On Calculation of Amplitudes in Quantum Electrodynamics

A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation of cross sections for different processes. The effectiveness of the method is shown on the cross-section calculation of Coulomb scattering, Compton scattering and electron-positron annihilation.Comment: 4 page

Chaos and Energy Redistribution the Nonlinear Interaction of Two Spatio-Temporal Wave Triplets

In this paper we examine the spatio-temporal dynamics of two nonlinearly coupled wave triplets sharing two common modes. Our basic findings are the following. When spatial dependence is absent, the homogeneous manifold so obtained can be chaotic or regular. If chaotic, it drives energy diffusion from long to small wavelengths as soon as inhomogeneous perturbations are added to the system. If regular, one may yet have two distinct cases: (i) energy diffusion is again present if the inhomogeneous modes are linearly unstable and triplets are effectively coupled; (ii) energy diffusion is absent if the inhomogeneous modes are linearly stable or the triplets are uncoupled.Comment: 21 pages, 5 figures, accepted for publication in Physica D (1997

Obfuscation methods of software code protection in computer systems

Thickening of formula feedings is part of the therapeutic approach for gastroesophageal reflux (GER) in infants. However, its mechanism of action, especially regarding the occurrence of nonacid (pH >4) GER, has not yet been clearly described. The aim of this randomized, placebo-controlled crossover study was to examine the influence of formula thickened with carob (St. John's bread) bean gum on acid and nonacid GER. METHODS: Infants with recurrent regurgitation and without other symptoms were fed alternately (A-B-A-B-A-B) with thickened (A) and nonthickened (B) but otherwise identical formula. Documentation of GER episodes during the study was performed by simultaneous intraesophageal impedance measurement (intraluminal electrical impedance,IMP) and pH monitoring. The IMP technique is able to detect bolus movements inside a luminal organ. The use of multiple measuring segments on a single catheter allowed the analysis of direction, height, and duration of the bolus transport. Continuous videorecording and visual surveillance of regurgitation frequency and amount resulted in a severity score. RESULTS: Fourteen infants (42 +/- 32 days old) were examined during 6 feeding intervals each. A total of 1130 GER episodes and 83 episodes of regurgitation were registered. Regurgitation frequency (17 vs 66 episodes) and amount were significantly lower after feedings with thickened formula. The difference regarding the occurrence of GER documented by IMP was also pronounced. Although not statistically significant, maximal height reached by the refluxate in the esophagus was decreased after thickened feedings. Mean GER duration and the frequency of acid (pH 4) GER episodes, but also because of a decrease of mean reflux height reached in the esophagus. However, the occurrence of acid GER is not reduced. The combination of IMP and pH monitoring allows the complete registration and description of these GER episodes. Thickening of formula feedings with carob bean gum is an efficient therapy for uncomplicated GER in infants