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《Discrete Mathematics》1986,58(3):317-321
In [4] Jung and Watkins proved that for a connected infinite graph X either κ∞(X) = ∞ holds or X is a strip, if Aut(X) contains a transitive abelian subgroup G. Here we prove the same result under weaker assumptions. 相似文献
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H. A. Jung 《Combinatorica》1981,1(3):285-288
Results involving automorphisms and fragments of infinite graphs are proved. In particular for a given fragmentC and a vertex-transitive subgroupG of the automorphism group of a connected graph there exists σ≠G such that σ[C] ⊂C. This proves the countable case of a conjecture of L. Babai and M. E. Watkins concerning graphs allowing a vertex-transitive
torsion group action.
Dedicated to Prof. K. Wagner on his 70th birthday 相似文献
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Youngjoon Cha Haseo Ki Young-One Kim 《Journal of Mathematical Analysis and Applications》2004,290(2):534-541
A sufficient condition for entire functions f and g to be such that the series ∑m=0∞f(m)(0)g(m)/m! represents an entire function is established; and in that case, the growth of the resulting function is described. 相似文献
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Chris D. Godsil Wilfried Imrich Norbert Seifter Mark E. Watkins Wolfgang Woess 《Graphs and Combinatorics》1989,5(1):333-338
LetX be a connected locally finite graph with vertex-transitive automorphism group. IfX has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup ofAUT(X) and the action ofAUT(X) onV(X) is imprimitive ifX is not finite. IfX has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic. 相似文献
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We present a construction of two infinite graphs and , and of an infinite set of graphs such that is an antichain with respect to the immersion relation and, for each graph in , both and are subgraphs of , but no graph properly immersed in admits an immersion of and of . This shows that the class of infinite graphs ordered by the immersion relation does not have the finite intertwine property. 相似文献
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Dongwen Qi 《Expositiones Mathematicae》2009,27(1):87-91
A new proof is given for the statement: For an irreducible, infinite Coxeter group (W,S) and w∈W, if wSw-1=S, then w=1 (the identity element of W). 相似文献
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Jaroslav Han?l Ond?ej Kolouch Simona Pulcerová Jan ?těpni?ka 《Czechoslovak Mathematical Journal》2012,62(3):613-623
The paper deals with several criteria for the transcendence of infinite products of the form $\prod\limits_{n = 1}^\infty {[{b_n}{a^{{a_n}}}]/{b_n}{a^{{a_n}}}} $ where α > 1 is a positive algebraic number having a conjugate α* such that α ≠ |α*| > 1, {a n } n=1 ∞ and {b n } n=1 ∞ are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P.Corvaja, U.Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mend`es France, Acta Math. 193, (2004), 175–191). 相似文献
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Liang-Xue Peng 《Topology and its Applications》2007,154(11):2223-2227
It is shown that if X is a countably compact space that is the union of a countable family of D-spaces, then X is compact. This gives a positive answer to Arhangel'skii's problem [A.V. Arhangel'skii, D-spaces and finite unions, Proc. Amer. Math. Soc. 132 (7) (2004) 2163-2170]. In this note, we also obtain a result that if a regular space X is sequential and has a point-countable k-network, then X is a D-space. 相似文献
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Uri Abraham 《Order》1987,4(2):107-125
If is a poset and every antichain is finite, and if the length of the well-founded poset of antichains is less than 2
1, then is the union of countably many chains. We also compute the length of the poset of antichains in the product of two ordinals, x. 相似文献
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A NOTE ON BEURLING-DENY FORMULAE IN INFINITE DIMENSIONAL SPACES 总被引:1,自引:0,他引:1
1.IntroductionandMainResultsAsisIvellknown,theBeurling-DenyformulaeplayimportalrolesinthetheoryofregularDirichletformsonlocallycompactseparablemetricspaces.See[4]forarecentnicerepreselltationinthisconnection.ThepurposeofthispaperistoextendtheBeurlingDenyformulaetoquasi-regularDirichletforms,inparticulartoDirichletformsoninfinitedimensionalstatespaces.RecallthataDirichletformisquasi-regularifandonlyifitisassociatedwitharightcontinuousstrongMarkovprocesslivingesselltiallyonametriZableLusin… 相似文献
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It is proved that if \(G\) is a (generalized) soluble group of infinite rank in which all proper subgroups of infinite rank are permodular, then the subgroup lattice of \(G\) is permodular. As a consequence of this theorem, we obtain shorter proofs for corresponding known results concerning normal or permutable subgroups of groups of infinite rank. 相似文献
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J. A. BurnsB. B. King 《Applied Mathematics Letters》1994,7(6):7-11
This note is concerned with the regularity of solutions of algebraic Riccati equations arising from infinite dimensional LQR control problems. We show that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smooths solutions of the corresponding Riccati equation. This analysis is motivated by the need to find specific representations for Riccati operators that can be used in the development of computational schemes for problems where the input and output operators are not Hilbert-Schmidt. This situation occurs in many boundary control problems and in certain distributed control problems associated with optimal sensor/actuator placement. 相似文献
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In this note we establish sufficient conditions for existence and uniqueness of solutions of terminal value problems for a class of fractional differential equations on infinite interval. Some illustrative examples are comprehended to demonstrate the proficiency and utility of our results. 相似文献
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The two-dimensional, incompressible flow past an infinite plate of a weakly conducting fluid in the presence of a transverse magnetic field is discussed when the suction velocity normal to the plate as well as the external flow velocity vary periodically with time. Expressions for the velocity and the skin-friction in the boundary layer have been obtained in a non-dimensional form. 相似文献