If we consider the quotient space of each tangent plane with respect to this equivalence relation, and the related quotient tangent bundle TS/∼1, a field FD : S −→ TS/∼1 maps each point on the surface to a direction. It is customary to take unit-length vectors as representatives of their equivalence classes, so that a direction field can be regarded as a vector field where the length of all vec...

The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that Π maps the set of polytopes in Rn into itself. We show that Π is the only non-trivial operator with these properties. MSC 2000: 52B45, 52A20

Given any space-time M without singularities and any event O, there is a natural continuous mapping f of a two dimensional sphere into any space-like slice T not containing O. The set of future null geodesics (or the set of past null geodesics) forms a 2-sphere S and the map f sends a point in S to the point in T which is the intersection of the corresponding geodesic with T . To require that f...

We study the numerical solutions to semi-infinite-domain two-point boundary value problems and initial value problems. A smooth, strictly monotonic transformation is used to map the semiinfinite domain x ∈ 0,∞ onto a half-open interval t ∈ −1, 1 . The resulting finite-domain twopoint boundary value problem is transcribed to a system of algebraic equations using ChebyshevGauss CG collocation, wh...

This paper proposes a new procedure for analyzing means-end chain data in marketing research. Most commonly the collected data is summarized in the Hierarchical Value Map (HVM) illustrating the main attribute-consequence-value linkages. This paper argues that traditionally constructed HVM may give an erroneous impression of the results of a means-end study. To justify the arguments, an alternat...

A general-purpose useful parameter in time series forecasting is the regressor, corresponding to the minimum number of variables necessary to forecast the future values of the time series. If the models used are non linear, the choice of this regressor becomes very difficult. We will show a quasiautomatic method using Curvilinear Component Analysis to build it. This method will be applied to el...

This article is devoted to the study cashflow maps used in the computation of value-at-risk (VaR). Properties and characteristics of the approaches found in the literature are presented and two new approaches are introduced. The goal of this paper is to study the quality of these maps. This is done by calculating the risk induced by the difference between the mapped cashflows and the original one.

The problem of finding the most probable explanation to a designated set of variables (the MAP problem) is a notoriously intractable problem in Bayesian networks, both to compute exactly and to approximate. It is known, both from theoretical considerations and from practical experiences, that low treewidth is typically an essential prerequisite to efficient exact computations in Bayesian networ...

The Lean Philosophy emphasizes one basic point – ‘Doing more with less’. This article outlines a simple-to-understand three step road-map that can help an organization embark on its journey towards lean transformation. The first is a cultural revamp of getting the lean spirit through to everyone. Step two is to develop the organization’s current state value stream map, scan for improvement oppo...

The Multidimensional Assignment Problem (MAP) is a higher-dimensional version of the Linear Assignment Problem that arises in the areas of data association, target tracking, resource allocation, etc. This paper elucidates the question of asymptotical behavior of the expected optimal value of the large-scale MAP whose assignment costs are independent identically distributed random variables with...