In this note we prove several duality theorems in lattice theory. We also discuss the connection between spectral spaces and Priestley spaces, and interpret Priestley duality in terms of spectral spaces. The organization of this note is as follows. In the first section we collect appropriate definitions and basic results common to many of the various topics. The next four sections consider Birk...

    Introduction: In the last few decades, a lot of monte carlo codes have been introduced for medical applications. For close - to - surface tumors, the surface of the skin can be used to increase the surface dose so that all or part of the bunch area can fall into bolus, thereby increasing the dose of the skin. The air gaps between bolus and skin can affect the dose of...

In coloured media, the index of refraction does not decrease monotonically with increasing wavelength, but behaves in a quite non-monotonical way. This behaviour is called anomalous dispersion and results from the fact that the absorption of a material influences its index of refraction. So far, this interesting fact has not been widely acknowledged by the graphics community. In this paper, we ...