Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms

In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the existing studies focusing on the case of non-degenerate diffusion, the new model with degenerate diffusion causes us some essential difficulty on the boundedness estimates and the propagation behavior of its compact support. In the presence of logistic damping, for the early stage before tumour cells spread to the whole body, we first estimate the expanding speed of tumour region as $O(t^{\beta})$ for $0<\beta<\frac{1}{2}$. Then, for the late stage of cell migration, we further prove that the asymptotic profile of the original system is just its corresponding steady state. The global convergence of the original weak solution to the steady state with exponential rate $O(e^{-ct})$ for some $c>0$ is also obtained

Medical condition, population density, and residents’ savings in China’s contiguous destitute areas

This paper uses the 2005–2012 spatial panel data of China’s 11 Contiguous Destitute Areas (CDAs) and different kinds of econometric regression models, we examines the implications of medical condition and population density for the residents’ savings in these 11 CDAs. We find that, the increase in population density not only would reduce residents’ savings through its own, but also has negative effect on residents’ savings through the way of medical condition, while medical condition has positively and significantly effect on the residents’ savings. This means that as a CDAs’ population density increases, the needs of medical condition will increase too, and then it will cause the medical condition to be deteriorating relatively, thereby reducing households’ precautionary savings. In most of the models, especially in the direct effects, indirect effects, and total effects, these results are roughly the same and robust. These findings mean that medical condition and population density not only have influence on residents’ savings on their own, but also will decrease the residents’ savings by their interactio

Developmental differences in the structure of executive function in middle childhood and adolescence

Although it has been argued that the structure of executive function (EF) may change developmentally, there is little empirical research to examine this view in middle childhood and adolescence. The main objective of this study was to examine developmental changes in the component structure of EF in a large sample (N = 457) of 7–15 year olds. Participants completed batteries of tasks that measured three components of EF: updating working memory (UWM), inhibition, and shifting. Confirmatory factor analysis (CFA) was used to test five alternative models in 7–9 year olds, 10–12 year olds, and 13–15 year olds. The results of CFA showed that a single-factor EF model best explained EF performance in 7–9-year-old and 10–12-year-old groups, namely unitary EF, though this single factor explained different amounts of variance at these two ages. In contrast, a three-factor model that included UWM, inhibition, and shifting best accounted for the data from 13–15 year olds, namely diverse EF. In sum, during middle childhood, putative measures of UWM, inhibition, and shifting may rely on similar underlying cognitive processes. Importantly, our findings suggest that developmental dissociations in these three EF components do not emerge until children transition into adolescence. These findings provided empirical evidence for the development of EF structure which progressed from unity to diversity during middle childhood and adolescence

A new characterization of fuzzy ideals of semigroups and its applications

In this paper, we develop a new technique for constructing fuzzy ideals of a semigroup. By using generalized Green\u27s relations, fuzzy star ideals are constructed. It is shown that the new fuzzy ideal of a semigroup can be used to investigate the relationship between fuzzy sets and abundance and regularity for an arbitrary semigroup. Appropriate examples of such fuzzy ideals are given in order to illustrate the technique. Finally, we explain when a semigroup satisfies conditions of regularity