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The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later…
The spectral flux density of stars can indicate their atmospheric physical properties. A detector can obtain any band flux density at the design stage. However, the band flux density is confirmed and fixed in the process of operation…
The four-component relativistic Fock space coupled cluster method is used to describe the magnetic hyperfine interaction in low-lying electronic states of the KCs molecule. Both diagonal and off-diagonal matrix elements as functions of the…
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
Cosmological random fields are often analysed in spherical Fourier-Bessel basis. Compared to the Cartesian Fourier basis this has an advantage of properly taking into account some of the relevant physical processes (redshift-space…
Using the tool of Hodge-Morrey decomposition of forms, we prove a new decomposition of symmetric rank-2 tensors on Ricci flat manifolds with boundary. Using this we reconstruct a new cosmological perturbation theory that allows for the…
A critical assessment of the quality of the Hipparcos data, partly supported by a completely new analysis of the raw data, is presented with the aim of clarifying reliability issues that have surfaced since the publication of the Hipparcos…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.
We re-examine the effects of redshift space distortion in all-sky galaxy redshift surveys in the formalism of spherical harmonics. Within this framework we show how one can treat both the large-scale linear effects, and the small-scale…
Angular and spectral differential imaging is an observational technique of choice to investigate the immediate vicinity of stars. The relative angular motion and spectral scaling between on-axis and off-axis sources are exploited by…
In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses --…
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the…
We present the formalism for calculating the femtoscopic correlation function directly in spherical harmonics. The numerator and denominator are stored as a set of one-dimensional histograms representing the spherical harmonic…
I report on the APOKASC catalog, a joint effort between the Kepler Asteroseismic Science Consortium and the SDSS-III APOGEE spectroscopic survey. It will contain both seismic and spectroscopic values for stars observed by both surveys. I…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an…