On the number of limit cycles in general planar piecewise linear systems of node–node types

We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles.     

二元三次样条空间S31,2(Δmn(2)) 的样条拟插值

本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2 型三角剖分上二元三次样条空间S₃^1,2(Δ_mn⁽²⁾)的若干样条拟插值算子. 这些变差缩减算子由样条函数B_ij¹支集上5 个网格点或中心和样条函数B_ij²支集上5 个网格点处函数值定义. 这些样条拟插值算子具有较好的逼近性,甚至算子V_mn（f） 能保持近最优的三次多项式性. 然后利用连续模,分析样条拟插值算子V_mn（f）一致逼近于充分光滑的实函数. 最后推导误差估计.     

Aragonite twinning in gastropod nacre

Aragonite twinning in gastropod nacre has been investigated using scanning electron microscopy (SEM), electron back-scattered diffraction (EBSD), and transmission electron microscopy (TEM) with the focused ion beam (FIB) sample preparation technique. At the growth front of nacre, Haliotis discus hannai and Omphalius rusticus form a “stack-of-coins” structures, which consist of pseudo-hexagonal and elliptical aragonite tablets, respectively. SEM, EBSD, and TEM analyses revealed that these tablets are monolithic single crystal and almost free of the {1 1 0} twins that are common in aragonite of biotic or abiotic origin. The longest diagonal of the hexagon and the longer axis of the ellipse are parallel to the a-axis of aragonite. The crystal orientation of each tablet in a stack, measured by TEM-Kikuchi pattern analysis, is almost the same but there is occasionally {1 1 0} twin-like relationship between adjacent tablets along the stacking. On the other hand, the fibrous aragonite layer formed prior to the nacreous structure is composed of polycrystalline aragonite with high density of {1 1 0} twins. TEM observation suggests that the interlamellar organic sheet prevents the inheritance of the twins, by selecting only single domain of the twins, through the mineral bridge.     

Multiplex bioanalytical methods for food and environmental monitoring

Recent advances in miniaturization of analytical systems and newly emerging technologies offer platforms with greater automation and multiplexing capabilities than traditional biological binding assays. Multiplexed bioanalytical techniques provide control agencies and food industries with new possibilities for improved, more efficient monitoring of food and environmental contaminants. This review deals with recent developments in planar-array and suspension-array technologies, and their applications in detecting pathogens, food allergens and adulterants, toxins, antibiotics and environmental contaminants.     

Design and implementation of an array of micro-electrochemical detectors for two-dimensional liquid chromatography—Proof of principle

Simultaneous two-dimensional liquid chromatography (2D-LC) is an implementation of two-dimensional liquid chromatography which has the potential to provide very fast, yet highly efficient separations. It is based on the use of time × space and space × space separation systems. The basic principle of this instrument has been validated long ago by the success of two-dimensional thin layer chromatography. The construction of a pressurized wide and flat column (100 mm × 100 mm × 1 mm) operated under an inlet pressure of up to 50 bar was described previously. However, to become a modern analytical method, simultaneous 2D-LC requires the development of detectors suitable for the monitoring of the composition of the eluent of this pressurized planar, wide column. An array of five equidistant micro-electrochemical sensors was built for this purpose and tested. Each sensor is a three-electrode system, with the working electrode being a 25 μm polished platinum micro-electrode. The auxiliary electrode is a thin platinum wire and the reference electrode an Ag/AgCl (3 M sat. KCl) electrode. In this first implementation, proof of principle is demonstrated, but the final instrument will require a much larger array.     

依赖型值的非奇异自适应三角剖分方法

1 引言 众所周知,三角剖分是在许多科学计算如曲面设计与拟合、有限元计算以及其他大型科学计算等领域中不可回避的问题.     

A vertex incremental approach for maintaining chordality

For a chordal graph G=(V,E), we study the problem of whether a new vertex u∉V and a given set of edges between u and vertices in V can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, specify a maximal subset of the proposed edges that can be added along with u, or conversely, a minimal set of extra edges that can be added in addition to the given set, so that the resulting graph is chordal. In order to do this, we give a new characterization of chordal graphs and, for each potential new edge uv, a characterization of the set of edges incident to u that also must be added to G along with uv. We propose a data structure that can compute and add each such set in O(n) time. Based on these results, we present an algorithm that computes both a minimal triangulation and a maximal chordal subgraph of an arbitrary input graph in O(nm) time, using a totally new vertex incremental approach. In contrast to previous algorithms, our process is on-line in that each new vertex is added without reconsidering any choice made at previous steps, and without requiring any knowledge of the vertices that might be added subsequently.     

子图识别的层分解方法

子图识别问题(SRP)就是在一个图G中确定并寻找是否存在和另一个图H相同构的子图．本文将引入图的层分解概念，并以此为基础建立识别图的同构子图的算法．该算法的复杂性为O(n(△-1)^k-1)，其中△是图G的度，即G中点的最大度，n，k分别是图G，H的阶．