Authors:Peng-Jie Wong Pages: 1 - 5 Abstract: Abstract We give a simple proof that critical values of any Artin L-function attached to a representation ℓ with character χℓ are stable under twisting by a totally even character χ, up to the dim ℓ-th power of the Gauss sum related to χ and an element in the field generated by the values of χℓ and χ over Q. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0134-16

Authors:Shaban Khidr; Osama Abdelkader Pages: 1 - 9 Abstract: Abstract Let D be a C d q-convex intersection, d ≥ 2, 0≤ q ≤ n − 1, in a complex manifold X of complex dimension n, n ≥ 2, and let E be a holomorphic vector bundle of rank N over X. In this paper, C k -estimates, k = 2, 3,...,∞, for solutions to the \(\bar \partial \) -equation with small loss of smoothness are obtained for E-valued (0, s)-forms on D when n − q ≤ s ≤ n. In addition, we solve the \(\bar \partial \) -equation with a support condition in C k -spaces. More precisely, we prove that for a \(\bar \partial \) -closed form f in \(C_{0{,_q}}^k\left( {X\backslash D,E} \right),{\kern 1pt} 1 \leqslant q \leqslant n - 2,{\kern 1pt} n \geqslant 3\) , with compact support and for ε with 0 < ε < 1 there exists a form u in \(C_{0{,_{q - 1}}}^k\left( {X\backslash D,E} \right)\) with compact support such that \(\bar \partial u = f{\kern 1pt} in{\kern 1pt} X\backslash \bar D\) . Applications are given for a separation theorem of Andreotti-Vesentini type in C k -setting and for the solvability of the \(\bar \partial \) -equation for currents. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0039-16

Authors:Hongfen Yuan Pages: 1 - 14 Abstract: Abstract Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera’s theorem and Painlevé theorem for super Dunklmonogenic functions. These results are nice generalizations of well-known facts in complex analysis. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0187-16

Authors:Kamal Paykan Pages: 1 - 7 Abstract: Abstract A ring R is called a right PS-ring if its socle, Soc(R R ), is projective. Nicholson and Watters have shown that if R is a right PS-ring, then so are the polynomial ring R[x] and power series ring R[[x]]. In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R[[x −1; α, δ]] and the skew polynomial ring R[x; α, δ], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0672-15

Authors:Azam Babai; Zeinab Akhlaghi Pages: 1 - 11 Abstract: Abstract Let G be a group and ω(G) be the set of element orders of G. Let k ∈ ω(G) and m k (G) be the number of elements of order k in G. Let nse(G) = {m k (G): k ∈ ω(G)}. Assume r is a prime number and let G be a group such that nse(G) = nse(S r ), where S r is the symmetric group of degree r. In this paper we prove that G ≅ S r , if r divides the order of G and r 2 does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0700-15

Authors:Jafar A'zami; Naser Pourreza Pages: 1 - 8 Abstract: Abstract Let (R,m) be a commutative Noetherian regular local ring of dimension d and I be a proper ideal of R such that mAss R (R/I) = Assh R (I). It is shown that the R- module Hht(I) I (R) is I-cofinite if and only if cd(I,R) = ht(I). Also we present a sufficient condition under which this condition the R-module H i I (R) is finitely generated if and only if it vanishes. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0116-16

Authors:Kwang-Soon Park Pages: 1 - 22 Abstract: Abstract As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h- Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0143-16

Authors:Janko Bračič; Lina Oliveira Pages: 1 - 10 Abstract: Abstract We show that for a linear space of operators M ⊆ B(H 1, H 2) the following assertions are equivalent. (i) M is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map Ψ = (ψ1, ψ2) on a bilattice Bil(M) of subspaces determined by M with P ≤ ψ1(P,Q) and Q ≤ ψ2(P,Q) for any pair (P,Q) ∈ Bil(M), and such that an operator T ∈ B(H1, H2) lies in M if and only if ψ2(P,Q)Tψ1(P,Q) = 0 for all (P,Q) ∈ Bil(M). This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0456-16

Authors:Adel Mahmoud Gomaa Pages: 1 - 27 Abstract: Abstract We give existence theorems for weak and strong solutions with trichotomy of the nonlinear differential equation (P) $$\dot x\left( t \right) = L\left( t \right)x\left( t \right) + f\left( {t,x\left( t \right)} \right),{\kern 1pt} t \in \mathbb{R}$$ where L(t): t ∈ R is a family of linear operators from a Banach space E into itself and f: R × E → E. By L(E) we denote the space of linear operators from E into itself. Furthermore, for a < b and d > 0, we let C([−d, 0],E) be the Banach space of continuous functions from [−d, 0] into E and f d : [a, b] × C([−d, 0],E) → E. Let \(\hat L:{\kern 1pt} \left[ {a,b} \right] \to L\left( E \right)\) be a strongly measurable and Bochner integrable operator on [a, b] and for t ∈ [a, b] define τ t x(s) = x(t + s) for each s ∈ [−d, 0]. We prove that, under certain conditions, the differential equation with delay (Q) $$\dot x\left( t \right) = \hat L\left( t \right)x\left( t \right) + {f^d}\left( {t,{\tau _t}x} \right){\kern 1pt} if{\kern 1pt} t \in \left[ {a,b} \right],$$ has at least one weak solution and, under suitable assumptions, the differential equation (Q) has a solution. Next, under a generalization of the compactness assumptions, we show that the problem (Q) has a solution too. PubDate: 2017-04-08 DOI: 10.21136/cmj.2017.0592-15

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: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