We calculate the Riemann curvature tensor and sectional curvature for the Lie group of volume-preserving diffeomorphisms of the Klein bottle and projective plane. In particular, we investigate the sign of the sectional curvature, and find a possible disagreement with a theorem of Lukatskii. We suggest an amendment to this theorem.

We present new explicit volume-preserving methods based on splitting for polynomial divergence-free vector fields. The methods can be divided in two classes: methods that distinguish between the diagonal part and the off-diagonal part and methods that do not. For the methods in the first class it is possible to combine different treatments of the diagonal and off-diagonal parts, giving rise to ...

In this paper, we consider an extension of the commonly used poverty gap measure that may be used to address he question of whether the elimination of poverty is a feasible objective, given sufficient political commitment. The resources potentially available to address poverty may be measured by the total amount by which the incomes of the non-poor exceed the same poverty line. The ratio of the...

We characterize a special class of unitary operators that preserve orthonormal wavelets. In the process we also prove that symmetric wavelet sets cover the real line.

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial derivatives, connected with volume-preserving diffeomorphisms. In this paper, we determine the structure space of the divergence-free Lie algebras associated with pair...

This paper introduces a new measure of quality for terrain surface simplification aiming at preserving the slope of the surface, as well as a new simplification algorithm which satisfies this measure. Experimental results and comparisons with other simplification algorithms show the effectiveness of proposed algorithm according to some quality measures.

The knowledge of the metric entropy of precompact subsets of operators on finite dimensional Euclidean space is important in particular in the probabilistic methods developped by E. D. Gluskin and S. Szarek for constructing certain random Banach spaces. We give a new argument for estimating the metric entropy of some subsets such as the Grassmann manifold equipped with natural metrics. Here, th...

Abstract. We establish that for q ≥ 1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local e...

FPE deconstructs and reframes basic neo-liberal assumptions and in the process refocuses economic theory and constructs alternatives. It uses a political economic approach, which is “the study of society as an integrated whole.” This approach identifies and analyzes “social relations as they relate to the economic system of production” (Drache 1978 as quoted in Bezanson and Luxton 2006, 12). A ...

Morphological connected set filters for extraction of filamentous details from medical images are developed. The advantages of these filters are that they are shape preserving and do not amplify noise. Two approaches are compared: (i) multi-scale filtering (ii) single-step shape filtering using connected set (or attribute) thinnings. The latter method highlights all filamentous structure in a s...