Passage to the limit in a chain of the muskat problems(II)

This paper is the continuation of the paper: “Passage to the limit in a chain of the Muskat problems(I)”. In spherically symmetric case one prove that for some class of initial data, generated by a chain of the Muskat problems, the solutions of smooth approximate problems converge to a weak solution of the Muskat problem. This weak solution can be regarded as interpretation of so-called finger phenomenon.     

初中生化学学科能力性别差异研究*

基于化学学科能力建构的基本框架,研究初中学生化学学科能力的分化水平和性别差异之间的关系。通过设计“初中化学学科能力”专项测试题,对132名男生、108名女生进行纸笔测试,并用SAS.9.4软件对测试结果进行量化处理,发现初中生的化学学科能力存在不同程度的分化现象,男生和女生在化学学科能力上存在性别差异,尤其在模型思维能力、定量化能力上男生比女生均有明显的优势。     

基于Lab view声卡音频演示拍现象

介绍了利用Lab view演示声波拍现象方法,设计基于声卡的Lab view双通道信号发生器产生两个频率接近的音频信号,分左右声道驱动两个喇叭,相当于两个振源,即形成拍音,并利用信号发生器测量拍频。     

硫脲甲醛聚合反应中的半结晶沉淀现象

首次报道了硫脲甲醛聚合反应中的半结晶沉淀现象.定量分析结果显示硫脲甲醛之间的聚合反应接近一种线性交替共聚反应过程.红外光谱的结果证明不同硫脲甲醛物质的量比反应条件下产物中始终存在较强的N—H特征振动吸收峰(v=3311cm-1,δ=1541cm-1).当甲醛用量较高和硫脲用量增加时分别在1008和1137cm-1处检测到较强的C—O—C和C=S伸缩振动吸收峰.结合XRD和核磁共振分析结果推测:硫脲甲醛聚合产物中存在着一种氢键导向型结晶结构;分子中含有醚键的聚合产物因具有复杂的氢键作用没有结晶性.扫描电镜分析显示较高硫脲用量反应条件下生成了层状半结晶碎片产物,而高甲醛比例条件得到的产物为细小的层状碎片交联聚集成的球形粒子.     

Monte Carlo study of the critical behavior and magnetic properties of La2/3Ca1/3MnO3 thin films

Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La_2/3Ca_1/3MnO₃ thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La_2/3Ca_1/3MnO₃ thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn³⁺-Mn³⁺(e_g-e_g′), Mn³⁺-Mn⁴⁺(e_g-d³) and Mn³⁺-Mn⁴⁺(e_g′-d³) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56±0.01, α=0.16±0.03, β=0.34±0.04γ and γ=1.17±0.05. These theoretical results are consistent with the Rushbrooke equalitiy α+2β+γ=2.     

The critical phenomenon and the re-entrance phenomenon in the anti-tumor model induced by the time delay

The effects of time delay τ on an anti-tumor model driven by a multiplicative noise and a periodic signal are investigated. The results obtained from the small delay approximation and numerical simulations indicate: (i) For the absence of the periodic signal in the system, the two-peak structure of the stationary probability distribution transforms into the single-peak structure with the increasing τ, and τ exists a critical value τc. For τ<τc, the stationary mean value 〈x〉_st of the cell population decreases as the noise intensity D increases, however, for τ>τc, the 〈x〉_st increases as the D increases; (ii) For the presence of the periodic signal in the system, the structure of the signal-to-noise ratio with changes of the D exhibits the transitions of one peak → two peaks → one peak as τ increases.     

Effects of friend-making resources/costs and remembering on acquaintance networks

We consider two overlooked yet important factors that affect acquaintance network evolution and formation—friend-making resources and remembering—and propose a bottom-up, network-oriented simulation model based on three rules representing human social interactions. Our proposed model reproduces many topological features of real-world acquaintance networks, including a small-world phenomenon and a sharply peaked connectivity distribution feature that mixes power-law and exponential distribution types. We believe that this is an improvement over fieldwork sampling methods that fail to capture acquaintance network node connectivity distributions. Our model may produce valuable results for sociologists working with social opinion formation and epidemiologists studying epidemic dynamics.     

On global solutions of the radial p-Laplace equation

We obtain blow-up conditions for solutions of the radial p$p$-Laplace equation.     

Generalized Hardy identity and relations to Gibbs-Wilbraham and Pinsky phenomena

We consider the Fourier series of the indicator functions of several dimensional balls. For the spherical partial sum of the Fourier series, we extract the Gibbs-Wilbraham (or Gibbs), Pinsky and the third phenomena as an extension of Hardy's identity. The third phenomenon has been shown by Kuratsubo recently. We prove the Gibbs-Wilbraham phenomenon for all dimensions and give another proof of the Pinsky phenomenon. Pinsky gave the order of the divergence for the Fourier inversion at the origin. We give the order of the divergence of the Fourier series at the origin and show that both orders coincide. We also investigate the uniform convergence for the Fourier series and the Fourier inversion.     

Friezes

The construction of friezes is motivated by the theory of cluster algebras. It gives, for each acyclic quiver, a family of integer sequences, one for each vertex. We conjecture that these sequences satisfy linear recursions if and only if the underlying graph is a Dynkin or an Euclidean (affine) graph. We prove the “only if” part, and show that the “if” part holds true for all non-exceptional Euclidean graphs, leaving a finite number of finite number of cases to be checked. Coming back to cluster algebras, the methods involved allow us to give formulas for the cluster variables in case Am and ; the novelty is that these formulas use 2 by 2 matrices over the semiring of Laurent polynomials generated by the initial variables (which explains simultaneously positivity and the Laurent phenomenon). One tool involved consists of the SL₂-tilings of the plane, which are particular cases of T-systems of Mathematical Physics.