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Sep
15
comment Construct function with known asymptotes
@Arthur, yeah, I think that would work for me. If I can play a bit with the maximum distance between the point where the lines cross and $f$. This is basically the answer by Martigan after his update.
Sep
15
comment Construct function with known asymptotes
And after back transformation that works for me. Thanks.
Sep
15
accepted Construct function with known asymptotes
Sep
15
comment Construct function with known asymptotes
Than I get, as per your answer, $a=2$ and $b=r_2-r_1$.
Sep
15
comment Construct function with known asymptotes
Is was thinking about (for $x_0=0$ and $y_0=0$) and then subtracting $(r_1+r_2)x/2$ from both functions?
Sep
15
comment Construct function with known asymptotes
Your hints are helping. Any thought on which transformation would work? Apart from the obvious translation to the origin.
Sep
15
revised Construct function with known asymptotes
added 5 characters in body
Sep
15
comment Construct function with known asymptotes
@Semiclassical I see your point, I will update the question accordingly.
Sep
15
revised Construct function with known asymptotes
Added two constraints
Sep
15
comment Construct function with known asymptotes
@Eleven-Eleven That would mean that either $r_1=0$ or $r_2=0$, which does not make sense for my case. Suppose $r_2>r_1>0$, would this test ever be an issue?
Sep
15
asked Construct function with known asymptotes
Sep
5
comment What is the difference between $\propto$ and $\sim$
@Marc Formally that is what I am doing, although the limit is implicitly taken (i.e. based on physical grounds).
Sep
5
comment What is the difference between $\propto$ and $\sim$
@Jean-ClaudeArbaut Thanks, I have the wiki-page open already :). For the first one I am quite certain, my doubt is mainly in the second one.
Sep
5
comment What is the difference between $\propto$ and $\sim$
@Marc I have a balance equation (momentum). Basically, I keep the largest terms on both sides. They are not equal anymore, and I think $\approx$ does not feel right, but I want to indicate that they more or less scale in the same way. I am wondering if $\sim$ would be appropriate. Someone told me $\propto$ and $\sim$ mean the same thing. But I am not convinced.
Sep
5
asked What is the difference between $\propto$ and $\sim$
Aug
29
comment Solving the 2D Poisson equation with variable boundary location
@rajb245 I think you have to decide that you want to eliminate $C$ from the pde :)
Jul
24
comment Determining the maximum value for the solution of this delay differential equation?
I need some time to understand everything I learned so far, gave me a lot new insights today. I will need some time to reevaluate everything now, but might be back with more questions later. Thanks anyhow up till now!
Jul
24
comment Determining the maximum value for the solution of this delay differential equation?
I think I did that implicity, by not using the $f''(\tau)$, but by working with $f''(t_{max})$. I think I now understand why you do it like that. Thanks for your update to your answer.
Jul
24
comment Determining the maximum value for the solution of this delay differential equation?
For $f''$ I found that $f''=-\alpha f'(t-\delta)$, so this last derivative can be bound from above, with the upper bound you already gave in this answer. (Again from $f''_{max}=(1-3f_{max}^2)f'(t_{max})-\alpha f'(t-\delta)$.