Wave Functional of the Universe and Time

A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the corresponding action operator. Its solution, the wave functional, is an invariant of general covariant transformations of spacetime. In the new formulation, the history of the evolution of the universe is described in terms of coordinate time together with arbitrary lapse and shift functions, which makes this description close to the formulation of the principle of general covariance in the classical theory of Einstein’s gravity. In the new formulation of quantum theory, an invariant parameter of the evolutionary time of the universe is defined, which is a generalization of the classical geodesic time measured by a standard clock along time-like geodesics.

The Relativistic Boltzmann Equation and Two Times

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ . If t ( τ ) increases with τ , the worldline may be associated with a normal particle, but if it is decreasing in τ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.

A PolSAR Scattering Power Factorization Framework and Novel Roll-Invariant Parameter-Based Unsupervised Classification Scheme Using a Geodesic Distance

© 1980-2012 IEEE. We propose a generic scattering power factorization framework (SPFF) for polarimetric synthetic aperture radar (PolSAR) data to directly obtain N scattering power components along with a residue power component for each pixel. Each scattering power component is factorized into similarity (or dissimilarity) using elementary targets and a generalized volume model. The similarity measure is derived using a geodesic distance between pairs of 4× 4 real Kennaugh matrices. In standard model-based decomposition schemes, the 3× 3 Hermitian-positive semi-definite covariance (or coherency) matrix is expressed as a weighted linear combination of scattering targets following a fixed hierarchical process. In contrast, under the proposed framework, a convex splitting of unity is performed to obtain the weights while preserving the dominance of the scattering components. The product of the total power (Span) with these weights provides the nonnegative scattering power components. Furthermore, the framework, along with the geodesic distance (GD) is effectively used to obtain specific roll-invariant parameters such as scattering-type parameter (αGD), helicity parameter (τ GD), and purity parameter (PGD). A PGD/αGD unsupervised classification scheme is also proposed for PolSAR images. The SPFF, the roll invariant parameters, and the classification results are assessed using C-band RADARSAT-2 and L-band ALOS-2 images of San Francisco.

A PolSAR Scattering Power Factorization Framework and Novel Roll-Invariant Parameter-Based Unsupervised Classification Scheme Using a Geodesic Distance

© 1980-2012 IEEE. We propose a generic scattering power factorization framework (SPFF) for polarimetric synthetic aperture radar (PolSAR) data to directly obtain N scattering power components along with a residue power component for each pixel. Each scattering power component is factorized into similarity (or dissimilarity) using elementary targets and a generalized volume model. The similarity measure is derived using a geodesic distance between pairs of 4× 4 real Kennaugh matrices. In standard model-based decomposition schemes, the 3× 3 Hermitian-positive semi-definite covariance (or coherency) matrix is expressed as a weighted linear combination of scattering targets following a fixed hierarchical process. In contrast, under the proposed framework, a convex splitting of unity is performed to obtain the weights while preserving the dominance of the scattering components. The product of the total power (Span) with these weights provides the nonnegative scattering power components. Furthermore, the framework, along with the geodesic distance (GD) is effectively used to obtain specific roll-invariant parameters such as scattering-type parameter (αGD), helicity parameter (τ GD), and purity parameter (PGD). A PGD/αGD unsupervised classification scheme is also proposed for PolSAR images. The SPFF, the roll invariant parameters, and the classification results are assessed using C-band RADARSAT-2 and L-band ALOS-2 images of San Francisco.

A New Newton Method with Memory for Solving Nonlinear Equations

A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of Newton method without memory by a variable self-accelerating parameter, we obtain a novel Newton method with memory. The convergence order of the new Newton method with memory is 1 + 2 . The acceleration of the convergence rate is attained without any additional function evaluations. The main innovation is that the self-accelerating parameter is constructed by a simple way. Numerical experiments show the presented method has faster convergence speed than existing methods.