Authors:Jafar A'zami; Naser Pourreza Pages: 733 - 740 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: 2017-09-01 DOI: 10.21136/cmj.2017.0116-16 Issue No:Vol. 67, No. 3 (2017)

Authors:Hongfen Yuan Pages: 795 - 808 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: 2017-09-01 DOI: 10.21136/cmj.2017.0187-16 Issue No:Vol. 67, No. 3 (2017)

Authors:Ruifang Chen; Xianhe Zhao Pages: 827 - 837 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: 2017-09-01 DOI: 10.21136/cmj.2017.0197-16 Issue No:Vol. 67, No. 3 (2017)

Authors:Martin Franců; Ron Kerman; Gord Sinnamon Pages: 1 - 23 Abstract: Abstract The least concave majorant, \(\widehat F\) , of a continuous function F on a closed interval, I, is defined by \(\widehat F\) (x) = inf{G(x): G ≥ F, G concave}, x ∈ I. We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on I. Given any function F ∈ C 4(I), it can be well-approximated on I by a clamped cubic spline S. We show that Ŝ is then a good approximation to \(\widehat F\) . We give two examples, one to illustrate, the other to apply our algorithm. PubDate: 2017-08-16 DOI: 10.21136/cmj.2017.0408-16

Authors:Doo Hyun Hwang; Eunmi Pak; Changhwa Woo Pages: 1 - 16 Abstract: Abstract We give a classification of Hopf real hypersurfaces in complex hyperbolic twoplane Grassmannians SU2,m /S(U 2·U m) with commuting conditions between the restricted normal Jacobi operator \(\overline R \) Nφ and the shape operator A (or the Ricci tensor S). PubDate: 2017-08-15 DOI: 10.21136/cmj.2017.0289-16

Authors:Byoung Soo Kim; Dong Hyun Cho Pages: 1 - 20 Abstract: Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t], and define a random vector Z n: C[0, t] → R n+1 by \({Z_n}\left( x \right) = \left( {x\left( 0 \right) + a\left( 0 \right),\int_o^{{t_1}} {h\left( s \right)dx\left( s \right) + x\left( 0 \right) + a\left( {{t_1}} \right),...,\int_0^{{t_n}} {h\left( s \right)dx\left( s \right) + x\left( 0 \right) + a\left( {{t_n}} \right)} } } \right)\) , where a ∈ C[0, t], h ∈ L 2[0, t], and 0 < t 1 <... < t n ≤ t is a partition of [0, t]. Using simple formulas for generalized conditional Wiener integrals, given Z n we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions F in a Banach algebra which corresponds to Cameron-Storvick’s Banach algebra S. Finally, we express the generalized analytic conditional Feynman integral of F as a limit of the non-conditional generalized Wiener integral of a polygonal function using a change of scale transformation for which a normal density is the kernel. This result extends the existing change of scale formulas on the classical Wiener space, abstract Wiener space and the analogue of the Wiener space C[0, t]. PubDate: 2017-08-12 DOI: 10.21136/cmj.2017.0248-15

Authors:Liang Zhang; Hui-Qiang Lu; Xiao-Mei Fu; Ze-Hua Zhou Pages: 1 - 15 Abstract: Abstract Let G be a locally compact group and let 1 ≤ p < 1. Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space L p(G) in terms of the weights. Sufficient and necessary conditions for disjoint hypercyclic and disjoint supercyclic powers of weighted translations generated by aperiodic elements on groups will be given. PubDate: 2017-08-10 DOI: 10.21136/cmj.2017.0204-16

Authors:Dishari Chaudhuri; Anupam Saikia Pages: 1 - 11 Abstract: Abstract Let G be a finite group G, K a field of characteristic p ≥ 17 and let U be the group of units in KG. We show that if the derived length of U does not exceed 4, then G must be abelian. PubDate: 2017-08-10 DOI: 10.21136/cmj.2017.0205-16

