Abstract:
Dynamics of solitons is considered in the framework of an extended nonlinear Schrodinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is a known ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order dispersion (SOD) and linear losses of HF waves. It is shown that wavenumber downshift by the pseudo-SRS may be compensated by upshift provided by SOD whose local strength is an exponentially decaying function of the coordinate. An analytical soliton solution with a permanent shape is found in an approximate form, and is verified by comparison with numerical results

Abstract:
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped low-frequency (LF) internal waves. The drive gives rise to a convective (but not absolute) instability in the system. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, which is a spatial-domain counterpart of the SRS term, a well-known ingredient of the temporal-domain NLSE in optics. Analysis of the field-momentum balance and direct simulations demonstrate that wavenumber downshift by the pseudo-SRS may be compensated by the upshift induced by the wind traction, thus maintaining robust bright solitons in both stationary and oscillatory forms; in particular, they are not destroyed by the underlying convective instability. Analytical soliton solutions are found in an approximate form and verified by numerical simulations. Solutions for soliton pairs are obtained in the numerical form.

Abstract:
Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.

Abstract:
In a previous paper we proposed a new model for the emission by amorphous astronomical dust grains, based on solid-state physics. The model uses a description of the Disordered Charge Distribution (DCD) combined with the presence of Two-Level Systems (TLS) defects in the amorphous solid composing the grains. The goal of this paper is to confront this new model to astronomical observations of different Galactic environments in the FIR/submm, in order to derive a set of canonical model parameters to be used as a Galactic reference to be compared to in future Galactic and extragalactic studies. We confront the TLS model with existing astronomical data. We consider the average emission spectrum at high latitudes in our Galaxy as measured with FIRAS and WMAP, as well as the emission from Galactic compact sources observed with Archeops, for which an inverse relationship between the dust temperature and the emissivity spectral index has been evidenced. We show that, unlike models previously proposed which often invoke two dust components at different temperatures, the TLS model successfully reproduces both the shape of the Galactic SED and its evolution with temperature as observed in the Archeops data. The best TLS model parameters indicate a charge coherence length of \simeq 13 nm and other model parameters in broad agreement with expectations from laboratory studies of dust analogs. We conclude that the millimeter excess emission, which is often attributed to the presence of very cold dust in the diffuse ISM, is likely caused solely by TLS emission in disordered amorphous dust grains. We discuss the implications of the new model, in terms of mass determinations from millimeter continuum observations and the expected variations of the emissivity spectral index with wavelength and dust temperature. The implications for the analysis of the Herschel and Planck satellite data are discussed.

Abstract:
The article is based on the assumption that the present state of writing for children in Kenya could in fact be reflecting the current condition of the entire Kenyan culture, particularly the culture of letters in the country. Using as a reference point the well-known book on Kenyan children's literature written in 1980s by Asenath Odaga, the author indicates the achievements made by Kenyan children's literature within the last two decades (e.g., efforts being made by both international and local publishers to increase the number of books and variety of titles suitable for different age groups), as well as problems still existing in the field (one of the major ones being the shortage of books in indigenous languages, with possible exception of Kiswahili). The author states that these problems could be applied to Kenyan writing culture in general. The article also proposes some guidelines towards the improvement of the current situation. Journal of Language, Technology & Entrepreneurship in Africa Vol. 1 (2) 2009: pp. 198-207

Abstract:
The rules of calculating three undetermined functions which defined a solution in the LTB model are used to study the class of exact nonhomogene\-ous models with $f^2(\mu) = 1$, $\Lambda = 0$. The parameter $\nu(\mu)$ defined the difference between LTB and FRW models is found out and the limit transformation to the FRW model is shown. The initial conditions are present throught density and Habble function at the moment of time $\tau = 0$. Two criteria of homogeneous of matter distribution are studied. The asimptotic of the present solution for $\tau \rightarrow +\infty$ is studied.

Abstract:
The Caushy problem in the LTB model is formulated. The rules of calculating three undetermined functions which defined a solution in the LTB model are presented. One example of exact nonhomogeneous model is studied. The limit transformation to the FRW model is shown.

Abstract:
The Cauchy problem in the LTB model is formulated. The rules of calculating three undetermined functions which defined a solution in the LTB model are presented. One example of exact nonhomogeneous model is studied. The limit transformation to the FRW model is shown.

Abstract:
Boundary problem for Tolman-Bondi model is formulated. One-to-one correspondence between singularities hypersurfaces and initial conditions of the Tolman-Bondi model is constructed.