A RIEMANN INTEGRAL APPROACH TO FEYNMANS PATH-INTEGRAL

It is a well known result that the Feynman's path integral (FPI) approach to quantum mechanics is equivalent to Schrodinger's equation when we use as integration measure the Wiener-Lebesgue measure. This results in little practical applicability due to the great algebraic complexibity involved, and the fact is that almost all applications of (FPI) - ''practical calculations'' - are done using a Riemann measure. In this paper we present an expansion to all orders in time of FPI in a quest for a representation of the latter solely in terms of differentiable trajetories and Riemann measure. We show that this expansion agrees with a similar expansion obtained from Schrodinger's equation only up to first order in a Riemann integral context, although by chance both expansions referred to above agree for the free. particle and harmonic oscillator cases. Our results permit, from the mathematical point of view, to estimate the many errors done in ''practical'' calculations of the FPI appearing in the literature and, from the physical point of view, our results supports the stochastic approach to the problem.

Study on the orientation degree of Pb1-xLaxTiO3 thin films by the rocking curve technique and its morphological aspects

Thin films of perovskite-type materials such as PbTiO3, BaTiO3, (Pb,La)TiO3, (Pb, La)(ZrTi)O-3, KNbO3, and Pb(Mg,Nb)03 have been attracting great interest for applications like non-volatile memories, ultrasonic sensors and optical devices. Thin film should be epitaxially grown or at least highly textured since the properties of this anisotropic material depend on the crystallographic orientation. For optical devices, in particular, an epitaxial thin film without defects are essential to reduce optical propagation losses. Pb1-xLaxTiO3 (PLT) where x=0, 13 and 27% thin films were prepared by a chemical method (polymeric precursors method), and deposited by the spin coating technique onto substrates of SrTiO3 (STO) and LaAlO3 (LAO). The films were then beat treated at 500 degrees C in a controlled atmosphere of 0,. The orientation degree of the thin films was obtained from rocking curve technique, by means of X-ray difftaction analysis. A microstructural study revealed that the films were crack-free, homogeneous and have low roughness. (c) 2006 Elsevier B.V. All rights reserved.

The caprine oxyhemoglobin dissociation curve

The caprine oxyhemoglobin dissociation curve has not been previously defined. Blood from 10 healthy goats was equilibrated in a tonometer with calibrated gas mixtures of oxygen at concentrations of 95%, 21%, 13%, 12%, 10%, 9%, 8%, 5%, 4% and 2.5%, 5% carbon dioxide, balance nitrogen. The pH, partial pressure of oxygen (PO2), partial pressure of carbon dioxide (PCO2), total hemoglobin, oxyhemoglobin saturation, carboxyhemoglobin, methemoglobin, and oxygen content were measured. The PO2/oxyhemoglobin and the PO2/oxygen content relationships were graphed with curve-fitting software and a formula for calculating oxyhemoglobin from PO2 was generated. The maximum oxygen content per gram of hemoglobin was 1.29 ml of oxygen per gram of hemoglobin. The PO2 at which hemoglobin was 50% saturated (P-50) from the PO2/oxyhemoglobin relationship was 28.6 +/- 1.5 mmHg and that from the PO2/oxygen content relationships was 29.1 +/- 1.6 mmHg. The Hill coefficient for the PO2/oxyhemoglobin data was 3.0 +/- 0.4. (c) 2005 Elsevier Ltd. All rights reserved.

Using shifts in the electronic emission curve to evaluate polymer surface degradation

The polymer surface degradation and/or modification evolution of Teflon FEP and Mylar C films caused by a low energy electron beam were analyzed using a new method that consists in measuring the second crossover energy shift in the electronic emission curve. Upon prolonged irradiation, the second crossover energy shifts irreversibly to lower values in Teflon FEP but to higher values in Mylar C, indicating distinct mechanisms of surface degradation for the two polymers. The method represents a relatively inexpensive way to monitor early stages of surface degradation since the secondary electron emission comes from a maximum depth below the geometric surface of 100 mn in insulators. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Electrogravimetric Real-Time and in Situ Michaelis-Menten Enzimatic Kinetics: Progress Curve of Acetylcholinesterase Hydrolysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparison of proton energy loss in thick absorbers in terms of a reduced calibration curve

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Application of dissociation curve analysis to radiation hybrid panel marker scoring: generation of a map of river buffalo (B-bubalis) chromosome 20

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Characteristics of the double-torsion test to determine the R-curve of ceramic materials

Double-torsion tests were carried out on a commercial ceramic floor tile to verify whether this test is suitable for determining the R-curve of ceramics. The instantaneous crack length was obtained by means of compliance calibration, and it was found that the experimental compliance underestimates the real crack length. The load vs. displacement curves were also found to drop after maximum loading, causing the stress intensity factor to decline. The R-curves were calculated by two methods: linear elastic fracture mechanics and the energetic method. It was obtained that the average values of crack resistance, R, and the double of the work of fracture, 2 · γwof, did not depend on notch length, a0, which is a highly relevant finding, indicating that these parameters were less dependent on the test specimen's geometry. The proposal was to use small notches, which produce long stable crack propagation paths that in turn are particularly important in the case of coarse microstructures.

Reduced calibration curve for proton computed tomography

The pCT deals with relatively thick targets like the human head or trunk. Thus, the fidelity of pCT as a tool for proton therapy planning depends on the accuracy of physical formulas used for proton interaction with thick absorbers. Although the actual overall accuracy of the proton stopping power in the Bethe-Bloch domain is about 1%, the analytical calculations and the Monte Carlo simulations with codes like TRIM/SRIM, MCNPX and GEANT4 do not agreed with each other. A tentative to validate the codes against experimental data for thick absorbers bring some difficulties: only a few data is available and the existing data sets have been acquired at different initial proton energies, and for different absorber materials. In this work we compare the results of our Monte Carlo simulations with existing experimental data in terms of reduced calibration curve, i.e. the range - energy dependence normalized on the range scale by the full projected CSDA range for given initial proton energy in a given material, taken from the NIST PSTAR database, and on the final proton energy scale - by the given initial energy of protons. This approach is almost energy and material independent. The results of our analysis are important for pCT development because the contradictions observed at arbitrary low initial proton energies could be easily scaled now to typical pCT energies. © 2010 American Institute of Physics.

Comparison of the GEANT4 releases 8.2 and 9.2 in terms of a pCT reduced calibration curve

The GEANT4 simulations are essential for the development of medical tomography with proton beams pCT. In the case of thin absorbers the latest releases of GEANT4 generate very similar final spectra which agree well with the results of other popular Monte Carlo codes like TRIM/SRIM, or MCNPX. For thick absorbers, however, the disagreements became evident. In a part, these disagreements are due to the known contradictions in the NIST PSTAR and SRIM reference data. Therefore, it is interesting to compare the GEANT4 results with each other, with experiment, and with diverse code results in a reduced form, which is free from this kind of doubts. In this work such comparison is done within the Reduced Calibration Curve concept elaborated for the proton beam tomography. © 2010 IEEE.

Sedenions of Cayley-Dickson and the Cauchy-Riemann like relations

This work is an extension to sedenions of the Cauchy-Riemann relations, following a similar earlier construction made by one of the authors (M. Borges) to quaternions and octonions, see [1], [2], [3]. © 2011 Academic Publications.

A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.