For a monoid M, we introduce M-nil-Armendariz rings, which are generalizations of nil-Armendariz rings and M-Armendariz rings, and we investigate their properties. We show that every NI ring is M-nil-Armendariz for any unique product monoid M, and if R is a 2-primal and M-Armendariz ring, then R is M × N-nil-Armendariz, where N is a unique product monoid. Moreover, we study the...

A nonlinear mathematical model for the spread of influenza A (H1N1) infectious diseases including the role of vaccination is proposed and analyzed. It is assumed that the susceptibles become infected by direct contact with infectives and exposed population. We take under consideration that only a susceptible person can be vaccinated and that the vaccine is not 100% efficient. The...

In this paper we show that if a ring R has finite Goldie dimension, then every finitely generated ideal of R consisting of zero-divisors has non-zero annihilator. We also construct an example of a ring of infinite Goldie dimension such that above condition does not hold.

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the...

In this paper, we investigate weak Hopf algebras introduced in Li (J Algebra 208:72–100, 1998; Commun Math Phys 225:191–217, 2002) corresponding to quantum algebras U q (f (K, H)) (see Wang et al. in Commun Algebra 30:2191–2211, 2002). A new class of algebras is defined, which is denoted by \({\mathfrak{w}U^{d}_q.}\) For d = ((1, 1) | (1, 1)), denote \({\mathfrak{w}U^{d}_q...

In this paper, the numerical solutions of doubly perturbed stochastic delay differential equations driven by Lèvy process are investigated. Using the Euler–Maruyama method, we define the numerical solutions, and show that the numerical solutions converge to the true solutions under the local Lipschitz condition. As a corollary, we give the order of convergence under the global...

This paper looks at the influence of slip conditions on heat transfer and the peristaltic flow of a Johnson–Segalman fluid in an inclined asymmetric channel under the supposition of long wave length. The asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Both analytical and numerical solutions are presented. The...

This paper studies the adaptive synchronization of two complex networks with non-delayed and delayed couplings, in which the coupling configuration matrices are not necessarily symmetric or irreducible. Considering the case of identical and nonidentical network topological structures, we obtain several criteria for synchronization of two complex networks based on the Lyapunov...

In this paper, we give and prove some coupled coincidence point theorems for mappings F : X × X → X and g : X → X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65:1379–1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4):16–24, 2010), Harjani et al...

In the present paper we introduce and investigate an interesting subclass \({\mathcal{K}_{s}^{(k)}(\lambda,h)}\) of analytic and close-to-convex functions in the open unit disk \({\mathbb{U}}\) . For functions belonging to the class \({\mathcal{K}_{s}^{(k)}(\lambda,h)}\) , we derive several properties as the inclusion relationships and distortion theorems. The various results...

In each of three exhaustive and distinct cases, it is found a distribution for which the correlation coefficient between the elements of the generalized order statistics (gos) is maximal. The corresponding result for the dual generalized order statistics (dgos) is derived for other three different distributions. Moreover, some interesting relations for the regression curves...

For a connected graph G = (V, E) of order n ≥ 2, a set \({S\subseteq V}\) is a 2-edge geodetic set of G if each edge \({e\in E - E(S)}\) lies on a u-v geodesic with d(u, v) = 2 for some vertices u and v in S. The minimum cardinality of a 2-edge geodetic set in G is the 2-edge geodetic number of G, denoted by eg2(G). It is proved that for any connected graph G, β1(G) ≤ eg2(G...

We consider the fundamental relations β and γ in simple and 0-simple semihypergroups, especially in connection with certain minimal cardinality questions. In particular, we enumerate and exhibit all simple and 0-simple semihypergroups having order 3 where β is not transitive, apart of isomorphisms. Moreover, we show that the least order for which there exists a strongly simple...

An estimate for the Hausdorff dimension of \({x\, \in \, \mathbb{R}}\) whose partial quotients of its regular continued fraction or minus continued fraction (MCF) are in \({E \, \subseteq \, \mathbb{N}}\) is given. This enables us to give a new proof for the Texan conjecture on \({[0,\,\frac{1}{2}]}\) which is valid for both regular and MCF. Also we show that if \({E \, \subseteq...

It is proven that each commutative arithmetical ring R has a finitistic weak dimension ≤ 2. More precisely, this dimension is 0 if R is locally IF, 1 if R is locally semicoherent and not IF, and 2 in the other cases.

The theory of R-smash products for Hopf quasigroups is developed.

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by t-multiplication. This paper investigates integral domains with Boolean t-class semigroup with an emphasis on the GCD and stability conditions. The main results establish t-analogues for well-known results on Prüfer domains and Bézout domains of...

Given any subgroup H of a group G, let Γ H (G) be the directed graph with vertex set G such that x is the initial vertex and y is the terminal vertex of an edge if and only if x ≠ y and \({xy\in H}\) . Furthermore, if \({xy\in H}\) and \({yx\in H}\) for some \({x,y\in G}\) with x ≠ y, then x and y will be regarded as being connected by a single undirected edge. In this paper, the...

We study the tensor category of modules over a semisimple bialgebra H under the assumption that irreducible H-modules of the same dimension > 1 are isomorphic. We consider properties of Clebsch–Gordan coefficients showing multiplicities of occurrences of each irreducible H-module in a tensor product of irreducible ones. It is shown that, in general, these coefficients cannot have...

For an integral domain R with quotient field K, an upper-type ideal of R[x] is an ideal of the form \({I_f = f({\rm x})K[{\rm x}] \cap R[{\rm x}]}\) for some polynomial \({f({\rm x}) \in K[{\rm x}] \backslash K}\). Clearly, I f = I rf for each nonzero \({r \in R}\). Hence one can always choose f (x) from R[x]. Such an ideal I f is said to be almost principal if there is a...

This paper aims to show that the “going-down ring” and the “divided ring” properties ascend along flat morphisms whose co-diagonal morphisms are flat, the so-called absolutely flat morphisms introduced by Olivier. But unibranchedness hypotheses are necessary as any henselization morphism shows. As a by-product, we get that the “unibranched divided ring” property is preserved by...

We discuss three different frameworks for a general theory of factorization in integral domains: τ-factorization, reduced τ-factorization and Γ-factorization. Let D be an integral domain, \({D^{\sharp}}\) the non-zero, non-units of D, and τ a symmetric relation on \({D^{\sharp}}\) . For \({a\in D^{\sharp}, a=\lambda a_{1}\cdots a_{n},\lambda}\) a unit, \({a_{i}\in D^{\sharp}, n...

The goal of this mainly expository paper is to develop the theory of the algebraic entropy in the basic setting of vector spaces V over a field K. Many complications encountered in more general settings do not appear at this first level. We will prove the basic properties of the algebraic entropy of linear transformations \({\phi:V \to V}\) of vector spaces and its...

It is known that a Prüfer domain either with dimension 1 or with finite character has the stacked bases property. Following Brewer and Klinger, some rings of integer-valued polynomials provide, for every n ≥ 2, examples of n-dimensional Prüfer domains without finite character which have the stacked bases property. But, the following question is still open: does the two...

Divisible modules over general rings are considered and a general notion of divisibility is defined. In order to study these divisible modules we generalize the notion of injectivity. One consequence is that rings for which every principal right ideal is projective can be characterized. In addition, a characterization is given of when a submodule of a projective module is...