On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Are There Nuclear Structure Effects on the Isoscalar Giant Monopole Resonance and Nuclear Incompressibility near A~90?

"Background-free" spectra of inelastic $\alpha$-particle scattering have been measured at a beam energy of 385 MeV in $^{90, 92}$Zr and $^{92}$Mo at extremely forward angles, including 0$^{\circ}$. The ISGMR strength distributions for the three nuclei coincide with each other, establishing clearly that nuclear incompressibility is not influenced by nuclear shell structure near $A\sim$90 as was claimed in recent measurements.Comment: 5 pages, 4 figures; accepted for publication in Phys. Lett.

Isoscalar Giant Monopole, Dipole, and Quadrupole Resonances in 90,92^{90,92}Zr and 92^{92}Mo

The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in $^{90, 92}$Zr, and $^{92}$Mo from "background-free" spectra of inelastic $\alpha$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including 0$^{\circ}$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influenced by nuclear shell structure near $A\sim$90, contrary to the claim in a recent measurement.Comment: 12 pages, 12 figures; Accepted for publication in Phys. Rev. C. arXiv admin note: text overlap with arXiv:1607.0219

A note on q-Bernoulli numbers and polynomials

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.Comment: 8 page

Evolution of the dipole polarizability in the stable tin isotope chain

The dipole polarizability of stable even-mass tin isotopes 112,114,116,118,120,124 was extracted from inelastic proton scattering experiments at 295 MeV under very forward angles performed at RCNP. Predictions from energy density functionals cannot account for the present data and the polarizability of 208Pb simultaneously. The evolution of the polarizabilities in neighboring isotopes indicates a kink at 120Sn while all model results show a nearly linear increase with mass number after inclusion of pairing corrections.Comment: 10 pages, 6 figures, submitted to Phys. Lett.