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

A Finite-Temperature Periodic Structure in (SUPER)STRING Theory

Using a Laurent series representation for the (super)string one-loop free energy, an explicit form for the analytic continuation of the Laurent series beyond the critical (Hagedorn) temperature is obtained. As an additional result, a periodic structure is found in (super)string thermodynamics. A brief physical discussion about the origin and meaning of such structure is carried out.Comment: 9 pages, LaTeX file, UB-ECM-PF 92/3

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

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

Optical Absorption and Scattering Phenomena in 'Jubileum' Plums in Relation to Their Colour Properties

Absorption and scattering of laser light pulse passing through the fruit determine among others, the optical properties of the product. Efforts have been made in the recent past to utilize innovative techniques such as time-resolved reflectance spectroscopy (TRS) to study the quality aspects of different fruit such as nectarines. These optical properties have been well related to firmness, sugars, acids and other quality attributes. TRS measurements were performed on ‘Jubileum’ plums at two different wavelengths: 670 nm and 758 nm. The fruit were harvested in Norway and brought to Italy under protected conditions. After sorting the fruit by size, TRS measurements were made and the fruit were randomized for different examinations of quality aspects. It was observed that the absorption coefficient (µa) increased for both wavelengths as ripening progressed towards the melting stage of the fruit. The µa values at 670 nm were higher than those at 758 nm. The higher rate in the µa was distinguishable from the third day onwards as the fruit ripened. Similarly, it was interesting to note that the internal colour measured after destructing the fruit related well with the TRS absorption coefficient (µa), i.e., a decrease in the CIE L* (towards darker region) and b* (towards blue) value along with an increase in a* (towards red) from third day of storag