Introduction It is a public fact that "shape" can only be defined in operational terms. "Shape" is only operationally defined. Thus things do not "have a shape" the way Santa Claus has a red suit. ---JAN KOENDERINK (1990) A shape can be observed or manufactured, and even its mere thought entails the possibility of a potential realization of such an act (an imagination in your mind's eye, a gesticulation). Shape as an attribute of an observable puts the very role of observation---generically the physical interaction with some kind of source---into focus. Ich werde [. . . ] in der transzendentalen Uberlegung meine Begriffe jederzeit nur unter den Bedingungen der Sinnlichkeit vergleichen mussen, und so werden Raum und Zeit nicht Bestimmungen der Dinge an sich, sondern der Erscheinungen sein: was die Dinge an sich sein mogen, weiß ich nicht, und brauche es auch nicht zu wissen,

The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scale-space paradigm. It is argued that the design of optic flow based

Abstract. The purpose of this article is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scale-space paradigm. It is argued that the design of optic flow based

We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates

Given a convex function φ: IR+ → IR, the Csiszár φ-divergence (Csiszár (1978)) is a function Iφ: IR n +×IR n + → IR, Iφ(p, q):=

to Lp generalizations of the space X . Our results elaborate on the well-known duality between Carleson measures and non-tangential maximal functions.

This paper studies a new representation of individ~l preferences termed the benefit function. The benetit function b(g; x,u) measures the amount that an individual is willing to trade, in terms of a specific reference commodity bundle g, for the opportunity to move from utility level a to a

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density toplologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman

Abstract. — In a former article [Les04], we construct a structure of measured quantum groupoid. We are now investigating duality theorem of these objects. More precisely, we give the definition of generalized measured quantum groupoids which is a category containing measured quantum groupoids

Extending the approach of Jouini et al. we define set–valued (convex) measures of risk and its acceptance sets. Using a new duality theory for set–valued convex functions we give dual representation theorems. A scalarization concept is introduced that has economical meaning in terms of prices