Blowup of solutions to a two-chemical substances chemotaxis system in the critical dimension

This paper deals with positive solutions of the fully parabolic system

$\{\begin{array}{cc}{u}_t=\mathrm{\Delta }u?\chi \mathrm{?}?(u\mathrm{?}v)\hfill & \mathrm{in}\mathrm{\Omega }\times (0,\infty ),\hfill \\ {\tau }_1{v}_t=\mathrm{\Delta }v?v+w\hfill & \mathrm{in}\mathrm{\Omega }\times (0,\infty ),\hfill \\ {\tau }_2{w}_t=\mathrm{\Delta }w?w+u\hfill & \mathrm{in}\mathrm{\Omega }\times (0,\infty )\hfill \end{array}$

under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain $\mathrm{\Omega }?{\mathbb{R}}^4$ with positive parameters ${\tau }_1,{\tau }_2,\chi >0$ and nonnegative smooth initial data $(u_0,v_0,w_0)$.Global existence and boundedness of solutions were shown if ${6u_{0}6}_{L^1(\mathrm{\Omega })}<{(8\pi )}^2/\chi$ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ${6u_{0}6}_{L^1(\mathrm{\Omega })}>{(8\pi )}^2/\chi$. This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has $8\pi /\chi$-dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in ${\mathbb{R}}^4$.     

The Gerber-Shiu penalty functions for two classes of renewal risk processes

In this paper, we study the Gerber-Shiu functions for a risk model with two independent classes of risks. We suppose that both of the two claim number processes are renewal processes with phase-type inter-claim times. By re-composing and analyzing the Markov chains associated with two given phase-type distributions, we obtain systems of integro-differential equations for two types of Gerber-Shiu functions. Explicit expressions for the Laplace transforms of the two types of Gerber-Shiu functions are established, respectively. And explicit results for the Gerber-Shiu functions are derived when the initial surplus is zero and when the two claim amount distributions are both from the rational family. Finally, an example is considered to illustrate the applicability of our main results.     

Rational torus-equivariant stable homotopy I: Calculating groups of stable maps

We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and show that it is of finite injective dimension. It can be used as a model for rational G-spectra in the sense that there is a homology theory

     

冷却速率对AZ91D镁合金半固态组织制备的影响

：研究了不同冷却速率(金属型、湿砂型和干砂型)对AZ91D镁合金半固态组织制备的影响．结果表明：增加冷却速率有利于初始凝固组织中存在的非平衡组织的分散细化．原始组织中的非平衡共晶组织在加热过程中大部分扩散溶解而溶入基体中,剩余部分在加热过程中首先熔化．冷却速率越大的试样在熔化过程中更容易发生二次枝晶臂之间的合并．提出了半固态熔化过程可分为成分均匀化、共晶熔化和部分初生相的熔化和球化三个阶段,不同熔化阶段时,控制性因素不同．熔化后的半固态组织中固态颗粒的尺寸和形貌主要与初始组织的形貌、加热过程中非平衡组织的溶解速度及加热速度有关。     

半固态AZ91D镁合金触变压铸充型过程的数值模拟

以半固态AZ91D镁合金浆料的流变性能的实验研究为基础,通过曲线拟合的方法建立半固态AZ91D镁合金的表观粘度的触变模型.根据此触变模型开发了半固态AZ91D镁合金触变压铸充型过程中的表观粘度计算程序,并嵌入在Castsoft软件中,实现了半固态AZ91D镁合金触变压铸过程的流场和温度场的模拟计算.模拟结果表明:充填速度和浆料温度对半固态AZ91D镁合金浆料的充填过程有显著影响, 最佳充填速度的范围为2～5m·s-1,半固态浆料的最佳温度范围为570～580℃.     

基于AT91RM9200的U-Boot的移植

主要介绍U-Boot在基于AT91RM9200硬件平台上移植.简略地分析了U-Boot的代码特点和启动机理后,对U-Boot在AT91RM9200目标板上移植的方法和过程作了详细的介绍,并验证其在目标板上运行的可靠性.     

P91钢中厚壁管焊接残余应力分析

针对管道试件规格不同所要求的焊接工艺不一致问题,讨论P91钢中厚壁管对接接头所要求的双人对称焊形式下的焊接残余应力分布规律．基于ANSYS分析软件,以双移动高斯热源结合单元生死技术,利用顺序耦合方法得到P91钢中厚壁管焊接残余应力．讨论热处理工艺对于P91钢中厚壁管焊接残余应力的影响．结果表明,由于焊接工艺在环向位置上的结构反对称性使得焊接残余应力在环向上呈反对称分布;即便经过较高温度的预热处理,没有焊后热处理时最大等效应力仍超过屈服极限;进行焊后整体热处理的P91钢中厚壁管焊接残余应力得到了有效的改善,平均应力数值下降了60%~70%．     

Abnormal Blood Glucose Concentration on Degradation Behavior of AZ31 Magnesium Alloy

In order to evaluate the effect of blood glucose concentration on the reliability of AZ31 magnesium alloy medical implant, the corrosion of AZ31 alloy was studied in a simulated physiological saline solution. It is found that when the glucose concentration is in the normal range of ca. 1 g/L, the corrosion of AZ31 alloy can be inhibited. However, when the glucose concentration becomes higher like that of diabetic patients, the degradation of AZ31 alloy is significantly accelerated. Therefore, for diabetic patients, the change in glucose concentration must be taken into consideration in order to ensure the reliability of AZ31 medical implants.     

基于AT91RM9200的点阵图形液晶模块接口设计

详细介绍了点阵图形液晶模块FYD12864-0402B的原理和AT91 RM9200的特性,具体阐述了FYD12864-0402B与AT91RM9200的硬件接口和驱动程序的设计,该接口结构简单,性能稳定,达到了设计要求,取得了良好的显示效果.