Authors:Amirhesam Zaeim; Parvane Atashpeykar Pages: 1 - 16 Abstract: 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. PubDate: 2018-02-14 DOI: 10.21136/cmj.2018.0502-16

Authors:Hejmadi Gopalakrishna Gadiyar; Ramanathan Padma Pages: 1 - 10 Abstract: We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative. PubDate: 2018-02-14 DOI: 10.21136/cmj.2018.0128-17

Authors:Enrico Jabara Pages: 1 - 6 Abstract: A group G has all of its subgroups normal-by-finite if H/HG 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/HG⩽ 2 for every subgroup H of G, then G contains an Abelian subgroup of index at most 8. PubDate: 2018-02-14 DOI: 10.21136/cmj.2018.0504-16

Authors:Zhanmin Zhu Pages: 1 - 20 Abstract: 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 F0,..., Fn-1 are finitely generated free and Kn-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. PubDate: 2018-02-10 DOI: 10.21136/cmj.2018.0494-16

Authors:Jun Yue; Meiqin Wei; Yan Zhao Pages: 1 - 16 Abstract: 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. PubDate: 2018-02-08 DOI: 10.21136/cmj.2018.0122-16

Authors:Benoit Florent Sehba Pages: 1 - 15 Abstract: We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given. PubDate: 2018-02-08 DOI: 10.21136/cmj.2018.0531-16

Authors:Yuzhuo Zhang; Xia Zhang Pages: 1 - 12 Abstract: 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 gc-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 gc-chromatic index of G, denoted by \(\chi '_{g_c } (G)\) , is the maximum number of colors such that a gc-coloring of G exists. Any simple graph G has the gc-chromatic index equal to δg(G) or δg(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. PubDate: 2018-02-08 DOI: 10.21136/cmj.2018.0477-16

Authors:Carlos S. Kubrusly; Bhagwati P. Duggal Pages: 1 - 16 Abstract: 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. PubDate: 2018-02-08 DOI: 10.21136/cmj.2018.0457-16

Authors:Suying Liu; Minghua Yang Pages: 1 - 17 Abstract: Let L be a non-negative self-adjoint operator acting on L2(ℝn) satisfying a pointwise Gaussian estimate for its heat kernel. Let w be an Ar weight on ℝn × ℝn, 1 < r < 1. In this article we obtain a weighted atomic decomposition for the weighted Hardy space H L,w p (ℝn×ℝn), 0 < p ⩽ 1 associated to L. Based on the atomic decomposition, we show the dual relationship between H L,w 1 (ℝn × ℝn) and BMOL,w(ℝn × ℝn). PubDate: 2018-02-07 DOI: 10.21136/cmj.2018.0469-16

Authors:Fuyuan Chen Pages: 1 - 29 Abstract: 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. PubDate: 2018-02-07 DOI: 10.21136/cmj.2018.0422-16

Authors:Monika Wrzosek; Maria Ziemlańska Pages: 1 - 17 Abstract: 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 L2-perturbations. PubDate: 2018-02-05 DOI: 10.21136/cmj.2018.0155-16

Authors:Addisalem Abathun; Rikard Bøgvad Pages: 1 - 11 Abstract: We prove that as n → ∞, the zeros of the polynomial $$_2 F_1 \left[ {\begin{array}{*{20}c} { - n,\alpha n + 1} \\ {\alpha n + 2} \\ \end{array} ;z} \right]$$ cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter α and partially proves a conjecture made by the authors in an earlier work. PubDate: 2018-02-02 DOI: 10.21136/cmj.2018.0055-17

Authors:Mojtaba Bakherad Pages: 1 - 13 Abstract: The Berezin symbol Ã of an operator A acting on the reproducing kernel Hilbert space H = H(Ω) over some (nonempty) set is defined by \(\tilde A(\lambda ) = \left\langle {A\hat k_\lambda ,\hat k_\lambda } \right\rangle \) , λ ∈ Ω, where \(\hat k_\lambda = k_\lambda /\left\ {k_\lambda } \right\ \) is the normalized reproducing kernel of H. The Berezin number of the operator A is defined by \(ber(A) = \mathop {\sup }\limits_{\lambda \in \Omega } \left {\tilde A(\lambda )} \right = \mathop {\sup }\limits_{\lambda \in \Omega } \left {\left\langle {A\hat k_\lambda ,\hat k_\lambda } \right\rangle } \right \) . Moreover, ber(A) ⩽ w(A) (numerical radius). We present some Berezin number inequalities. Among other inequalities, it is shown that if \(T = \left[ {\begin{array}{*{20}c} A & B \\ C & D \\ \end{array} } \right] \in \mathbb{B}(\mathcal{H}(\Omega _1 ) \oplus \mathcal{H}(\Omega _2 ))\) , then $$ber(T) \leqslant \frac{1} {2}(ber(A) + ber(D)) + \frac{1} {2}\sqrt {(ber(A) - ber(D))^2 + \left( {\left\ B \right\ + \left\ C \right\ } \right)^2 } .$$ PubDate: 2018-02-01 DOI: 10.21136/cmj.2018.0048-17

Authors:Chunyue Wang; Qingcheng Zhang Pages: 1 - 11 Abstract: We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras. PubDate: 2018-02-01 DOI: 10.21136/cmj.2018.0627-16

Authors:Zahra Barati Pages: 1 - 9 Abstract: We define the generalized outerplanar index of a graph and give a full characterization of graphs with respect to this index. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0365-16

Authors:Srinivas Kotyada; Subramani Muthukrishnan Pages: 1 - 9 Abstract: 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 OK under the assumption of the abc-conjecture for number fields. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0485-16

Authors:Maryam Khatami; Azam Babai Pages: 1 - 10 Abstract: Let G be a finite group. An element g ∈ G is called a vanishing element if there exists an irreducible complex character χ of G such that χ(g)= 0. Denote by Vo(G) the set of orders of vanishing elements of G. Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let G be a finite group and M a finite nonabelian simple group such that Vo(G) = Vo(M) and G = M . Then G ≌ M. We answer in affirmative this conjecture for M = Sz(q), where q = 22n+1 and either q − 1, \(q - \sqrt {2q} + 1\) or q + \(\sqrt {2q} + 1\) is a prime number, and M = F4(q), where q = 2 n and either q4 + 1 or q4 − q2 + 1 is a prime number. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0355-16

Authors:Atossa Parsapour; Khadijeh Ahmad Javaheri Pages: 1 - 16 Abstract: Let (L,∧, ∨) be a finite lattice with a least element 0. AG(L) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L, and two distinct vertices I and J are adjacent if and only if I ∧ J = 0. We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by L(AG(L)), is a planar or projective graph. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0635-15

Authors:Victor Bovdi; Mohammed Salim Pages: 1 - 8 Abstract: We give a full description of locally finite 2-groups G such that the normalized group of units of the group algebra FG over a field F of characteristic 2 has exponent 4. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0386-16

Authors:Ruifang Liu; Jie Xue Pages: 1 - 18 Abstract: Let G be a connected graph with vertex set V(G) = {v1, v2,..., v n }. The distance matrix D(G) = (d ij )n×n is the matrix indexed by the vertices of G, where d ij denotes the distance between the vertices v i and v j . Suppose that λ1(D) ≥ λ2(D) ≥... ≥ λ n (D) are the distance spectrum of G. The graph G is said to be determined by its D-spectrum if with respect to the distance matrix D(G), any graph having the same spectrum as G is isomorphic to G. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their D-spectra. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0505-15