Frequenz} {die} \formuladef vf {\vec{f}} {Vektorfeld} {ein} \formuladef fa {\freq_a} {Abtastfrequenz} {die} \formuladef fgrund {\freq_{ext}} {Anregungsfrequenz der Schwingung} {die} \formuladef fstrob {\freq_s} {Blitzfrequenz des Stroboskops} {die} \formuladef fvirt {\freq_v} {virtuelle Frequenz} {die} \formuladef vfO {\vf(\vO)} {Vektorfeld f im Ursprung} {} \formuladef FE {G} {freie Enthalpie} {die} \formuladef FEO {\FE_0} {temperaturunabh\"angiger Anteil der freien Energie} {} \formuladef h {\text{h}} {Probendicke} {die} \formuladef Hrel {H_r} {relative Helligkeit eines Videobildes} {die} \formuladef IH {I} {elektrische Stromst\"arke} {die} \formuladef Itot {\IH_{tot}} {Gesamtstromst\"arke} {die} \formuladef ICnl {\IH_{\Cnl}} {Strom durch die nichtlineare Kapazit\"at} {der} \formuladef IRp {\IH_{\Rp}} {Strom durch den Parallelverlustwiderstand \Rp} {der} \formuladef je {j} {Stromdichte} {die} \formuladef Lx {\text{L}} {Induktivit\"at der linearen Spule} {die} \formuladef vO {\vec{o}} {Nullvektor} {der} \formuladef Par {p} {} {} \formuladef vp {\vec{\Par}} {Modellparameter} {die} \formulaarg Para {\Par_} {} {} {i} \formuladef Parai {\Para{1}, \Para{2}, \cdots} {Komponenten der Modellparameter} {die} \formuladef Pol {P} {Polarisation} {die} \formuladef Poinc {\mathfrak{P}} {Poincar\'e-Ebene} {die} \formuladef Pols {\Pol_s} {spontane Polarisation} {die} \formuladef Lad {Q} {elektrische Ladung} {die} \formuladef Rz {\mathbb{R}} {reeller Raum} {} \formuladef Rx {\text{R}} {Widerstand} {} \formuladef RCnl {\Rx_{\Cnl}} {linearer Widerstand in der Ersatzschaltung der Probe} {} \formuladef RL {\Rx_{\Lx}} {Verlustwiderstand der Spule} {der} \formuladef Rlin {\Rx_{lin}} {linearer Verlustwiderstand; \Rlin = \RL + \Rmess} {} \formuladef Rmess {\Rx_m} {linearer Me\ss{}widerstand} {} \formulaarg Rn {\Rz^} {n-dimensionaler reeller Raum} {} {n} \formuladef Rp {\Rx_p} {Parallelverlustwiderstand der nichtlinearen Kapazit\"at} {der} \formuladef Rs {\Rx_s} {Serienverlustwiderstand der nichtlinearen Kapazit\"at} {der} \formuladef Spur {\text{Spur}} {Spur einer Matrix} {die} \formuladef tx {t} {Zeit} {die} \formuladef T {T} {Periodendauer} {die} \formuladef Te {\text{T}} {Temperatur} {die} \formuladef ta {\tx_a} {Abtastzeit} {die} \formuladef te {\tx_e} {Delay-Zeit} {die} \formuladef Tgrund {\T_0} {Periodendauer der Anregung} {die} \formuladef TC {\Te_C} {absolute Curie-Temperatur} {die} \formuladef TCrit {\Te_{crit}} {kritische absolute Temperatur} {die} \formuladef Ux {U} {Spannung} {die} \formuladef Umg {\mathbb{U}} {Umgebung} {} \formuladef Ueff {\Ux_{ef\kern-1pt{f}}} {Effektivwert der Anregungsspannung} {der} \formuladef Uext {\Ux_{ext}} {externe Spannung} {die} \formuladef UCnl {\Ux_{\Cnl}} {Spannung \"uber \Cnl} {die} \formuladef URL {\Ux_{\RL}} {Spannung \"uber \RL} {die} \formuladef URs {\Ux_{\Rs}} {Spannung \"uber \Rs} {die} \formuladef