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Given an ST-triple (C , D , M) one can associate a co-t-structure on C and a t-structure on D . It is shown that the discreteness of C with respect to the co-t-structure is equivalent to the discreteness of D with respect to the t-structure. As a special case, the discreteness of D b (mod A) in the sense of Vossieck is equivalent to the discreteness of Kb(projA) in a dual sense, where A is a finite-dimensional algebra. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of achieving node-to-node consensus (NNC) in two-layer multiple-input-multiple-output (MIMO) multi-agent systems (MASs) with Lipschitz nonlinear dynamics and intermittent directed networks, where the cooperative goal is to make each follower to track a specified leader. By using the relative outputs, discontinuous observers are given to reconstruct the full states of followers and then feedback controllers are designed. Furthermore, some NNC criteria are given by investigating stability of the error system. To verify the obtained results, a simulation is performed. [ABSTRACT FROM AUTHOR]

In this paper, a class of disturbed networked Euler-Lagrangian systems is investigated to track a general virtual signal under a general directed communication network. Firstly, a class of fixed-time distributed observer is constructed to estimate the leader's state. Secondly, a local anti-disturbance tracking control based on the previous distributed observer is proposed for each follower to achieve the tracking consensus in a fixed time. A simulation example is finally conducted to verify the proposed algorithm. [ABSTRACT FROM AUTHOR]

Multiferroic properties of La-modified four-layered perovskite BiLaFeCoTiO (0 ≤ x ≤ 1) ceramics were investigated, by analyzing the magnetodielectric effect, magneto-polarization response and magnetoelectric conversion. X-ray diffraction indicated the formation of pure Aurivillius ceramics, and Raman spectroscopy revealed the Bi ions displacement and the crystal structure variation. The enhancement of ferromagnetic and ferroelectric properties was observed in BiLaFeCoTiO after La modification. The evidence for enhanced ME coupling was determined by magnetic field-induced marked variations in the dielectric constant and polarization. A maximum ME coefficient of 1.15 mV/cm·Oe was achieved in BiLaFeCoTiO ceramic, which provides the possible promise for novel magnetoelectric device application. [ABSTRACT FROM AUTHOR]

In this paper, we considered the torsionless modules over cluster-titled algebras of type A. For this type of algebras we deduced some properties and characterizations of the torsionless modules. Moreover, it is nicely showed that M is an indecomposable torsionless module if and only if M is an indecomposable projective module or M = L( α), where α : x → y is a cyclic arrow and $P(y)\stackrel {P(\alpha )}\rightarrow P(x)\rightarrow L(\alpha )\rightarrow 0$. The Auslander-Reiten structure is also investigated. [ABSTRACT FROM AUTHOR]

J. Wei recently proposed a concept of *-modules which is another generalization of *-modules besides *-modules [J. Algebra, 2005, 291: 312-324]. In this paper, we consider the co-*-modules and give some characterizations and properties. It is found that the class of co-*-modules contains co-selfsmall injective cogenerators. The relations between co-*-modules and co-*-modules are also considered. [ABSTRACT FROM AUTHOR]