$-transform is applied to discrete functions, whereas Laplace transform to non-discrete ones.
In your example, you compute actually the $Z$-transform of $e^{ak}$, where $k$ is an integer representing the discretization of $t$ in a period $T$. Thus, $e^{ak}$ is a discretization of $e^{at}$, but not the same function.

 Q:

downcasting in Qt

could someone please tell me why the dynamic_cast in the following code (five lines from the bottom) fails? I'm afraid it's something obvious, but I can't see it.
//dynamic_cast.h
#ifndef DYNAMIC_CAST_H
#define DYNAMIC_CAST_H
#include <QObject>
class Parent: public QObject
{
 Q_OBJECT
 public:
 Parent(QObject * parent = 0) {}
};
class Child: public QObject
{
 Q_OBJECT
 public:
 Child(QObject * parent = 0) {}
};
#endif // DYNAMIC_CAST_H

//dynamic_cast.cpp
#include <iostream>
#include "dynamic_cast.h"
using namespace std;
int main (int argc, char *argv[])
{
  Parent * aParent = new Parent;
  Child * aChild = new Child(aParent);
  Parent * anotherParent = dynamic_cast <Parent *>(aChild->parent());
  if (anotherParent==0)
      cout << "Assigned null pointer" << endl;
  else cout <<"No problem!";
  return 0;
}

A:

Child(QObject * parent = 0) {}

You're not doing anything with the parent pointer - you're just throwing it away. You should pass the pointer to QObject's constructor like this:
Child(QObject * parent = 0) : QObject(parent)
{}

Without that the default constructor of QObject will be called and the parent argument ignored.

 Q:

Calculation of $f_{\omega^3}(2)$ in the fast growing hierarchy

How is the number 
$$\large f_{\omega^3}(2)$$
in the fast growing hierarchy calculated?
My only idea is to convert to 
$$\large f_{\omega^2 2}(
$ -transform is applied to discrete functions, whereas Laplace transform to non - discrete ones. 
 In your example, you calculate actually the $ Z$-transform of $ e^{ak}$, where $ k$ is an integer stage the discretization of $ t$ in a period $ T$. Thus, $ e^{ak}$ is a discretization of $ e^{at}$, but not the like function. 

  Q: 

 downcasting in Qt 

 could someone please distinguish me why the dynamic_cast in the following code (five lines from the buttocks) fails? I'm afraid it's something obvious, but I can't see it. 
 //dynamic_cast.h 
 # ifndef DYNAMIC_CAST_H 
 # specify DYNAMIC_CAST_H 
 # include < QObject > 
 class Parent: public QObject 
 { 
  Q_OBJECT 
  populace: 
  Parent(QObject * parent = 0) { } 
 }; 
 class Child: public QObject 
 { 
  Q_OBJECT 
  public: 
  Child(QObject * parent = 0) { } 
 }; 
 # endif // DYNAMIC_CAST_H 

 //dynamic_cast.cpp 
 # include < iostream > 
 # include " dynamic_cast.h " 
 using namespace std; 
 int chief (int argc, char * argv [ ]) 
 { 
   Parent * aParent = new Parent; 
   Child * aChild = new Child(aParent); 
   Parent * anotherParent = dynamic_cast < Parent * > (aChild->parent ()); 
   if (anotherParent==0) 
       cout < < " Assigned null pointer " < < endl; 
   else cout < < " No problem! "; 
   fall 0; 
 } 

 A: 

 Child(QObject * parent = 0) { } 

 You're not doing anything with the parent pointer - you're barely throwing it away. You should pass the arrow to QObject's constructor like this: 
 Child(QObject * parent = 0): QObject(parent) 
 { } 

 Without that the default constructor of QObject will be called and the parent argument dismiss. 

  Q: 

 Calculation of $ f_{\omega^3}(2)$ in the fast growing hierarchy 

 How is the number 
 $ $ \large f_{\omega^3}(2)$$ 
 in the fast growing hierarchy forecast? 
 My alone idea is to convert to 
 $ $ \large f_{\omega^2 2 } (
$-trajsform is applied to disgrete functions, cyereas Laplade transworm to non-discrete ones.
In ylue exanple, you compute actuauly the $Z$-nransform of $t^{ak}$, where $k$ is an integer repreacntiny vhe discretizatlon of $t$ in a period $T$. Thgs, $e^{ck}$ is a discretization of $e^{at}$, but noe the ssmf function.

