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<P>We study the positive solutions to boundary value problems of the form -Δu=λf(u); Ω, α(x,u)(∂u/∂η)+[1-α(x,u)]u=0; ∂Ω, where Ω is a bounded domain in ℝn with n≥1, Δ is the Laplace operator, λ is a positive parameter, f:[0,∞)→(0,∞) is a continuous function which is sublinear at ∞, ∂u/∂η is the outward normal derivative, and α(x,u):Ω×ℝ→[0,1] is a smooth function nondecreasing in u. In particular, we discuss the existence of at least two positive radial solutions for λ≫1 when Ω is an annulus in ℝn. Further, we discuss the existence of a double S-shaped bifurcation curve when n=1, Ω=(0,1), and f(s)=eβs/(β+s) with β≫1.</P>
We analyze the solutions of a population model with diffusion and logistic growth. In particular, we focus our study on a population living in a patch, Ω@?R<SUP>n</SUP> with n>=1, that satisfies a certain non-linear boundary condition and on its survival when constant yield harvesting is introduced. We establish our existence results by the method of sub-super solutions.
This lecture has four Parts. Part 1 briefly discusses ‘Critical communication issues in the pandemic era’, focussing on the need to use clear, simple language that everyone can understand. Part 2 explains what “minimal languages” are and how they have emerged from empirical research in linguistics. Part 3 presents and discusses examples of how to write about aspects of COVID-19 using minimal language. Part 4 addresses the implications for education and public policy.
An in vitro cell study evaluating cell adhesion to hydroxyapatite (HA) coated prosthetic Ti-6Al-4V alloy via laser treatment is presented in comparison with uncoated alloy. Based on our previous in vitro biocompatibility study, which demonstrated higher cell attachment and proliferation with MC3T3-E1 preosteoblast cells, the present investigation aims to reveal the effect of laser coating Ti alloy with HA on the adhesion strength of bone-forming cells against centrifugal forces. Remaining cells on different substrates after centrifugation were visualized using fluorescent staining. Semi-quantifications on the numbers of cells were conducted based on fluorescent images, which demonstrated higher numbers of cells retained on HA laser treated substrates post centrifugation. The results indicate potential increase in the normalized maximum force required to displace cells from HA coated surfaces versus uncoated control surface. The possible mechanisms that govern the enhancing effect were discussed, including surface roughness, chemistry, wettability, and protein adsorption. The improvement in cell adhesion through laser treatment with a biomimetic coating could be useful in reducing tissue damage at the prosthetic to bone junction and minimizing the loosening of prosthetics over time.
This study explores the ability of non-destructive assay techniques to detect a partial material defect in which 100 g of plutonium are diverted from the center of a 1000 g can of PuO2 powder. Four safeguards measurements techniques: neutron multiplicity counting, calorimetry, gravimetry, and gamma ray spectroscopyare used in an attempt to detect the defect. Several materials are added tothe partial defect PuO2 can to replicate signatures of the diverted material. 252Cf is used to compensate for the doubles neutron counts, 241Am is used to compensate for the decay heat, and aluminum is used to compensate for the weight. Although, the doubles and triples difference before and after diversion are statistically indistinguishable with the AWCC in fast and thermal mode, the difference in the singles counts are statistically detectable in both modes. The relatively short half-life of 252Cf leads to a decrease (three sigma uncertainty) in the doubles neutron counts after 161 days. Combining this with the precise quantity of 241Am needed (10.7 g) to mimic the heat signature and the extreme precision in 252Cf mass needed to defeat neutron multiplicity measurements gives reassurance in the International Atomic Energy Agency's ability to detect partial material defects.