Proper 1-immersions of graphs triangulating the plane

In this paper we study what planar graphs are “rigid” enough such that they can not be drawn on the plane with few (1, 2, or 3) crossings per edge. A graph drawn on the plane is k$k$-immersed in the plane if each edge is crossed by at most k$k$ other edges. By a proper  k$k$-immersion of a graph we mean a k$k$-immersion of the graph in the plane such that there is at least one crossing point. We give a characterization (in terms of forbidden subgraphs) of 4-connected graphs which triangulate the plane and have a proper 1-immersion. We show that every planar graph has a proper 3-immersion.     

The trigonometric triangle

A procedure is presented by which the integration of a function such as cos ⁿ (x) or sin ⁿ (x) with n = 1, 2, 3, 4 … is facilitated.     

Hamiltonian map approach to 1D Anderson model

A one-dimensional diagonal tight binding electronic system is analyzed with the Hamiltonian map approach to study analytically the inverse localization length of an infinite sample. Both the uncorrelated and the dichotomic correlated random potential sequences are considered in the evaluations of the inverse localization length. Analytical expressions for the invariant measure or the angle density distribution are the main motivation of this work in order to derive analytical results. The well-known uncorrelated weak disorder result of the inverse localization length is derived with a clear procedure. In addition, an analytical expression for high disorder is obtained near the band edge. It is found that the inverse localization length goes to 1 in this limit. Following the procedure used in the uncorrelated situation, an analytical expression for the inverse localization length is also obtained for the dichotomic correlated sequence in the small disorder situation.     

Origin of the X‐ray magnetic circular dichroism at the L‐edges of the rare‐earths in RxR1−x′Al2 systems

An X‐ray magnetic circular dichroism (XMCD) study performed at the rare‐earth L_2,3‐edges in the R_xR_1?x′Al₂ compounds is presented. It is shown that both R and R′ atoms contribute to the XMCD recorded at the L‐edges of the selected rare‐earth, either R or R′. The amplitude of the XMCD signal is not directly correlated to the magnetization or to the value of the individual (R, R′) magnetic moments, but it is related to the molecular field acting on the rare‐earth tuned in the photoabsorption process. This result closes a longstanding study of the origin of the XMCD at the L‐edge of the rare‐earths in multi‐component systems, allowing a full understanding of the exact nature of these signals.     

Homogeneity and the disjoint arcs property

Some previous results of the author towards a classification of homogeneous metric continua are improved. The disjoint arcs property is fully revealed in this context. In particular, closed -manifolds, , are characterized as those homogeneous continua which do not have the disjoint arcs property.

     

Disjoint Paths in Graphs III,Characterization

Let G be a graph, $ \{a, b, c\}\subseteq V(G) $, and $ \{a', b', c'\}\subseteq V(G) $ such that $ \{a, b, c\}\neq \{a', b', c'\} $. We say that $ (G, \{a, c\}, \{a', c'\}, (b, b')) $ is an obstruction if, for any three vertex disjoint paths from {a, b, c} to {a', b', c'} in G, one path is from b to b'. In this paper we characterize obstructions. As a consequence, we show that no obstruction can be 8-connected, unless b = b' or {a, c} = {a', c'}.AMS Subject Classification: 05C38.     

Localization-delocalization transition in chains with long-range correlated disorder

We investigated numerically localization properties of electron eigenstates in a chain with long-range correlated diagonal disorder. A tight-binding one-dimensional model with on-site energies exhibiting long-range correlated disorder (LCD) was used with various disorder strength W. LCD was defined so that it gave a power-law spectral density of the form S(k)αk^-p, where p determines the roughness of the potential landscape. Numerical results on the correlation length ξ of eigenstates shows the existence of the localization-delocalization transition at p=2. It is found that the critical values for disorder strength W_c and also the critical exponent ν for localization length change with the values of p.     

Mechanistic Investigations of Surface Modification of Carbon Black and Silica by Plasma Polymerisation

Carbon black is widely used as an active filler in the rubber industry to improve the physical properties of rubber. The surface energy of carbon black is high compared to that of various elastomers like styrene–butadiene rubber (SBR), butadiene rubber (BR) and ethylene–propylene–diene rubber (EPDM). The work aims at reducing the surface energy of carbon black by modifying its surface for application especially in rubber blends. The present paper looks into the possibility of using plasma polymerisation of acetylene as a surface modification technique for carbon black in comparison with silica. Thermogravimetric analysis, wetting behaviour with various liquids of known surface tension and time of flight secondary ion mass spectrometry (ToF-SIMS) were used to characterise the carbon black before and after surface modification. The study shows that surface modification of carbon black by plasma polymerisation is difficult in comparison with silica, unless treated for long duration. The mechanistic aspects of the surface modification and the importance of active sites on the carbon black surface for effective modification are discussed in the paper.     

弹性约束边界圆环板面内自由振动的二维弹性解

基于二维线弹性理论,应用哈密顿原理导出弹性约束边界圆环板面内自由振动的控制微分方程。采用微分求积法(DQM)数值研究了弹性约束边界圆环板面内自由振动的频率特性。通过设置弹性刚度系数为0或∞,问题退化为四种典型边界圆环板的面内自由振动,与已有文献的计算数值结果进行比较,证实本文的分析求解方法行之有效。最后全面考虑了圆环板边界条件、几何系数及刚度系数对自振频率的影响。