Legendre Transformation for Regularizable Lagrangians in Field Theory

Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail.     

Ionization penalty in nonlinear Raman neuroimaging

Light-assisted ionization accompanying coherent anti-Stokes Raman scattering (CARS) of ultrashort laser pulses in brain tissue is shown to manifest itself in a detectable blueshift of the anti-Stokes signal. This blueshift can serve as an indicator of ionization processes in CARS-based neuroimaging.     

Scattering-induced changes in the temporal coherence length and the pulse duration of a partially coherent plane-wave pulse

The scattering of a partially coherent plane-wave pulse on a Gaussian-correlated, quasi-homogeneous random medium is investigated. The analytical expressions for the temporal coherence length and the pulse duration of the scattered field are derived. We demonstrate that the scattering-induced changes in the temporal coherence length and the pulse duration may be used to determine the correlation function of the scattering potential of the medium.     

Enhanced reactivity of nanoscale iron particles through a vacuum annealing process

A reactivity study was undertaken to compare and assess the rate of dechlorination of chlorinated aliphatic hydrocarbons (CAHs) by annealed and non-annealed nanoscale iron particles. The current study aims to resolve the uncertainties in recently published work studying the effect of the annealing process on the reduction capability of nanoscale Fe particles. Comparison of the normalized rate constants (m²/h/L) obtained for dechlorination reactions of trichloroethene (TCE) and cis-1,2-dichloroethene (cis-1,2-DCE) indicated that annealing nanoscale Fe particles increases their reactivity ~30-fold. An electron transfer reaction mechanism for both types of nanoscale particles was found to be responsible for CAH dechlorination, rather than a reduction reaction by activated H₂ on the particle surface (i.e., hydrogenation, hydrogenolysis). Surface analysis of the particulate material using X-ray diffraction (XRD) and transmission electron microscopy (TEM) together with surface area measurement by Brunauer, Emmett, Teller (BET) indicate that the vacuum annealing process decreases the surface area and increases crystallinity. BET surface area analysis recorded a decrease in nanoscale Fe particle surface area from 19.0 to 4.8 m²/g and crystallite dimensions inside the particle increased from 8.7 to 18.2 nm as a result of annealing.     

Reputation-based network selection mechanism using game theory

Current and future wireless environments are based on the coexistence of multiple networks supported by various access technologies deployed by different operators. As wireless network deployments increase, their usage is also experiencing a significant growth. In this heterogeneous multi-technology multi-application multi-terminal multi-user environment users will be able to freely connect to any of the available access technologies. Network selection mechanisms will be required in order to keep mobile users “always best connected” anywhere and anytime. In such a heterogeneous environment, game theory techniques can be adopted in order to understand and model competitive or cooperative scenarios between rational decision makers. In this work we propose a theoretical framework for combining reputation-based systems, game theory and network selection mechanism. We define a network reputation factor which reflects the network’s previous behaviour in assuring service guarantees to the user. Using the repeated Prisoner’s Dilemma game, we model the user–network interaction as a cooperative game and we show that by defining incentives for cooperation and disincentives against defecting on service guarantees, repeated interaction sustains cooperation.     

Spin and quark states in the probability representation of quantum mechanics

A short review of the general principles of constructing tomograms of spin and quark states is presented.     

Experimental demonstration of a narrowband, angular tolerant, polarization independent, doubly periodic resonant grating filter

Resonant grating filters are promising components for free-space narrowband filtering. Unfortunately, due to their weak angular tolerance, their performances are strongly deteriorated when they are illuminated with a standard collimated beam. Yet this problem can be overcome by resorting to a complex periodic pattern known as the doubly periodic grating [Lemarchand et al., Opt. Lett.23, 1149 (1998)]. We report what we believe to be the first experimental fabrication and characterization of a bidimensional doubly periodic grating filter. We obtained a 0.5 nm bandpass polarization independent reflection filter for telecom wavelengths (1520-1570 nm) that presents a transmittivity minimum of 18% with a standard incident collimated beam.     

Astrogeometry: Toward mathematical foundations

Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes.