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8</script></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">3.4. 
9Run
10</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch03s03.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><th width="60%" align="center">Chapter 3. 
11Toolkit Fundamentals
12</th><td width="20%" align="right"> <a accesskey="n" href="ch03s05.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr></table><hr></div><div class="sect1" lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sect.Run"></a>3.4. 
13Run
14</h2></div></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.Run.Basic"></a>3.4.1. 
15Basic concept of <span class="emphasis"><em>Run</em></span>
16</h3></div></div></div><p>
17In Geant4, <span class="emphasis"><em>Run</em></span> is the largest unit of simulation. A run
18consists of a sequence of events. Within a run, the detector
19geometry, the set up of sensitive detectors, and the physics
20processes used in the simulation should be kept unchanged. A run is
21represented by a <span class="emphasis"><em>G4Run</em></span> class object. A run starts with
22<code class="literal">BeamOn()</code> method of <span class="emphasis"><em>G4RunManager</em></span>.
23</p><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Basic.Rep"></a>3.4.1.1. 
24Representation of a run
25</h4></div></div></div><p>
26<span class="emphasis"><em>G4Run</em></span> represents a run. It has a run identification
27number, which should be set by the user, and the number of events
28simulated during the run. Please note that the run identification
29number is not used by the Geant4 kernel, and thus can be
30arbitrarily assigned at the user's convenience.
31</p><p>
32<span class="emphasis"><em>G4Run</em></span> has pointers to the tables
33<span class="emphasis"><em>G4VHitsCollection</em></span>
34and <span class="emphasis"><em>G4VDigiCollection</em></span>. These tables are associated
35in case <span class="emphasis"><em>sensitive detectors</em></span> and
36<span class="emphasis"><em>digitizer modules</em></span> are
37simulated, respectively. The usage of these tables will be
38mentioned in <a href="ch04s04.html" title="4.4. 
39Hits
40">Section 4.4</a> and <a href="ch04s05.html" title="4.5. 
41Digitization
42">Section 4.5</a>.
43</p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Basic.Manage"></a>3.4.1.2. 
44Manage the run procedures
45</h4></div></div></div><p>
46<span class="emphasis"><em>G4RunManager</em></span> manages the procedures of a run. In the
47constructor of <span class="emphasis"><em>G4RunManager</em></span>, all of the manager classes in
48Geant4 kernel, except for some static managers, are constructed.
49These managers are deleted in the destructor of
50<span class="emphasis"><em>G4RunManager</em></span>. <span class="emphasis"><em>G4RunManager</em></span>
51must be a singleton, and
52the pointer to this singleton object can be obtained by the
53<code class="literal">getRunManager()</code> static method.
54</p><p>
55As already mentioned in <a href="ch02.html#sect.HowToDefMain" title="2.1. 
56How to Define the main() Program
57">Section 2.1</a>, all of the
58<span class="emphasis"><em>user initialization</em></span> classes and
59<span class="emphasis"><em>user action</em></span> classes
60defined by the user should be assigned to <span class="emphasis"><em>G4RunManager</em></span>
61before starting initialization of the Geant4 kernel. The
62assignments of these user classes are done by
63<code class="literal">SetUserInitialization()</code> and <code class="literal">SetUserAction()</code>
64methods. All user classes defined by the Geant4 kernel will be
65summarized in <a href="ch06.html" title="Chapter 6. 
66User Actions
67">Chapter 6</a>.
68</p><p>
69<span class="emphasis"><em>G4RunManager</em></span> has several public methods, which are listed
70below.
71
72</p><div class="variablelist"><p class="title"><b></b></p><dl><dt><span class="term"><code class="literal">Initialize()</code></span></dt><dd>
73 All initializations required by the Geant4 kernel are triggered
74 by this method. Initializations are:
75
76 <div class="itemizedlist"><ul type="disc" compact><li><p>
77 construction of the detector geometry and set up of sensitive
78 detectors and/or digitizer modules,
79 </p></li><li><p>
80 construction of particles and physics processes,
81 </p></li><li><p>
82 calculation of cross-section tables.
