Recent content by Carla1985

Hi all, I am hoping someone can help me understand a PDE. I am reading a paper and am trying to follow the math. My experience with PDEs is limited though and I am not sure I am understanding it all correctly. I have 3 coupled PDEs, for $n$, $f$ and $c$, that are written in general form, and I...

I think when they say 'determine the exact solution' they mean the composite asymptotic solution. I will give you a brief outline of what is required. As $\epsilon$ is multiplying the highest order term we have a singular perturbation problem so have multiple layers. For the outer layer no...

Hi all, I am trying to understand some examples given to me by my supervisor but am struggling with some bits. The part I don't understand is: if the equation $$ax+b\lambda=\bar{a}x-\bar{d}y$$ holds for any $x,y\in V$, an open neighbourhood of the origin, and $\lambda$ is a mapping from $V$ to...

$\alpha$ and $\beta$ are grouped parameters from how I did the nondimensionalisation. Basically the system is a type of drug-receptor binding system. After nondimensionalising I have 3 parameters: $\alpha$, $\beta$ and $\gamma$. We know that $\alpha$ is $O(1)$ but have limit information about...

Hi all, I have this (nondimensionalised) system of ODEs that I am trying to analyse: \[ \begin{align} \frac{dr}{dt}= &\ - \left(\alpha+\frac{\epsilon}{2}\right)r + \left(1-\frac{\epsilon}{2}\right)\alpha p - \alpha^2\beta r p + \frac{\epsilon}{2} \\ \frac{dp}{dt}= &\...

Yes $A$ is constant. The only variables are $X,Y$ and $Z$

Hi, Yes, sorry, I should have explained better, D is a constant value. The only other constraints are $\alpha, \beta, k_+, k_-\geq 0$. I will work through your suggestions. Thank you very much for the help. Regards Carla

Hi all, I have the system of nonlinear ODEs: $$ \begin{align} \frac{dX}{dt}=&-k_+ A X+k_-Y \\ \frac{dY}{dt}=&\ k_+ A X-k_-Y-\alpha k_+ X Y +\beta Z \\ \frac{dZ}{dt}=&\ \alpha k_+ X Y -\beta Z \end{align} $$ I also have a conservation law that says $D=X+Y+2Z$. Obviously it is not possible to...

That's fab, thank you so much. I'll work though that method. Again, thank you.

I am trying to prove that $$ x^4+4096y^4+450x^2y^2-2304xy^3-36x^3y $$ is positive for all positive $x$ and $y$. I also have the condition $x>16y$ though I don't believe this is needed to prove positivity as I've plotted the function for varying $x$ and $y$ and it always seems to be positive...

Ok, I think I've got it. So I have 2 right angle triangles with triples $(17,h,x)$ and $(10, 21-x,h)$. From pythag I get: $$h^2+x^2=289$$ $$h^2+x^2-42x=-341$$ Subbing in $h^2$ into the second equation gives me $x=15$ and $h=8$. This gives me an area of $84$. Thanks for the help!

That would make things a whole lot easier. Thank you for your help!

Thanks but that just gives me the angle between the two straight lines. My impression was that $\gamma$ was the part of the angle up to the edge of the circle.

Can I have an opinion on this question, please? Personally I would use the cosine & sine rules to work out the angles then use trig to calculate the height. However, the question asks for Pythag to be used. Can someone please explain what method I should be using to answer this? Thanks Thanks Carla

Hi, could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one. Thanks