Poles of Zeta Functions on Normal Surfaces

Let (S, 0) be a normal surface germ and Let f a non-constantregular function on Let (S, 0) with Let f(0) = 0. Using anyadditive invariant on complex algebraic varieties one can associatea zeta function to these data, where the topological and motiviczeta functions are the roughest and the finest zeta functions,respectively. In this paper we are interested in a geometricdetermination of the poles of these functions. The second authorhas already provided such a determination for the topologicalzeta function in the case of non-singular surfaces. Here wegive a complete answer for all normal surfaces, at least onthe motivic level. The topological zeta function however seemsto be too rough for this purpose, although for negative poles,which are the only ones in the non-singular case, we are ableto prove exactly the same result as for non-singular surfaces. We also give and verify a (natural) definition for when a rationalnumber is a pole of the motivic zeta function. 2000 MathematicsSubject Classification 14B05, 14E15, 14J17 (primary), 32S50(secondary).     

Formation of p-cresol:piperazine complex in solution monitored by spin-lattice relaxation times and pulsed field gradient NMR diffusion measurements

A study of the nature of the anthelmintic p-cresol:piperazine complex in chloroform solution has been conducted using different NMR techniques: self-diffusion coefficients using DOSY; NOE, NULL, and double-selective T1 measurements to determine inter-molecular distances; and selective and non-selective T1 measurements to determine correlation times. The experimental results in solution and CP-MAS were compared to literature X-ray diffraction data using molecular modeling. It was shown that the p-cresol:piperazine complex exists in solution in a very similar manner as it does in the solid state, with one p-cresol molecule hydrogen bonded through the hydroxyl hydrogen to each nitrogen atom of piperazine. The close correspondence between the X-ray diffraction data and the inter-proton distances obtained by NULL and double selective excitation techniques indicate that those methodologies can be used to determine inter-molecular distances in solution.     

On the kinetics and energetics of one-electron oxidation of 1,3,5-triazines

One-electron oxidation of 1,3,5-triazines is observed with both excited uranyl ion (*UO2(2+)) and sulfate radical anion (SO4.-) in aqueous solution, but not with Tl2+, indicating that the standard reduction potentials E degree of 1,3,5-triazine radical cations are = 2.3 +/- 0.1 V vs. NHE, consistent with theoretical calculations; this suggests that if triazines inhibit electron transfer during photosynthesis, they would need to act on the reductive part of the electron transport chain.     

Mössbauer study of Brazilian columbite

Columbite mineral from Lavra de Golconda in Governador Valadares, Minas Gerais, Brazil has been characterized by X-ray diffraction and electron microscopy. It has short prismatic nonconducting crystals with noninherent impurities of quartz, and exhibits one set of perfect cleavage. The reflectance is lowest normal to the cleavage surface, almost black. The surface is uneven and has small particles in a regular manner. On the other cleavage surface there is a regular pattern of white adherent impurity. The chemical composition of (Fe_0.32Mn_0.68)Nb₂O₆ was determined by mass spectrometry. The mineral has been studied by Mössbauer spectroscopy down to liquid nitrogen temperature. The isomer shift is 1.15 mm/sec and is almost temperature independent, but, the quadrupole splitting (1.55 mm/s at room temperature) is strongly temperature dependent (2.23 mm/s at liquid nitrogen temperature with large linewidth). This temperature dependence is explained in terms of relatively small crystal-field splitting of the t_2g levels.     

A Proposed Entropy Measure for Assessing Combat Degradation

This paper describes a method for assessing the combat degradation of an army, based on the Shannon entropy measure. It is shown that this measure is useful for analysing combat degradation due to casualties, since it is in broad agreement with the values established from past battle experience. It is also shown that the measure can be used to evaluate the degree of confidence in the outcome of training manoeuvres when weapons simulators are employed.     

Ablation of molybdenum and niobium with a HyBrID copper laser

A hydrogen bromide in discharge (HyBrID) copper laser with 12 W of maximum average power, 16 kHz repetition rate and 35 ns pulse duration, emitting simultaneously in 512 and 578 nm, was used to study molybdenum and niobium ablation. A modified Balzer QMG-311 mass spectrometer was used for monitoring presence of metal vapor and a pair of polarized flat electrodes placed parallel to the metal vapor stream was used in order to observe electric charges formation. Thin films on BK-7 optical-quality flats allowed the estimation of deposition rate. The measured ablation thresholds of 6.9 and 5.4 J/cm² for Mo and Nb, respectively, agreed well with theoretical estimations. Charge formation was observed for laser fluencies below the vapor formation thresholds and this was attributed to thermoionic emission. The maximum film growth rate in our experimental facility was measured to be about 16 Å/min for Mo and 11 Å/min for Nb.     

Low temperature magnetotransport properties of La0.55Ho0.15Sr0.3MnO3

Magnetotransport data measured in thin films of La_0.55Ho_0.15Sr_0.3MnO₃ down to very low temperatures (0.25 K) are reported. The samples presented colossal magnetoresistance with a T_C close to 200 K. A minimum in the resistance vs. T curve and a drop in the ZFC magnetization were also observed. It was also found a T-dependent relaxation effect after the magnetic field was either applied or removed. These results can be understood within the framework where electronic scattering occurs across magnetic domain walls in a reentrant spin-glassy-like phase.     

Plane wave expansion and extended plane wave expansion formulations for Mindlin-Reissner elastic metamaterial thick plates

The plane wave expansion (PWE) and the extended plane wave expansion (EPWE) formulations are derived in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators. These new formulations are useful to obtain more accurate results at higher frequencies than those based on Kirchhoff-Love thin plate theory. Multiple periodic resonators with multiple degrees of freedom (M-DOF) attached to metamaterial thick plates broaden the applications for wave attenuation in high frequencies.     

The meaning of time in the theory of relativity and “Einstein's later view of the Twin Paradox”

The purpose of the present paper is to reply to a misleading paper by M. Sachs entitled Einstein's later view of the Twin Paradox (TP) (Found. Phys. 15, 977 (1985)). There, by selecting some passages from Einstein's papers, he tried to convince the reader that Einstein changed his mind regarding the asymmetric aging of the twins on different motions. Also Sachs insinuates that he presented several years ago convincing mathematical arguments proving that the theory of relativity does not predict asymmetrical aging in the TP. Here we give a definitive treatment to the clocks problem showing that Sachs' convincing mathematical arguments are non sequitur. Also, by properly quoting Einstein, we show that his later view of the TP coincides with the one derived from the rigorous theory of time developed in this paper.