Abstract: Let \((R,\mathfrak{m})\) be a local ring, a an ideal of R and M a nonzero Artinian R-module of Noetherian dimension n with hd(a, M) = n. We determine the annihilator of the top local homology module \(H^{\mathfrak{a}}_{n}(M)\) . In fact, we prove that $$\text{Ann}_R(H^{\mathfrak{a}}_{n}(M))=\text{Ann}(N(\mathfrak{a},M)),$$ where \(N(\mathfrak{a},M)\) denotes the smallest submodule of M such that \(\text{hd}(\mathfrak{a},M/N(\mathfrak{a},M))<n\) . As a consequence, it follows that for a complete local ring \((R,\mathfrak{m})\) all associated primes of \(H^{\mathfrak{a}}_{n}(M)\) are minimal. PubDate: 2019-03-01

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 to a smaller subgroup of G are obtained. PubDate: 2019-03-01

Abstract: We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014). PubDate: 2019-03-01

Abstract: For a digraph D, the niche hypergraph \(N\mathcal{H}(D)\) of D is the hypergraph having the same set of vertices as D and the set of hyperedges \(E(N\mathcal{H}(D)) = \{ e \subseteq V(D): e \geqslant 2\) and there exists a vertex v such that \(e = \mathop N\nolimits_D^ - (v)\) or \(\left. {e = {\rm{ }}N_D^ + (v)} \right\}\) . A digraph is said to be acyclic if it has no directed cycle as a subdigraph. For a given hypergraph \(\mathcal{H}\) , the niche number \(\hat n(\mathcal{H})\) is the smallest integer such that \(\mathcal{H}\) together with \(\hat n(\mathcal{H})\) isolated vertices is the niche hypergraph of an acyclic digraph. C.Garske, M. Sonntag and H.M.Teichert (2016) conjectured that for a linear hypercycle \(\mathcal{C}_m,\;m\geqslant2\) , if \(\min \left\{ {\left e \right :e \in E({\mathcal{C}_m})} \right\} \geqslant 3\) , then \(\hat n(\mathcal{C}_m)=0\) . In this paper, we prove that this conjecture is true. PubDate: 2019-03-01

Abstract: Let R be an associative unital ring and let a ∈ R be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results. PubDate: 2019-03-01

Abstract: We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral. PubDate: 2019-03-01

Abstract: We prove that the universal central extension of a direct limit of perfect Hom- Lie algebras \((\mathcal{L_i,\;\alpha_{\mathcal{L}_i}})\) is (isomorphic to) the direct limit of universal central extensions of \((\mathcal{L_i,\;\alpha_{\mathcal{L}_i}})\) . As an application we provide the universal central extensions of some multi-plicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras {(slk \((\mathcal{A})\) , αk)}k∈I and describe the universal central extension of its direct limit. PubDate: 2019-03-01

Abstract: Let R be a graded ring and n ⩾ 1 an integer. We introduce and study n-strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m-strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever n > m. Many properties of the n-strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate the relations between the graded and the ungraded n-strongly Gorenstein injective (or flat) modules. In addition, the connections between the n-strongly Gorenstein gr-projective, gr-injective and gr-flat modules are considered. PubDate: 2019-03-01

Abstract: The aim of this paper is to extend the study of Riesz transforms associated to Dunkl Ornstein-Uhlenbeck operator considered by A. Nowak, L. Roncal and K. Stempak to higher order. PubDate: 2019-03-01

Abstract: We obtain the fundamental solution kernel of dyadic diffusions in ℝ+ as a central limit of dyadic mollification of iterations of stable Markov kernels. The main tool is provided by the substitution of classical Fourier analysis by Haar wavelet analysis. PubDate: 2019-03-01

