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In cluster physics a single particle potential to determine the microscopic part of the total energy of a collective configuration is necessary to calculate the shell- and pairing effects. In this paper we investigate the properties of the Riesz fractional integrals and compare their properties with the standard Coulomb and Yukawa potentials commonly used. It is demonstrated, that Riesz potentials may serve as a promising extension of standard potentials and may be reckoned as a smooth transition from Coulomb to Yukawa like potentials, depending of the fractional parameter $alpha$. For the macroscopic part of the total energy the Riesz potentials treat the Coulomb-, symmetry- and pairing-contributions from a generalized point of view, since they turn out to be similar realizations of the same fractional integral at distinct $alpha$ values.
In this paper, we study the general orthogonal Radon transform $R_{p,q}^k$ first studied by R.S Strichartz in cite{Stri}. An sharp existence condition of $R_{p,q}^k f$ on $L^p$-spaces will be given. Then we devote to the relation formulas connecting
For $sgeqslant d$, we obtain the leading term as $Nto infty$ of the maximal weighted $N$-point Riesz $s$-polarization (or Chebyshev constant) for a certain class of $d$-rectifiable compact subsets of $mathbb{R}^p$. This class includes compact subsets
We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main to
Advanced electromagnetic potentials are indigenous to the classical Maxwell theory. Generally however they are deemed undesirable and are forcibly excluded, destroying the theorys inherent time-symmetry. We investigate the reason for this, pointing o
Multiple bases are presented for the conclusion that potentials are fundamental in electrodynamics, with electric and magnetic fields as quantities auxiliary to the scalar and vector potentials -- opposite to the conventional ordering. One foundation