Orthonormal spin-flavor wave functions of Lorentz covariant quark models of the Bakamjian-Thomas type are constructed for nucleon resonances. Three different bases are presented. The manifestly Lorentz covariant Dirac-Melosh basis is related to the Pauli-Melosh basis and the symmetrized Bargmann-Wigner basis that are manifestly orthogonal.

In this paper we calibrate the stationary Gaussian Musiela model to time series of market data using the Karhunen-Loeve expansion in order to get an ortonormal basis (classically known as EOF, empirical orthonormal functions) in a separable Hilbert space. The basis found is optimal for representing the covariance of the invariant measure of the forward rates’ process.

We use special functions and orthonormal wavelet bases on the real line to construct wavelet-like bases. With these wavelets we can construct polynomial bases on the interval; moreover, we can use them for the numerical resolution of degenerate elliptic operators.

Tightness of bounds on rates of approximation by feedforward neural networks is investigated in a more general context of nonlinear approximation by variable-basis functions. Tight bounds on the worst case error in approximation by linear combinations of elements of an orthonormal variable basis are derived.

The use of orthonormal functions and consistency relationships to identify models of multivariable processes and their uncertainty descriptions, is discussed in this paper. The norm-bounded uncertainty can be obtained from the covariance matrix of the parameters. Using a-priori consistency relationships, unstructured uncertainty may be converted to a structured one. The μ analysis shows that th...

Motivated by recent developments in quantum simulation of synthetic dimensions, e.g., optical lattices ultracold atoms, we discuss here d-dimensional periodic, gapped systems for d ≤ 4, with a focus on the topology occupied energy states. We perform this analysis asking whether spectral subspace below gap can be spanned smooth and periodic Bloch functions, corresponding to localized Wannier fun...

We introduce two new non-iterative approaches towards passivity enforcement for scalar rational transfer functions. The first is based on the projection of the Herglotz-Cauer representation of the transfer function on the orthonormal Laguerre basis. The second is based on the rational approximation by means of Talbot-Gauss quadrature of a pertinent integral related to the Cauer transform kernel.

We compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on Fq[[T ]]. In particular, we show a close relation between them as orthonormal bases. Moreover, parallel to Carlitz’s coefficient formula, we give the closed formula for the expansion coefficients in terms of the digit derivatives.

In this paper linear prediction process is applied to frequency warped signals. The warping is realized by using orthonormal FAM' functions. The general formulation of WLP is given and effective realizations with allpass filters are studied. The application of auditory WLP to speech coding and speech recognition has given good results.