in this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. following this, we establish the minkowski and brunn-minkowski inequalities for volumes difference function of the projection and intersection bodies.

BACKGROUND Nipple creation using the C-V flap technique is often the final step in breast reconstruction. The aim of this study was to subjectively and objectively assess the cosmetic outcomes and satisfaction of patients undergoing C-V flap nipple reconstruction. METHODS Subjective assessments of patient satisfaction with the neo-nipple were recorded by visual analogue scoring (VAS; 0...

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. 2000 Mathematics Subject Classification. 52A40, 52A20.

An open research question is how to define a useful metric on SE(n) with respect to (1) the choice of coordinate frames and (2) the units used to measure linear and angular distances. We present two techniques for approximating elements of the special Euclidean group SE(n) with elements of the special orthogonal group SO(n+1). These techniques are based on the singular value and polar decomposi...