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...

It is well known that Zk,m(t) is related to the virial coefficients of a quantum system of obstacles K at inverse temperature t. For example, G. E. Uhlenbeck [15] calculated the asymptotic behaviour of Zk,m(t) as t → ∞ in the special case where k = 1, m = 3, and K is a ball. I. McGillivray [14] obtained the full asymptotic series as t → ∞ for k = 1, m ≥ 3, and K an arbitrary, non-polar compact ...

There has been a general understanding that Mycobacterium smegmatis produces only apolar glycopeptidolipid (GPL), similar in structure to serovar non-specific GPL of Mycobacterium avium. In this study, synthesis of polar GPL in carbon-starved M. smegmatis is reported. Mass spectrometric analysis suggests the polar GPL to be a hyperglycosylated species. The earlier structural studies of polar GP...

The design of robust omniphobic surfaces, which are not wetted by low-surface-tension liquids such as octane (γlv=21.6 mN/m) and methanol (γlv=22.7 mN/m), requires an appropriately chosen surface micro/nanotexture in addition to a low solid-surface energy (γsv). 1H,1H,2H,2H-Heptadecafluorodecyl polyhedral oligomeric silsesquioxane (fluorodecyl POSS) offers one of the lowest solid-surface energy...

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X−E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F -harmonic functions (solutions) wh...

Sometimes information in a network model is based on multi-agent, multi-attribute, multi-object, multi-polar information or uncertainty rather than a single bit. An m-polar fuzzy model is useful for such network models which gives more and more precision, flexibility, and comparability to the system as compared to the classical, fuzzy and bipolar fuzzy models. In this research article, we intro...

Let Cm×n, Cm×n r , C m ≥ , C m > , and In denote the set of m × n complex matrices, subset of Cm×n consisting of matrices with rank r, set of the Hermitian nonnegative definite matrices of order m, subset of C ≥ consisting of positive-definite matrices and n × n unit matrix, respectively. Without specification, we always assume that m > n >max{r, s} and the given weight matrices M ∈ C > ,N ∈ C ...

In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arıkan’s polarization technique applied individually to each user transforms independent uses of a m-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: (i) the ‘uniform sum rate’ of the original MAC is pr...