For a given (n − 1)-dimensional hypersurface x : M → R, consider the Laguerre form Φ, the Laguerre tensor L and the Laguerre second fundamental form B of the immersion x. In this article, we address the case when the Laguerre form of x is parallel, i.e., ∇Φ ≡ 0. We prove that ∇Φ ≡ 0 is equivalent to Φ ≡ 0, provided that either L+λB+μg = 0 for some smooth function λ and μ, or x has constant Lagu...

Dendritic macromolecules’ have attracted much attention as organic examples of well-defined nanostructures. These molecules are ideal model systems for studying how physical properties depend on molecular size and architecture. In this paper using a simple result, some GAP programs are prepared to compute Wiener and hyper Wiener indices of dendrimers.

We provide examples of flat Laguerre planes of Kleinewillinghöfer type E, thus completing the classification of flat Laguerre planes with respect to Laguerre translations in B. Polster and G.F. Steinke, Results Maths. (2004). These planes are obtained by a method for constructing a new flat Laguerre plane from three given Laguerre planes devised in B. Polster and G. Steinke, Canad. Math. Bull. ...

A new time-domain model order reduction method based on the Laguerre function expansion of the impulse response is presented. The Laguerre coefficients of the impulse response of the reduced-order model, which is calculated using a projection whose matrices form basis of appropriate Krylov subspaces, match, up to a given order, those of the original system. In addition, it is shown that the obt...

A Wiener model is a fairly simple, well known, and often used nonlinear block-oriented black-box model. A possible generalization of the class of Wiener models lies in the parallel Wiener model class. This paper presents a method to estimate the linear time-invariant blocks of such parallel Wiener models from input/output data only. The proposed estimation method combines the knowledge obtained...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless nonlinearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The param...

Introduction: Block-oriented structures are useful to model a nonlinear system. Applications range from RF amplifiers over chemical processes to physiological systems [1]. A block-oriented model consists of two types of blocks: Linear Time Invariant (LTI) and static nonlinear blocks. The most simple block-oriented model structures are the Wiener (a LTI block followed by a static nonlinear block...

The paper presents a model predictive control method for continuous-time systems based on subspace identification. It’s developed by reformulating the continuous-time systems using Laguerre filters to obtain the subspace prediction output. Then, the subspace predictors are derived by QR decomposition from input-output and Laguerre matrices. The subspace predictive controller is designed with th...

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The para...

In this paper, ‎the multi-sensor fault diagnosis in the exhaust temperature sensors of a V94.2 heavy duty gas turbine is presented‎. ‎A Laguerre network-based fuzzy modeling approach is presented to predict the output temperature of the gas turbine for sensor fault diagnosis‎. Due to the nonlinear dynamics of the gas turbine, in these models the Laguerre filter parts are related to the linear d...