Parametric Relation

[monir]

Hello;

1) Having the relation:
r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t)
where:
a, b, c, d, h, k, m are real
m > 0
t > 0
r > 0
"." represents multiplication sign

2) Is there a practical way (even with the help of a system Algebraic
package) to derive the parametric relation between "m" on one side and
the rest of parameters on the other side from the condition:
r(t + 2pi.n) > r(t)
where "n" is an integer > 0

Your expert help would be greatly appreciated.

Regards.
Monir

[monir]

Correction:
===========
Independant variable "t" in item 1) of my OP should read:
t >= 0

Regards.
Monir

[monir]

> Monir- Hide quoted text -
>
> - Show quoted text -

Hello;
Here are some limited trial and error numerical results that satisfy
the condition r(t+2pi.n) > r(t) where:

r(t) = { a + b.t + c.t^2 + d.t^3 + h.t^4 + k.t^5 }.Exp(m.t)

The results do not cover all cases with all parameters since couldn't
do such cases manually!

CASE 1:
t-range 0 to 6.407576:
a = 0.00101695
b = - 0.0004745
c = 0.00012327
d = 0
h = 0
k = 0
m = 0.10

CASE 2:
t-range 0 to 10.2939339:
a = 0.00146937
b = - 0.0002298
c = 3.3017E-05
d = 0
h = 0
k = 0
m = 0.10

CASE 3:
t-range 0 to 16.8304665:
a = 0.00232341
b = - 0.0003554
c = 5.6636E-05
d = -2.215E-06
h = 0
k = 0
m = 0.10

CASE 4:
t-range 0 to 19.5654517:
a = 0.00233668
b = - 0.0004121
c = 3.133E-05
d = -8.068E-07
h = 0
k = 0
m = 0.18

Your help in deriving the parametric relation(s) would be greatly
appreciated.

Regards.
Monir