Related papers: The usefulness of analytic response functions
Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many of the statistical methods used to account for autocorrelation can be viewed as regression models that include basis…
An analytical function for the spectrum of spinning dust emission is presented. It is derived through the application of careful approximations, with each step tested against numerical calculations. This approach ensures accuracy while…
In scattering theory the far field pattern describes the directional dependence of a time-harmonic wave scattered by an obstacle or inhomogeneous medium, when observed sufficiently far away from these objects. Considering plane wave…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
We carry out a theoretical study of the polarization of the solar Mg II h-k doublet (including its extended wings) and the subordinate UV triplet around 280 nm. These lines are of great diagnostic interest, as they encode information on the…
The argon spectral function is constructed and applied to neutrino-argon cross section computations in the plane wave impulse approximation with the Pauli blocking final state interaction effect taken into account. The approximations of the…
We examine the analytic properties of the photon polarization function in a background magnetic field, using the technique of inverse Mellin transform. The photon polarization function is first expressed as a power series of the photon…
Surface Patterson Functions have been derived by direct inversion of experimental Low-Energy Electron Diffraction I-V spectra measured at multiple incident angles. The direct inversion is computationally simple and can be used to…
The structure of the solar chromosphere is believed to be governed by magnetic fields, even in quiet-Sun regions that have a relatively weak photospheric field. During the past decade inversion methods have emerged as powerful tools for…
In this work we study the qualitative properties of real analytic bounded maps defined in the infinite complex strip. The main tool is approximation by continued g-fractions of Wall. As an application, the ABC flow system is considered…
Stellar models often use relations between the temperature $T$ and optical depth $\tau$ to evaluate the structure of their optically-thin outer layers. We fit a novel analytic function to the Hopf function $q(\tau)$ of a radiation-coupled…
We provide analytical functions approximating $\int e^{-x^2} dx$, the basis of which is the kink soliton and which are both accurate (error $< 0.2 %$) and simple. We demonstrate our results with some applications, particularly to the…
Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…
Magnetic reconnection is an important driving mechanism of many chromospheric phenomena, e.g., UV bursts and chromospheric jets. Information about magnetic field is indispensable for analyzing chromospheric magnetic reconnection, which is…
We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres of compact stars, which are simple enough to allow practical implementation and still preserve all important physical effects. We take into…
We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE,…
Obtaining the magnetic properties of non-resolved structures in the solar photosphere is always challenging and problems arise because the inversion is carried out through the numerical minimization of a merit function that depends on the…
Diagnostics for the solar chromosphere are relatively few compared to other parts of the atmosphere. Despite this, hundreds of Rydberg lines emitted by neutrals in this region have been observed at UV wavelengths. Here, we investigate their…
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More…