Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group. Mathematics Subject Classification (1991): 49L25, 35J70, 35J67, 22E30.

Let P be a property (or, equivalently, a class) of topological spaces. A space X is called P-bounded if every subspace of X with (or in) P has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω-bounded. In this paper we present a systematic study of the interrelations of these two known “boundedness” concepts with P-boundedness where P is ...

this paper is a part of study about the impact of the microclimate on the space use and the user’s behaviours. the purpose of our study is to get an in-depth understanding of how people use out door public spaces in different climatic conditions, how their behaviour and perception of the space change with the climatic variations. we have employed a multi-method approach which combines a “qualit...

Using X-ray temperature and surface brightness profiles of the hot intracluster medium (ICM) derived from ASCA and ROSAT observations we place constraints on the dark matter (DM) and baryon fraction distributions in the poor clusters Abell 1060 (A1060) and AWM 7. Although their total mass distributions are similar, AWM 7 has twice the baryon fraction of A1060 in the best-fit models. The functio...

Abstract. With a map f : Ω → R,Ω ⊂ R, that belongs to the John Ball classAp,q(Ω) where n − 1 < p < n and q ≥ p/(p − 1) one can associate a set valued map F whose values F (x) ⊂ R are subsets ofR describing the topological character of the singularity of f at x ∈ Ω. Šverak conjectured that Hn−1(F (S)) = 0, where S is the set of points at which f is not continuous andHn−1 is the Hausdorff measure...

Here we discuss some variations of Nagata’s conjecture on linear systems of plane curves. The most relevant concerns non-effectivity (hence nefness) of certain rays, which we call good rays, in the Mori cone of the blowup Xn of the plane at n ≥ 10 general points. Nagata’s original result was the existence of a good ray for Xn with n ≥ 16 a square number. Using degenerations, we give examples of...

We make a model-independent analysis of all available data that indicate neutrino oscillations. Using probability diagrams, we connrm that a mass spectrum with two nearly degenerate pairs of neutrinos separated by a mass gap of ' 1 eV is preferred over a spectrum with one mass eigenstate separated from the others. We derive some new relations among the four-neutrino mixing matrix elements. We d...

In this article, we present a detailed study of the complex calculus of variations introduced in [4]. This calculus is analogous to the conventional calculus of variations, but is applied here to C functions in C. It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions to complex Hamilton-Jacobi equations, i...