Dear Newsgroup:

http://mathforum.org/kb/thread.jspa?...39373&tstart=0

It is difficult to imagine that a simple formula like Riccati
differential equation (RDE):

dx/dt+x^2=g(t)

will represent the sole mathematical formula of the universe.

Yes, all majestic edifice of mathematics can indeed be reduced to a
RDE (or many of them).

Sounds like impossible to visualize.

But this is result of my 25 years extensive research experiences,
after Cambridge graduation.

That is more than 5 times of time required from B.Sc. to Ph.D. degrees
(5 years average), bearing in mind my intuition in the subject is
about 10 times more than those of academics in top schools.

They are conventional researchers within mainstream research, some
practicing obsolete mathematical sciences.

Let us look at the Math-chart again (as enclosed).

1-I have declared that polynomials are included in RDE.

Not only we systematically extract solving polynomials to Riccati, but
also general polynomial can be included in a RDE, with the residue
having solutions according to ODE or PDE existence theorems for
systems of differential equations.

Indeed many developments and applications demonstrate that.

2- linear differential equations of higher order of variable
coefficients (LDE).

In fact once we have a general polynomial, a LDE can be constructed
based on it.

Also we can see on my classical solving equations, I imbed a RDE
within a LDE and then manipulate the result to solve
The Riccati.

One can say there is a kind of inverse relations happening here.

3- Non-linear differential equations are similarly imbedded within a
higher order LDE, or systems.

The solving will apply to systems of algebraic equations as well.

4-Integrals are special part of a RDE anyway. But manipulating whole
system around RDE will as well solve many integrals particularly
Elliptic.

5-Numerical applications are direct applications of results obtained
with many solved parametric algebraic equations or differential
equations, as well as difference equations.

All I see the Math-Chart is correct and you need to have 5 years of
international research to experience personally this new world of math
computations.

I will renew the offer after each five years!

Well, all this means that, once you start your research here, there is
no way out of RDE.

About other algebraic branches in mathematics, eventually they will be
out of business or have a very small influence on the subject.

Dr.M.Basti

Dear Newsgroup:

I have to clarify that most of my arguments are based of existence
theorems of ODE and PDE for systems of ODE ,PDE and algebraic
equations.

Once the method is applied, they all confirm that they are indeed
linked with the Riccati.

Then only massive systematic practical and concrete applications prove
the claim.

Indeed, this is the only way; we can really get to know the complexity
of the universe.

The other equations (as a base) will simply not working.

Dr.M.Basti