3,334 research outputs found
Analysis of a mathematical model for the growth of cancer cells
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 and is controlled by an internal cell pressure . We
assume that the tumor occupies a strip-like domain with a fixed boundary at
and a free boundary , where is a -periodic
function. First, we prove the existence of solutions 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
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 âValue of Childrenâ. We assume that the âValue of Childrenâ 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 âValue of Childrenâ and fertility intentions. We use data from the original âValue of Children Studiesâ, 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 âValue of Childrenâ 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 âValue of Childrenâ on fertility intentions is limited
Spectral Properties of Grain Boundaries at Small Angles of Rotation
We study some spectral properties of a simple two-dimensional model for small
angle defects in crystals and alloys. Starting from a periodic potential , we let in the right half-plane
and in the left half-plane , where is the usual matrix describing
rotation of the coordinates in by an angle . As a main result,
it is shown that spectral gaps of the periodic Schr\"odinger operator fill with spectrum of as . 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
- âŚ