Related papers: Pulsar timing array analysis in a Legendre polynom…
Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite…
The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials. We show how the use of the well known integral…
In this paper, we explore a new type of smooth and well-behaved polynomial redshift function that can avoid a future singularity. Using this function, we have proposed different redshift parametrizations of the dark energy equation of…
Pulsar-timing collaborations have recently reported evidence for the detection of an isotropic stochastic gravitational-wave background consistent with one sourced by a population of inspiralling supermassive black hole binaries. However, a…
Additional pulsation modes have been discovered in many Cepheids, RR Lyrae, and other variable stars. Fourier transforms are used to find, fit and subtract the main pulsation period and its harmonics to reveal additional modes. Commonly,…
We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a…
We extend our previous work on applying CMB techniques to the mapping of gravitational-wave backgrounds to backgrounds which have non-GR polarisations. Our analysis and results are presented in the context of pulsar-timing array…
We investigate the cross-correlation between astrometric and timing-residual observables for distant sources, such as pulsars and galaxies, and equivalent observables for nearby solar system bodies. Using the unified spin-weighted formalism…
The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically problematic. Indeed, it has long been suggested,…
In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp…
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density…
The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…
With evidence for a nanohertz gravitational-wave background now established by Pulsar Timing Arrays, the search focuses on identifying individual supermassive black hole binaries. We show that these binaries produce a distinct spatial…
In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…
After large galaxies merge, their central supermassive black holes are expected to form binary systems whose orbital motion generates a gravitational wave background (GWB) at nanohertz frequencies. Searches for this background utilize…
Pulsar Timing Arrays have yet to convincingly observe gravitational waves. Some time ago it was pointed out by one of the authors that a dramatic enhancement of the signal would take place for particular values of the angle subtended by the…
A new Bayesian method for the analysis of folded pulsar timing data is presented that allows for the simultaneous evaluation of evolution in the pulse profile in either frequency or time, along with the timing model and additional…
Integrals involving derivatives of Legendre polynomials frequently arise in applications ranging from multipole expansions for processes involving electromagnetic probes to spectral methods in numerical physics. Despite their practical…
Pulsar Timing Array (PTA) observations have recently gathered substantial evidence for the existence of a gravitational wave background in the nHz frequency band. Searching for anisotropies in this signal is key to determining its origin,…
We introduce an extended d-variate Farlie-Gumbel-Morgenstern (FGM) copula that incorporates additional parameters based on Legendre polynomials to enhance the representation of multivariate dependence structures. Within an i.i.d. framework,…