Authors:Farrokh Shirjian; Ali Iranmanesh Pages: 1 - 8 Abstract: Abstract Let G be a finite group. Let X 1(G) be the first column of the ordinary character table of G. We will show that if X 1(G) = X1(PGU3(q 2)), then G ≅ PGU3(q 2). As a consequence, we show that the projective general unitary groups PGU3(q 2) are uniquely determined by the structure of their complex group algebras. PubDate: 2017-08-10 DOI: 10.21136/cmj.2017.0194-16

Authors:Bertram A. F. Wehrfritz Pages: 1 - 10 Abstract: Abstract Let R be a commutative ring, M an R-module and G a group of R-automorphisms of M, usually with some sort of rank restriction on G. We study the transfer of hypotheses between M/C M (G) and [M,G] such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose [M,G] is R-Noetherian. If G has finite rank, then M/C M (G) also is R-Noetherian. Further, if [M,G] is R-Noetherian and if only certain abelian sections of G have finite rank, then G has finite rank and is soluble-by-finite. If M/C M (G) is R-Noetherian and G has finite rank, then [M,G] need not be R-Noetherian. PubDate: 2017-08-09 DOI: 10.21136/cmj.2017.0193-16

Authors:Lewen Ji; Zhenbing Zeng Pages: 1 - 15 Abstract: Abstract We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals. PubDate: 2017-08-09 DOI: 10.21136/cmj.2017.0180-16

Authors:Xiaoqi Wei; Yan Gu Pages: 1 - 14 Abstract: Abstract Let Δ n,d (resp. Δ′ n,d ) be the simplicial complex and the facet ideal I n,d = (x 1... x d, x d−k+1... x 2d−k ,..., x n−d+1... x n ) (resp. J n,d = (x 1... x d , x d−k+1... x 2d−k ,..., x n−2d+2k+1... x n−d+2k , x n−d+k+1... x n x 1... x k)). When d ≥ 2k + 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/J n,d and S/I n,d t for all t ≥ 1. When d = 2k, we compute the depth and Stanley depth of quotient rings S/Jn,d and S/I n,d , and give lower bounds for the depth and Stanley depth of quotient rings S/I n,d t for all t ≥ 1. PubDate: 2017-08-08 DOI: 10.21136/cmj.2017.0172-16

Authors:Somayeh Bandari; Ali Soleyman Jahan Pages: 1 - 12 Abstract: Abstract Let Δ be a pure simplicial complex on the vertex set [n] = {1,..., n} and I Δ its Stanley-Reisner ideal in the polynomial ring S = K[x 1,..., x n]. We show that Δ is a matroid (complete intersection) if and only if S/I Δ (m) (S/I Δ (m)) is clean for all m ∈ N and this is equivalent to saying that S/I Δ (m) (S/I Δ (m), respectively) is Cohen-Macaulay for all m ∈ N. By this result, we show that there exists a monomial ideal I with (pretty) cleanness property while S/I m or S/I m is not (pretty) clean for all integer m ≥ 3. If dim(Δ) = 1, we also prove that S/I Δ (2) Δ (S/I Δ 2) is clean if and only if S/I Δ (2) (S/I Δ 2, respectively) is Cohen-Macaulay. PubDate: 2017-08-08 DOI: 10.21136/cmj.2017.0173-16

Authors:Qinghou Zeng; Jianfeng Hou Pages: 1 - 12 Abstract: Abstract Let G be a weighted hypergraph with edges of size at most 2. Bollobás and Scott conjectured that G admits a bipartition such that each vertex class meets edges of total weight at least (w 1−Δ1)/2+2w 2/3, where wi is the total weight of edges of size i and Δ1 is the maximum weight of an edge of size 1. In this paper, for positive integer weighted hypergraph G (i.e., multi-hypergraph), we show that there exists a bipartition of G such that each vertex class meets edges of total weight at least (w 0−1)/6+(w 1−Δ1)/3+2w 2/3, where w 0 is the number of edges of size 1. This generalizes a result of Haslegrave. Based on this result, we show that every graph with m edges, except for K 2 and K 1,3, admits a tripartition such that each vertex class meets at least [2m/5] edges, which establishes a special case of a more general conjecture of Bollobás and Scott. PubDate: 2017-07-14 DOI: 10.21136/cmj.2017.0147-16

Authors:Keli Zheng; Yongzheng Zhang Pages: 1 - 15 Abstract: Abstract We study some properties of generalized reduced Verma modules over ℤ-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for ℤ-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules. PubDate: 2017-07-13 DOI: 10.21136/cmj.2017.0050-16

Authors:Yi Liu; Wen Yuan Pages: 1 - 18 Abstract: Abstract Let θ ∈ (0, 1), λ ∈ [0, 1) and p, p 0, p 1 ∈ (1,∞] be such that (1 − θ)/p 0 + θ/p 1 = 1/p, and let φ, φ0, φ1 be some admissible functions such that φ, φ0 p/p0 and φ1 p/p1 are equivalent. We first prove that, via the ± interpolation method, the interpolation L φ0 p0),λ (X), L φ1 p1), λ (X), θ> of two generalized grand Morrey spaces on a quasi-metric measure space X is the generalized grand Morrey space L φ p),λ (X). Then, by using block functions, we also find a predual space of the generalized grand Morrey space. These results are new even for generalized grand Lebesgue spaces. PubDate: 2017-07-13 DOI: 10.21136/cmj.2017.0081-16

Authors:Xiang Han; Jizhu Nan; Chander K. Gupta Pages: 1 - 44 Abstract: Abstract We investigate the invariant rings of two classes of finite groups G ≤ GL(n, F q) which are generated by a number of generalized transvections with an invariant subspace H over a finite field F q in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with different invariant subspaces which have the same dimension. We provide a explicit classification of these groups and calculate their invariant rings. PubDate: 2017-07-12 DOI: 10.21136/cmj.2017.0044-16

Authors:Malkhaz Ashordia Pages: 1 - 30 Abstract: Abstract A general theorem (principle of a priori boundedness) on solvability of the boundary value problem dx = dA(t) · f(t, x), h(x) = 0 is established, where f: [a, b]×R n → R n is a vector-function belonging to the Carathéodory class corresponding to the matrix-function A: [a, b] → R n×n with bounded total variation components, and h: BVs([a, b],R n ) → R n is a continuous operator. Basing on the mentioned principle of a priori boundedness, effective criteria are obtained for the solvability of the system under the condition x(t1(x)) = B(x) · x(t 2(x))+c 0, where t i: BVs([a, b],R n ) → [a, b] (i = 1, 2) and B: BVs([a, b], R n ) → R n are continuous operators, and c 0 ∈ R n . PubDate: 2017-07-11 DOI: 10.21136/cmj.2017.0144-11

Authors:Xiaoying Du Pages: 1 - 9 Abstract: Abstract For any positive integer D which is not a square, let (u 1, v 1) be the least positive integer solution of the Pell equation u 2 − Dv 2 = 1, and let h(4D) denote the class number of binary quadratic primitive forms of discriminant 4D. If D satisfies 2 ł D and v 1h(4D) ≡ 0 (mod D), then D is called a singular number. In this paper, we prove that if (x, y, z) is a positive integer solution of the equation x y + y x = z z with 2 z, then maximum max{x, y, z} <480000 and both x, y are singular numbers. Thus, one can possibly prove that the equation has no positive integer solutions (x, y, z). PubDate: 2017-07-11 DOI: 10.21136/cmj.2017.0645-15

Authors:Songxiao Li; Ruishen Qian; Jizhen Zhou Pages: 1 - 15 Abstract: Abstract In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space. PubDate: 2017-07-11 DOI: 10.21136/cmj.2017.0481-15