Related papers: Comment to Comment on Cartesian expressions for su…
Recently published formulas for the surface and regular solid spherical harmonics and for the expansion of the product of two normalized associated Legendre functions with different centers in ellipsoidal coordinates (Telhat Ozdogan, Metin…
The comments of Guseinov are critically analyzed. Contrary to his comments, it is pointed out that our formula for two-center overlap integrals over Slater type orbitals have been derived independently, not derived from the earlier works of…
In a recent publication (Telhat Ozdogan, Int. J. Quantum Chem., 92 (2003) 419), we presented a unified algorithm for the evaluation of multicenter multielectron integrals over Slater type orbitals with noninteger principal quantum numbers,…
The comments of Guseinov on our paper (T. Ozdogan, S. Gumus and M. Kara, J. Math. Chem., 33 (2003) 181) are critically analyzed. Contrary to his comments, it is proved that the expansion formula for the product of two normalized associated…
Ozdogan (Int. J. Quantum Chem., 92 (2003) 419) published formulas for evaluating the multielectron multicenter molecular integrals over Slater-type orbitals (STOs). It is demonstrated that the formulas presented in this work are not…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
The behavior of geodesic curves on even seemingly simple surfaces can be surprisingly complex. In this paper we use the Hamiltonian formulation of the geodesic equations to analyze their integrability properties. In particular, we examine…
The question raised by [Bastin and Martin 2003 J. Phys. B: At. Mol. Opt. Phys. 36, 4201] is examined and used to explain in more detail a key point of our calculations. They have sought to rebut criticisms raised by us of certain techniques…
We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never…
We develop a systematic approach to deriving addition theorems for, and some other bilocal sums of, spin spherical harmonics. In this first part we establish some necessary technical results. We discuss the factorization of orbital and spin…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
We introduce a new basis function (the spherical gaussian) for electronic structure calculations on spheres of any dimension $D$. We find \alert{general} expressions for the one- and two-electron integrals and propose an efficient…
A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…
The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
Recently we have reanalyzed the consistency of the solutions of the space fractional Schr\"odinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
Comments are made on some recently published papers on matter collineations of plane symmetric, cylindrically symmetric and spherically symmetric spacetimes.
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for $\mathbb{CP}^n$ and $\mathbb{CH}^n$,…