Authors:Erzsébet Lukács; András Magyar Pages: 1 - 29 Abstract: Let A be a standard Koszul standardly stratified algebra and X an A-module. The paper investigates conditions which imply that the module Ext* A (X) over the Yoneda extension algebra A* is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras. PubDate: 2017-10-25 DOI: 10.21136/cmj.2017.0546-16

Authors:Sheng-Liang Yang; Yan-Xue Xu; Tian-Xiao He Pages: 1 - 18 Abstract: For integers m > r ≥ 0, Brietzke (2008) defined the (m, r)-central coefficients of an infinite lower triangular matrix G = (d, h) = (d n,k ) n,k∈N as d mn+r,(m−1)n+r , with n = 0, 1, 2,..., and the (m, r)-central coefficient triangle of G as $${G^{\left( {m,r} \right)}} = {\left( {{d_{mn + r,\left( {m - 1} \right)n + k + r}}} \right)_{n,k \in \mathbb{N}}}.$$ It is known that the (m, r)-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = (d, h) with h(0) = 0 and d(0), h′(0) ≠ 0, we obtain the generating function of its (m, r)-central coefficients and give an explicit representation for the (m, r)-central Riordan array G (m,r) in terms of the Riordan array G. Meanwhile, the algebraic structures of the (m, r)-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of m and r. As applications, we determine the (m, r)-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach. PubDate: 2017-10-24 DOI: 10.21136/cmj.2017.0165-16

Authors:Li Zu; Daqing Jiang; Donal O'Regan Pages: 1 - 24 Abstract: We consider a single-species stochastic logistic model with the population’s nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation. PubDate: 2017-10-24 DOI: 10.21136/cmj.2017.0350-15

Authors:Pengfei Guo; Jianjun Liu Pages: 1 - 10 Abstract: A group G is said to be a C-group if for every divisor d of the order of G, there exists a subgroup H of G of order d such that H is normal or abnormal in G. We give a complete classification of those groups which are not C-groups but all of whose proper subgroups are C-groups. PubDate: 2017-10-20 DOI: 10.21136/cmj.2017.0542-16

Authors:Catarina P. Avelino; Altino F. Santos Pages: 1 - 28 Abstract: A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed. The combinatorial structure of each tiling is also analysed. PubDate: 2017-10-19 DOI: 10.21136/cmj.2017.0610-15

Authors:Hossein Shahsavari; Behrooz Khosravi Pages: 1 - 9 Abstract: For a finite group G, the intersection graph of G which is denoted by Γ(G) is an undirected graph such that its vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H ∩ K ≠ 1. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of Aut(Γ(G)). PubDate: 2017-10-18 DOI: 10.21136/cmj.2017.0446-16

Authors:Swarup Kumar Panda Pages: 1 - 11 Abstract: A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in H which possess unicyclic inverses. We present a characterization of unicyclic graphs in H which possess bicyclic inverses. PubDate: 2017-10-12 DOI: 10.21136/cmj.2017.0429-16

Authors:Amiran Gogatishvili; Rza Mustafayev; Tuğçe Ünver Pages: 1 - 28 Abstract: In this paper, characterizations of the embeddings between weighted Copson function spaces \(Co{p_{{p_1},{q_1}}}\left( {{u_1},{v_1}} \right)\) and weighted Cesàro function spaces \(Ce{s_{{p_2},{q_2}}}\left( {{u_2},{v_2}} \right)\) are given. In particular, two-sided estimates of the optimal constant c in the inequality $${\left( {\int_0^\infty {{{\left( {\int_0^t {f{{\left( \tau \right)}^{{p_2}}}{v_2}\left( \tau \right)d\tau } } \right)}^{{q_2}/{p_2}}}{u_2}\left( t \right)dt} } \right)^{1/{q_2}}} \leqslant c{\left( {\int_0^\infty {{{\left( {\int_t^\infty {f{{\left( \tau \right)}^{{p_1}}}{v_1}\left( \tau \right)d\tau } } \right)}^{{q_1}/{p_1}}}{u_1}\left( t \right)dt} } \right)^{1/{q_1}}},$$ where p 1, p 2, q 1, q 2 ∈ (0,∞), p 2 ≤ q 2 and u 1, u 2, v 1, v 2 are weights on (0,∞), are obtained. The most innovative part consists of the fact that possibly different parameters p 1 and p 2 and possibly different inner weights v 1 and v 2 are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities. PubDate: 2017-10-11 DOI: 10.21136/cmj.2017.0424-16

Authors:Zujin Zhang Pages: 1 - 7 Abstract: We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of u 3 and ω 3, which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M.Pokorný (2004). PubDate: 2017-10-10 DOI: 10.21136/cmj.2017.0419-16

Authors:Roksana Słowik Pages: 1 - 9 Abstract: Consider T n (F)—the ring of all n × n upper triangular matrices defined over some field F. A map φ is called a zero product preserver on T n (F) in both directions if for all x, y ∈ T n (F) the condition xy = 0 is satisfied if and only if φ(x)φ(y) = 0. In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map φ may act in any bijective way, whereas for the zero divisors and zero matrix one can write φ as a composition of three types of maps. The first of them is a conjugacy, the second one is an automorphism induced by some field automorphism, and the third one transforms every matrix x into a matrix x′ such that {y ∈ T n (F): xy = 0} = {y ∈ T n (F): x′y = 0}, {y ∈ T n (F): yx = 0} = {y ∈ T n (F): yx′ = 0}. PubDate: 2017-10-09 DOI: 10.21136/cmj.2017.0416-16

Authors:Francisco Javier González Vieli Pages: 1 - 12 Abstract: Given a distribution T on the sphere we define, in analogy to the work of Łojasiewicz, the value of T at a point ξ of the sphere and we show that if T has the value τ at ξ, then the Fourier-Laplace series of T at ξ is Abel-summable to τ. PubDate: 2017-10-06 DOI: 10.21136/cmj.2017.0403-16

Authors:Azam Babai; Ali Mahmoudifar Pages: 1 - 10 Abstract: For a finite group G denote by N(G) the set of conjugacy class sizes of G. In 1980s, J.G.Thompson posed the following conjecture: If L is a finite nonabelian simple group, G is a finite group with trivial center and N(G) = N(L), then G ≅ L. We prove this conjecture for an infinite class of simple groups. Let p be an odd prime. We show that every finite group G with the property Z(G) = 1 and N(G) = N(A i ) is necessarily isomorphic to A i , where i ∈ {2p, 2p + 1}. PubDate: 2017-10-05 DOI: 10.21136/cmj.2017.0396-16

Authors:Ahmad Khojali Pages: 1 - 9 Abstract: We consider the annihilator of certain local cohomology modules. Moreover, some results on vanishing of these modules will be considered. PubDate: 2017-10-04 DOI: 10.21136/cmj.2017.0313-16

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: 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: 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: 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: 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:Xiaoqi Wei; Yan Gu Pages: 1 - 14 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: 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