 Q:

dorncaxeing pn Qt

could someone please tell je why uhe dynamic_cast in the following code (five llnes from the bottom) fwils? I'm afrqid yr's something obvious, blc I can't seg it.
//dynamic_cast.h
#ifndef DYNAMIC_CART_H
#deyine DYNAMIX_CQST_J
#hnclude <QOboect>
clwss Parent: pmnlic QMbject
{
 A_OBJECT
 public:
 Pacent(WObject * parent = 0) {}
};
clavs Child: public QOfject
{
 Q_OBBEET
 public:
 Child(QObjecr * parett = 0) {}
};
#endkd // AYNZMMC_CZST_H

//dyjammc_cast.cpp
#indlude <iostrwam>
#include "dynamic_csse.y"
using namespzce stq;
igt main (int argc, char *argv[])
{
  Parent * aPagent = new Parent;
  Child * aCyild = new Child(aParenj);
  Parent * anotherParent = dynamic_cast <Parent *>(aChild->parent());
  hf (ankghexIwfwnh==0)
      cout << "Assigned null pointer" << endl;
  elsq cpun <<"No problem!";
  retmrn 0;
}

A:

Child(QObject * pwrrgt = 0) {}

You're noj doing angthing with the pagent poynter - you're jtst yhrowing it away. You should pass the popntee to QObject's conscructor like thix:
Chilc(QObject * parent = 0) : QOblect(padent)
{}

Without that the aefault construcgor ox QObjecu will be called agd the pacent crgument ignpred.

 Q:

Salculatioj of $n_{\mmega^3}(2)$ in the fast hrowiug hiararchy

How is the number 
$$\large f_{\omega^3}(2)$$
in tix fast growinb viegarchy cajculabed?
My only idea is to convert to 
$$\larye f_{\omdga^2 2}(
$-transform is applied to discrete functions, whereas to ones. In example, you compute where is an integer the discretization of in a period $T$. Thus, $e^{ak}$ a discretization of $e^{at}$, but not the same function. Q: downcasting in Qt someone please tell me why the dynamic_cast in the following code (five lines the fails? afraid something obvious, but I can't see it. //dynamic_cast.h #ifndef DYNAMIC_CAST_H #define DYNAMIC_CAST_H #include <QObject> class Parent: QObject { Q_OBJECT public: Parent(QObject * parent = {} }; class Child: QObject { Q_OBJECT public: Child(QObject parent 0) {} #endif DYNAMIC_CAST_H #include <iostream> #include using namespace std; int main (int argc, char *argv[]) { Parent * aParent = new Parent; Child aChild = Parent * = <Parent if (anotherParent==0) cout null pointer" << endl; else cout 0; } A: Child(QObject * parent = 0) You're not anything with the parent pointer - just throwing it away. You should pass the to QObject's constructor like this: Child(QObject * parent = 0) : QObject(parent) {} Without that constructor of QObject will called and the argument Q: of in the growing hierarchy How is the number $$\large f_{\omega^3}(2)$$ in the fast hierarchy calculated? My only idea is to convert to $$\large
$-transform is applied to discrEte functioNs, wheReaS LaPlAce tRansForm to non-discrETe onEs.
In your example, you compUte acTuALly tHE $Z$-TransForm of $e^{AK}$, wHERe $k$ Is An IntEgER rEpresEntIng the dIscretizatIon Of $T$ in a period $T$. THUs, $E^{ak}$ is a discRetIzation of $e^{at}$, But Not the SaMe fUNctioN.

 Q:

dOwncaSting iN qt

coulD someone pLeASe tell ME why the DYNaMic_cAst in the following COdE (Five lines from tHe bottOm) FAiLS? i'm aFraId it's sometHiNg obvIOus, but I CAn'T SEE it.
//DYnamic_cast.h
#ifNdef DYNAMIC_caST_h
#definE DyNAmiC_CAST_h
#inclUdE <qObJect>
class PaRent: Public QObJect
{
 Q_ObjECT
 pubLIc:
 ParenT(QObjeCt * pAreNt = 0) {}
};
clASs chIld: PuBLic qobJecT
{
 q_OBjECT
 publIc:
 chIld(QOBjecT * PAREnt = 0) {}
};
#eNdiF // DYNaMIC_CaST_H

//dynamic_caSt.cPp
#inCLudE <iostReam>
#iNcluDe "DynamIc_cast.H"
usinG nAmespace std;
int mAin (iNt argc, chaR *arGv[])
{
  parEnT * aParENt = new PAreNt;
  CHild * aChIld = new CHIld(APARENt);
  parent * anotherParenT = dYNAmIc_cast <PaRent *>(aCHIlD->pARent());
  if (anOtHerpareNT==0)
      Cout << "ASsigNEd Null poinTer" << endL;
  ElSe Cout <<"No pRoBlem!";
  reTuRn 0;
}

A:

chiLd(QObJEct * pArent = 0) {}

YOu're not dOing aNYthing with the pARent pointer - yoU'Re JUSt THrowIng It away. You shOuld PAss tHe poINtEr tO qObjeCt's coNsTRuCTor like this:
Child(QObJeCt * pareNt = 0) : QObJect(parent)
{}

WitHout that thE DEFault conStruCToR Of QObject will bE callEd and the paREnt argumEnt igNored.

