Unbounded B-Fredholm operators on Hilbert spaces

This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given in terms of the sum of a Drazin closed operator and a finite-rank operator. We analyse the properties of the powers Tm of a closed B-Fredholm operator and we establish a spectral mapping theorem

B-Weyl spectrum and poles of the resolvent

AbstractLet T be a bounded linear operator acting on a Banach space and let σBW(T)={λ∈Csuch thatT−λIis not a B-Fredholm operator of index0} be the B-Weyl spectrum of T. Define also E(T) to be the set of all isolated eigenvalues in the spectrum σ(T) of T, and Π(T) to be the set of the poles of the resolvent of T. In this paper two new generalized versions of the classical Weyl's theorem are considered. More precisely, we seek for conditions under which an operator T satisfies the generalized Weyl's theorem: σBW(T)=σ(T)⧹E(T), or the version II of the generalized Weyl's theorem: σBW(T)=σ(T)⧹Π(T)

Tableaux Modulo Theories Using Superdeduction

We propose a method that allows us to develop tableaux modulo theories using the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. This method is presented in the framework of the Zenon automated theorem prover, and is applied to the set theory of the B method. This allows us to provide another prover to Atelier B, which can be used to verify B proof rules in particular. We also propose some benchmarks, in which this prover is able to automatically verify a part of the rules coming from the database maintained by Siemens IC-MOL. Finally, we describe another extension of Zenon with superdeduction, which is able to deal with any first order theory, and provide a benchmark coming from the TPTP library, which contains a large set of first order problems.Comment: arXiv admin note: substantial text overlap with arXiv:1501.0117

Abstract Weyl-type theorems

summary:In this paper, we give a new approach to the study of Weyl-type theorems. Precisely, we introduce the concepts of spectral valued and spectral partitioning functions. Using two natural order relations on the set of spectral valued functions, we reduce the question of relationship between Weyl-type theorems to the study of the set difference between the parts of the spectrum that are involved. This study solves completely the question of relationship between two spectral valued functions, comparable for one or the other order relation. Then several known results about Weyl-type theorems become corollaries of the results obtained

Imposed Switching Frequency Direct Torque Control of Induction Machine Using Five Level Flying Capacitors Inverter

The paper proposes a new control structure for sensorless induction motor drive based on a five-level voltage source inverter (VSI). The output voltages of the five-level VSI can be represented by nine groups. Then, the amplitude and the rotating velocity of the flux vector can be controlled freely. Both fast torque and optimal switching logic can be obtained. The selection is based on the value of the stator flux and the torque. This paper investigates a new control structure focused on controlling switching frequency and torque harmonics contents. These strategies, called ISFDTC, indeed combines harmoniously both these factors, without compromising the excellence of the dynamical performances typically conferred to standard DTC strategies. The validity of the proposed control technique is verified by Matlab/Simulink. Simulation results presented in this paper confirm the validity and feasibility of the proposed control approach and can be tested on experimental setup.Peer reviewe