83 </p></li></ul></div>
84
85 This method is thus mandatory before proceeding to the first run.
86 This method will be invoked automatically for the second and later
87 runs in case some of the initialized quantities need to be updated.
88 </dd><dt><span class="term"><code class="literal">BeamOn(G4int numberOfEvent)</code></span></dt><dd>
89 This method triggers the actual simulation of a run, that is,
90 an event loop. It takes an integer argument which represents the
91 number of events to be simulated.
92 </dd><dt><span class="term"><code class="literal">GetRunManager()</code></span></dt><dd>
93 This static method returns the pointer to the
94 <span class="emphasis"><em>G4RunManager</em></span> singleton object.
95 </dd><dt><span class="term"><code class="literal">GetCurrentEvent()</code></span></dt><dd>
96 This method returns the pointer to the <span class="emphasis"><em>G4Event</em></span> object
97 which is currently being simulated. This method is available only
98 when an event is being processed. At this moment, the application
99 state of Geant4, which is explained in the following sub-section,
100 is <span class="emphasis"><em>"EventProc"</em></span>. When Geant4 is in a state other than
101 <span class="emphasis"><em>"EventProc"</em></span>, this method returns
102 <code class="literal">null</code>.
103 Please note that the return value of this method is
104 <code class="literal">const G4Event *</code> and thus you cannot modify the
105 contents of the object.
106 </dd><dt><span class="term"><code class="literal">SetNumberOfEventsToBeStored(G4int nPrevious)</code></span></dt><dd>
107 When simulating the "pile up" of more than one event, it is
108 essential to access more than one event at the same moment. By
109 invoking this method, <span class="emphasis"><em>G4RunManager</em></span> keeps <code class="literal">nPrevious
110 G4Event</code> objects. This method must be invoked before proceeding
111 to <code class="literal">BeamOn()</code>.
112 </dd><dt><span class="term"><code class="literal">GetPreviousEvent(G4int i_thPrevious)</code></span></dt><dd>
113 The pointer to the <code class="literal">i_thPrevious G4Event</code> object can be
114 obtained through this method. A pointer to a <code class="literal">const</code> object
115 is returned. It is inevitable that <code class="literal">i_thPrevious</code> events
116 must have already been simulated in the same run for getting the
117 <code class="literal">i_thPrevious</code> event. Otherwise, this method returns
118 <code class="literal">null</code>.
119 </dd><dt><span class="term"><code class="literal">AbortRun()</code></span></dt><dd>
120 This method should be invoked whenever the processing of a run
121 must be stopped. It is valid for <span class="emphasis"><em>GeomClosed</em></span> and
122 <span class="emphasis"><em>EventProc</em></span> states. Run processing will be safely aborted even
123 in the midst of processing an event. However, the last event of the
124 aborted run will be incomplete and should not be used for further
125 analysis.
126 </dd></dl></div><p>
127</p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Basic.UserRunAction"></a>3.4.1.3. 
128<span class="emphasis"><em>G4UserRunAction</em></span>
129</h4></div></div></div><p>
130<span class="emphasis"><em>G4UserRunAction</em></span> is one of the <span class="emphasis"><em>user action</em></span>
131classes from which you can derive your own concrete class. This base class
132has two virtual methods, as follows:
133
134
135</p><div class="variablelist"><p class="title"><b></b></p><dl><dt><span class="term"><code class="literal">BeginOfRunAction()</code></span></dt><dd>
136 This method is invoked at the beginning of the
137 <code class="literal">BeamOn()</code> method but after confirmation of the conditions
138 of the Geant4 kernel. Likely uses of this method include:
139
140 <div class="itemizedlist"><ul type="disc" compact><li><p>
141 setting a run identification number,
142 </p></li><li><p>
143 booking histograms,
144 </p></li><li><p>
145 setting run specific conditions of the sensitive detectors
146 and/or digitizer modules (e.g., dead channels).
