elastic energy of seismic wave is lost through propagation into the earth. various factors affect seismic energy. some of them are frequency independent and recovered in processing steps. but other factors such as intrinsic absorption of medium are frequency dependent and cannot be recovered by processing methods. lost energy caused by these factors is called attenuation. there are various meth...

Recently there has been renewed interest in applications of the so-called phase-space formulation of quantum mechanics’) for both equilibrium2) and non-equilibrium phenomena3). Its basic feature is to provide a framework for the treatment of quantum mechanical problems in terms of classical phasespace language. Following the appearance of the well-known Wigner distribution function’), many othe...

A discrete-time, discrete-frequency Wigner distribution is derived using a group-theoretic approach. It is based upon a study of the Heisenberg group generated by the integers mod N , which represents the group of discrete-time and discrete-frequency shifts. The resulting Wigner distribution satis es several desired properties. An example demonstrates that it is a full-band time-frequency repre...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

After a century of neglect the dilogarithm appeared twenty years ago in works of Gabrielov-Gelfand-Losik [GGL] on a combinatorial formula for the first Pontryagin class, Bloch on K-theory and regulators [Bl1] and Wigner on Lie groups. The dilogarithm has a single-valued cousin : the Bloch Wigner function L2(z) := ImLi2(z) + arg(1− z) log |z|. Let r(x1, ..., x4) be the cross-ratio of 4 distinct ...

We introduce a time-frequency representation of linear signal spaces which we call the Wigner distribution (WO) ofa linear signal space. Similar to the WD of a signal, the WD of a linear signal space describes the space’s energy distribution over the time-frequency plane. The WD of a signal space can be defined both in a deterministic and in a stochastic framework, and it can be expressed in a ...

It has been known that the Wigner representation theory for positive energy orbits permits a useful localization concept in terms of certain lattices of real subspaces of the complex Hilbert -space. This ”modular localization” is not only useful in order to construct interactionfree nets of local algebras without using non-unique ”free field coordinates”, but also permits the study of propertie...

. . . may prove an interesting tool to extract physical quantities of the fireball, once the formation process has been understood. We assume an emission function of the form [1] with gaussian source parametrization and local thermal equilibrium distributions for nucleons in the hot, central reaction region. Using a Wigner function coalescence mechanism [2], we obtain a formula for the invarian...

We define and present an example of a deformation quantization product on a Hida space of test functions endowed with a Wick product.

The Wigner distribution function formalism is applied to the description of transport properties of spintronic multilayer nanodevice. The central layer of the nanodevice is doped with magnetic impurities. The current-voltage characteristics and the spin polarisation of current are calculated.