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SmoothTransitionFunctions

Guides

  • Guide to ZigangPan`SmoothTransitionFunctions`

Symbols

  • Arztanfunction
  • flexibledeadzonefunction
  • mylegendPlot
  • SATF
  • simplesmoothfunction
  • smoothAsaturationfunction
  • smoothdeadzonefunction
  • smoothgrowthfunction
  • smoothsaturationfunction
  • smoothtransitionEfunction
  • smoothtransitionfunction
ZigangPan`SmoothTransitionFunctions`
SATF
​
SATF
[x,p]
for constant p>0 is a smooth function on ×(0,+∞). It equals to x when |x|≤10p/11. Its absolute value is always less than and equals to |x| and p, ∀x ∈ . It is monotonically increasing in the first argument with Limit[SATF[x,p],x-∞]=-p and Limit[SATF[x,p],x+∞]=p.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
In[1]:=
SATF
[x,2]
Out[1]=
2
20-11x

20
11
-x+x
x
2
>
10
11
x
x
2
≥0||2(20+11x)≥0
2
20+11x

-
20
11
-x+x
True
In[2]:=
Plot
SATF
[x,2],{x,-4,4}
Out[2]=
SeeAlso
smoothtransitionfunction
 
▪
simplesmoothfunction
 
▪
smoothtransitionEfunction
 
▪
smoothgrowthfunction
 
▪
smoothsaturationfunction
 
▪
smoothAsaturationfunction
 
▪
Arztanfunction
""

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