Vnl {V_{nl}} {nichtlineares Potential} {} \formuladef x {x} {beliebige skalare physikalische Gr\"o\ss{}e} {} \formuladef dxdt {\dot x} {Ableitung von x nach der Zeit} {} \formuladef vx {\vec{x}} {beliebige vektorielle physikalische Gr\"o\ss{}e} {} \formuladef vX {\vec{X}} {Fouriertransformierte der vektoriellen Gr\"o\ss{}e \vx} {} \formuladef xO {x_0} {} {} \formuladef vxO {\vec{\xO}} {} {} \formulaarg PotK {\alpha_} {} {} {i} \formuladef PotKo {\PotK{2}, \PotK{4}} {Koeffizienten des nichtlinearen Potentials \Vnl} {die} \formulaarg LanK {\tilde{\alpha}_} {} {} {i} \formuladef LanKo {\LanK{1}, \LanK{2}, \cdots} {Entwicklungskoeffizienten der Landau-Entwicklung} {die} \formuladef Feige {\delta} {Feigenbaum-Konstante} {die} \formuladef Abli {\partial_i} {Ableitungsoperator nach der $i$-ten Koordinate} {der} \formuladef eps {\varepsilon} {Dielektrizit\"atskonstante} {die} \formuladef epsO {\eps_0} {Influenzkonstante $\epsO = 8.84\cdot 10^{-12}\AsVm$} {die} \formuladef epsr {\eps_r} {relative Dielektrizit\"atskonstante} {die} \formuladef OP {\eta} {Ordnungsparameter} {der} \formuladef Ev {\eta} {mit Index: Komponente des Eigenvektors} {der} \formuladef vEv {\vec{\Ev}} {Eigenvektor} {der} \formuladef GOP {\OP^{*}} {Gleichgewichtswert des Ordnungsparameters} {der} \formuladef Ewl {\lambda} {Eigenwert} {der} \formuladef phistrob {\varphi_s} {Phasenwinkel des Stroboskops} {der} \formuladef TGrdC {\vartheta} {Temperatur in Celsius} {die} \formuladef ThC {\TGrdC_C} {Curie-Temperatur} {die} \formuladef ThCrit {\TGrdC_{crit}} {kritische Temperatur} {die} \formuladef oC {\omega} {Kreisfrequenz $\oC = 2\pi\freq$} {die} \formuladef oO {\oC_0} {Grundfrequenz} {die} \formuladef siehe {\rightarrow} {siehe} {} \formuladef drf {\Rightarrow} {daraus folgt} {} \fi% end of predefinition \def\formulaunit#1 #2 #3 #4 #5{% \globaldefs=1% \expandafter\newcommand\expandafter{\csname#1\endcsname}% {\relax\ensuremath{\text{\,#2}#3\text{#4}}\xspace}% \expandafter\newcommand\expandafter{\csname#1doc\endcsname} {{\em x}\csname#1\endcsname & #5\\}% \expandafter\newcommand\expandafter{\csname#1txt\endcsname} {#5}% description of units in words \expandafter\newcommand\expandafter{\csname#1my\endcsname}% {{\em x\tt\char92#1} & \csname#1doc\endcsname} \globaldefs=0}% \ifpredefinition \formulaunit mn {} {} min {\eorg{minute}{Minute}} \formulaunit sek {} {} s {\eorg{second}{Sekunde}} \formulaunit msek {m} {} s {Millisekunde} \formulaunit musek {} {\text{\textmu}} s {Mikrosekunde} \formulaunit m {} {} m {Meter} \formulaunit cm {c} {} m {Zentimeter} \formulaunit mm {m} {} m {Millimeter} \formulaunit mum {} {\text{\textmu}} m {Mikrometer} \formulaunit nm {n} {} m {Nanometer} \formulaunit li {} {} l {Liter} \formulaunit ml {m} {} l {Milliliter} \formulaunit g {} {} g {Gramm} \formulaunit kg {k} {} g {Kilogramm} \formulaunit Hz {} {} Hz {Hertz} \formulaunit