Abstract: Let σ = {σi: i ∈ I} be some partition of the set of all primes ℙ, G be a finite group and σ(G) = {σi: σi ∩ π(G)≠Ø}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every non-identity member of H is a Hall σi-subgroup of G and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ(G). G is said to be σ-full if G possesses a complete Hall σ-set. A subgroup H of G is σ-permutable in G if G possesses a complete Hall σ-set H such that HAx= AxH for all A ∈ H and all x ∈ G. A subgroup H of G is σ-permutably embedded in G if H is σ-full and for every σi ∈ σ(H), every Hall σi-subgroup of H is also a Hall σi-subgroup of some σ-permutable subgroup of G. By using the σ-permutably embedded subgroups, we establish some new criteria for a group G to be soluble and supersoluble, and also give the conditions under which a normal subgroup of G is hypercyclically embedded. Some known results are generalized. PubDate: 2019-03-01

Abstract: The paper deals with the existence of a Kneser solution of the n-th order nonlinear differential inclusion $${x^{(n)}}(t) \in - {A_1}(t,x,(t),...,{x^{(n - 1)}}(t)){x^{(n - 1)}}(t) - ... - {A_n}(t,x(t),...,{x^{(n - 1)}}(t))x(t)\;\text{for}\;\text{a.a.}\;t\; \in [a,\infty ),$$ where a ∈ (0,∞), and Ai: [a,∞) × ℝn → ℝ, i = 1,..., n, are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem. PubDate: 2019-03-01

Abstract: We are concerned with the boundedness of generalized fractional integral operators Iϱ,τ from Orlicz spaces LΦ(X) near L1(X) to Orlicz spaces LΨ(X) over metric measure spaces equipped with lower Ahlfors Q-regular measures, where Φ is a function of the form Φ(r) = rl(r) and l is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials. PubDate: 2019-03-01

Abstract: In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, \(\bar \partial \) -Dirichlet functionals of harmonic mappings are also investigated. PubDate: 2019-03-01

Abstract: Let R be a commutative Noetherian ring, I an ideal of R. Let t ∈ ℕ0 be an integer and M an R-module such that Ext R i (R/I,M) is minimax for all i ⩽ t+1. We prove that if H I i (M) is FD⩽1 (or weakly Laskerian) for all i < t, then the R-modules H I i (M) are I-cominimax for all i < t and Ext R i (R/I,H I t (M) is minimax for i = 0, 1. Let N be a finitely generated R-module. We prove that Ext R j (N,H I i (M)) and Tor j R (N,H I i (M)) are I-cominimax for all i and j whenever M is minimax and H I i (M) is FD⩽1 (or weakly Laskerian) for all i. PubDate: 2019-03-01

Abstract: Let ζ(s) be the Riemann zeta-function. If t ⩾ 6.8 and σ > 1/2, then it is known that the inequality ζ(1 − s) > ζ(s) is valid except at the zeros of ζ(s). Here we investigate the Lerch zeta-function L(λ, α, s) which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters λ = α it is still possible to obtain a certain version of the inequality L(λ, λ, \(1 - \bar s\) ) > L(λ, λ, s) . PubDate: 2019-03-01

Abstract: Let G be a finite group with exactly two nonlinear non-faithful irreducible characters. We discuss the properties of G and classify finite p-groups with exactly two nonlinear non-faithful irreducible characters. PubDate: 2019-03-01

Abstract: We compute the torsion group explicitly over quadratic fields and number fields of degree coprime to 6 for a family of elliptic curves of the form E: y2 = x3 + c, where c is an integer. PubDate: 2019-03-01

Abstract: We give a characterization of the Hölder-Zygmund spaces Cσ(G) (0 < σ < ∞) on a stratified Lie group G in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on G, in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces on stratified Lie groups. PubDate: 2019-03-01

Abstract: An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent. Firstly, we show that Jacobson’s lemma does not hold for nil-clean elements in a ring, answering a question posed by Koşan, Wang and Zhou (2016). Secondly, we present new counter-examples to Diesl’s question whether a nil-clean element is clean in a ring. Lastly, we give new examples of unit-regular elements that are not clean in a ring. The rings under consideration in our examples are particular subrings of \(\mathbb{M}_{2}(\mathbb{Z})\) . PubDate: 2019-03-01