# stable

1. ### Finding roots in marginally stable system modeled by complex number

A system can be modeled by (z + 3)(z + 2)(z + 1) + C = 0, where C > 0, and z = x + iy. When it is marginally stable Re(z) = 0. What are the values of the roots in marginally stable condition? At what values of C do they occur? Please give me help, as I don't know how to go about this question...
2. ### Understanding for a system why not asymptotically stable when $\epsilon = 0$ at the o

Consider the system $$x' = (\epsilon x+2y)(z+1)$$ $$y' = (-x+\epsilon y)(z+1)$$ $$z' = -z^3$$ Show that the origin is not asymptotically stable when $\epsilon = 0$. I am told if we start with z = 0, z remains at 0 and the system reduces to $$x' = 2y$$ $$y' = −x$$ (1). My question...
3. ### Why is outer product not backward stable?

So I am new to the topic of numerical analysis and was trying to figure out why the outer product of 2 vectors is not backwards stable. I understand the equation would be f(a,b) = ab* and that the resulting matrix is of rank 1. My book says that it is not backwards compatible simply because...
4. ### Stable Distribution in Queueing Model (but, it's really a binomial coef problem)

Hello, This is coming up in a solution of a detailed balance equation. I'm fine with the theory, I'm just missing something silly here: I have the detailed balance eqn: πjuj = λ(K-(j-1))πj-1 So this turns into something like: πj = (λ/u) * (K-j+1) / j * πj-1 And then: πj = \binom {K}{j}...
5. ### Stable region for Adams- Bashforth method

Dears, I want to plot the stability region of Adams- Bashforth method with 4th order, Thanks for all
6. ### why is my function so stable at multiples of 22?

hey everyone, in my never ending quest to find interesting maths based animations i created a trig function but dont understand it. the function is y = sin(x) where x = x+k*sin(x). k has a starting value of 20 and x starts at 180 (or PI). the function iterates once every frame. have a look...
7. ### Determining whether motion under a central force is stable

The question asks me to use the effective pontential to show that the motion in a circle of radius a under a central force \frac{b}{r^{2}}+\frac{c}{r^{4}} per unit mass (with b and c positive) is stable if a^{2}b < c. How would I go about doing this? What's the condition required for an orbit to...
8. ### Are pullbacks stable under left invertible maps (split monos)?

I know that pullbacks are stable under monomorphisms. I have a case where f: A -> B is not only a mono, but even a left invertible, i.e., there exists an l: B -> A with l \circ f = id_A. My question is whether pullbacks are also stable in this case, i.e., whether the corresponding projection in...
9. ### Tempered Stable Distributions - Computing R(dx)

Im trying to compute R(dx) from a paper by Jan Rosinski, which can be found here, (also here using slightly different notation). In the paper on page 3 we have the following theorem Theorem 2.3. The Levy measure M of a tempered alpha stable distribution can be written in the form M(A)...
10. ### Ordering resisters for the most stable circuit

i have to connect 50 resistors in a series circuit. each resistor has a different value of resistance. i must arrange them in a certain way so that my electrical circuit will be most stabile. although this seems to be an electronical issue, my problem is purely mathematical. the resistors have...
11. ### Stable Matching

Prove that if man x is paired with woman a in some stable matching, then a does not reject x in the proposal algorithm with men proposing. (Hint: Consider the first occurrence of such a rejection.) Conclude that among all stable matchings, every man is happiest in the matching produced by this...
12. ### Stable infinite union

Hello, Let G be the system of subsets A \subset \mathbb{R} such that A can be written as A = (a1 , b1 ] ∪ (a2 , b2 ] ∪ · · · ∪ (an , bn ] where -\infty\le a_1 \le b_1 \le ... \le a_n \le b_n \le \infty Why (if we consider A_1, ..., A_n \in G) \cup_{i\ge 0} A_i \notin G ? thanks
13. ### SOLVED Stable by but not Asymptotically Stable

Show that the equilibrium point x_0=0 for the differential equation x^{\prime}=0 is stable but not asymptotically stable.
14. ### Discrete Time Systems, stable solutions?

Not too sure if this question belongs in this part of the forum. Does the discrete time system: 5x_{n+1}-19x_n-22x_{n-1}+4x_{n-2}=0 have unstable time solutions? I've done this before with quadratics, but this looks a bit confusing.
15. ### Unconditionally stable scheme for solving first order system of PDEs

Hello, I would like to numerically solve the following system of PDEs using a stable computational scheme. The system involves three equations and three unknowns (q_x, q_y, and p). I've tried to solve this system using an explicit scheme, but I found that the solution could become unstable...
16. ### Equilibrium stable or unstable - differential euqation

So this is actually a physics problem but im having problem with the math again. My function is: y'' + y*sin(a)*k^2 = 0 , where a and k are constants. from this I get the following solution; y = y(max)*cos(w*t + a) where w = sin(a)*k. This far I understand everything. However after...
17. ### What is the range of (real) values of r for which the filter is stable?

hi i am totally new to this forum and i am in desperate need of serious help with this question What is the range of (real) values of r for which the filter is stable? (1-r)^2 + (r^2 - 1)z^-2 --------------------------------------… 1 - 2r cos (WcT) z^-1 + r^2 z^-2 p.s. r^2 means...
18. ### stable fixed point

The map X(n+1) = [X(n)]^3 + a*Xn has a fixed point at the origin. For what values of a is this fixed point stable? So stable meaning is will always gradually be along the line of 0? So would a have to be -[X(n)]^2 ?
19. ### alpha stable

Suppose \alpha: X \times X \to X . A subset A \subseteq X is called \alpha -stable if and only if x,y \in A \Rightarrow \alpha(x,y) \in A . What is the point of considering \psi_{\alpha}(\psi_{\alpha}(A)) = \psi_{\alpha}(A) ? Is there any significance?
20. ### Stable, but not asymptotically stable

Hi everyone. My task from difference equations is: Lets suppose we have a nonlinear dynamic system x(t+1) = f(x(t)) , the status space X from R (real) and a fixed point xHAT. Find a function f from C1 and a set X from R (real) , so that f ' (xHAT) = 1 and xHAT is stable, but NOT ASYMPTOTICALLY...