Feedforward neural networks based on PPS-wavelet activation functions

Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. Neural networks and wavenets have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. In this paper, it is shown how feedforward neural networks can be built using a different type of activation function referred to as the PPS-wavelet. An algorithm is presented to generate a family of PPS-wavelets that can be used to efficiently construct feedforward networks for function approximation.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

Psychophysical power functions for estimates of area: Effects of age and educational levels

The purpose of the present study was to verify the memory exponents of power function for area in observers of different age and educational levels (elementary school, high school or undergraduate school), using the psychophysics method of magnitude estimation. For the age level I (17 to 30 years old) there was no difference among educational levels, although for the age level II (45 to 60 years old) the differences were significant. Tn the age level II, there was a tendency for greater variability of the responses for lower educational levels. The data obtained for the age level I did not show the same results, although a significant difference among the three educational levels was observed. We call conclude that the mnemonic processes present different results when we observe the answers from observers with different ages. This result leads us to suppose that the motivational factor related to the stimulus used can interact with the mnemonic processes.

Modelling frequency distributions of 5 minute-averaged solar radiation indexes using Beta probability functions

Five minute-averaged values of sky clearness, direct and diffuse indices, were used to model the frequency distributions of these variables in terms of optical air mass. From more than four years of solar radiation observations it was found that variations in the frequency distributions of the three indices of optical air mass for Botucatu, Brazil, are similar to those in other places, as published in the literature. The proposed models were obtained by linear combination of normalized Beta probability functions, using the observed distributions derived from three years of data. The versatility of these functions allows modelling of all three irradiance indexes to similar levels of accuracy. A comparison with the observed distributions obtained from one year of observations indicate that the models are able to reproduce the observed frequency distributions of all three indices at the 95% confidence level.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

MAPPING CORRELATION-FUNCTIONS OF SCHWINGER AND AXIAL MODELS

We show that all Green's functions of the Schwinger and axial models can be obtained one from the other. In particular, we show that the two models have the same chiral anomaly. Finally it is demonstrated that the Schwinger model can keep gauge invariance for an arbitrary mass, dispensing with an additional gauge group integration.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Perturbative bosonization from two-point correlation functions

Here we address the problem of bosonizing massive fermions without making expansions in the fermion masses in both massive QED(2) and QED(3) with N fermion flavors including also a Thirring coupling. We start from two-point correlators involving the U(1) fermionic current and the gauge field. From the tensor structure of those correlators we prove that the U(1) current must be identically conserved (topological) in the corresponding bosonized theory in both D=2 and D=3 dimensions. We find an effective generating functional in terms of bosonic fields which reproduces these two-point correlators and from that we obtain a map of the Lagrangian density (ψ) over bar (r)(ipartial derivative-m)psi(r) into a bosonic one in both dimensions. This map is nonlocal but it is independent of the electromagnetic and Thirring couplings, at least in the quadratic approximation for the fermionic determinant.

Kinetic aspects of ion exchange in KhFek[Fe(CN)(6)](l)center dot mH(2)O compounds: A combined electrical and mass transfer functions approach

The present paper quantifies and develops the kinetic aspects involved in the mechanism of interplay between electron and ions presented elsewhere(1) for KhFek[Fe(CN)(6)](l)center dot mH(2)O (Prussian Blue) host materials. Accordingly, there are three different electrochemical processes involved in the PB host materials: H3O+, K+, and H+ insertion/extraction mechanisms which here were fully kinetically studied by means of the use of combined electronic and mass transfer functions as a tool to separate all the processes. The use of combined electronic and mass transfer functions was very important to validate and confirm the proposed mechanism. This mechanism allows the electrochemical and chemical processes involved in the KhFek[Fe(CN)(6)](l)center dot mH(2)O host and Prussian Blue derivatives to be understood. In addition, a formalism was also developed to consider superficial oxygen reduction. From the analysis of the kinetic processes involved in the model, it was possible to demonstrate that the processes associated with K+ and H+ exchanges are reversible whereas the H3O+ insertion process was shown not to present a reversible pattern. This irreversible pattern is very peculiar and was shown to be related to the catalytic proton reduction reaction. Furthermore, from the model, it was possible to calculate the number density of available sites for each intercalation/deintercalation processes and infer that they are very similar for K+ and H+. Hence, the high prominence of the K+ exchange observed in the voltammetric responses has a kinetic origin and is not related to the amount of sites available for intercalation/deintercalation of the ions.