147 </p></li></ul></div></dd><dt><span class="term"><code class="literal">EndOfRunAction()</code></span></dt><dd>
148 This method is invoked at the very end of the <code class="literal">BeamOn()</code>
149 method. Typical use cases of this method are
150
151 <div class="itemizedlist"><ul type="disc" compact><li><p>
152 store/print histograms,
153 </p></li><li><p>
154 manipulate run summaries.
155 </p></li></ul></div></dd></dl></div><p>
156</p></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.Run.StateMac"></a>3.4.2. 
157Geant4 as a state machine
158</h3></div></div></div><p>
159Geant4 is designed as a state machine. Some methods in Geant4 are
160available for only a certain state(s). <span class="emphasis"><em>G4RunManager</em></span> controls
161the state changes of the Geant4 application. States of Geant4 are
162represented by the enumeration <span class="emphasis"><em>G4ApplicationState</em></span>. It has
163six states through the life cycle of a Geant4 application.
164
165
166</p><div class="variablelist"><p class="title"><b></b></p><dl><dt><span class="term"><span class="emphasis"><em>G4State_PreInit</em></span> state</span></dt><dd>
167 A Geant4 application starts with this state. The application
168 needs to be initialized when it is in this state. The application
169 occasionally comes back to this state if geometry, physics
170 processes, and/or cut-off have been changed after processing a
171 run.
172 </dd><dt><span class="term"><span class="emphasis"><em>G4State_Init</em></span> state</span></dt><dd>
173 The application is in this state while the
174 <code class="literal">Initialize()</code> method of <span class="emphasis"><em>G4RunManager</em></span>
175 is being invoked. Methods defined in any
176 <span class="emphasis"><em>user initialization</em></span> classes
177 are invoked during this state.
178 </dd><dt><span class="term"><span class="emphasis"><em>G4State_Idle</em></span> state</span></dt><dd>
179 The application is ready for starting a run.
180 </dd><dt><span class="term"><span class="emphasis"><em>G4State_GeomClosed</em></span> state</span></dt><dd>
181 When <code class="literal">BeamOn()</code> is invoked, the application proceeds to
182 this state to process a run. Geometry, physics processes, and
183 cut-off cannot be changed during run processing.
184 </dd><dt><span class="term"><span class="emphasis"><em>G4State_EventProc</em></span> state</span></dt><dd>
185 A Geant4 application is in this state when a particular event
186 is being processed. <code class="literal">GetCurrentEvent()</code> and
187 <code class="literal">GetPreviousEvent()</code> methods of
188 <span class="emphasis"><em>G4RunManager</em></span> are
189 available only at this state.
190 </dd><dt><span class="term"><span class="emphasis"><em>G4State_Quit</em></span> state</span></dt><dd>
191 When the destructor of <span class="emphasis"><em>G4RunManager</em></span> is invoked, the
192 application comes to this "dead end" state. Managers of the Geant4
193 kernel are being deleted and thus the application cannot come back
194 to any other state.
195 </dd><dt><span class="term"><span class="emphasis"><em>G4State_Abort</em></span> state</span></dt><dd>
196 When a <span class="emphasis"><em>G4Exception</em></span> occurs, the application comes to this
197 "dead end" state and causes a core dump. The user still has a hook
198 to do some "safe" opperations, e.g. storing histograms, by
199 implementing a user concrete class of <span class="emphasis"><em>G4VStateDependent</em></span>. The
200 user also has a choice to suppress the occurence of
201 <span class="emphasis"><em>G4Exception</em></span> by a UI command
202 <span class="emphasis"><em>/control/suppressAbortion</em></span>. When abortion is suppressed, you
203 will still get error messages issued by G4Exception, and there is
204 NO guarantee of a correct result after the G4Exception error
205 message.
206 </dd></dl></div><p>
207
208<span class="emphasis"><em>G4StateManager</em></span> belongs to the <span class="emphasis"><em>intercoms</em></span>
209category.
210</p></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.Run.UserHook"></a>3.4.3. 
