This article introduces a new concept, ‘frontiers of existence’, to highlight and demand more attention be placed on the lives human other-than-human beings whose possibilities exist are extinguished or radically negatively transformed at resource commodity frontiers this. What happens existences these places has not been central focus in prior studies utilizing political economy, ecology, othe...

We provide a new class of counter-examples to existence in a simple moral hazard problem in which the first-order approach is valid. In contrast to the Mirrlees example, unbounded likelihood ratios on the signal technology are not central. Rather, our examples center around the behavior of the utility function as utility diverges to negative infinity. For any utility function, such as ln(w), in...

We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized...

In a series of papers, D. Gordon and C. Pomerance demonstrated that pseudoprimes on elliptic curves behave in many ways very similar to pseudoprimes related to Lucas sequences. In this paper we give an answer to a challenge that was posted by D. Gordon in 1989. The challenge was to either prove that a certain composite N ≡ 1 mod 4 did not exist, or to explicitly calculate such a number. In this...

We study the existence of positive solutions for a system of two elliptic equations of the form  −∆u = a1(x)F1 (x, u, v) in Ω −∆v = a2(x)F2 (x, u, v) in Ω u = v = 0 on ∂Ω where Ω ⊂ RN (N ≥ 2) is a bounded domain in RN with a smooth boundary ∂Ω or Ω = RN (N ≥ 3). A non-existence result is obtained for radially symmetric solutions. Our proofs are based primarily on the sub and super-solution met...