27,676 research outputs found
Hopf algebra actions on differential graded algebras and applications
Let be a finite dimensional semisimple Hopf algebra, a differential
graded (dg for short) -module algebra. Then the smash product algebra
is a dg algebra. For any dg -module , there is a quasi-isomorphism of
dg algebras: \mathrm{RHom}_A(M,M)\#H\longrightarrow \mathrm{RHom}_{A\#H}(M\ot
H,M\ot H). This result is applied to -Koszul algebras, Calabi-Yau algebras
and AS-Gorenstein dg algebrasComment: to appear in Bull. Belg. Math So
Robust fault detection for networked systems with distributed sensors
Copyright [2011] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the robust fault detection problem for a class of discrete-time networked systems with distributed sensors. Since the bandwidth of the communication channel is limited, packets from different sensors may be dropped with different missing rates during the transmission. Therefore, a diagonal matrix is introduced to describe the multiple packet dropout phenomenon and the parameter uncertainties are supposed to reside in a polytope. The aim is to design a robust fault detection filter such that, for all probabilistic packet dropouts, all unknown inputs and admissible uncertain parameters, the error between the residual (generated by the fault detection filter) and the fault signal is made as small as possible. Two parameter-dependent approaches are proposed to obtain less conservative results. The existence of the desired fault detection filter can be determined from the feasibility of a set of linear matrix inequalities that can be easily solved by the efficient convex optimization method. A simulation example on a networked three-tank system is provided to illustrate the effectiveness and applicability of the proposed techniques.This work was supported by national 973 project under Grants 2009CB320602 and 2010CB731800, and the NSFC under Grants
60721003 and 60736026
Deformations of Koszul Artin-Schelter Gorenstein algebras
We compute the Nakayama automorphism of a PBW-deformation of a Koszul
Artin-Schelter Gorenstein algebra of finite global dimension, and give a
criterion for an augmented PBW-deformation of a Koszul Calabi-Yau algebra to be
Calabi-Yau. The relations between the Calabi-Yau property of augmented
PBW-deformations and that of non-augmented cases are discussed. The Nakayama
automorphisms of PBW-deformations of Koszul Artin-Schelter Gorenstein algebras
of global dimensions 2 and 3 are given explicitly. We show that if a
PBW-deformation of a graded Calabi-Yau algebra is still Calabi-Yau, then it is
defined by a potential under some mild conditions. Some classical results are
also recovered. Our main method used in this paper is elementary and based on
linear algebra. The results obtained in this paper will be applied in a
subsequent paper.Comment: to appear at Manuscripta Mat
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