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

Authors:Mohammad Ramezanpour Pages: 1 - 13 Abstract: We study the notion of character Connes amenability of dual Banach algebras and show that if A is an Arens regular Banach algebra, then A** is character Connes amenable if and only if A is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension of Banach algebras. These help us to give examples of dual Banach algebras which are not Connes amenable. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0451-16

Authors:Saifallah Ghobber Pages: 1 - 15 Abstract: The aim of this paper is to prove a quantitative version of Shapiro’s uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0445-16

Authors:Xiaoli Chao; Yusha Lv Pages: 1 - 23 Abstract: We deal with complete submanifolds with weighted Poincaré inequality. By assuming the submanifold is δ-stable or has sufficiently small total curvature, we establish two vanishing theorems for L p harmonic 1-forms, which are extensions of the results of Dung-Seo and Cavalcante-Mirandola-Vitório. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0415-16

Authors:Wenxu Ge; Feng Zhao Pages: 1 - 20 Abstract: Suppose that λ1, λ2, λ3, λ4 are nonzero real numbers, not all negative, δ > 0, V is a well-spaced set, and the ratio λ1/λ2 is algebraic and irrational. Denote by E(V,N, δ) the number of v ∈ V with v ≤ N such that the inequality $$\left {{\lambda _1}p_1^2 + {\lambda _2}p_2^3 + {\lambda _3}p_3^4 + {\lambda _4}p_4^5 - \upsilon } \right < {\upsilon ^{ - \delta }}$$ has no solution in primes p1, p2, p3, p4. We show that $$E\left( {\upsilon ,N,\delta } \right) \ll {N^{1 + 2\delta - 1/72 + \varepsilon }}$$ for any ɛ > 0. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0388-16

Authors:Gladis Pradolini; Jorgelina Recchi Pages: 1 - 18 Abstract: Let μ be a nonnegative Borel measure on R d satisfying that μ(Q) ⩽ l(Q)n for every cube Q ⊂ R n , where l(Q) is the side length of the cube Q and 0 < n ⩽ d. We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function B in the context of non-homogeneous spaces related to the measure μ. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W.Wang, C. Tan, Z. Lou (2012). PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0337-16

Authors:Yu Sun; Jian Xu Pages: 1 - 15 Abstract: We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0474-16

Authors:Alexander Grigor'yan; Rolando Jimenez; Yuri Muranov Pages: 1 - 31 Abstract: We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory of digraphs, we transfer the results to the category of graphs. As a corollary we obtain the corresponding results for the fundamental groups of digraphs and graphs. We give an application to graph coloring. PubDate: 2018-01-26 DOI: 10.21136/cmj.2018.0683-15

Authors:Xiaoyou Chen; Mark L. Lewis Pages: 1 - 3 Abstract: We determine the groups with exactly two nonlinear non-faithful irreducible characters whose kernels intersect trivially. PubDate: 2017-12-14 DOI: 10.21136/cmj.2017.0348-17

Authors:Vasile Lauric Pages: 1 - 6 Abstract: The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar’s construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar’s theory does not lead to the extension that would provide a positive answer to the question. PubDate: 2017-12-13 DOI: 10.21136/cmj.2017.0129-17

Authors:Akshaa Vatwani Pages: 1 - 25 Abstract: We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings. PubDate: 2017-12-12 DOI: 10.21136/cmj.2017.0410-16

Authors:Hao Sun Pages: 1 - 11 Abstract: We give an estimation for the arithmetic genus of an integral space curve which is not contained in a surface of degree k−1. Our main technique is the Bogomolov-Gieseker type inequality for P3 proved by Macrì. PubDate: 2017-12-08 DOI: 10.21136/cmj.2017.0093-17

Authors:Hong Pan Pages: 1 - 4 Abstract: A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper, we extend one main result of Kong and Liu (2014). PubDate: 2017-12-08 DOI: 10.21136/cmj.2017.0067-17

Authors:Haimiao Chen; Yueshan Xiong; Zhongjian Zhu Pages: 1 - 13 Abstract: A metacyclic group H can be presented as 〈α, β: α n = 1, β m = α t , βαβ-1 = αr〉 for some n, m, t, r. Each endomorphism σ of H is determined by σ(α) = \({\alpha ^{{x_1}}}{\beta ^{{y_1}}}\) , σ(β) = \({\alpha ^{{x_2}}}{\beta ^{{y_2}}}\) for some integers x1, x2, y1, y2. We give sufficient and necessary conditions on x1, x2, y1, y2 for σ to be an automorphism. PubDate: 2017-12-07 DOI: 10.21136/cmj.2017.0656-16

Authors:Josef Janyška Pages: 1 - 23 Abstract: Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds. PubDate: 2017-12-06 DOI: 10.21136/cmj.2017.0626-16