Related papers: Calculation of oblate spheroidal wave functions wi…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
Cosmological parameter estimation requires that the likelihood function of the data is accurately known. Assuming that cosmological large-scale structure power spectra data are multivariate Gaussian-distributed, we show the accuracy of…
We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf…
Context. The QUBIC collaboration is building a bolometric interferometer dedicated to the detection of B-mode polarization fluctuations in the Cosmic Microwave Background. Aims. We introduce a self-calibration procedure related to those…
Accurate estimates of Instrument Spectral Response Functions (ISRFs) are crucial in order to have a good characterization of high resolution spectrometers. Spectrometers are composed of different optical elements that can induce errors in…
We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological…
This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…
Let $D_{T}$ and $B_{\Omega }$ denote the operators which cut the time content outside $T$ and the frequency content outside $\Omega $, respectively. The prolate spheroidal functions are the eigenfunctions of the operator $P_{T,\Omega…
Parameter estimation on gravitational wave signals from compact binary coalescence (CBC) requires the evaluation of computationally intensive waveform models, typically the bottleneck in the analysis. This cost will increase further as low…
Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…
It is shown for two electron atoms that ground-state wavefunctions of the form \begin{equation} \Psi(\vec{r_{1}}, \vec{r_{2}})=\phi(\vec{r_{1}})\phi(\vec{r_{2}})(\cosh ar_{1}+\cosh ar_{2})(1+0.5 r_{12}e^{-b r_{12}}) \end{equation} where…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
This report describes the computation of gradients by algorithmic differentiation for statistically optimum beamforming operations. Especially the derivation of complex-valued functions is a key component of this approach. Therefore the…
The expressions of the autocorrelation functions (CF) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and (a + b r2)1/2, a and…
The Fock expansion [1] describes the $S$-state wave function of the two-electron atomic system in the vicinity of the triple coalescence point. The present work constitutes the additional appendix to our paper [2] devoted to refinement and…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…
We develop a singular pseudodifferential calculus. The symbols that we consider do not satisfy the standard decay with respect to the frequency variables. We thus adopt a strategy based on the Calderon-Vaillancourt Theorem. The remainders…