Adaptive variational curve smoothing based on level set method

This paper presents an adaptive method for variational curve smoothing based on level set implementation. A suitable cost functional is minimized via solving the derived Euler–Lagrangian equation, of which the discretization is conducted on unstructured triangular meshes by employing a simple and effective finite volume scheme. Through adaptive refinement of the mesh, the geometry features of the given curve can be well resolved in a cost-effective way. Various numerical experiments demonstrate the effectiveness and efficiency of the proposed approach.     

应用曲面镜成像原理仿真高温超导体磁悬浮力

文章首次探讨了应用曲面镜成像原理 ,对高温超导体悬浮力进行仿真计算 ,并且比较了实验数据与计算结果 ,结果表明了此方法的有效性。文章还讨论了此方法今后的工作方向。     

Geometric tools to determine the hyperbolicity of limit cycles

In this paper we present a new method to study limit cycles' hyperbolicity. The main tool is the function ν=([V,W]∧V)/(V∧W), where V is the vector field under investigation and W a transversal one. Our approach gives a high degree of freedom for choosing operators to study the stability. It is related to the divergence test, but provides more information on the system's dynamics. We extend some previous results on hyperbolicity and apply our results to get limit cycles' uniqueness. Liénard systems and conservative + dissipative systems are considered among the applications.     

On joint universality of periodic Hurwitz zeta-functions

We prove a joint universality theorem for a collection of periodic Hurwitz zeta-functions with algebraically independent parameters over the field of rational numbers.     

Bifurcation analysis of a plant-herbivore model with toxin-determined functional response

A system of ordinary differential equations is considered which models the plant-herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically.     

Central limit behavior in the Kuramoto model at the “edge of chaos”

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.     

共聚焦拉曼光谱研究ZnSO_4微液滴的风化过程

通过共聚焦拉曼原位光谱技术在分子水平上研究了沉积在聚四氟乙烯基底上的ZnSO_4微液滴的风化过程.根据获得的高信噪比的Raman光谱,详细探讨了湿度降低时ZnSO_4微液滴中Zn~(2+)和SO_4~2离子的缔合行为,即经由单齿、双齿最终转化为复杂的链状或网状接触离子对.利用曲线拟合技术对其光谱的ν1-SO_4~2峰进行分峰,获得了不同湿度下ZnSO_4微液滴中各组分的量化信息:高湿度时,液滴中主要包含自由的水合SO_4~(2-);随着湿度降低,自由SO_4~(2-)逐渐向单齿、双齿接触离子对转化,并在湿度为66%和34%时分别达到其最大值;继续降低湿度,复杂的链状或网状接触离子对逐渐成为液滴中的主要成分.     

机会约束规划在岩土工程中的应用

采用极限平衡理论分析土坡稳定性, 搜索确定其潜在的滑动面与确立可靠度分析模型是理论研究与应用的两个重要方面。应用“确定的”方法, 构筑由随机变量决定的约束条件, 根据机会约束规模理论, 分析土坡的稳定性与可靠性。并用土坡实例进行计算。     

具有二个焦点的二次系统极限环的分布与个数

本文证明了具有二个焦点的二次系统必在其中一个焦点外围至多有一个极限环这一猜想．从而得到具有二个焦点的二次系统之极限环必是（Ｏ,ｉ）或（１,ｉ）分布（ｉ＝ ０, １, ２,）．     

Limit分子格

通过在完全分配格上引入理想收敛,给出ｌｉｍｉｔ分子格及其范畴,证明了其是包含拓扑分子格范畴为全反射范畴的笛卡儿闭范畴．