Difference between revisions of "Format notes"

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=General format for time scale pages=
 
=General format for time scale pages=
 
{| class="wikitable"
 
{| class="wikitable"
−
|+$\mathbb{T}=*********$
+
|+$\mathbb{T}=$THETIMESCALE
 
|-
 
|-
 
|[[Forward jump]]:
 
|[[Forward jump]]:
−
|$\sigma(t)=*********$
+
|$\sigma(t)=$
 +
|[[Derivation of forward jump for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Forward graininess]]:
 
|[[Forward graininess]]:
−
|$\mu(t)=*********$
+
|$\mu(t)=$
 +
|[[Derivation of forward graininess for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Backward jump]]:
 
|[[Backward jump]]:
−
|$\rho(t)=*********$
+
|$\rho(t)=$
 +
|[[Derivation of backward jump for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Backward graininess]]:
 
|[[Backward graininess]]:
−
|$\nu(t)=*********$
+
|$\nu(t)=$
 +
|[[Derivation of backward graininess for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Delta derivative | $\Delta$-derivative]]
 
|[[Delta derivative | $\Delta$-derivative]]
−
|$f^{\Delta}(t)=*********$
+
|$f^{\Delta}(t)=$
 +
|[[Derivation of delta derivative for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Nabla derivative | $\nabla$-derivative]]
 
|[[Nabla derivative | $\nabla$-derivative]]
−
|$f^{\nabla}(t) =*********$
+
|$f^{\nabla}(t)=$
 +
|[[Derivation of nabla derivative for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Delta integral | $\Delta$-integral]]
 
|[[Delta integral | $\Delta$-integral]]
−
|$\displaystyle\int_s^t f(\tau) \Delta \tau = *********$
+
|$\displaystyle\int_s^t f(\tau) \Delta \tau$
 +
|[[Derivation of delta integral for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Nabla derivative | $\nabla$-derivative]]
 
|[[Nabla derivative | $\nabla$-derivative]]
−
|$\displaystyle\int_s^t f(\tau) \nabla \tau = *********$
+
|$\displaystyle\int_s^t f(\tau) \nabla \tau$
 +
|[[Derivation of nabla integral for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|[[Delta exponential | $e_p(t,s)=$]]  
+
|[[Delta hk|$h_k(t,s)$]]
−
| $*********$
+
|$h_k(t,s)=$
−
([[Derivation of delta exponential T=******|derivation]])
+
|[[Derivation of delta hk for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|[[Nabla exponential | $\hat{e}_p(t,s)=$]]
+
|[[Nabla hk|$\hat{h}_k(t,s)$]]
−
|$*********$
+
|$\hat{h}_k(t,s)=$
−
([[Derivation of nabla exponential T=*********|derivation]])
+
|[[Derivation of nabla hk for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Delta gk|$g_k(t,s)$]]
 +
|$g_k(t,s)=$
 +
|[[Derivation of delta gk for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Nabla gk|$\hat{g}_k(t,s)$]]
 +
|$\hat{g}_k(t,s)=$
 +
|[[Derivation of nabla gk for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Delta exponential | $e_p(t,s)$]]
 +
|$e_p(t,s)=$
 +
|[[Derivation of delta exponential T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Nabla exponential | $\hat{e}_p(t,s)$]]
 +
|$\hat{e}_p(t,s)=$
 +
|[[Derivation of nabla exponential T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Gaussian bell]]
 +
|$\mathbf{E}(t)=$
 +
|[[Derivation of Gaussian bell for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Delta sine | $\mathrm{sin}_p(t,s)=$]]
 