kHz {k} {} Hz {Kilohertz} \formulaunit MHz {M} {} Hz {Megahertz} \formulaunit MV {M} {} V {Megavolt} \formulaunit kV {k} {} V {Kilovolt} \formulaunit Vo {} {} V {Volt} \formulaunit mV {m} {} V {Millivolt} \formulaunit Ohm {} {\text{\textohm}} {} {Ohm} \formulaunit kOhm {k} {\text{\textohm}} {} {Kiloohm} \formulaunit MOhm {M} {\text{\textohm}} {} {Megaohm} \formulaunit muF {} {\text{\textmu}} F {Mikrofarad} \formulaunit nF {n} {} F {Nanofarad} \formulaunit pF {p} {} F {Picofarad} \formulaunit He {} {} H {Henry} \formulaunit mH {m} {} H {Millihenry} \formulaunit K {} {} K {Kelvin} \formulaunit grd {} {\text{\textdegree}} {} {Grad} \formulaunit grdC {} {\text{\textcelsius}} {} {Grad Celsius} \formulaunit J {} {} {J} {Joule} \formulaunit muJ {} {\text{\textmu}} {J} {Mikrojoule} \formulaunit mW {m} {} {W} {Milliwatt} \formulaunit W {} {} {W} {Watt} \formulaunit Bit {} {} Bit {Bit} \formulaunit Byte {} {} HByte {Byte} \formulaunit kByte {k} {} Byte {Kilobyte} \formulaunit MByte {M} {} Byte {Megabyte} \formulaunit Bilderprosek {} {} {\eorg{images}{Bilder}/s} {\eorg{Bilder pro Sekunde}{images per second}} \formulaunit Bilder {} {} {\eorg{images}{Bilder}} {\eorg{images}{Bilder}} \formulaunit dpi {} {} {dpi} {\eorg{dots per inch}{Punkte pro Zoll}} \formulaunit Prozent {} {} {\%} {\eorg{per cent}{Prozent}} \formulaunit Upromin {} {} {U/min} {Umdrehungen pro Minute} \formulaunit AsVm {} {} {\ensuremath{\frac{\text{As}}{\text{Vm}}}} {Amperesekunden pro Voltmeter} \formulaunit DM {} {} {DM} {DM} \formulaunit TDM {T} {} {DM} {tausend DM} \fi% end predefinition \newcommand{\Odif}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\odif}[2]{\relax\ensuremath{\Odif{#1}{#2}}} \newcommand{\Pdif}[2]{\left( \odif{#1}{#2} \right)} \newcommand{\pdif}[2]{\relax\ensuremath{\Pdif{#1}{#2}}} \newcommand{\OSdif}[2]{\frac{\partial^2 #1}{\partial #2^2}} \newcommand{\osdif}[2]{\relax\ensuremath{\OSdif{#1}{#2}}} \newcommand{\OOdif}[3]{\frac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\oodif}[3]{\relax\ensuremath{\OOdif{#1}{#2}{#3}}} \newcommand{\PPdif}[3]{\left( \oodif{#1}{#2}{#3} \right)} \newcommand{\ppdif}[3]{\relax\ensuremath{\PPdif{#1}{#2}{#3}}} \newcommand{\OOOdif}[4]{\frac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\ooodif}[4]{\relax\ensuremath{\OOOdif{#1}{#2}{#3}{#4}}} \newcommand{\PPPdif}[4]{\left( \ooodif{#1}{#2}{#3}{#4} \right)} \newcommand{\pppdif}[4]{\relax\ensuremath{\PPPdif{#1}{#2}{#3}{#4}}} \newcommand{\OOSdif}[3]{\frac{\partial^3 #1}{\partial #2^2\partial #3}} \newcommand{\oosdif}[3]{\relax\ensuremath{\OOSdif{#1}{#2}{#3}}} \newcommand{\beq}{\begin{equation}} \newcommand{\eeq}{\end{equation}} \newcommand{\bea}{\begin{eqnarray}} \newcommand{\eea}{\end{eqnarray}} \def\be*{\begin{eqnarray*}} \def\ee*{\end{eqnarray*}} \def\buildrul#1\over #2{\mathrel {\mathop {#1}\limits_{#2}}} \endinput %% %% End of file `formula.sty'.