Large time behavior of solutions to a degenerate parabolic equation not in divergence form

In this paper, we investigate positive solutions of the degenerate parabolic equation not in divergence form: ut=upΔu+auq−bur, subject to the null Dirichlet boundary condition. We at first discuss the existence and nonexistence of global solutions to the problem, and then study the large time behavior for the global solutions. When the positive source dominates the model, we prove that the global solutions uniformly tend to the positive steady state of the problem as t→∞. In particular, we establish the uniform asymptotic profiles for the decay solutions when the problem is governed by the nonlinear diffusion or absorption.     

有向网络下多个体系统的整体行为

研究非时变有向通讯网络背景下一阶线性多个体动力学系统的整体行为.根据通讯网络的结构,系统可以区分为独立基本子系统和非独立基本子系统.当系统的控制规则为一类平凡的线性类型时,系统的独立基本子系统将趋于自身的一致状态,也即子系统中的每个个体趋于子系统的带权中心.独立基本子系统带权中心由子系统的系数矩阵的零特征根归一化左特征向量确定.非独立子系统中个体将趋于独立基本子系统带权中心的凸集内.当且仅当系统的独立基本子系统唯一时,系统实现一致性行为.     

kth Order convergence for a semilinear elliptic boundary value problem in the divergence form

The convergence problem of approximate solutions for a semilinear elliptic boundary value problem in the divergence form is studied. By employing the method of quasilinearization, a sequence of approximate solutions converging with the kth (k ? 2) order convergence to a weak solution for a semilinear elliptic problem is obtained via the variational approach.     

The critical group of <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> × <Emphasis Type="Italic">C</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

In this paper, the structure of the critical group of the graph K _m × C _n is determined, where m, n ≥ 3.     

具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.     

水泥聚苯模壳格构式混凝土墙体的抗侧性能试验及分析

论文介绍6片不同高宽比的水泥聚苯模壳格构式混凝土墙体在轴压力和水平往复侧推力作用下的试验,分析这种墙体的抗侧强度、刚度和延性等力学性能.试验表明,高宽比大于1的墙体破坏时表现为墙体跟部的单一水平裂缝,其他部位完好;高宽比3∶4的墙体破坏时存在多条通过格构梁柱的斜向裂缝,墙体裂缝分布密集,变形能力好.     

初中化学教科书表格呈现方式及其教学功能价值的研究

以现行4个版本的义务教育化学教科书为研究对象,根据教科书中表格功能的不同,将其分为实验记录型表格、归纳总结型表格、习题型表格、资料卡片型表格等4类,对4类不同表格的教学功能价值进行了分析说明。并以沪教版为例,对当前初中化学教师使用教科书表格进行教学的情况进行了抽样调查与分析,由此提出3点教学建议。     

光杠杆实验中尺读望远镜视场部分不清晰的成因和改善

对光杠杆实验中经常见到的尺读望远镜视场部分不清晰的成因作了深入的分析和实验验证,证明是因为背景光进入尺读望远镜,降低了直尺在尺读望远镜中的像的对比度所致,提出慢慢将物镜向像不清晰那个方向调整就能改善.     

Cocyclic Hadamard matrices from forms over finite Frobenius rings

We give a construction of cocyclic Butson-Hadamard matrices from bilinear forms over finite Frobenius rings, which generalizes previous constructions. We then prove a classification result, showing that the resulting matrices depend only on the additive group of the underlying module of the form.     

Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.