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In this paper, we generalize the main results of Guo and Isaacs, Archiv der Mathematik 105 (2015) 215-222. We also obtain some criteria for -nilpotency of a finite group. [ABSTRACT FROM AUTHOR]

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points. [ABSTRACT FROM AUTHOR]

The structure of groups in which many subgroups have a certain property χ has been investigated for several choices of the property χ. In particular, groups whose non-normal subgroups are supersoluble are studied in this paper. Moreover, groups with only finitely many normalizers of non-supersoluble groups are considered. [ABSTRACT FROM AUTHOR]

Fix , let be the loop Lie algebra over with basis and relations , where . In this paper, a formal distribution Lie algebra of is constructed. Then the associated conformal algebra is studied, where has a -basis with -brackets and . In particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules. [ABSTRACT FROM AUTHOR]

In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient condition is given for the graded path category to admit a DG category structure. [ABSTRACT FROM AUTHOR]

An ideal I of a ring R is strongly separative provided that for all finitely generated projective R-modules A, B with A=AI and B=BI, if 2A ≅ A ⊕ B, then A ≅ B. We prove in this paper that a regular ideal I of a ring R is strongly separative if and only if each a ∈ 1+I satisfying (1-a)R ∝ r(a) is unit-regular, if and only if each a ∈ 1+I satisfying (1-a2)R ∝ r(a2) is unit-regular, if and only if each a ∈ 1+I satisfying R(1-a)R=R r(a) is unit-regular, if and only if each a ∈ 1+I satisfying R(1-a2)R=R r(a2) is unit-regular. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of non-weight modules for some algebras related to the Virasoro algebra: The algebra (a, b), the twisted deformative Schrödinger-Virasoro Lie algebras and the Schrödinger algebra. We study the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank 1 for these algebras. Moreover, the simplicities of these modules are determined. [ABSTRACT FROM AUTHOR]

In the present paper, the σ-derivations of ℂ[x±1,y±1] are determined, and their applications are considered. [ABSTRACT FROM AUTHOR]

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied. [ABSTRACT FROM AUTHOR]

Ramanujan's formula for the number r24(n) of representations of a positive integer n as a sum of 24 squares asserts that where and Ramanujan's function τ(n) is given by In this paper, we determine a class of formulae analogous to Ramanujan's formula for r24(n). [ABSTRACT FROM AUTHOR]