All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.

We present some statistical features of the large number of Lyα absorption lines detected in high redshift quasar spectra, obtained by using the multifractal approach. In the analysed sample of 12 QSO sight–lines, 11 show scaling behaviour with a crossover between two distinct regimes: a non-homogeneous regime at small scales and a homogeneous regime at large scales. The correlation length show...

Temper rolling or skin pass rolling is one of cold rolling processes composed of a horizontal pass cold rolling mill stand. In this process, the thick strip is subjected to very light reduction (0.5–4%) in thickness in the presence of high friction amplitudes. One of the basic parameters of strip rolling processes is temper rolling force. A new rolling force model has been proposed for temper r...

By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and is suitable for obtaining both the linear and nonlinear equations describing the e...

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wi...

The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of...

Introduction Polymer gel dosimeters offer a practical solution to 3D dose verification for conventional radiotherapy as well as intensity-modulated and stereotactic radiotherapy. In this study, EGSnrc calculated and PAGAT polymer gel dosimeter measured dose profiles from single shot irradiation with 18 mm collimator of Gamma Knife in homogeneous and inhomogeneous phantoms were compared with eac...

─ This paper presents a new method to model inhomogeneous media in commercial electromagnetics software, especially FEKO. In this method, the inhomogeneous medium is fragmented to some homogeneous pieces. If the size of these pieces is chosen correctly, then the electromagnetic behaviors of them and inhomogeneous medium are the same. Since creating these homogeneous pieces in FEKO manually is v...

We have investigated steady, radial gas outflows (or winds) from galaxies and the development of thermal instability in the hot gas. In order to see the maximum influence of the instability on the global structure of the galactic outflows, we study inhomogeneous comoving flows and the non-linear fate of the fluctuations in the flows. We compare the results with solutions for homogeneous flows. ...

the microstructure of dual phase steels can be considered as a matrix of ferrite phase reinforced by martensite particles. recent measurements show that the mechanical properties of the ferrite phase are changed with the distance from the martensite grains. in this paper, a new method has been proposed to consider this phenomenon in finite element modeling of dual phase steels microstructure. i...