Authors:Daowei Lu; Shuanhong Wang Pages: 1 - 9 Abstract: Abstract Let H be a finite-dimensional bialgebra. In this paper, we prove that the category LR(H) of Yetter-Drinfeld-Long bimodules, introduced by F.Panaite, F. Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category \(\begin{array}{*{20}{c}} {H \otimes H*} \\ {H \otimes H*} \end{array}YD\) over the tensor product bialgebra \(H \otimes H*\) as monoidal categories. Moreover if H is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results. PubDate: 2017-03-03 DOI: 10.21136/cmj.2017.0666-15

Authors:Ruifang Chen; Xianhe Zhao Pages: 1 - 11 Abstract: Abstract Let G be a finite group. A normal subgroup N of G is a union of several G-conjugacy classes, and it is called n-decomposable in G if it is a union of n distinct G-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5. PubDate: 2017-03-02 DOI: 10.21136/cmj.2017.0197-16

Authors:Zhi-Wei Li Pages: 1 - 9 Abstract: Abstract We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category F such that the homotopy category of this model structure is equivalent to the stable category F as triangulated categories. This seems to be well-accepted by experts but we were unable to find a complete proof for it in the literature. When F is a weakly idempotent complete (i.e., every split monomorphism is an inflation) Frobenius category, the model structure we constructed is an exact (closed) model structure in the sense of Gillespie (2011). PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0582-15

Authors:Abdoreza R. Armakan; Mohammed Reza Farhangdoost Pages: 1 - 12 Abstract: Abstract We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra g by another hom-Lie algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie algebras, i.e., we show that in order to have an extendible hom-Lie algebra, there should exist a trivial member of the third cohomology. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0576-15

Authors:Miloš Arsenović; Miroslav Pavlović Pages: 1 - 8 Abstract: Abstract We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0562-15

Authors:Tomasz Beberok Pages: 1 - 13 Abstract: Abstract We investigate the Bergman kernel function for the intersection of two complex ellipsoids {(z, w 1, w 2) ∈ C n+2: z 1 2+...+ z n 2+ w 1 q < 1, z 1 2+...+ z n 2+ w 2 r < 1}. We also compute the kernel function for {(z 1,w 1,w 2) ∈ C3: z 1 2/n + w 1 q < 1, z 1 2/n + w 2 r < 1} and show deflation type identity between these two domains. Moreover in the case that q = r = 2 we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0073-16

Authors:Ji-Cai Liu Pages: 1 - 7 Abstract: Abstract Euler’s pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler’s pentagonal number theorem. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0063-16

Authors:Lai-Yi Zhu; Da-Peng Zhou Pages: 1 - 13 Abstract: Abstract Using undergraduate calculus, we give a direct elementary proof of a sharp Markov-type inequality p' [−1,1] ≤ 1/2 p [−1,1] for a constrained polynomial p of degree at most n, initially claimed by P. Erdős, which is different from the one in the paper of T.Erdé lyi (2015). Whereafter, we give the situations on which the equality holds. On the basis of this inequality, we study the monotone polynomial which has only real zeros all but one outside of the interval (−1, 1) and establish a new asymptotically sharp inequality. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0256-16

Authors:Raul Quiroga-Barranco; Armando Sanchez-Nungaray Pages: 1 - 16 Abstract: Abstract We consider separately radial (with corresponding group T n ) and radial (with corresponding group U(n)) symbols on the projective space P n (C), as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the C*-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the C*-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between T n and U(n). PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0293-16

Authors:Shaohui Wang; Bing Wei Pages: 1 - 4 Abstract: Abstract Let γ(G) and i(G) be the domination number and the independent domination number of G, respectively. Rad and Volkmann posted a conjecture that i(G)/γ(G) 6 ≤ ∆(G)/2 for any graph G, where ∆(G) is its maximum degree (see N. J.Rad, L.Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than ∆(G)/2 are provided as well. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0068-16

Authors:Nahid Ashrafi; Marjan Sheibani; Huanyin Chen Pages: 1 - 9 Abstract: Abstract A ring R is (weakly) nil clean provided that every element in R is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let R be abelian, and let n ∈ N. We prove that M n (R) is nil clean if and only if R/J(R) is Boolean and M n (J(R)) is nil. Furthermore, we prove that R is weakly nil clean if and only if R is periodic; R/J(R) is Z3, B or Z3 ⊕ B where B is a Boolean ring, and that M n (R) is weakly nil clean if and only if M n (R) is nil clean for all n > 2. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0677-15

