FULL POLARIZABILITY MATRIX EXTRACTION FORMULAS FOR ELECTRICALLY SMALL PARTICLES VIA REFLECTION/TRANSMISSION COEFFICIENTS

Matrix Formulas for Nonstationary ARIMA Signal Extraction

The paper provides general matrix formulas for minimum mean squared error signal extraction, for a finitely sampled time series whose signal and noise components are nonstationary ARIMA processes. These formulas are quite practical; as well as being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters. We also ex...

Matrix Formulas for Nonstationary Signal Extraction

The paper provides general matrix formulas for extraction of a nonstationary signal in nonstationary noise, for a finitely sampled time series. These formulas are quite practical, in that they provide a ready intuition for the filtering operation, as well as being simple to implement on a computer. Applications to signal extraction diagnostics are discussed. Disclaimer This report is released t...

Quadrature formulas for Fourier coefficients

Radiative corrections to the polarizability tensor of an electrically small anisotropic dielectric particle.

Radiative corrections to the polarizability tensor of isotropic particles are fundamental to understand the energy balance between absorption and scattering processes. Equivalent radiative corrections for anisotropic particles are not well known. Assuming that the polarization within the particle is uniform, we derived a closed-form expression for the polarizability tensor which includes radiat...

Exact Formulas for Coefficients of Jacobi Forms

In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...