211User's hook for state change
212</h3></div></div></div><p>
213In case the user wants to do something at the moment of state
214change of Geant4, the user can create a concrete class of the
215<span class="emphasis"><em>G4VStateDependent</em></span> base class. For example, the user can
216store histograms when G4Exception occurs and Geant4 comes to the
217<span class="emphasis"><em>Abort</em></span> state, but before the actual core dump.
218</p><p>
219The following is an example user code which stores histograms
220when Geant4 becomes to the <span class="emphasis"><em>Abort</em></span> state. This class object
221should be mabe in, for example <span class="emphasis"><em>main()</em></span>, by the user code.
222This object will be automatically registered to
223<span class="emphasis"><em>G4StateManager</em></span> at its construction.
224</p><div class="example"><a name="programlist_Run_1"></a><p class="title"><b>Example 3.1. 
225Header file of UserHookForAbortState
226</b></p><div class="example-contents"><pre class="programlisting">
227#ifndef UserHookForAbortState_H
228#define UserHookForAbortState_H 1
229
230#include "G4VStateDependent.hh"
231
232class UserHookForAbortState : public G4VStateDependent
233{
234 public:
235 UserHookForAbortState(); // constructor
236 ~UserHookForAbortState(); // destructor
237
238 virtual G4bool Notify(G4ApplicationState requiredState);
239};
240</pre></div></div><br class="example-break"><div class="example"><a name="programlist_Run_2"></a><p class="title"><b>Example 3.2. 
241Source file of UserHookForAbortState
242</b></p><div class="example-contents"><pre class="programlisting">
243#include "UserHookForAbortState.hh"
244
245UserHookForAbortState::UserHookForAbortState() {;}
246UserHookForAbortState::~UserHookForAbortState() {;}
247
248G4bool UserHookForAbortState::Notify(G4ApplicationState requiredState)
249{
250 if(requiredState!=Abort) return true;
251
252 // Do book keeping here
253
254 return true;
255}
256</pre></div></div><br class="example-break"></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.Run.Custom"></a>3.4.4. 
257Customizing the Run Manager
258</h3></div></div></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Custom.VirMeth"></a>3.4.4.1. 
259Virtual Methods in the Run Manager
260</h4></div></div></div><p>
261<code class="literal">G4RunManager</code> is a concrete class with a complete set of
262functionalities for managing the Geant4 kernel. It is the only
263manager class in the Geant4 kernel which must be constructed in the
264<code class="literal">main()</code> method of the user's application. Thus, instead of
265constructing the <code class="literal">G4RunManager</code> provided by Geant4, you are
266free to construct your own <code class="literal">RunManager</code>. It is recommended,
267however, that your <code class="literal">RunManager</code> inherit
268<code class="literal">G4RunManager</code>. For this purpose, <code class="literal">G4RunManager</code> has
269various virtual methods which provide all the functionalities
270required to handle the Geant4 kernel. Hence, your customized run
271manager need only override the methods particular to your needs;
272the remaining methods in <code class="literal">G4RunManager</code> base class can still
273be used. A summary of the available methods is presented here:
274
275
276</p><div class="variablelist"><p class="title"><b></b></p><dl><dt><span class="term"><code class="literal">public: virtual void Initialize();</code></span></dt><dd>
277 main entry point of Geant4 kernel initialization
278 </dd><dt><span class="term"><code class="literal">protected: virtual void InitializeGeometry();</code></span></dt><dd>
279 geometry construction
280 </dd><dt><span class="term"><code class="literal">protected: virtual void InitializePhysics();</code></span></dt><dd>
281 physics processes construction
282 </dd><dt><span class="term"><code class="literal">public: virtual void BeamOn(G4int n_event);</code></span></dt><dd>
283 main entry point of the event loop
284 </dd><dt><span class="term"><code class="literal">protected: virtual G4bool ConfirmBeamOnCondition();</code></span></dt><dd>
285 check the kernel conditions for the event loop
286 </dd><dt><span class="term"><code class="literal">protected: virtual void RunInitialization();</code></span></dt><dd>
287 prepare a run
288 </dd><dt><span class="term"><code class="literal">protected: virtual void DoEventLoop(G4int n_events);</code></span></dt><dd>
289 manage an event loop
290 </dd><dt><span class="term"><code class="literal">protected: virtual G4Event* GenerateEvent(G4int i_event);</code></span></dt><dd>
291 generation of <span class="emphasis"><em>G4Event</em></span> object
292 </dd><dt><span class="term"><code class="literal">protected: virtual void AnalyzeEvent(G4Event* anEvent);</code></span></dt><dd>
293 storage/analysis of an event
294 </dd><dt><span class="term"><code class="literal">protected: virtual void RunTermination();</code></span></dt><dd>
295 terminate a run
296 </dd><dt><span class="term"><code class="literal">public: virtual void DefineWorldVolume(G4VPhysicalVolume * worldVol);</code></span></dt><dd>
297 set the world volume to <span class="emphasis"><em>G4Navigator</em></span></dd><dt><span class="term"><code class="literal">public: virtual void AbortRun();</code></span></dt><dd>
298 abort the run
299 </dd></dl></div><p>
300</p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Custom.EventLoop"></a>3.4.4.2. 
