The paper is devoted to the study of metallic Riemannian structures. An integrability condition and curvature properties for these structures by means of a Φ-operator applied to pure tensor fields are presented. Examples of these structures are also given. [ABSTRACT FROM AUTHOR]
In this paper we prove that spacelike and timelike magnetic trajectories corresponding to the para-Kähler 2-form on a para-Kähler manifold (M, p, g) are circles on M. We then classify all para-Kähler magnetic curves in pseudo-Euclidean spaces E2nn. [ABSTRACT FROM AUTHOR]
This paper deals with the global attractivity of positive solutions of the second-order nonlinear difference equationxn+1 = axkn + bk-1Σj=1xjnxk-jn-1 + cxkn-1/Axkn + Bk-1Σj=1xjnxk-jn-1 + Cxkn-1, k = 3, 4; ..., n = 0, 1, ..., where the parameters a, b, c, A, B, C and the initial values x0, x-1 are arbitrary positive real numbers. [ABSTRACT FROM AUTHOR]
An almost null ring is a ring R in which for all a, b ∊ R, a³ = 0, Ma² = 0 for some square-free integer M that depends on a and ab = ka² = lb² for some integers k, l. This paper is devoted to the classification of the almost null rings. [ABSTRACT FROM AUTHOR]
Golchin and Rezaei (Commun Algebra 2009; 37: 1995-2007) introduced the weak version of Condition (PWP) for S -posets, called Condition (PWP)w. In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the S -poset A(I) satisfies Condition (PWP)w. Furthermore, we characterize pomonoids S over which all cyclic (Rees factor) S -posets satisfy Condition (PWP)w, and pomonoids S over which all Rees factor S -posets satisfying Condition (PWP)w have a certain property. Finally, we consider direct products of S -posets satisfying Condition (PWP)w. [ABSTRACT FROM AUTHOR]
Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption. [ABSTRACT FROM AUTHOR]