Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions

In this work, we study the Neumann initial boundary value problem for a three-component chemotaxis model in any dimensional bounded and smooth domains; this model is used to describe the branching of capillary sprouts during angiogenesis. First, we find three qualitatively simple sufficient conditions for qualitative global boundedness, and then, we establish two types of global stability for bounded solutions in qualitative ways. As a consequence of our findings, the underlying system without chemotaxis and the effect of ECs mitosis can not give rise to pattern formations. Our findings quantify and extend significantly previous studies, which are set in lower dimensional convex domains and are with no qualitative information.Comment: 43 pages, under review in a journa

Targeting Acid-Sensing Ion Channels by Peptide Toxins

Acid-sensing ion channels (ASICs) are proton-gated ion channels that are highly expressed in the nervous system and play important roles in physiological and pathological conditions. They are also expressed in non-neuronal tissues with different functions. The ASICs rapidly respond to a reduction in extracellular pH with an inward current that is quickly inactivated despite the continuous presence of protons. Recently, protons have been identified as neurotransmitters in the brain. Until now, six different isoforms (ASIC1a, 1b, 2a, 2b, 3 and 4) in rodents have been discovered and they can be assembled into homotrimers or heterotrimers to form an ion channel. Peptide toxins targeting ASICs have been found from the venoms of spider Psalmotoxin-1 (PcTx1), sea anemones (APETx2 and PhcrTx1) and snakes (MitTx and mambalgins). They reveal different pharmacological properties and are selective blockers of ASICs, except for MitTx, which is a potent activator of ASICs. In this mini review, the structure, pharmacology and effects of peptide toxins on ASICs will be introduced and their therapeutic potentials for neurological and psychological diseases will be discussed

A study of China's overseas investment

A study of China's overseas investment Induction Chapter 1. The concept of overseas investment and the relevant theories 1.1 What is an overseas investment 1.2 Reviews of international theories of overseas investment 1.2.1 Traditional theories of overseas investment 　　 1.2.2 New theories of multinationals 1.3 Advantages of overseas investment 1.4 The disadvantages of overseas investment Chapter 2. China’s overseas investment 2.1 China’s financial system 2.2 Advantages of China’s overseas investment 2.3 Characteristics of China’s overseas investment Chapter 3. The development of China’s overseas overseas mergers and acquisitions 3.1 Analyses of the situation 3.2 Risk analysis of the Chinese enterprises’ overseas mergers and acquisitions 3.3 Improvements of China’s enterprises overseas M & A performance 3.4 Performance analyses of China’s enterprises overseas M & A 3.4.1 A brief introduction to research methods of enterprises M & A performance 3.4.2 Designing of the research methods 3.4.3 Evaluation of sample score 3.4.4 research conclusion Chapter 4. Case analyses of successful overseas investment — TCL’s investment in Vietnam 4.1 Introduction to TCL and the economic and trade development between China and Vietnam 4.2 The diverse aspects of Chinese investment in Vietnam 4.3 General profile of the Vietnamese market 4.4 The conditions of success for TCL’s overseas investment in Vietnam 4.4.1 The long history between China and Vietnam provides the basic conditions for the development of TCL 4.4.2 TCL positions its development as the internationalized operation 4.4.3 The successful strategies of self-owned brands 4.5 How to improve China’s overseas investment? Conclusion Acknowledgement references Appendi

Pressure Effects in Supercooled Water: Comparison between a 2D Model of Water and Experiments for Surface Water on a Protein

Experiments in bulk water confirm the existence of two local arrangements of water molecules with different densities, but, because of inevitable freezing at low temperature $T$, can not ascertain whether the two arrangements separate in two phases. To avoid the freezing, new experiments measure the dynamics of water at low $T$ on the surface of proteins, finding a crossover from a non-Arrhenius regime at high $T$ to a regime that is approximately Arrhenius at low $T$. Motivated by these experiments, Kumar et al. [Phys. Rev. Lett. 100, 105701 (2008)] investigated, by Monte Carlo simulations and mean field calculations, the relation of the dynamic crossover with the coexistence of two liquid phases in a cell model for water and predict that: (i) the dynamic crossover is isochronic, i.e. the value of the crossover time $\tau_{\rm L}$ is approximately independent of pressure $P$; (ii) the Arrhenius activation energy $E_{\rm A}(P)$ of the low-$T$ regime decreases upon increasing $P$; (iii) the temperature $T^*(P)$ at which $\tau$ reaches a fixed macroscopic time $\tau^*\geq \tau_{\rm L}$ decreases upon increasing $P$; in particular, this is true also for the crossover temperature $T_{\rm L}(P)$ at which $\tau=\tau_{\rm L}$. Here, we compare these predictions with recent quasi elastic neutron scattering (QENS) experiments performed by X.-Q. Chu {\it et al.} on hydrated proteins at different values of $P$. We find that the experiments are consistent with these three predictions.Comment: 18 pages, 5 figures, to appear on J. Phys.: Cond. Ma

Fourth-order modified method for the Cauchy problem for the Laplace equation

AbstractWe consider the Cauchy problem for the Laplace equation in the half plane x>0,y∈R where the Cauchy data is given at x=0 and the solution is sought in the interval 0<x⩽1. The problem is ill-posed: the solution (if it exists) does not depend continuously on the data. In order to solve the problem numerically, it is necessary to modify the equation so that a bound on the solution is imposed. We study a modification of the equation, where a fourth-order mixed derivative term is added. Error estimates for this equation are given, which show that the solution of the modified equation is an approximation of the solution of the Cauchy problem for the Laplace equation, and it is shown that when the data error tends to zero, the error in the approximate solution tends to zero logarithmically. Numerical implementation is considered and a simple example is given

Fourier regularization for a backward heat equation

AbstractIn this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively