As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a
version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that decompositio
n process can be done by iterative procedure(s), each step of which is reduced to solution of some auxiliary PDEs system(s) for one dependent variable. Moreover, we find on this way the explicit expression of the first-order PDE(s) for first integral of decomposable initial PDE. Remarkably that this first-order PDE is linear if initial PDE is linear in its highest derivatives. The developed method is implemented in Maple procedure, which can really solve many of different order PDEs with different number of independent variables. Examples of PDEs with calculated their general solutions demonstrate a potential of the method for automatic solving of nonlinear PDEs.
In this paper we show how to compute the $Lambda_{alpha}$ norm, $alphage 0$, using the dyadic grid. This result is a consequence of the description of the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
The intelligent acoustic emission locator is described in Part I, while Part II discusses blind source separation, time delay estimation and location of two simultaneously active continuous acoustic emission sources. The location of acoustic emissi
on on complicated aircraft frame structures is a difficult problem of non-destructive testing. This article describes an intelligent acoustic emission source locator. The intelligent locator comprises a sensor antenna and a general regression neural network, which solves the location problem based on learning from examples. Locator performance was tested on different test specimens. Tests have shown that the accuracy of location depends on sound velocity and attenuation in the specimen, the dimensions of the tested area, and the properties of stored data. The location accuracy achieved by the intelligent locator is comparable to that obtained by the conventional triangulation method, while the applicability of the intelligent locator is more general since analysis of sonic ray paths is avoided. This is a promising method for non-destructive testing of aircraft frame structures by the acoustic emission method.
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging method, using a
recent development of this theory for perturbed integrable equations. This general approach enables us not only to improve known results on the adiabatic evolution of isolated solitary waves and periodic wave trains in the presence of variable topography and bottom friction, modeled by the Chezy law, but also importantly, to study the effects of these factors on the propagation of undular bores, which are essentially unsteady in the system under consideration. In particular, it is shown that the combined action of variable topography and bottom friction generally imposes certain global restrictions on the undular bore propagation so that the evolution of the leading solitary wave can be substantially different from that of an isolated solitary wave with the same initial amplitude. This non-local effect is due to nonlinear wave interactions within the undular bore and can lead to an additional solitary wave amplitude growth, which cannot be predicted in the framework of the traditional adiabatic approach to the propagation of solitary waves in slowly varying media.
Neutrinoless double beta decay is one of the most sensitive approaches in non-accelerator particle physics to take us into a regime of physics beyond the standard model. This article is a brief review of the experiments in search of neutrinoless doub
le beta decay from 76Ge. Following a brief introduction of the process of double beta decay from 76Ge, the results of the very first experiments IGEX and Heidelberg-Moscow which give indications of the existence of possible neutrinoless double beta decay mode has been reviewed. Then ongoing efforts to substantiate the early findings are presented and the Majorana experiment as a future experimental approach which will allow a very detailed study of the neutrinoless decay mode is discussed.
A novel way of picturing the processing of quantum information is described, allowing a direct visualization of teleportation of quantum states and providing a simple and intuitive understanding of this fascinating phenomenon. The discussion is aimed
at providing physicists a method of explaining teleportation to non-scientists. The basic ideas of quantum physics are first explained in lay terms, after which these ideas are used with a graphical description, out of which teleportation arises naturally.
The results of the spectral, energetical and temporal characteristics of radiation in the presence of the photonic flame effect are presented. Artificial opal posed on Cu plate at the temperature of liquid nitrogen boiling point (77 K) being irradiat
ed by nanosecond ruby laser pulse produces long- term luminiscence with a duration till ten seconds with a finely structured spectrum in the the antistocks part of the spectrum. Analogous visible luminescence manifesting time delay appeared in other samples of the artificial opals posed on the same plate. In the case of the opal infiltrated with different nonlinear liquids the threshold of the luminiscence is reduced and the spatial disribution of the bright emmiting area on the opal surface is being changed. In the case of the putting the frozen nonlinear liquids on the Cu plate long-term blue bright luminiscence took place in the frozen species of the liquids. Temporal characteristics of this luminiscence are nearly the same as in opal matrixes.
We analyze the possibility of probing non-standard neutrino interactions (NSI, for short) through the detection of neutrinos produced in a future galactic supernova (SN).We consider the effect of NSI on the neutrino propagation through the SN envelop
e within a three-neutrino framework, paying special attention to the inclusion of NSI-induced resonant
We describe a new algorithm, the $(k,\\ell)$-pebble game with colors, and use\nit obtain a characterization of the family of $(k,\\ell)$-sparse graphs and\nalgorithmic solutions to a family of problems concerning tree decompositions of\ngraphs. Spe
cial instances of sparse graphs appear in rigidity theory and have\nreceived increased attention in recent years. In particular, our colored\npebbles generalize and strengthen the previous results of Lee and Streinu and\ngive a new proof of the Tutte-Nash-Williams characterization of arboricity. We\nalso present a new decomposition that certifies sparsity based on the\n$(k,\\ell)$-pebble game with colors. Our work also exposes connections between\npebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and\nWestermann and Hendrickson.\n
