Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

The retreat of Arctic summer sea ice has been dramatic in recent years as recorded by satellite images. But it also appears that the thickness of ice has also experienced equally significant shrinkage. Most computer models predict ice-free summer conditions by 2040 to 2100 but real conditions appear to be moving faster than this. The British Catlin Arctic Survey, which got underway in February,...

We developed an equation of state (EOS) by Ihm, Song, and Mason (ISM) for polar fluids. The model consists of four parameters, namely, the second virial coefficient, an effective van der Waals co-volume, a scaling factor, and the reduced dipole moment. The second virial coefficient is calculated from a correlation that uses the heat of vaporization, and the liquid density at the normal boiling ...

Ozone is observed to be present in the polar regions of Mars and to have a seasonal variation. In the summer, the amount present in the polar atmosphere is less than 3 micrometer-atmospheres. In the fall, ozone increases in amount and is found in association with the formation of the polar hood. In winter, the maximum amount of ozone is present, 57 micrometer-atmospheres over the polar hood and...

The changes in the nonnegative and positive polar factors of generalized polar decomposition and polar decomposition are studied under the additive perturbation. Some new perturbation bounds are obtained. These bounds are different from precious ones in form and measure and, in some cases, may be smaller than the corresponding existing ones. Furthermore, the corresponding perturbation bounds fo...

[1] The polar cap index (PCI) has been shown to be quite useful as an index of the electrodynamic processes within the high-latitude ionosphere. Here we use between 150 and 180 magnetometers to model the high-latitude electrodynamics with the assimilative mapping of ionospheric electrodynamics (AMIE) technique for all of 1997–2001. We compare AMIE calculations of the cross polar cap potential (...