Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L_1=-\lap+V_1 and L_2=-\lap+V_2, with $V_1$, $V_2$ constant, in a D-dimensional compact smooth manifold $M_D$, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for $D$ odd and for D=2. An application to the one-loop effective potential of the O(2) self-interacting scalar model is outlined.Comment: LaTeX, 17 pages, 3 figures. Small corrections, two new formulas, and an addition to the references. To appear in Commun. Math. Phy

Black hole and de Sitter solutions in a covariant renormalizable field theory of gravity

It is shown that Schwarzschild black hole and de Sitter solutions exist as exact solutions of a recently proposed relativistic covariant formulation of (power-counting) renormalizable gravity with a fluid. The formulation without a fluid is also presented here. The stability of the solutions is studied and their corresponding entropies are computed, by using the covariant Wald method. The area law is shown to hold both for the Schwarzschild and for the de Sitter solutions found, confirming that, for the $\beta=1$ case, one is dealing with a minimal modification of GR.Comment: 7 paages, latex fil

Influence of cold storage time on the softening prediction in Spring Bright nectarines

With Time-resolved Reflectance Spectroscopy (TRS) the maturity of nectarines at harvest can be assessed by measuring the absorption coefficient at 670 nm (µa 670) in the fruit flesh. A kinetic model has been developed linking the optical properties as measured by TRS with the models of µa 670 and firmness decay in shelf-life at 20°C, making the prediction of the softening time for individual fruit possible. In order to study the influence of cold storage time prior to shelf life on the softening prediction, 540 (year 2003) and 870 (year 2004) ‘Spring Bright’ nectarines were measured at harvest with TRS; then fruit were put in shelf life after various periods of cold storage at 0°C (4 and 10 d, year 2003; 6, 13 and 20 days, year 2004). During the 5-day period of shelf life at 20°C, fruit were analysed for firmness by pressure test after 30, 48, 54, 72, 78, 96, 102 and 120h in 2003 and after 36, 43, 62, 87, 108 and 135h in 2004. For each year and cold storage time, the parameters of the logistic model of softening as a function of µa 670 at harvest were computed. The cold storage up to 13 days did not significantly influence the estimates of the softening rate constant (kf), of the maximum firmness at minus infinite time (Fmax) and of parameter alpha (a) in both years, whereas parameter beta (ß) in 2003 significantly decreased from -1.867 at day 4 to -2.237 at day 10. The further 7 days of cold storage in 2004 significantly affected kf, which decreased from 0.00084 at days 6 and 13 to 0.00069 at day 20, and ß which increased from -2.395 at day 6 to -2.053 at day 20. Our results indicate that the cold storage time significantly influences the softening prediction of nectarines as the longer the cold storage, the lower the softening rat

Hawking Radiation as Tunneling: the D-dimensional rotating case

The tunneling method for the Hawking radiation is revisited and applied to the $D$ dimensional rotating case. Emphasis is given to covariance of results. Certain ambiguities afflicting the procedure are resolved.Comment: Talk delivered at the Seventh International Workshop Quantum Field Theory under the influence of External Conditions, QFEXT'05, september 05,Barcelona, Spain. To appear in Journal of Phys.

TRS-measurements as a nondestructive method assessing stage of maturity and ripening in plum (Prunus domestica L.)

n plum fruit with dark red or blue blush colour covering the whole fruit, the change in ground colour from green to yellow during maturation and ripening is masked. Hence, the maturity stage is difficult to judge. Time-resolved reflectance spectroscopy (TRS) has been used as a nondestructive method to assess changes in important internal quality factors in ‘Jubileum’ plums (Prunus domestica L.). Absorption coefficients (µa) and scattering coefficients (µs) were measured at both 670 and 758 nm during 5 days of storage. The changes in soluble solids content, titratable acidity and firmness were as expected. No change in soluble solids content was observed, while the plums became less acid and softer during storage. The TRS-measurements of plums indicated that TRS could give interesting information on internal quality factors in plums as the absorption at 670 nm was closely related to firmness, TA and TSS at the time of picking. Absorption at 758 nm was more closely related to the quality parameters after storage. The study did not indicate that scattering could be used in assessing maturity stage in plum