Authors:Wei Meng; Hailou Yao Pages: 1 - 11 Abstract: Let N denote the class of nilpotent Lie algebras. For any finite-dimensional Lie algebra L over an arbitrary field F, there exists a smallest ideal I of L such that L/I 2 N. This uniquely determined ideal of L is called the nilpotent residual of L and is denoted by L N . In this paper, we define the subalgebra S(L) = ∩H≤L I L(H N ). Set S0(L) = 0. Define Si+1(L)/S i (L) = S(L/S i (L)) for i > 1. By S∞(L) denote the terminal term of the ascending series. It is proved that L = S∞(L) if and only if L N is nilpotent. In addition, we investigate the basic properties of a Lie algebra L with S(L) = L. PubDate: 2018-04-27 DOI: 10.21136/cmj.2018.0006-17

Authors:Victor J. W. Guo Pages: 1 - 4 Abstract: We give a new and elementary proof of Jackson’s terminating q-analogue of Dixon’s identity by using recurrences and induction. PubDate: 2018-04-16 DOI: 10.21136/cmj.2018.0052-17

Authors:Ryôhei Kakizawa Pages: 1 - 19 Abstract: We discuss the validity of the Helmholtz decomposition of the Muckenhoupt A p -Weighted L p -Spaces (L p w (Ω)) n for any domain Ω in R n , n ∈ Z, n > 2, 1 < p < ∞ and Muckenhoupt A p -weight w ∈ A p . Set p′:= p/(p − 1) and w′:= w−1/(p−1). Then the Helmholtz decomposition of (L p w (Ω)) n and (L p′ w′ (Ω)) n and the variational estimate of L p w,π(Ω) and L p′ w′,π(Ω) are equivalent. Furthermore, we can replace L p w,π(Ω) and L p′ w′,π(Ω) by L p w,σ(Ω) and L p′ w′,σ(Ω), respectively. The proof is based on the reflexivity and orthogonality of L p w,π(Ω) and L p w,σ(Ω) and the Hahn-Banach theorem. As a corollary of our main result, we obtain the extrapolation theorem with the aid of the Helmholtz projection of (L p w (Ω)) n . PubDate: 2018-04-16 DOI: 10.21136/cmj.2018.0646-16

Authors:Qiang Zhou Pages: 1 - 5 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 this paper, some interesting results with weakly-supplemented minimal subgroups or Sylow subgroups of G are obtained. PubDate: 2018-04-13 DOI: 10.21136/cmj.2018.0301-17

Authors:Petteri Harjulehto; Peter Hästö Pages: 1 - 10 Abstract: We prove that the associate space of a generalized Orlicz space Lϕ(·) is given by the conjugate modular ϕ* even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling Φ-function is equivalent to a doubling Φ-function. As a consequence, we conclude that Lϕ(·) is uniformly convex if ϕ and ϕ* are weakly doubling. PubDate: 2018-04-13 DOI: 10.21136/cmj.2018.0054-17

Authors:Jana Coroničová Hurajová; Tomáš Madaras Pages: 1 - 14 Abstract: We study graphs whose vertices possess the same value of betweenness centrality (which is defined as the sum of relative numbers of shortest paths passing through a given vertex). Extending previously known results of S. Gago, J. Hurajová, T. Madaras (2013), we show that, apart of cycles, such graphs cannot contain 2-valent vertices and, moreover, are 3-connected if their diameter is 2. In addition, we prove that the betweenness uniformity is satisfied in a wide graph family of semi-symmetric graphs, which enables us to construct a variety of nontrivial cubic betweenness-uniform graphs. PubDate: 2018-04-13 DOI: 10.21136/cmj.2018.0087-16

Authors:Ivica Bošnjak; Rozália Madarász Pages: 1 - 14 Abstract: For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined. PubDate: 2018-04-13 DOI: 10.21136/cmj.2018.0552-16

Authors:Asma Ilkhanizadeh Manesh; Ahmad Mohammadhasani Pages: 1 - 11 Abstract: For X, Y ∈ Mn,m it is said that X is gut-majorized by Y, and we write X ≺gut Y, if there exists an n-by-n upper triangular g-row stochastic matrix R such that X = RY. Define the relation ≺gut as follows. X ~gut Y if X is gut-majorized by Y and Y is gut-majorized by X. The (strong) linear preservers of ≺gut on Rn and strong linear preservers of this relation on Mn,m have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of ~gut on Rn and Mn,m. PubDate: 2018-04-11 DOI: 10.21136/cmj.2018.0648-16

Authors:Péter Kórus Pages: 1 - 10 Abstract: We extend the results of paper of F.Móricz (2010), where necessary conditions were given for the L1-convergence of double Fourier series. We also give necessary and sufficient conditions for the L1-convergence under appropriate assumptions. PubDate: 2018-04-10 DOI: 10.21136/cmj.2018.0043-17

