Ellipsoids of U(3) model

Intersection of Ellipsoids

Surface Area of Ellipsoids

A. We study the surface area of an ellipsoid in E as the function of the lengths of theirmajor semi-axes. Wewrite down an explicit formula as an integral over Sn−1, use the formula to derive convexity properties of the surface area, to sharpen the estimates given [6], to produce asymptotic formulas in large dimensions, and to give an expression for the surface in terms of the Lauricella ...

VC dimension of ellipsoids

We will establish that the vc dimension of the class of d-dimensional ellipsoids is (d +3d)/2, and that maximum likelihood estimate with N -component d-dimensional Gaussian mixture models induces a geometric class having vc dimension at least N(d + 3d)/2.

Isolation and characterization of three rat U3 RNA pseudogenes colinear with U3 RNA.

Three different 15-kilobase rat genomic clones that contained sequences colinear with U3 RNA were isolated. These inserts hybridized only to U3 RNA in a mixture of total cellular 4-8 S RNA labeled in vivo which showed that genes or pseudogenes for most other small RNAs were absent in these U3 DNA clones. DNA sequence analysis showed that the three subcloned genes contained full-length U3-coding...

Plane Intersections of Rotational Ellipsoids

This result could have been proved by the Greeks more than two thousand years ago, so we certainly did not expect it to be a new theorem. However, since we found it (1996) we have asked a large number of experts, we have searched the literature, and we have posted queries on the internet, all without finding anyone who has heard of the theorem. We thus feel comfortable in concluding that the th...