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...

one of the important discussions in the science of principles of jurisprudence is generalization and restriction. implication of generality from proper nouns and sentences is through premises of wisdom. there are different viewpoints about generic nouns in terms of conventionality of their reference to generality or their being based . on premises of wisdom, like proper nouns and sentences. pre...

We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external differences that occur, and were first defined in the context of classifying optimal strong algebraic manipulation detection codes. We establish new necessary conditions for the existence of (n,m, k, λ)-SEDFs; in particular giving a near-co...

conclusions our results validate that telephonic confirmation of clinic appointment plays a significant role in reducing the nar in paediatric out-patient clinic setting. patients and methods nar was reviewed for 6 months (february-july 2013) and compared with the nar for similar duration in 2014 (before and after implementation of telephone reminders). within 2014 data, comparison was also mad...

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