Nilradical of a Lie algebra: Difference between revisions

Revision as of 03:13, 25 April 2013

Given an atomic DEVS model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states. (see Behavior of DEVS). [Zeigler84] originally introduced the algorithms that handle time variables related to lifespan $t_{s} \in [0, \infty]$ and elapsed time $t_{e} \in [0, \infty)$ by introducing two other time variables, last event time, $t_{l} \in [0, \infty)$ , and next event time $t_{n} \in [0, \infty]$ with the following relations:

t_{e} = t - t_{l}

and

t_{s} = t_{n} - t_{l}

where $t \in [0, \infty)$ denotes the current time. And the remaining time,

t_{r} = t_{s} - t_{e}

is equivalently computed as

t_{r} = t_{n} - t

, apparently

t_{r} \in [0, \infty]

.

Since the behavior of a given atomic DEVS model can be defined in two different views depending on the total state and the external transition function (refer to Behavior of DEVS), the simulation algorithms are also introduced in two different views as below.

Common parts

Regardless of two different views of total states, algorithms for initialization and internal transition cases are commonly defined as below.

DEVS-simulator
  variables:
    parent // parent coordinator
     $t_{l}$      // time of last event
     $t_{n}$      // time of next event
     $A = (X, Y, S, t a, δ_{e x t}, δ_{i n t}, λ)$ // the associated Atomic DEVS model 
  when receive init-message(Time  $t$ )
      $t_{l} \leftarrow t;$ 
      $t_{n} \leftarrow t_{l} + t a (s);$ 
  when receive star-message(Time  $t$ )
     if  $t \neq t_{n}$  then
        error: bad synchronization;
      $y \leftarrow λ (s);$ 
     send y-message( $y, t$ ) to parent;
      $s \leftarrow δ_{i n t} (s)$ 
      $t_{l} \leftarrow t;$ 
      $t_{n} \leftarrow t_{l} + t a (s);$

View 1: total states = states * elapsed times

As addressed in Behavior of Atomic DEVS, when DEVS receives an input event, right calling $δ_{e x t}$ , the last event time, $t_{l}$ is set by the current time, $t$ , thus the elapsed time $t_{e}$ becomes zero because $t_{e} = t - t_{l}$ .

  when receive x-message( $x \in X$ , Time  $t$ )
     if  $(t_{l} \leq t$  and  $t \leq t_{n})$  == false then
        error: bad synchronization;
      $s \leftarrow δ_{e x t} (s, t - t_{l}, x)$ 
      $t_{l} \leftarrow t;$ 
      $t_{n} \leftarrow t_{l} + t a (s);$

View 2: total states = states * lifespans * elapsed times

Notice that as addressed in Behavior of Atomic DEVS, depending on the value of $b$ return by $δ_{e x t}$ , last event time, $t_{l}$ , and next event time, $t_{n}$ ,consequently, elapsed time, $t_{e}$ , and lifespan $t_{n}$ , are updated (if $b = 1$ ) or preserved (if $b = 0$ ).

  when receive x-message( $x \in X$ , Time  $t$ )
     if  $(t_{l} \leq t$  and  $t \leq t_{n})$  == false then
        error: bad synchronization;
      $(s, b) \leftarrow δ_{e x t} (s, t - t_{l}, x)$ 
     if  $b = 1$  then 
         $t_{l} \leftarrow t;$ 
         $t_{n} \leftarrow t_{l} + t a (s);$

References

[Zeigler84] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
[ZKP00] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

