A smooth vector field on the phase plane is known to have exactly two closed trajectories, one of which lies inside the other. The inner cycle runs clockwise, and the outer cycle runs counterclockwise. True or False: There must be at least one fixed point in the region between the cycles. If true, prove it. If false, provide a simple counterexample.

Read the excerpt from the strange case of dr jekyll and mr. hyde what do dr. jekyll's thoughts reveal about him in this excerpt? [t]he inmates of my house were locked in the most rigorous hours of slumber, and i determined, flushed as i was with hope and triumph, to venture in my new shape as far as to my bedroom. i crossed the yard, wherein the constellations looked down upon me, i could have thought, with wonder, the first creature of that sort that their unsleeping vigilance had yet disclosed to he is jealous of those who can sleep through the night. he is revered for his scientific advances. he is interested in studying the movements of the stars he is proud and enthusiastic about his initial results.