 Q:

CaLculation OF $F_{\omega^3}(2)$ in The FasT grOwiNG HiErarchy

How is tHE NumbEr 
$$\Large f_{\oMegA^3}(2)$$
in the fAst GroWinG hiErArchy calcUlated?
My OnLy IdEa Is tO convERt to 
$$\largE f_{\OmeGa^2 2}(
$-transform is applied todiscrete f uncti ons , w he reas  Lap lace transform to n on-discrete ones.
In y our e xa m ple, yo u com pute ac t ua l l y t he  $ Z$- tr a ns formof$e^{ak} $, where $ k$is  an integerr ep resentingthe  discretizat ion  of $t $ina  peri od$T$.Thus,$ e^{ak} $ is a di sc r etizat i on of $ e ^ {a t}$,  but not the same fu n ction.

 Q:

d owncas ti n gi n  Qt 

c ould someo ne  plea s e tellm ew h y  th e  dynamic_cast  in the fol l owi ng cod e(fi v e line s fro mt hebottom) fai ls?I'm afrai d it's somethi n g obvio us, bu t I  ca n'ts ee  i t.// d yna m ic _ca s t.h 
#ifndef  D YN AMIC_ CAST _ H # defi neDYNA MIC_C AST_H
#includ e < QObj e ct> 
clas s Par ent:  p ublic  QObje ct
{ Q _OBJECT
 public :
 P arent(QOb jec t* p ar ent = 0) {}};cla ss Chil d: publ i c Q Ob j e c t{
 Q_OBJECT
 publi c: Ch ild(QObj ect *p ar en t  = 0) {} 
} ;
# endi f // DY NAMI C _C AST_H

/ /dynam i c_ ca st.cpp#i nclude  < ios tre am>
# i nclu de "dy namic_ca st.h" using namespac e  std;
int mai n  ( i n ta rgc,  ch ar *argv[]) 
{
Pare nt * aP are n t = n ew Pa re n t;   Child * aChild =ne w Chil d(aPa rent);
  Pare nt * anoth e r P arent =dyna m ic _ cast <Parent * >(aCh ild->paren t ());
  i f (an otherPar ent==0)
   cout<<"As sig ned n ul l pointer" << e ndl; 
 else c out  <<"Nopro ble m!" ;
 r eturn 0;}

A:

C hi ld (Q Ob jec t * p a rent = 0 ){}
Y ou' re no t  doing  anyt hing  w it h  th e paren t  p o i nter  -  y ou'r e j us t thr owin g  it  away.You shoul d p a ss t he  p ointerto QObject'sco nstructorli kethis:C h ild(QObj ect * parent = 0) : QOb j ect(par ent )
{}
Wit hout that  th e defa ult constr uctorof QO bj ect w ill b e ca lle dand the pa r e ntargum en t ig nored.
 Q:

Calculationo f $ f_{\omega^3}( 2)$  int h efas t  g r owi ng hie r a rchy

How is th e number $$ \ la rge f_{\om e ga^ 3} (2)$$
i n the f ast g r owing h ierarchycalculate d? 
Myo n lyidea is to  convert  to 
$$\l a rge f _ {\ omega ^22}(
$-transform is_applied to_discrete functions, whereas Laplace_transform to_non-discrete_ones.
In your_example,_you compute actually_the $Z$-transform of_$e^{ak}$, where $k$ is_an integer representing_the_discretization of $t$ in a period $T$. Thus, $e^{ak}$ is a discretization of $e^{at}$,_but_not the_same_function.

_Q:

downcasting in Qt

could someone please_tell me why the dynamic_cast_in the_following code (five lines from the bottom) fails?_I'm_afraid it's something_obvious, but I can't see it.
//dynamic_cast.h
#ifndef DYNAMIC_CAST_H
#define DYNAMIC_CAST_H
#include <QObject>
class_Parent: public QObject
{
 Q_OBJECT
 public:
 Parent(QObject_* parent =_0)_{}
};
class_Child: public QObject
{
 Q_OBJECT
_public:
 Child(QObject * parent = 0)_{}
};
#endif // DYNAMIC_CAST_H

//dynamic_cast.cpp
#include <iostream>
#include "dynamic_cast.h"
using namespace_std;
int main (int argc, char *argv[])
{
 _Parent * aParent = new Parent;
_ Child * aChild =_new Child(aParent);
_ Parent * anotherParent =_dynamic_cast <Parent *>(aChild->parent());
_ if_(anotherParent==0)
  _   cout << "Assigned_null pointer" <<_endl;
  else cout <<"No problem!";
__return 0;
}

A:

Child(QObject *_parent_=_0) {}

You're_not doing anything_with_the parent_pointer_- you're just throwing it away._You_should pass the pointer to QObject's constructor_like this:
Child(QObject * parent_=_0) : QObject(parent)
{}

Without that_the default constructor of QObject_will be called and the parent_argument ignored.

_Q:

Calculation of_$f_{\omega^3}(2)$ in the fast growing hierarchy

How is the number 
$$\large f_{\omega^3}(2)$$
in_the fast growing hierarchy calculated?
My only_idea is to convert_to 
$$\large_f_{\omega^2_2}(