|[[Delta sine | $\mathrm{sin}_p(t,s)=$]]
−
|$*********$
+
|$\sin_p(t,s)=$
−
([[Derivation of sin sub p for T=*********|derivation]])
+
|[[Derivation of delta sin sub p for T=THETIMESCALE|derivation]]
 +
|-
 +
|$\mathrm{\sin}_1(t,s)$
 +
|$\sin_1(t,s)=$
 +
|[[Derivation of delta sin sub 1 for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Nabla sine|$\widehat{\sin}_p(t,s)$]]
 +
|$\widehat{\sin}_p(t,s)=$
 +
|[[Derivation of nabla sine sub p for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Delta cosine|$\mathrm{\cos}_p(t,s)$]]
 +
|$\cos_p(t,s)=$
 +
|[[Derivation of delta cos sub p for T=THETIMESCALE|derivation]]
 +
|-
 +
|$\mathrm{\cos}_1(t,s)$
 +
|$\cos_1(t,s)=$
 +
|[[Derivation of delta cos sub 1 for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Nabla cosine|$\widehat{\cos}_p(t,s)$]]
 +
|$\widehat{\cos}_p(t,s)=$
 +
|[[Derivation of nabla cos sub 1 for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|$\mathrm{\sin}_1(t,0)$
+
|[[Delta sinh|$\sinh_p(t,s)$]]
−
|$*********$
+
|$\sinh_p(t,s)=$
−
([[Derivation of sin sub 1 for T=*********|derivation]])
+
|[[Derivation of delta sinh sub p for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|$\mathrm{\cos}_p(t,s)$
+
|[[Nabla sinh|$\widehat{\sinh}_p(t,s)$]]
−
|$*********$
+
|$\widehat{\sinh}_p(t,s)=$
−
([[Derivation of cos sub p for T=*********|derivation]])
+
|[[Derivation of nabla sinh sub p for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|$\mathrm{\cos}_1(t,0)$
+
|[[Delta cosh|$\cosh_p(t,s)$]]
−
|$*********$
+
|$\cosh_p(t,s)=$
−
([[Derivation of cos sub 1 for T=*********|derivation]])
+
|[[Derivation of delta cosh sub p for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|[[Hilger circle]]  
+
|[[Nabla cosh|$\widehat{\cosh}_p(t,s)$]]
 +
|$\widehat{\cosh}_p(t,s)=$
 +
|[[Derivation of nabla cosh sub p for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Gamma function]]
 +
|$\Gamma_{THETIMESCALESYMBOL}(x,s)=$
 +
|[[Derivation of gamma function for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Euler-Cauchy logarithm]]
 +
|
 +
|[[Derivation of Euler-Cauchy logarithm for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Bohner logarithm]]
 +
|
 +
|[[Derivation of the Bohner logarithm for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Jackson logarithm]]
 +
|
 +
|[[Derivation of the Jackson logarithm for T=THETIMESCALE|derivation]]
 +
|-
 +
|[[Mozyrska-Torres logarithm]]
 
|
 
|
 +
|[[Derivation of the Mozyrska-Torres logarithm for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|[[Laplace transform]]
 
|[[Laplace transform]]
−
|$\mathscr{L}_{\mathbb{R}}\{f\}(z;s)=*********$
+
|$\mathscr{L}_{THETIMESCALESYMBOL}\{f\}(z;s)=$
 +
|[[Derivation of Laplace transform for T=THETIMESCALE|derivation]]
 
|-
 
|-
−
|[[Gamma function]]
+
|[[Hilger circle]]  
−
|$\Gamma_{\mathbb{T}}(x,s)=*********$
+
|
 +
|[[Derivation of Hilger circle for T=THETIMESCALE|derivation]]
 
|-
 
|-
 
|}
 
|}

Revision as of 00:09, 22 May 2015

This is a list of common code templates and styles we use at timescalewiki.

Theorem/proof box template

The code 

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
<strong>THEOREM/LEMMA/PROPOSITION:</strong> STATEMENT OF THEOREM
<div class="mw-collapsible-content">
<strong>Proof:</strong> proof goes here █ 
</div>
</div>

creates

THEOREM/LEMMA/PROPOSITION: STATEMENT OF THEOREM

Proof: proof goes here █

Generic list of time scales

The code 

{| class="wikitable"
|+Time Scale foo Functions
|-
|$\mathbb{T}$
|
|-
|[[Real_numbers | $\mathbb{R}$]]
|$foo(t)=  $
|-
|[[Integers | $\mathbb{Z}$]]
|$foo(t) = $
|-
|[[Multiples_of_integers | $h\mathbb{Z}$]]
| $foo(t) = $
|-
| [[Square_integers | $\mathbb{Z}^2$]]
| $foo(t) = $
|-
|[[Quantum_q_greater_than_1 | $\overline{q^{\mathbb{Z}}}, q > 1$]]
| $foo(t) = $
|-
|[[Quantum_q_less_than_1 | $\overline{q^{\mathbb{Z}}}, q < 1$]]
| $foo(t) =$
|-
|[[Harmonic_numbers | $\mathbb{H}$]]
|$foo(t) = $
|}

generates

Time Scale foo Functions
$\mathbb{T}$
$\mathbb{R}$ $foo(t)= $
$\mathbb{Z}$ $foo(t) = $
$h\mathbb{Z}$ $foo(t) = $
$\mathbb{Z}^2$ $foo(t) = $
$\overline{q^{\mathbb{Z}}}, q > 1$ $foo(t) = $
$\overline{q^{\mathbb{Z}}}, q < 1$ $foo(t) =$
$\mathbb{H}$ $foo(t) = $

