3,334 research outputs found

    Analysis of a mathematical model for the growth of cancer cells

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    In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or cell dead. The growth process is caused by a diffusing nutrient concentration σ\sigma and is controlled by an internal cell pressure pp. We assume that the tumor occupies a strip-like domain with a fixed boundary at y=0y=0 and a free boundary y=ρ(x)y=\rho(x), where ρ\rho is a 2π2\pi-periodic function. First, we prove the existence of solutions (σ,p,ρ)(\sigma,p,\rho) and that the model allows for peculiar stationary solutions. As a main result we establish that these equilibrium points are locally asymptotically stable under small perturbations.Comment: 15 pages, 2 figure

    Fertility intentions in a cross-cultural view: the value of children reconsidered

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    This paper seeks to explain the differences in fertility intentions between Turkey and Japan, based on a theoretical modification of the social-psychological concept of the ‘Value of Children’. We assume that the ‘Value of Children’ consists of their support for their parents in order to achieve general human goals. We investigate the causal structure between individual socio-economic characteristics and the ‘Value of Children’ and fertility intentions. We use data from the original “Value of Children Studies”, including women in their reproductive age, with children born in wedlock. Based on confirmatory factor analyses and structural equation models, we find that in both countries fertility intentions are related to the instrumentality of children to their parents as well as to socio-economic characteristics and institutionally defined opportunities. The ‘Value of Children’ is in part determined by socio-economic independent variables; however, we also observe direct effects that can not be reduced to the instrumentality of children. Therefore, the endogenization of the effects of the ‘Value of Children’ on fertility intentions is limited

    Spectral Properties of Grain Boundaries at Small Angles of Rotation

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    We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential V ⁣:R2→RV \colon \R^2 \to \R, we let Vθ(x,y)=V(x,y)V_\theta(x,y) = V(x,y) in the right half-plane {x≥0}\{x \ge 0\} and Vθ=V∘M−θV_\theta = V \circ M_{-\theta} in the left half-plane {x<0}\{x < 0\}, where Mθ∈R2×2M_\theta \in \R^{2 \times 2} is the usual matrix describing rotation of the coordinates in R2\R^2 by an angle θ\theta. As a main result, it is shown that spectral gaps of the periodic Schr\"odinger operator H0=−Δ+VH_0 = -\Delta + V fill with spectrum of Rθ=−Δ+VθR_\theta = -\Delta + V_\theta as 0≠θ→00 \ne \theta \to 0. Moreover, we obtain upper and lower bounds for a quantity pertaining to an integrated density of states measure for the surface states.Comment: 22 pages, 3 figure
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