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2.
Christian Bosse 《Discrete Mathematics》2019,342(12):111595
The Hadwiger number of a graph , denoted , is the largest integer such that contains as a minor. A famous conjecture due to Hadwiger in 1943 states that for every graph , , where denotes the chromatic number of . Let denote the independence number of . A graph is -free if it does not contain the graph as an induced subgraph. In 2003, Plummer, Stiebitz and Toft proved that for all -free graphs with , where is any graph on four vertices with , , or is a particular graph on seven vertices. In 2010, Kriesell subsequently generalized the statement to include all forbidden subgraphs on five vertices with . In this note, we prove that for all -free graphs with , where denotes the wheel on six vertices. 相似文献
3.
Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002 相似文献
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A. Khrennikov 《Annalen der Physik》2003,12(10):575-585
We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations. 相似文献
6.
Liyue Liu Yingge Yang Yafei Zhang 《Physica E: Low-dimensional Systems and Nanostructures》2004,24(3-4):343-348
The electrical conductivity was investigated for multi-walled carbon nanotubes (MWNTs) dissolved in chloroform and toluene, respectively. The electrical conductivity remarkably increased with increase in the content of MWNTs, which is in accordance with Archie's equation . Furthermore, a hypothesis of the electronic transport process was proposed to explain the difference between the solution and the solid compound. In addition, the temperature dependence of the electrical conductivity shows that log σ vs. 1/T exist in a good linear relationship. The activation energy of the electrical conductivity decreased with increase in concentration and an inflexion was observed at 60 °C in MWNT/toluene solution. 相似文献
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1 INTRODUCTION Carbon nanotubes have many potential applica- tions due to their unique structures and properties[1~4]. Physicists have been studying their electrical, me- chanical and other properties since their discove- ries[5, 6]. Recently, chemists are interested in carbon nanotubes because their properties can be altered by chemical functionalization[7~14], and these functiona- lized nanotubes can undergo further chemical trea- tment. So the potential application range of such na- … 相似文献
9.
《Magnetic resonance in chemistry : MRC》2003,41(6):417-430
A systematic study of the one‐bond and long‐range J(C,C), J(C,H) and J(H,H) in the series of nine bicycloalkanes was performed at the SOPPA level with special emphasis on the coupling transmission mechanisms at bridgeheads. Many unknown couplings were predicted with high reliability. Further refinement of SOPPA computational scheme adjusted for better performance was carried out using bicyclo[1.1.1]pentane as a benchmark to investigate the influence of geometry, basis set and electronic correlation. The calculations performed demonstrated that classical ab initio SOPPA applied with the locally dense Dunning's sets augmented with inner core s‐functions used for coupled carbons and Sauer's sets augmented with tight s‐functions used for coupled hydrogens performs perfectly well in reproducing experimental values of different types of coupling constants (the estimated reliability is ca 1–2 Hz) in relatively large organic molecules of up to 11 carbon atoms. Additive coupling increments were derived for J(C,C), J(C,H) and J(H,H) based on the calculated values of coupling constants within SOPPA in the model bicycloalkanes, in reasonably good agreement with the known values obtained earlier on pure empirical grounds. Most of the bridgehead couplings in all but one bicycloalkane appeared to be essentially additive within ca 2–3 Hz while bicyclo[1.1.1]pentane demonstrated dramatic non‐additivity of ?14.5 Hz for J(C,C), +16.6 Hz for J(H,H) and ?5.5 Hz for J(C,H), in line with previous findings. Non‐additivity effects in the latter compound established at the SOPPA level should be attributed to the through‐space non‐bonded interactions at bridgeheads due to the essential overlapping of the bridgehead rear lobes which provides an additional and effective non‐bonding coupling path for the bridgehead carbons and their protons in the bicyclopentane framework. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
10.
Zuo LIU Zhen De WU 《数学学报(英文版)》2005,21(5):997-1000
Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP(ξ^κ)] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given. 相似文献