Recent content by JJacquelin

By inspection one observes that the shape of the whole curve looks like two arcs of hyperbolas : on the first figure the blue curve for small x and the green curve for large x. Thus the whole model function can be presented as a picewise function. The equation writen on the second figure...

Polynomial regression z = Ax^2 + Bxy + Cy^2 + Dx + Ey + F, in order to evaluate the coefficients A to F is a LINEAR regression because z is linear with respect to the unknowns A to F . Of course the function $z(x)$ is non-linear, but we are not looking for z or for x since they are given data...

One of the best answer in : https://mathoverflow.net/questions/48067/is-square-of-delta-function-defined-somewhere

Hi, Duo Who Ow you seem embarrassed by the "appropriate initial guess" necessary to start the iterative process currently used in the usual methods of non-linear regression. Why not using a method where no initial guess is necessary ? This is possible in the case of the fitting of the...

Hi Jimit ! Unfortunately, nothing change. Special functions remain a matter of brute force for the memory. As it is written as a joke at the end of the paper quoted above : << When the best-seller "Phylogenetic Classification of the Special Functions" will appear ? >> . There is no indication...

@ sounouhid : One cannot answer to your question without a clear description of your problem. What kind of "theoretical model" are you talking about ? What kind of data ? And more details on the context of the problem are essential. The fitting methods are numerous and depends on the context. A...

Laplace transform is an efficient tool when linear operations are involves (sum, derivative, integral). But it is not so, and generaly very complicated, when non-linear operations are involved (multiplication, division, power). Even in the simplest cases convolution is requiered, which is...

There are several typo in my first answer; I suppose that you can correct them.

In order to understand what happen when ##\omega## tends to ##\omega_0## , let ##\omega=\omega_0+\epsilon## ##\omega^2-\omega_0^2=(\omega+\omega_0)\epsilon \simeq 2\omega_0\epsilon## ##\sin(\omega t)=\sin(\omega_0 t+\epsilon t)=\sin(\omega_0 t)\cos(\epsilon t)+\cos(\omega_0 t)\sin(\epsilon t)...

That's typical answer of Mathematicians a century ago !

First you wrote that ##G## is constant : Now, if ##G## is function of ##t## the general solution of the PDE , before any further condition, becomes: ## n(t,L,p)=F\left( \left( L - \int G(p,t)dt \right)\:,\: p\: \right) ## where ##F## is any differentiable function of two variables. Well, it...

Frist you wrote that ##G## is constant : Now, If ##G## is fonction of ##t## , the general solution of the PDE, before any further conditions is : ## n(t,L,p)=F \left( \left( -\int G(t)dt \right)\:,\: p\: \right) ## where ##F## is any differentiable function of two variables. But it is not...

## \frac {\partial n(t,L,p)}{\partial t} = -G(p)\cdot\frac {\partial n(t,L,p)}{\partial L} ## General solution : ## \quad n(t,L,p)=F\left(\left(L-G(p)\:t\;\right)\:,\:p\right)## where ## F ## is any differentiable function of two variables. The goal now is to find which function(s) ##F##...

The wording of the question is very bad. In the first PE it appears that $n$ is a function of at least two variables t and L. In the boundary condition n(t,0,p) they are now three variables. The vatiable p is new. We don't know what variable is equal to 0. Then, a new "given variable" appears C...

This is not a reply to the question about numerical calculus. In fact the analytical solving is not so hard : Thanks to the characteristics method of solving PDEs, the general solution expressed on implicite form is : \rho=F\left( x-v_{max} \left(\rho-\frac{\rho^2}{\rho_{max} } \right) t \right)...