Authors:Michal Hrbek; Pavel Růžička Pages: 1 - 11 Abstract: Abstract A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0632-15

Authors:Chao Wang; Xiaoyan Yang Pages: 1 - 18 Abstract: Abstract Let \(\Lambda = \left( {\begin{array}{*{20}{c}} A&M \\ 0&B \end{array}} \right)\) be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ-modules under the condition that M is a cocompatible (A,B)-bimodule, we establish a recollement of the stable category \(\overline {Ginj\left( \Lambda \right)} \) . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ. PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0346-16

Authors:Jiří Tomáš Pages: 1 - 20 Abstract: Abstract Let M be an m-dimensional manifold and A = D k r /I = R⊕N A a Weil algebra of height r. We prove that any A-covelocity T x A f ∈ T x A* M, x ∈ M is determined by its values over arbitrary max{widthA,m} regular and under the first jet projection linearly independent elements of T x A M. Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result T A* M ~ T r* M without coordinate computations, which improves and generalizes the partial result obtained in Tomáš (2009) from m ≥ k to all cases of m. We also introduce the space J A (M,N) of A-jets and prove its rigidity in the sense of its coincidence with the classical jet space J r (M,N). PubDate: 2017-03-01 DOI: 10.21136/cmj.2017.0566-15

Authors:Dariusz Idczak Pages: 1 - 25 Abstract: Abstract We introduce a notion of a function of finite fractional variation and characterize such functions together with their weak σ-additive fractional derivatives. Next, we use these functions to study differential equations of fractional order, containing a σ-additive term—we prove existence and uniqueness of a solution as well as derive a Cauchy formula for the solution. We apply these results to impulsive equations, i.e. equations containing the Dirac measures. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0455-15

Authors:Yunhee Euh; JeongHyeong Park; Kouei Sekigawa Pages: 1 - 18 Abstract: Abstract We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional case under a slightly more general setting. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0540-15

Authors:Yaning Wang Pages: 1 - 14 Abstract: Abstract A necessary and sufficient condition for the Reeb vector field of a three dimensional non-Kenmotsu almost Kenmotsu manifold to be minimal is obtained. Using this result, we obtain some classifications of some types of (k, μ, v)-almost Kenmotsu manifolds. Also, we give some characterizations of the minimality of the Reeb vector fields of (k, μ, v)-almost Kenmotsu manifolds. In addition, we prove that the Reeb vector field of an almost Kenmotsu manifold with conformal Reeb foliation is minimal. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0377-15

Authors:Nijjwal Karak Pages: 1 - 8 Abstract: Abstract In many recent articles, medians have been used as a replacement of integral averages when the function fails to be locally integrable. A point x in a metric measure space (X, d, μ) is called a generalized Lebesgue point of a measurable function f if the medians of f over the balls B(x, r) converge to f(x) when r converges to 0. We know that almost every point of a measurable, almost everywhere finite function is a generalized Lebesgue point and the same is true for every point of a continuous function. We show that a function f ∈ M s,p (X), 0 < s ≤ 1, 0 < p < 1, where X is a doubling metric measure space, has generalized Lebesgue points outside a set of \(\mathcal{H}^h\) -Hausdorff measure zero for a suitable gauge function h. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0405-15

Authors:Zhinan Xia Pages: 1 - 19 Abstract: Abstract In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic PC-mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic PC-mild solution of a two-dimensional impulsive fractional predator-prey system with diffusion are investigated. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0398-15

Authors:Mojgan Afkhami; Kazem Khashyarmanesh; Zohreh Rajabi Pages: 1 - 19 Abstract: Abstract Let R be a commutative ring. The annihilator graph of R, denoted by AG(R), is the undirected graph with all nonzero zero-divisors of R as vertex set, and two distinct vertices x and y are adjacent if and only if ann R (xy) ≠ ann R (x) ∪ ann R (y), where for z ∈ R, ann R (z) = {r ∈ R: rz = 0}. In this paper, we characterize all finite commutative rings R with planar or outerplanar or ring-graph annihilator graphs. We characterize all finite commutative rings R whose annihilator graphs have clique number 1, 2 or 3. Also, we investigate some properties of the annihilator graph under the extension of R to polynomial rings and rings of fractions. For instance, we show that the graphs AG(R) and AG(T(R)) are isomorphic, where T(R) is the total quotient ring of R. Moreover, we investigate some properties of the annihilator graph of the ring of integers modulo n, where n ⩾ 1. PubDate: 2017-02-24 DOI: 10.21136/cmj.2017.0436-15