301Customizing the Event Loop
302</h4></div></div></div><p>
303In <code class="literal">G4RunManager</code> the event loop is handled by the
304virtual method <code class="literal">DoEventLoop()</code>. This method is implemented
305by a <code class="literal">for</code> loop consisting of the following steps:
306
307</p><div class="orderedlist"><ol type="1" compact><li><p>
308 construct a <code class="literal">G4Event</code> object and assign to it primary
309 vertex(es) and primary particles. This is done by the virtual
310 <code class="literal">GeneratePrimaryEvent()</code> method.
311 </p></li><li><p>
312 send the <code class="literal">G4Event</code> object to <code class="literal">G4EventManager</code>
313 for the detector simulation. <span class="emphasis"><em>Hits</em></span> and
314 <span class="emphasis"><em>trajectories</em></span> will
315 be associated with the <code class="literal">G4Event</code> object as a
316 consequence.
317 </p></li><li><p>
318 perform bookkeeping for the current <code class="literal">G4Event</code> object.
319 This is done by the virtual <code class="literal">AnalyzeEvent()</code> method.
320 </p></li></ol></div><p>
321</p><p>
322<code class="literal">DoEventLoop()</code> performs the entire simulation of an
323event. However, it is often useful to split the above three steps
324into isolated application programs. If, for example, you wish to
325examine the effects of changing discriminator thresholds, ADC gate
326widths and/or trigger conditions on simulated events, much time can
327be saved by performing steps 1 and 2 in one program and step 3 in
328another. The first program need only generate the hit/trajectory
329information once and store it, perhaps in a database. The second
330program could then retrieve the stored <code class="literal">G4Event</code> objects and
331perform the digitization (analysis) using the above threshold, gate
332and trigger settings. These settings could then be changed and the
333digitization program re-run without re-generating the
334<code class="literal">G4Event</code>s.
335</p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Custom.Geometry"></a>3.4.4.3. 
336Changing the Detector Geometry
337</h4></div></div></div><p>
338The detector geometry defined in your
339<span class="emphasis"><em>G4VUserDetectorConstruction</em></span> concrete class can be changed
340during a run break (between two runs). Two different cases are
341considered.
342</p><p>
343The first is the case in which you want to delete the entire
344structure of your old geometry and build up a completely new set of
345volumes. For this case, you need to set the new world physical
346volume pointer to the <span class="emphasis"><em>RunManager</em></span>. Thus, you should proceed
347in the following way.
348
349</p><div class="informalexample"><pre class="programlisting">
350 G4RunManager* runManager = G4RunManager::GetRunManager();
351 runManager-&gt;DefineWorldVolume( newWorldPhys );
352</pre></div><p>
353
354Presumably this case is rather rare. The second case is more
355frequent for the user.
356</p><p>
357The second case is the following. Suppose you want to move
358and/or rotate a particular piece of your detector component. This
359case can easily happen for a beam test of your detector. It is
360obvious for this case that you need not change the world volume.