BiBTeX

Place all references at the bottom of the document below a 

=References=

inside of 

<bibtex>....</bibtex>

tags. Use the following code as a template: 

<div id="deots"></div><bibtex>
 @inproceedings{MR1843232,
   title="Dynamic equations on time scales",
   author="Bohner, Martin and Peterson, Allan",
   booktitle="Birkhäuser Boston, Inc., Boston, MA",
   year="2001",
   doi="10.1007/978-1-4612-0201-1",
   url="http://dx.doi.org/10.1007/978-1-4612-0201-1"
 }
</bibtex>

creates

<bibtex> 
@inproceedings{deots,
  title="Dynamic equations on time scales",
  author="Bohner, Martin and Peterson, Allan",
  booktitle="Birkhäuser Boston, Inc., Boston, MA",
  year="2001",
  doi="10.1007/978-1-4612-0201-1",
  url="http://dx.doi.org/10.1007/978-1-4612-0201-1"
}

</bibtex>

We use the code 

<sup>[[#***ABC*** | pp.##]]</sup>

to create a link in the main text that looks like pp.##

which links to the reference next to 
<div id="***ABC***">

General format for time scale pages

$\mathbb{T}=$THETIMESCALE
Forward jump: $\sigma(t)=$ derivation
Forward graininess: $\mu(t)=$ derivation
Backward jump: $\rho(t)=$ derivation
Backward graininess: $\nu(t)=$ derivation
$\Delta$-derivative $f^{\Delta}(t)=$ derivation
$\nabla$-derivative $f^{\nabla}(t)=$ derivation
$\Delta$-integral $\displaystyle\int_s^t f(\tau) \Delta \tau$ derivation
$\nabla$-derivative $\displaystyle\int_s^t f(\tau) \nabla \tau$ derivation
$h_k(t,s)$ $h_k(t,s)=$ derivation
$\hat{h}_k(t,s)$ $\hat{h}_k(t,s)=$ derivation
$g_k(t,s)$ $g_k(t,s)=$ derivation
$\hat{g}_k(t,s)$ $\hat{g}_k(t,s)=$ derivation
$e_p(t,s)$ $e_p(t,s)=$ derivation
$\hat{e}_p(t,s)$ $\hat{e}_p(t,s)=$ derivation
Gaussian bell $\mathbf{E}(t)=$ derivation
$\mathrm{sin}_p(t,s)=$ $\sin_p(t,s)=$ derivation
$\mathrm{\sin}_1(t,s)$ $\sin_1(t,s)=$ derivation
$\widehat{\sin}_p(t,s)$ $\widehat{\sin}_p(t,s)=$ derivation
$\mathrm{\cos}_p(t,s)$ $\cos_p(t,s)=$ derivation
$\mathrm{\cos}_1(t,s)$ $\cos_1(t,s)=$ derivation
$\widehat{\cos}_p(t,s)$ $\widehat{\cos}_p(t,s)=$ derivation
$\sinh_p(t,s)$ $\sinh_p(t,s)=$ derivation
$\widehat{\sinh}_p(t,s)$ $\widehat{\sinh}_p(t,s)=$ derivation
$\cosh_p(t,s)$ $\cosh_p(t,s)=$ derivation
$\widehat{\cosh}_p(t,s)$ $\widehat{\cosh}_p(t,s)=$ derivation
Gamma function $\Gamma_{THETIMESCALESYMBOL}(x,s)=$ derivation
Euler-Cauchy logarithm derivation
Bohner logarithm derivation
Jackson logarithm derivation
Mozyrska-Torres logarithm derivation
Laplace transform $\mathscr{L}_{THETIMESCALESYMBOL}\{f\}(z;s)=$ derivation
Hilger circle derivation
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