CHORD POWER INTEGRALS OF SIMPLICES

In this paper, we obtain a formula relating the chord power integrals of a simplex K and the dual quermassintegrals of its difference body DK. As interesting applications, we express the volumes of difference body DK and polar projection body Π*K in terms of the volume of simplex K. Santaló-type inequality for chord power integrals of simplex is also established.

VOLUME INEQUALITIES FOR Lp-JOHN ELLIPSOIDS AND THEIR DUALS

In this paper, we establish some inequalities among the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual, which are the strengthened version of known results. We also prove inequalities among the polar of the Lp-centroid body, the Lp-polar projection body, the Lp-John ellipsoid and its dual.

Part 1: Chapter 3 Svalbard's geological frame

This chapter gives an outline of the geology of Svalbard, an introduction to the principles applied in this work and a preview of the interpretations and conclusions that have come out of these studies.The key position of Svalbard in relation to other Arctic lands is shown in a Polar projection (Fig. 3.1).3.1 The space frame: Svalbard's structural frame3.1.1 Solid outcropsThe conventional geological map of Svalbard shows in outline the outcrop areas according to age. (Fig. 3.2). Although rock ages are matters of interpretation, the diagrammatic map is at least consistent with the conclusions in this work. It differs from most maps in the larger outcrop of Vendian rocks within the basement. The outcrop pattern ignores Quaternary deposits, i.e. it is a solid geology map. It is diagrammatic because detail is impossible to show on this scale. The larger ice masses which obscure the exposure are also diagrammatic.3.1.2 Regional descriptive sectorsBecause the intention in this work is generally to describe rocks before interpreting their history and so not to begin with too many assumptions, the rocks are described in Part 2 of this work in the eight sectors or regions (Chapters 4 to 11) as shown in Fig. 3.3. Their boundaries are not fixed because it is convenient to treat some geological matters together in one chapter, even when they might overlap onto another. They are not terranes. Where strata are described the succession is presented as observed with the youngest at the top (as

Rosannia manika gen. et sp. nov. from the Edmonton Formation (Maestrichtian), Alberta, Canada

The form-genus Rosannia is designated for triorate pollen, having only one polar projection and three equatorial projections. Rosannia manika n. sp. Is described from the Edmonton Formation (Maestrichtian), Alberta, and is designed as the type species of the genus.