The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomial...

A novel power series representation of the generalized Marcum Q-function of positive order involving generalized Laguerre polynomials is presented. The absolute convergence of the proposed power series expansion is showed, together with a convergence speed analysis by means of truncation error. A brief review of related studies and some numerical results are also provided.

Moments and transforms are the scalar quantities that characterise a function and capture its significant properties. More specifically, these are the descriptors that correspond to the projection of the function on a specific basis function, where the type or characteristic of the basis function gives the name to the moment or transform [82]. Normally, moments and transforms are treated separa...

As for the Encryption protection of 3D digital model, 3D digital watermark technology is inevitably the preferred plan. However, due to the curved surface property and three-dimension property in 3D model itself, there are no better plans that can effectively defend all kinds of watermark attacks among the numerous 3D digital watermark algorithms so far. Thus in this paper a modified algorithm ...

This work demonstrates the use of Latin Hypercube Sampling and Proper Orthogonal Decomposition in combination with a Radial Basis Function model to perform on vehicle prediction coupled fluid–thermal–structure. We regarded Mach number, flight altitude angle attack as input parameters established rapid model. The basic process numerical simulation hypersonic fluid–thermal–structure was studied o...

We recount previous development of d-fold doubling of orthogonal polynomial sequences and give new results on rational function coefficients, recurrence formulas, continued fractions, Rodrigues’ type formulas, and differential equations, for the general case and, in particular, for the d-fold Hermite orthogonal rational functions.

We construct Tchebyshev-II (second kind) weighted orthogonal polynomials U (γ) n,r (u, v, w), γ > −1, on the triangular domain T. We show that U (γ) n,r (u, v, w), n = 0, 1, 2, . . . , r = 0, 1, . . . , n, form an orthogonal system over T with respect to the Tchebyshev-II weight function. AMS Subject Classification: 42C05, 33C45, 33C70

In this paper, we construct generalized Tschebyscheff-type weighted orthogonal polynomials U n,r (u,v,w), γ > −1, in the Bernstein-Bézer form over the simplicial domain. We show that U n,r (u,v,w), r = 0,1, . . . ,n; n= 0,1,2, . . . , form an orthogonal system over a triangular domain with respect to the generalized weight function.

An effective numerical approach is developed for orthogonal waveform design for Multiple-Input Multiple-Output (MIMO) radar. The Doppler shift tolerance is considered in the design cost function. The design results indicate that the Doppler tolerance of the designed orthogonal waveforms is markedly improved. Keywords-MIMO radar; waveform design; Doppler effect;