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91.
The chromatic polynomial PG(q) of a loopless graph G is known to be non-zero (with explicitly known sign) on the intervals (−∞,0), (0,1) and (1,32/27]. Analogous theorems hold for the flow polynomial of bridgeless graphs and for the characteristic polynomial of loopless matroids. Here we exhibit all these results as special cases of more general theorems on real zero-free regions of the multivariate Tutte polynomial ZG(q,v). The proofs are quite simple, and employ deletion–contraction together with parallel and series reduction. In particular, they shed light on the origin of the curious number 32/27. 相似文献
92.
Abbas Heydari 《Linear algebra and its applications》2008,429(7):1744-1757
Let H be a simple graph with n vertices and G be a sequence of n rooted graphs G1,G2,…,Gn. Godsil and McKay [C.D. Godsil, B.D. McKay, A new graph product and its spectrum, Bull. Austral. Math. Soc. 18 (1978) 21-28] defined the rooted product H(G), of H by G by identifying the root vertex of Gi with the ith vertex of H, and determined the characteristic polynomial of H(G). In this paper we prove a general result on the determinants of some special matrices and, as a corollary, determine the characteristic polynomials of adjacency and Laplacian matrices of H(G).Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97-117] computed the characteristic polynomials and the spectrum of adjacency and Laplacian matrices of a class of balanced trees. As an application of our results, we obtain their conclusions by a simple method. 相似文献
93.
In this paper, some utilities for the developement of asymmetrical circular arc tapes are described. Basing on a polygon-approximation of characteristic impedance a method for to determine the geometrical parameters of the taper is explained. The applicability of the method presented here is proved by extensive measurements. 相似文献
94.
In this paper, a new method for numerically solving nonlinear convection-dominated diffusion problems is devised and analysed. The discrete time approximations with time stepping along charactcristics are cstablished and solved in spaces posscssing reproducing kernel functions. At each time step, the exact solution of the approximate problem is given by explicit expression. The computational advantage of this method is that the schemes are absolutely stable, and are explicitly solvable as well. The stability and error estimates are derived. Some numerical results are given. 相似文献
95.
Gan Danyan 《数学年刊B辑(英文版)》1996,17(3):257-262
51.IntroductionOne0ftheinterestingproblemsneartheheartof4dimensionaltopologyistodecidewhich2-dimensionalhomology/homotoPyclasscanberepresentedbyasmo0thlyembedded2-sphereinagivensmooth4-dimensionalmanifold.ItwasRohlin[19]wh0pointed0utintheearly195Ostousthatnotevery2-dimensionalhthmology/hom0topyclasscanbesorepresented.TheimportanceoftheproblemwasexplainedbyKervaireandMilnorl11].Onedecadelater,theystartedthestudyin1961,followedbyBoardm..I1]?Wall[25]5Tri.t..m[23]tHsiangandSzczarba[1o],andRoh… 相似文献
96.
Let BG be the classifying space for stable spherical fibrations, and let V be a finite dimensional vector subspace of the cohomology algebra H1(BG; 2). We prove that V may be realized by a Poincaré duality space P, which means that if v:P→BG is the Spivak fibration, then v1 maps V isomorphically onto its image in H1(P;2). By construction, P is the product of a certain Grassman manifold and a spherical fiber space over a closed smooth manifold. 相似文献
97.
设G为n阶κ正则简单连通图(κ≥2),λ是图G的次根,d(G)是图G的直径,如果G不是二部图,且d(G)≠2,则d(G)≤[log(n-1)/log(κ/λ)],并且当G≌时,这一上界可达. 相似文献
98.
99.
Considering the htermal conduction through molecular collisions an expression for the effective thermal conductivityλ
e
of loose and granular two-phase materials at different interstitial air pressure has been derived. The dependence ofλ
e
on pore and particle sizes, characteristic pressure and radiative heat transfer is also discussed. Calculated values ofλ
e
of glass beads and loose building materials are compared with reported results. 相似文献
100.
James P. Kahan 《Mathematical Social Sciences》1980,1(1):11-37
Eighteen groups of subjects each participated in five different computer-controlled superadditive 3-person characteristic function games with sidepayments, that modeled negotiable conflicts in which two of the players are weak and one is considerably stronger. Both the degree to which the strong player was powerful and the type of communication were experimentally manipulated. The 90 game outcomes rejected any solution concept that predicts a single payoff vector for a given coalition structure, but supported the recently developed single-parameter α-power model that allows range predictions. Both the degree of power and type of communication were found to affect game outcomes and to determine the predictive power of models that make point predictions in 3-person games. 相似文献