introduction: variable resolution x-ray (vrx) ct is a new type of ct that can image objects at various spatial resolutions. in a vrx ct scanner, the spatial resolution increases at the cost of reduction in the field of view (fov). an important factor that limits the spatial resolution of the vrx ct is the effect of focal spot size. also, the optimum magnification is different at each incident a...

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose ‘lifts’ to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize p...

We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case R −→ R, we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent (Definition 3.2) to the ...

In the category Top of topological spaces and continuous functions we prove that descent morphisms with respect to the class IE of continuous bijections are exactly the descent mor phisms providing a new characterization of the latter in terms of sub brations IE X of the basic bration given by Top X which are essentially complete lattices Also e ective descent morphisms are characterized in ter...

Topological groupoids admit various types of morphisms. We push these notions to the level continuous groupoid actions obtain action Some dynamical properties and their relation morphisms are studied. Among them recurrence, forms transitivity, minimality, limit, recurrent, periodic almost points.

In this paper, we construct quasi-morphisms on the group of symplectomorphisms closed disk D. These are extensions Ruelle invariant and Gambaudo-Ghys quasi-morphisms. As a corollary, show that second bounded cohomology Hb2(Symp(D)) is infinite dimensional.