The Riemann hypothesis for certain integrals of Eisenstein series

This paper studies the non-holomorphic Eisenstein series E(z,s) for the modular surface, and shows that integration with respect to certain non-negative measures gives meromorphic functions of s that have all their zeros on the critical line Re(s) = 1/2. For the constant term of the Eisenstein series it shows that all zeros are on the critical line for fixed y= Im(z) \ge 1, except possibly for two real zeros, which are present if and only if y > 4 \pi e^{-\gamma} = 7.0555+. It shows the Riemann hypothesis holds for all truncation integrals with truncation parameter T \ge 1. For T=1 this proves the Riemann hypothesis for a zeta function recently introduced by Lin Weng, attached to rank 2 semistable lattices over the rationals.Comment: 23 pages; corrected residues of functions in theorem 1 and 2, added reference; v3 small corrections, removed uncited references; v4 more small correction

Large basis ab initio shell model investigation of 9-Be and 11-Be

We are presenting the first ab initio structure investigation of the loosely bound 11-Be nucleus, together with a study of the lighter isotope 9-Be. The nuclear structure of these isotopes is particularly interesting due to the appearance of a parity-inverted ground state in 11-Be. Our study is performed in the framework of the ab initio no-core shell model. Results obtained using four different, high-precision two-nucleon interactions, in model spaces up to 9\hbar\Omega, are shown. For both nuclei, and all potentials, we reach convergence in the level ordering of positive- and negative-parity spectra separately. Concerning their relative position, the positive-parity states are always too high in excitation energy, but a fast drop with respect to the negative-parity spectrum is observed when the model space is increased. This behavior is most dramatic for 11-Be. In the largest model space we were able to reach, the 1/2+ level has dropped down to become either the first or the second excited state, depending on which interaction we use. We also observe a contrasting behavior in the convergence patterns for different two-nucleon potentials, and argue that a three-nucleon interaction is needed to explain the parity inversion. Furthermore, large-basis calculations of 13-C and 11-B are performed. This allows us to study the systematics of the position of the first unnatural-parity state in the N=7 isotone and the A=11 isobar. The 11-B run in the 9\hbar\Omega model space involves a matrix with dimension exceeding 1.1 x 10^9, and is our largest calculation so far. We present results on binding energies, excitation spectra, level configurations, radii, electromagnetic observables, and 10-Be+n overlap functions.Comment: 17 pages, 12 figures To be published in Phys. Rev. C Resubmitted version. Minor change

Immediate versus water-storage performance of Class V flowable composite restoratives

Objectives The aims of this investigation were to clarify the effects of 24 h water-storage and finishing time on mechanical properties and marginal adaptation to a Class V cavity of eight modern flowable resin-composites. Methods Eight flowable composites, plus two controls (one microfilled and one hybrid composite), were investigated with specimen sub-groups (n = 10) for each property measured. The principal series of experiments was conducted in model Class V cavities with interfacial polishing either immediately (3 min) after setting or after 24 h water-storage. After the finishing procedure, each tooth was sectioned in a buccolingual direction through the center of the restoration, and the presence or absence of marginal-gaps was measured (and then summed for each cavity) at 14 points (each 0.5 mm apart) along the cavity restoration interface (n = 10 per group; total points measured = 140). The shear bond-strengths to enamel and to dentin, and flexural strengths and moduli data were also measured at 3 min and after 24 h water-storage. Results For all flowable composites, polished immediately after setting, 14–30 summed gaps were observed (controls: 64 and 42). For specimens polished after 24 h, a significantly (p &#60; 0.05) reduced number of 8–17 summed gaps occurred for only 3 flowable composites; whereas for 5 flowable composites there were non-significantly-different (p &#62; 0.05) numbers (11–17) of summed gaps (controls: 28 and 22). After 24 h storage, shear bond-strengths to enamel and to dentin, flexural strengths and moduli increased highly significantly (p &#60; 0.001) for all materials, except Silux Plus. Significance A post-cure interval of 24 h resulted in enhanced mechanical and adhesive properties of flowable dental composites. In a minority of cases there was also a reduced incidence of marginal-gap formation. However the latter effect may be partly attributed to 24 h delayed polishing, even though such a delay is not usual clinical practice.</p