Hi Guys,
I know that I'm going against regulations of this forum, but I don´t know where else to turn.
Two hours from now I will be picked by a ambulance because I´m going to have an operation in my heart.
Anyway I have these math problems here which have caused me some trouble. I have made a deal with a teaching assistant that he will picked my assignments up within the hour.
But I'm affried that if I don't finish them in time it will put to much strain on my heart.
Therefore I will be forever greatful if there is some kind soul who would be so kind and help solve what I have typed below.
(a)
(I use the triangle inequality in (1) and (3)?)
Let I be a open interval and f: I \rightarrow \mathbb{R}^n be a continious function.
Let || \cdot || be a given norm on \mathbb{R}^n.
Show the following:
1) If there exists a C>0 then ||x|| \leq C ||C||_1; x \in \mathbb{R}^n, ||x|| _1 = \sum _{j=1} ^n |x_j|
2) The mapping I \ni t \rightarrow ||f(t)|| \in \mathbb{R} is continious on.
3) for all t1,t2 \in \ || \int_{t_1} ^{t_2} f(t) dt|| \leq | \int_{t_1} ^{t_2} ||f(t)||dt|
(b)
Looking at the system(*) of equations,
x1' = (a-bx2)* x1
x2' = (cx1 -d)*x2
open the open Quadrant K; here a,b,c and d er positive constants.
I need to show that the system can be integrated. Which means I need to show that there exist a C^1 -function, with the properties F:U \rightarrow \mathbb{R}, where U \subseteq K is open and close in K(close means that for every point in K, is a limit point for q sequence, whos elements belongs to K). Such that gradient F \notequal 0 for alle x \in U and such that F is constant for trajectories of system.
Finally I need to conclude that every max trajectory is contained in a compact subset of K, and that the system (*) field X: R \rightarrow \mathbb{R}^2.
Sincerely Yours and God bless You all,
Maria Thomson 25
p.s. I promis that if there is some kind soul who can help, then I will NEVER ask for so much again !
I know that I'm going against regulations of this forum, but I don´t know where else to turn.
Two hours from now I will be picked by a ambulance because I´m going to have an operation in my heart.
Anyway I have these math problems here which have caused me some trouble. I have made a deal with a teaching assistant that he will picked my assignments up within the hour.
But I'm affried that if I don't finish them in time it will put to much strain on my heart.
Therefore I will be forever greatful if there is some kind soul who would be so kind and help solve what I have typed below.
(a)
(I use the triangle inequality in (1) and (3)?)
Let I be a open interval and f: I \rightarrow \mathbb{R}^n be a continious function.
Let || \cdot || be a given norm on \mathbb{R}^n.
Show the following:
1) If there exists a C>0 then ||x|| \leq C ||C||_1; x \in \mathbb{R}^n, ||x|| _1 = \sum _{j=1} ^n |x_j|
2) The mapping I \ni t \rightarrow ||f(t)|| \in \mathbb{R} is continious on.
3) for all t1,t2 \in \ || \int_{t_1} ^{t_2} f(t) dt|| \leq | \int_{t_1} ^{t_2} ||f(t)||dt|
(b)
Looking at the system(*) of equations,
x1' = (a-bx2)* x1
x2' = (cx1 -d)*x2
open the open Quadrant K; here a,b,c and d er positive constants.
I need to show that the system can be integrated. Which means I need to show that there exist a C^1 -function, with the properties F:U \rightarrow \mathbb{R}, where U \subseteq K is open and close in K(close means that for every point in K, is a limit point for q sequence, whos elements belongs to K). Such that gradient F \notequal 0 for alle x \in U and such that F is constant for trajectories of system.
Finally I need to conclude that every max trajectory is contained in a compact subset of K, and that the system (*) field X: R \rightarrow \mathbb{R}^2.
Sincerely Yours and God bless You all,
Maria Thomson 25
p.s. I promis that if there is some kind soul who can help, then I will NEVER ask for so much again !