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  • Articles  (507)
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  • Articles  (507)
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  • 1
    Publication Date: 2018-03-06
    Description: We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to the Sasaki lifts, horizontal lifts and complete lifts of the metrics under study.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
    Published by Springer
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  • 2
    Publication Date: 2018-03-06
    Description: A group G has all of its subgroups normal-by-finite if H / H G is finite for all subgroups H of G . The Tarski-groups provide examples of p -groups ( p a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a 2-group with every subgroup normal-by-finite is locally finite. We also prove that if H / H G ⩽ 2 for every subgroup H of G , then G contains an Abelian subgroup of index at most 8.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 3
    Publication Date: 2018-03-06
    Description: Let R be a ring. A subclass T of left R -modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let T be a weak torsion class of left R -modules and n a positive integer. Then a left R -module M is called T -finitely generated if there exists a finitely generated submodule N such that M/N ∈ T ; a left R -module A is called ( T , n )-presented if there exists an exact sequence of left R -modules $$0 \to K_{n - 1} \to F_{n - 1} \to \ldots \to F_1 \to F_0 \to M \to 0$$ such that F 0 ,..., F n -1 are finitely generated free and K n -1 is T -finitely generated; a left R -module M is called ( T , n )-injective, if Ext R n ( A,M ) = 0 for each ( T , n +1)-presented left R -module A ; a right R -module M is called ( T , n )-flat, if Tor n R ( M,A ) = 0 for each ( T , n +1)-presented left R -module A . A ring R is called ( T , n )-coherent, if every ( T , n +1)-presented module is ( n + 1)-presented. Some characterizations and properties of these modules and rings are given.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
    Published by Springer
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  • 4
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    Springer
    Publication Date: 2018-03-06
    Description: This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbertspace operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly l -sequentially supercyclic, and (iii) weak l -sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators: (iv) the point spectrum of the normed-space adjoint of a power bounded supercyclic operator is either empty or is a singleton in the open unit disk, (v) weak l -sequential supercyclicity coincides with supercyclicity for compact operators, and (vi) every compact weakly l -sequentially supercyclic operator is quasinilpotent.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 5
    Publication Date: 2018-03-06
    Description: In 1966, Gallai conjectured that all the longest paths of a connected graph have a common vertex. Zamfirescu conjectured that the smallest counterexample to Gallai’s conjecture is a graph on 12 vertices. We prove that Gallai’s conjecture is true for every connected graph G with α ’( G ) ⩽ 5, which implies that Zamfirescu’s conjecture is true.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 6
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    Springer
    Publication Date: 2018-03-06
    Description: We define the generalized outerplanar index of a graph and give a full characterization of graphs with respect to this index.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 7
    Publication Date: 2018-03-06
    Description: Let K /Q be an algebraic number field of class number one and let O K be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in O K under the assumption of the abc -conjecture for number fields.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 8
    Publication Date: 2018-03-06
    Description: Let G be a simple graph, let d ( v ) denote the degree of a vertex v and let g be a nonnegative integer function on V ( G ) with 0 ⩽ g ( v ) ⩽ d ( v ) for each vertex v ∈ V ( G ). A g c -coloring of G is an edge coloring such that for each vertex v ∈ V ( G ) and each color c , there are at least g ( v ) edges colored c incident with v . The g c -chromatic index of G , denoted by \(\chi '_{g_c } (G)\) , is the maximum number of colors such that a g c -coloring of G exists. Any simple graph G has the g c -chromatic index equal to δ g ( G ) or δ g ( G )–1, where \(\delta _g (G) = \mathop {\min }\limits_{v \in V(G)} \left\lfloor {d(v)/g(v)} \right\rfloor\) . A graph G is nearly bipartite, if G is not bipartite, but there is a vertex u ∈ V ( G ) such that G – u is a bipartite graph. We give some new sufficient conditions for a nearly bipartite graph G to have \(\chi '_{g_c } (G) = g(G)\) . Our results generalize some previous results due to Wang et al. in 2006 and Li and Liu in 2011.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 9
    Publication Date: 2018-03-06
    Description: An edge-colored graph G is proper connected if every pair of vertices is connected by a proper path. The proper connection number of a connected graph G , denoted by pc( G ), is the smallest number of colors that are needed to color the edges of G in order to make it proper connected. In this paper, we obtain the sharp upper bound for pc( G ) of a general bipartite graph G and a series of extremal graphs. Additionally, we give a proper 2-coloring for a connected bipartite graph G having δ( G ) ⩾ 2 and a dominating cycle or a dominating complete bipartite subgraph, which implies pc( G ) = 2. Furthermore, we get that the proper connection number of connected bipartite graphs with δ ⩾ 2 and diam( G ) ⩽ 4 is two.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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  • 10
    Publication Date: 2018-03-06
    Description: We apply an approximation by means of the method of lines for hyperbolic stochastic functional partial differential equations driven by one-dimensional Brownian motion. We study the stability with respect to small L 2 -perturbations.
    Print ISSN: 0011-4642
    Electronic ISSN: 1572-9141
    Topics: Mathematics
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