361Rather, it should be said that your world volume (experimental hall
362for your beam test) should be big enough for moving/rotating your
363test detector. For this case, you can still use all of your
364detector geometries, and just use a <code class="literal">Set</code> method of a
365particular physical volume to update the transformation vector as
366you want. Thus, you don't need to re-set your world volume pointer
367to <span class="emphasis"><em>RunManager</em></span>.
368</p><p>
369If you want to change your geometry for every run, you can
370implement it in the <code class="literal">BeginOfRunAction()</code> method of
371<span class="emphasis"><em>G4UserRunAction</em></span> class, which will be invoked at the
372beginning of each run, or, derive the <code class="literal">RunInitialization()</code>
373method. Please note that, for both of the above mentioned cases,
374you need to let <span class="emphasis"><em>RunManager</em></span> know "the geometry needs to be
375closed again". Thus, you need to invoke
376
377</p><div class="informalexample"><pre class="programlisting">
378 runManager-&gt;GeometryHasBeenModified();
379</pre></div><p>
380
381before proceeding to the next run. An example of changing geometry
382is given in a Geant4 tutorial in Geant4 Training kit #2.
383</p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.Run.Custom.SwitchPhys"></a>3.4.4.4. 
384Switch physics processes
385</h4></div></div></div><p>
386In the <code class="literal">InitializePhysics()</code> method,
387<code class="literal">G4VUserPhysicsList::Construct</code> is invoked in order to
388define particles and physics processes in your application.
389Basically, you can not add nor remove any particles during
390execution, because particles are static objects in Geant4 (see
391<a href="ch02s04.html" title="2.4. 
392How to Specify Particles
393">Section 2.4</a> and
394<a href="ch05s03.html" title="5.3. 
395Particles
396">Section 5.3</a> for details).
397In addition, it is very difficult to add and/or remove physics
398processes during execution, because registration procedures are
399very complex, except for experts (see <a href="ch02s05.html" title="2.5. 
400How to Specify Physics Processes
401">Section 2.5</a>
402and <a href="ch05s02.html" title="5.2. 
403Physics Processes
404">Section 5.2</a>).
405This is why the <code class="literal">initializePhysics()</code> method is assumed
406to be invoked at once in Geant4 kernel initialization.
407</p><p>
408However, you can switch on/off physics processes defined in your
409<span class="emphasis"><em>G4VUserPhysicsList</em></span> concrete class and also change parameters
410in physics processes during the run break.
411</p><p>
412You can use <code class="literal">ActivateProcess()</code> and
413<code class="literal">InActivateProcess()</code> methods of <span class="emphasis"><em>G4ProcessManager</em></span>
414anywhere outside the event loop to switch on/off some process. You
415should be very careful to switch on/off processes inside the event
416loop, though it is not prohibited to use these methods even in the
417<span class="emphasis"><em>EventProc</em></span> state.
418</p><p>
419It is a likely case to change cut-off values in a run. You can
420change <code class="literal">defaultCutValue</code> in
421<span class="emphasis"><em>G4VUserPhysicsList</em></span>
422during the <span class="emphasis"><em>Idle</em></span> state. In this case, all cross section
423tables need to be recalculated before the event loop. You should use the
424<code class="literal">CutOffHasBeenModified()</code> method when you change cut-off
425values so that the <code class="literal">SetCuts</code> method of your
426<span class="emphasis"><em>PhysicsList</em></span> concrete class will be invoked.
427</p></div></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch03s03.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><td width="20%" align="center"><a accesskey="u" href="ch03.html"><img src="AllResources/IconsGIF/up.gif" alt="Up"></a></td><td width="40%" align="right"> <a accesskey="n" href="ch03s05.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr><tr><td width="40%" align="left" valign="top">3.3. 
428System of units
429 </td><td width="20%" align="center"><a accesskey="h" href="index.html"><img src="AllResources/IconsGIF/home.gif" alt="Home"></a></td><td width="40%" align="right" valign="top"> 3.5. 
430Event
431</td></tr></table></div></body></html>
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