Solutions to Take-Home Part of Math 317 Exam #1

Cytokine responses andmath performance: The role of stereotype threat and anxiety reappraisals

• Female college students take a math exam described as gender-fair or gender-biased. • In one condition, participants directed to reappraise physiological arousal. • Performance on math exam and post-exam levels of the cytokine IL-6 were measured. • Reappraisal of physiological arousal buffers inflammatory responses to exam across conditions. • Reappraisal of arousal especially effective buffe...

Improving the security of quantum exam against cheating

The security of quantum exam [Phys. Lett. A 350 (2006) 174] is analyzed and it is found that this protocol is secure for any eavesdropper except for the “students” who take part in the exam. Specifically, any student can steal other examinees’ solutions and then cheat in the exam. Furthermore, a possible improvement of this protocol is presented.

MATH 127 Solutions to Final Exam

Existence and Nonexistence of Global Positive Solutions to Nonlinear Diffusion Problems with Nonlinear Absorption through the Boundary

This paper deals with the existence and nonexistence of global positive solutions to ut = ∆ ln(1 + u) in Ω× (0,+∞), ∂ ln(1 + u) ∂n = √ 1 + u(ln(1 + u)) on ∂Ω× (0,+∞), and u(x, 0) = u0(x) in Ω. Here α ≥ 0 is a parameter, Ω ⊂ RN is a bounded smooth domain. After pointing out the mistakes in Global behavior of positive solutions to nonlinear diffusion problems with nonlinear absorption through the...

Math 317 HW #5 Solutions

Proof. I intend to use the Monotone Convergence Theorem, so my goal is to show that (xn) is decreasing and bounded. To do so, I will prove by induction that, for any n ∈ {1, 2, 3, . . .}, 0 < xn+1 < xn < 4. Base Case When n = 1, we have that x1 = 3 and x2 = 1 4−3 = 1, so 0 < x2 < x1. Inductive Step Suppose 0 < xk+1 < xk < 4; our goal is to show that this implies that 0 < xk+2 < xk+1 < 4. Since ...