Upper bounds for the eigenvalues of Hessian equations

We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur

49Cr: Towards full spectroscopy up to 4 MeV

The nucleus 49Cr has been studied analysing gamma-gamma coincidences in the reaction 46Ti(alpha,n)49Cr at the bombarding energy of 12 MeV. The level scheme has been greatly extended at low excitation energy and several new lifetimes have been determined by means of the Doppler Shift Attenuation Method. Shell model calculations in the full pf configuration space reproduce well negative-parity levels. Satisfactory agreement is obtained for positive parity levels by extending the configuration space to include a nucleon-hole either in the 1d3/2 or in the 2s1/2 orbitals. A nearly one-to-one correspondence is found between experimental and theoretical levels up to an excitation energy of 4 MeV. Experimental data and shell model calculations are interpreted in terms of the Nilsson diagram and the particle-rotor model, showing the strongly coupled nature of the bands in this prolate nucleus. Nine values of K(pi) are proposed for the levels observed in this experiment. As a by-result it is shown that the values of the experimental magnetic moments in 1f7/2 nuclei are well reproduced without quenching the nucleon g-factors.Comment: 13 pages, 8 figure

Transition rates and nuclear structure changes in mirror nuclei 47Cr and 47V

Lifetime measurements in the mirror nuclei 47Cr and 47V were performed by means of the Doppler-shift attenuation method using the multidetector array EUROBALL, in conjunction with the ancillary detectors ISIS and the Neutron Wall. The determined transition strengths in the yrast cascades are well described by full pf shell model calculations.Comment: Latex2e, 11 pages, 3 figure

Band termination in the N=Z Odd-Odd Nucleus 46V

High spin states in the odd-odd N=Z nucleus 46V have been identified. At low spin, the T=1 isobaric analogue states of 46Ti are established up to I = 6+. Other high spin states, including the band terminating state, are tentatively assigned to the same T=1 band. The T=0 band built on the low-lying 3+ isomer is observed up to the 1f7/2-shell termination at I=15. Both signatures of a negative parity T=0 band are observed up to the terminating states at I = 16- and I = 17-, respectively. The structure of this band is interpreted as a particle-hole excitation from the 1d3/2 shell. Spherical shell model calculations are found to be in excellent agreement with the experimental results.Comment: 5 pages, 4 figure

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Demand for the quality conservation of Venice, Italy, according to different nationalities.

This paper focuses on visitor demand for the quality conservation of Venice according to different nationalities. The vast majority of visitors to Venice are foreigners (both tourists and day-visitors) who come from all over the world. In this research they are mainly categorized as non-Italian Europeans or non-Europeans. A specific theoretical model, in which quality conservation is provided publicly and also privately through donations, is presented for nationals and for foreigners. The data are obtained from a contingent valuation survey carried out in Venice, the aim of which was to estimate visitors' willingness to donate (WTD) to the Venice flood defence programme. Demand functions are estimated by applying a twostage regression model. The authors show that the majority of visitors are willing to donate. On average, Italians and non-Europeans would donate more than non-Italian Europeans. As expected, these visitor categories have different mean WTD and different behavioural functions which are affected by attitudinal and economic variables. Bequest value is the main donation motive. Those who identify this as a donation motive, on average, state the highest WTD and the highest degree of certainty to donate. This result seems to confirm empirically the validity of the sustainable development principle applied to the management of Venice as a cultural tourist site

Excited States in 52Fe and the Origin of the Yrast Trap at I=12+

Excited states in 52Fe have been determined up to spin 10\hbar in the reaction 28Si + 28Si at 115 MeV by using \gamma-ray spectroscopy methods at the GASP array. The excitation energy of the yrast 10+ state has been determined to be 7.381 MeV, almost 0.5 MeV above the well known \beta+-decaying yrast 12+ state, definitely confirming the nature of its isomeric character. The mean lifetimes of the states have been measured by using the Doppler Shift Attenuation method. The experimental data are compared with spherical shell model calculations in the full pf-shell.Comment: 9 pages, RevTeX, 7 figures include

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Experimental evidence for 56Ni-core breaking from the low-spin structure of the N=Z nucleus 58Cu

Low-spin states in the odd-odd N=Z nucleus 58Cu were investigated with the 58Ni(p,n gamma)58Cu fusion evaporation reaction at the FN-tandem accelerator in Cologne. Seventeen low spin states below 3.6 MeV and 17 new transitions were observed. Ten multipole mixing ratios and 17 gamma-branching ratios were determined for the first time. New detailed spectroscopic information on the 2+,2 state, the Isobaric Analogue State (IAS) of the 2+,1,T=1 state of 58Ni, makes 58Cu the heaviest odd-odd N=Z nucleus with known B(E2;2+,T=1 --> 0+,T=1) value. The 4^+ state at 2.751 MeV, observed here for the first time, is identified as the IAS of the 4+,1,T=1 state in 58Ni. The new data are compared to full pf-shell model calculations with the novel GXPF1 residual interaction and to calculations within a pf5/2 configurational space with a residual surface delta interaction. The role of the 56Ni core excitations for the low-spin structure in 58Cu is discussed.Comment: 15 pages, 7 figures, submitted to Phys. Rev.