Laguerre geometry provides a simple approach to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from arbitrary rational curves or surfaces with help of a geometric transformation which describes a change between two models of Laguerre geometry. Closely related to that is their optical interpretation as anticaustics o...

In this paper a novel Laguerre based controller is proposed to control the velocity of an electro hydraulic servo system (EHSS). The proposed Laguerre based controller is a kind of IIR structure which has the benefits of both FIR and IIR structures and can solve their limitations in stability and compelexity. The controller can control the velocity of EHSS appropriately and consumes small compu...

The linearization problem of a second-order ordinary differential equation by the generalized Sundman transformation was considered earlier by Duarte, Moreira and Santos using the Laguerre form. The results obtained in the present paper demonstrate that their solution of the linearization problem for a second-order ordinary differential equation via the generalized Sundman transformation is not...

We present a new passive model reduction algorithm based on the Laguerre expansion of the time response of interconnect networks. We derive expressions for the Laguerre coefficient matrices that minimize a weighted square of the approximation error, and show how these matrices can be computed efficiently using Krylov subspace methods. We discuss the connections between our method and other meth...

The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...

We generalized the nonparaxial field components of Laguerre-Gaussian and flattened Gaussian beams obtained using the angular spectrum method to include symmetric radial and angular expansions and simplified them using an approximate evaluation of the integral equations for the field components. These field components possess series expressions in orders of a natural expansion parameter, which c...

We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for re...

1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...

In this article, the quasi-Laguerre iteration is established in the spirit of Laguerre's iteration for solving polynomial f with all real zeros. The new algorithm, which maintains the monotonicity and global convergence of the Laguerre iteration, no longer needs to evaluate f". The ultimate convergence rate is + 1. When applied to approximate the eigenvalues of a symmetric tridiagonal matrix, t...