Ramp model: Difference between revisions

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<math>
<math>
u(r) = \left\{ \infty & {\rm if}\; r < \sigma  
u(r) = \left\{  
W_r - (W_r-W_a)\frac{r-\sigma}{d_a-\sigma} {\rm if}\;\sigma\leq r \leq
\begin{array}{ll}
d_a  
\infty & {\rm if} \; r < \sigma \\
W_a - W_a\frac{r-d_a}{d_c-d_a} & {\rm if}\;d_a < r \leq d_c
W_r - (W_r-W_a) \frac{r-\sigma}{d_a-\sigma} & {\rm if} \; \sigma \leq r \leq d_a \\
0  {if}\; r > d_c \right</math>
W_a - W_a \frac{r-d_a}{d_c-d_a} & {\rm if} \; d_a < r \leq d_c \\
0 & {\rm if} \; r > d_c
\end{array} \right.
</math>
 
where <math>W_r > 0</math> and <math>W_u < 0</math>.
where <math>W_r > 0</math> and <math>W_u < 0</math>.


Revision as of 12:40, 16 March 2007

The model:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u(r) = \left\{ \begin{array}{ll} \infty & {\rm if} \; r < \sigma \\ W_r - (W_r-W_a) \frac{r-\sigma}{d_a-\sigma} & {\rm if} \; \sigma \leq r \leq d_a \\ W_a - W_a \frac{r-d_a}{d_c-d_a} & {\rm if} \; d_a < r \leq d_c \\ 0 & {\rm if} \; r > d_c \end{array} \right. }

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W_r > 0} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle W_u < 0} .


References

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