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91.
We give an inequality for the group chromatic number of a graph as an extension of Brooks’ Theorem. Moreover, we obtain a structural theorem for graphs satisfying the equality and discuss applications of the theorem. 相似文献
92.
Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero Z
3-flow and Jaeger et al. [Group connectivity of graphs–a nonhomogeneous analogue of nowhere-zero flow properties, J. Combin.
Theory Ser. B 56 (1992) 165-182] further conjectured that every 5-edge-connected graph is Z
3-connected. These two conjectures are in general open and few results are known so far. A weaker version of Tutte’s conjecture
states that every 4-edge-connected graph with each edge contained in a circuit of length at most 3 admits a nowhere-zero Z
3-flow. Devos proposed a stronger version problem by asking if every such graph is Z
3-connected. In this paper, we first answer this later question in negative and get an infinite family of such graphs which
are not Z
3-connected. Moreover, motivated by these graphs, we prove that every 6-edge-connected graph whose edge set is an edge disjoint
union of circuits of length at most 3 is Z
3-connected. It is a partial result to Jaeger’s Z
3-connectivity conjecture.
Received: May 23, 2006. Final version received: January 13, 2008 相似文献
93.
Jin Bai Kim 《数学研究及应用》1985,5(3):11-13
We give a characterization of a regular Boolean matrix and prove that AB = I Implies that BA = I, where A and B are Boolean matrices whose elements belong to a Boolean algebra of a set with more than two elements. 相似文献
94.
95.
The magnetic susceptibilities (χ) of several natural single crystals of iron pyrite (FeS2) have been measured between 4.2 and 620 K with a force magnetometer. The measured susceptibilities are shown to related to the magnetic impurities present in the samples. For a pure sample, χ = 1.7 × 10?7 emu/g at room temperature, with a small monotonic increase of χ with temperature. The results for a pure sample are interpreted in terms of contributions from diamagnetism and Van Vleck paramagnetism. 相似文献
96.
H.W Gould 《Journal of Combinatorial Theory, Series A》1977,23(3):351-353
In this paper a general identity is proved which includes among its special cases a recurrence formula for Catalan numbers given by J. Touchard in 1924. 相似文献
97.
This paper presents a computational framework for the optimization and sensitivity analysis of a process whose state depends upon several parameter functions. Assuming that the process is described by a system of quasilinear, parabolic, partial differential equations, we show how determining the problem parameters so as to improve an associated objective functional is directly related to knowing the state function sensitivities. An expression for the gradient of the objective functional in terms of the solutions of an adjoint system enables one to bypass the calculation of state function sensitivities. These concepts are illustrated for a simple model of cooperative processes in chemical kinetics. Since sensitivity analysis and model optimization are important tools for investigating parameter dependence and validating mathematical models, research developments in such diverse fields as optimal design theory, chemical kinetics, and parameter identification are important motivations for this paper.This author would like to gratefully acknowledge Dr. M. Delle Donne, EGG, for several helpful discussions.This author was partially supported by NSF Grant No. CMS-80-05677. 相似文献
98.
Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related
to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders
greater than some numberN
0 vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property
holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular
operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant
function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would
need to introduce cumulant tensors. 相似文献
99.
The following results are obtained. (i) Let p, d, and k be fixed positive integers, and let G be a graph whose vertex set can be partitioned into parts V1, V2,…, Va such that for each i at most d vertices in V1 … Vi have neighbors in Vi+1 and r(Kk, Vi) p | V(G) |, where Vi denotes the subgraph of G induced by Vi. Then there exists a number c depending only on p, d, and k such that r(Kk, G)c | V(G) |. (ii) Let d be a positive integer and let G be a graph in which there is an independent set I V(G) such that each component of G−I has at most d vertices and at most two neighbors in I. Then r(G,G)c | V(G) |, where c is a number depending only on d. As a special case, r(G, G) 6 | V(G) | for a graph G in which all vertices of degree at least three are independent. The constant 6 cannot be replaced by one less than 4. 相似文献
100.
For a natural crystal of marcasite, an energy gap of 0.34 eV and an acceptor level at 0.052 eV are determined from temperature-dependent (53–370 K) electrical resistivity measurements. Magnetic susceptibilities and dielectric constants of marcasite and pyrite are compared in view of the large difference in their energy gaps. 相似文献