Authors:Yukihide Enaka; Masakazu Onitsuka Pages: 1 - 16 Abstract: This paper is concerned with the oscillatory behavior of the damped half-linear oscillator (a(t)φp(x′))′ + b(t)φp(x′) + c(t)φp(x) = 0, where φp(x) = x p−1 sgn x for x ∈ R and p > 1. A sufficient condition is established for oscillation of all nontrivial solutions of the damped half-linear oscillator under the integral averaging conditions. The main result can be given by using a generalized Young’s inequality and the Riccati type technique. Some examples are included to illustrate the result. Especially, an example which asserts that all nontrivial solutions are oscillatory if and only if p≠2 is presented. PubDate: 2018-04-04 DOI: 10.21136/cmj.2018.0645-16

Authors:Imed Feki; Ameni Massoudi; Houda Nfata Pages: 1 - 28 Abstract: The main purpose of this article is to give a generalization of the logarithmic-type estimate in the Hardy-Sobolev spaces Hk,p(G); k ∈ N*, 1 ≤ p ≤ 1 and G is the open unit disk or the annulus of the complex space C. PubDate: 2018-03-28 DOI: 10.21136/cmj.2018.0466-16

Authors:Huanyin Chen; Marjan Sheibani; Nahid Ashrafi Pages: 1 - 6 Abstract: We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; Z3 ⊕ Z3; Z3 ⊕ B where B is a Boolean ring; local ring with nil Jacobson radical; M2(Z2) or M2(Z3); or the ring of a Morita context with zero pairings where the underlying rings are Z2 or Z3. PubDate: 2018-03-22 DOI: 10.21136/cmj.2018.0554-16

Authors:Boban Karapetrović Pages: 1 - 18 Abstract: We show that if α > 1, then the logarithmically weighted Bergman space \(A_{{{\log }^\alpha }}^2\) is mapped by the Libera operator L into the space \(A_{{{\log }^{\alpha - 1}}}^2\) , while if α > 2 and 0 < ε ⩽ α−2, then the Hilbert matrix operator H maps \(A_{{{\log }^\alpha }}^2\) into \(A_{{{\log }^{\alpha - 2 - \varepsilon }}}^2\) . We show that the Libera operator L maps the logarithmically weighted Bloch space \({B_{{{\log }^\alpha }}}\) , α ∈ ℝ, into itself, while H maps \({B_{{{\log }^\alpha }}}\) into \({B_{{{\log }^{\alpha + 1}}}}\) . In Pavlović’s paper (2016) it is shown that L maps the logarithmically weighted Hardy-Bloch space \(B_{{{\log }^\alpha }}^1\) , α > 0, into \(B_{{{\log }^{\alpha - 1}}}^1\) . We show that this result is sharp. We also show that H maps \(B_{{{\log }^\alpha }}^1\) , α ⩾ 0, into \(B_{{{\log }^{\alpha - 1}}}^1\) and that this result is sharp also. PubDate: 2018-03-06 DOI: 10.21136/cmj.2018.0555-16

Authors:Yanjiong Yang; Xiaoguang Yan Pages: 1 - 10 Abstract: In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective. PubDate: 2018-03-06 DOI: 10.21136/cmj.2018.0621-16

Authors:Mehri Nasehi; Mansour Aghasi Pages: 1 - 18 Abstract: In this paper we first classify left-invariant generalized Ricci solitons on some solvable extensions of the Heisenberg group in both Riemannian and Lorentzian cases. Then we obtain the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. We also calculate the energy of an arbitrary left-invariant vector field X on these spaces and obtain all vector fields which are critical points for the energy functional restricted to vector fields of the same length. Furthermore, we determine all homogeneous Lorentzian structures and their types on these spaces and give a complete and explicit description of all parallel and totally geodesic hypersurfaces of these spaces. The non-existence of harmonic maps in the non-abelian case is proved and it is shown that the existence of Einstein, Einstein-like metrics and some equations in the Riemannian case can not be extended to their Lorentzian analogues. PubDate: 2018-03-02 DOI: 10.21136/cmj.2018.0635-16

Authors:Haixian Chen; Ying Wang Pages: 1 - 15 Abstract: Let q(n) be a simple strange Lie superalgebra over the complex field ℂ. In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over ℂ and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but p(n) is an exception. In this paper, we introduce the definition of the local superderivation on q(n), give the structures and properties of the local superderivations of q(n), and prove that every local superderivation on q(n), n > 3, is a superderivation. PubDate: 2018-03-02 DOI: 10.21136/cmj.2018.0597-16

Authors:Temha Erkoç; Utku Yilmaztürk; İsmail Ş. Güloğlu Pages: 1 - 10 Abstract: In the literature, there are several graphs related to a finite group G. Two of them are the character degree graph, denoted by Δ(G), and the prime graph, Γ(G). In this paper we classify all finite groups whose character degree graphs are disconnected and coincide with their prime graphs. As a corollary, we find all finite groups whose character degree graphs are square and coincide with their prime graphs. PubDate: 2018-03-02 DOI: 10.21136/cmj.2018.0553-16

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: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