Related papers: Pulsar timing array analysis in a Legendre polynom…
We consider the Mellin transforms of certain Legendre functions based upon the ordinary and associated Legendre polynomials. We show that the transforms have polynomial factors whose zeros lie all on the critical line Re $s=1/2$. The…
The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a…
The standard technique for very low-frequency gravitational wave detection is mainly based on searching for a specific spatial correlation in the variation of the times of arrival of the radio pulses emitted by millisecond pulsars with…
A short review will be made of elliptic integrals, widely applied in GPS (Global Positioning System) communications (accounting for General Relativity Theory-effects), cosmology, Black hole physics and celestial mechanics. Then a novel…
Double-mode RR Lyrae variables (i.e. radial variables which are simultaneously pulsating in both fundamental and first overtone modes) appear a fundamental tool for investigating the mass of old Population II Horizontal Branch (HB) stars.…
We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…
Precision pulsar timing is integral to the detection of the nanohertz stochastic gravitational-wave background as well as understanding the physics of neutron stars. Conventional pulsar timing often uses fixed time and frequency-averaged…
Arrays of precisely-timed millisecond pulsars are used to search for gravitational waves with periods of months to decades. Gravitational waves affect the path of radio pulses propagating from a pulsar to Earth, causing the arrival times of…
Pulsar timing arrays (PTAs) will enable the detection of nanohertz gravitational waves (GWs) from a population of supermassive binary black holes (SMBBHs) in the next $\sim 3-7$ years. In addition, PTAs provide a rare opportunity to probe…
We have constructed timing solutions for 81 gamma-ray pulsars covering more than five years of Fermi data. The sample includes 37 radio-quiet or radio-faint pulsars which cannot be timed with other telescopes. These timing solutions and the…
In pulsar astronomy, detecting effective pulsar signals among numerous pulsar candidates is an important research topic. Starting from space X-ray pulsar signals, the two-dimensional autocorrelation profile map (2D-APM) feature modelling…
Millisecond and binary pulsars are the most stable astronomical standards of frequency. They can be applied to solving a number of problems in astronomy and time-keeping metrology including the search for a stochastic gravitational wave…
In our previous work \cite{PTA2} we calculated the overlap reduction function for the tensor polarization without employing the short wavelength approximation, this was done by obtaining a power series of nested sums which is valid for all…
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
An astrophysical population of supermassive black hole binaries is thought to be the strongest source of gravitational waves in the frequency range covered by Pulsar Timing Arrays (PTAs). A potential cause for concern is that the standard…
We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…
Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…
We report results on various techniques which allow to compute the expansion into Legendre (or in general Gegenbauer) polynomials in an efficient way. We describe in some detail the algebraic/symbolic approach already presented in Ref.1 and…
We prove that every multiplier sequence for the Legendre basis which can be interpolated by a polynomial has the form $\{h(k^2+k)\}_{k=0}^{\infty}$, where $h\in\mathbb{R}[x]$. We also prove that a non-trivial collection of polynomials of a…