Broken Glass by Arthur Miller

By Arthur Miller

Set in Brooklyn, this gripping secret starts while appealing, level-headed Sylvia Gellburg without notice loses her skill to stroll. the one clue to her mysterious sickness lies in her obsession with information money owed from Germany.

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When t2 − 4d > 0, the matrix A has two real eigenvalues with the same sign, λ1 > λ2 . Therefore if t < 0, then E s = R2 and E u = E c = {0}; and if t > 0, then E u = R2 and E s = E c = {0}. 7, depending on t. The corresponding phase portrait of the system x˙ = Ax is obtained by a linear transformation. The origin is called an asymptotically stable node if t < 0, and an asymptotically unstable node if t > 0. When t2 − 4d = 0, there exists a unique eigenvalue λ, which is real, and the real Jordan normal form of A is λ 0 λ 1 J= or J = .

Therefore, Φ(s, x) = P −1 Ψ(s, P x). 8) From this we obtain the expressions of the flow of any planar linear system. 6. Consider the flow Φ(t, x) of the linear system x˙ = Ax, with A ∈ L(R2 ), d = det(A) and t = trace(A). Let J be the real Jordan normal form of A and P be the matrix such that J = P AP −1 . (a) If t2 − 4d > 0, then esλ1 0 Φ (s, x) = P −1 0 esλ2 P x. (b) If t2 − 4d = 0, then either Φ (s, x) = esλ x or Φ (s, x) = P −1 esλ 0 s esλ P x, depending on whether J is diagonal or not. (c) If t2 − 4d < 0, then Φ (s, x) = esα P −1 cos (βs) − sin (βs) sin (βs) cos (βs) P x.

We see that the origin, which is a focus type singular point, is a global attractor. Also, two separatrices born at the two saddles at infinity are observed. The remaining singular points at infinity are two nodes. 326 KΩ one has T = 0. 6(h). Now the global attractor, namely, the singular point at the origin, is replaced by a central region foliated by periodic orbits (bounded period annulus). The remainder of the phase portrait persists without changes. 326 KΩ we have that T > 0. 9(g). As it can be observed, the period annulus disappears and only one periodic solution persists.

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