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41.
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-immersed in the plane if each edge is crossed by at most k other edges. By a proper k-immersion of a graph we mean a 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. 相似文献
42.
Ya'akov Nahir 《International Journal of Mathematical Education in Science & Technology》2013,44(4):614-624
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. 相似文献
43.
44.
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. 相似文献
45.
Jesús Chaboy María ángeles Laguna‐Marco Cristina Piquer Roberto Boada Neculai Plugaru Hiroshi Maruyama Naomi Kawamura 《Journal of synchrotron radiation》2009,16(3):405-412
An X‐ray magnetic circular dichroism (XMCD) study performed at the rare‐earth L2,3‐edges in the RxR1?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. 相似文献
46.
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.
47.
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. 相似文献
48.
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 Wc and also the critical exponent ν for
localization length change with the values of p. 相似文献
49.
T. Mathew R. N. Datta W. K. Dierkes J. W. M. Noordermeer W. J. van Ooij 《Plasma Chemistry and Plasma Processing》2008,28(2):273-287
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. 相似文献
50.