@@ Line 1: / Line 1: @@
-I am 18 years old and my name is Brodie Cornish. I life in Mittermoos (Austria).<br>xunjie パレ·ド·トーキョー博物館ディスプレイブシュロン（ブシュロン）に2013年5月29 MAISON Auclert、
+Given an [[DEVS#Atomic DEVS|atomic DEVS]] model, simulation algorithms are methods to generate the model's legal behaviors which are trajectories not to reach to illegal states. (see [[Behavior of DEVS]]). [[Simulation_Algorithms_for_Atomic_DEVS#References|[Zeigler84]]] originally introduced the algorithms that handle time variables related to ''lifespan'' <math>t_s \in [0,\infty]</math> and ''elapsed time'' <math>t_e\in [0,\infty)</math> by introducing two other time variables, ''last event time'', <math>t_l\in [0,\infty)</math>, and ''next event time'' <math> t_n\in [0,\infty]</math> with the following relations:
-単純な単調でこれを行いますが、
+<center><math> \, t_e = t - t_l </math></center>
-需要と供給の側面を助ける。 [http://www.hps-heerbrugg.ch/admin/eddie/editor/chrome/ �����ϩ`�� �ԥ��� ���`���] 皮膚「ベビー柔らかい筋肉の手術を防ぐ（図） _情報_中国ボディケアアパレルネットワー<br>�た
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-都市部の女性のファッションライフスタイルや生活にパーソナライズされたアプローチを推進しています。 [http://www.karatedoshotokai.com/ckeditor/e/Paul.php �ݩ`�륹�ߥ� ؔ�� ����] ディオールのファッション店に点滅し、
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+and
+<center><math>\, t_s = t_n - t_l </math></center>
+where <math>t\in [0,\infty)</math> denotes the ''current time''. And the ''remaining time'',
+ <center><math>\,t_r=t_s-t_e</math></center> is equivalently computed as
+<center><math>\, t_r = t_n - t</math></center>, apparently <math> t_r \in [0,\infty]</math>.
+Since the behavior of a given atomic DEVS model can be defined in two different views depending on the total state and the external transition function (refer to [[Behavior of DEVS]]), the simulation algorithms are also introduced in two different views as below.
+== Common parts ==
+Regardless of two different views of total states, algorithms for initialization and internal transition cases are commonly defined as below.
+ DEVS-simulator
+   variables:
+     parent // parent coordinator
+     <math>t_l</math>     // time of last event
+     <math>t_n</math>     // time of next event
+     <math>A=(X,Y,S,ta, \delta_{ext}, \delta_{int}, \lambda) </math>// the associated [[DEVS#Atomic DEVS|Atomic DEVS]] model
+   when receive init-message(Time <math>t</math>)
+      <math> t_l \leftarrow t;</math>
+      <math> t_n \leftarrow t_l + ta(s); </math>
+   when receive star-message(Time <math>t</math>)
+      if <math> t \ne t_n </math> then
+         error: bad synchronization;
+      <math> y \leftarrow \lambda(s);</math>
+      send y-message(<math>y,t</math>) to parent;
+      <math> s \leftarrow \delta_{int}(s)</math>
+      <math> t_l \leftarrow t;</math>
+      <math> t_n \leftarrow t_l + ta(s); </math>
+== View 1: total states = states * elapsed times ==
+As addressed in [[Behavior of Atomic DEVS]], when DEVS receives an input event, right calling <math>\delta_{ext}</math>, the last event time,<math>t_l</math> is set by the current time,<math>t</math>, thus the elapsed time<math>t_e</math> becomes zero because <math>t_e = t - t_l</math>.
+   when receive x-message(<math>x \in X</math>, Time <math>t</math>)
+      if <math>( t_l \le t </math> and <math> t \le t_n )</math> == false then
+         error: bad synchronization;
+      <math> s \leftarrow \delta_{ext}(s,t-t_l, x)</math>
+      <math> t_l \leftarrow t;</math>
+      <math> t_n \leftarrow t_l + ta(s); </math>
+==View 2: total states = states * lifespans * elapsed times==
+Notice that as addressed in [[Behavior of Atomic DEVS]], depending on the value of <math>b</math> return by <math> \delta_{ext}</math>, last event time,<math>t_l</math>, and next event time,<math>t_n</math>,consequently, elapsed time, <math>t_e</math>, and lifespan<math>t_n</math>, are updated (if <math>b=1</math>) or preserved (if <math>b=0</math>).
+   when receive x-message(<math>x \in X</math>, Time <math>t</math>)
+      if <math>( t_l \le t </math> and <math> t \le t_n )</math> == false then
+         error: bad synchronization;
+      <math> (s,b) \leftarrow \delta_{ext}(s, t-t_l, x)</math>
+      if <math> b = 1 </math> then
+         <math> t_l \leftarrow t;</math>
+         <math> t_n \leftarrow t_l + ta(s); </math>
+==See also==
+* [[DEVS#Atomic DEVS|Atomic DEVS]]
+* [[Behavior of atomic DEVS]]
+* [[Simulation algorithms for coupled DEVS]]
+== References ==
+* [Zeigler84] {{cite book|author = Bernard Zeigler | year = 1984| title = Multifacetted Modeling and Discrete Event Simulation | publisher = Academic Press, London; Orlando | id = ISBN 978-0-12-778450-2  }}
+* [ZKP00] {{cite book|author = Bernard Zeigler, Tag Gon Kim, Herbert Praehofer| year = 2000| title = Theory of Modeling and Simulation| publisher = Academic Press, New York  | id= ISBN 978-0-12-778455-7 |edition=second}}
+[[Category:Algorithms]]

Nilradical of a Lie algebra: Difference between revisions

Revision as of 03:13, 25 April 2013

Contents

Common parts

View 1: total states = states * elapsed times

View 2: total states = states * lifespans * elapsed times

See also

References

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Nilradical of a Lie algebra: Difference between revisions

Revision as of 03:13, 25 April 2013

Common parts

View 1: total states = states * elapsed times

View 2: total states = states * lifespans * elapsed times

See also

References

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