SL (m, C)-equivariant and translation covariant continuous tensor valuations

The space of continuous, -equivariant, , and translation covariant valuations taking values in the space of real symmetric tensors on of rank is completely described. The classification involves the moment tensor valuation for and is analogous to the known classification of the corresponding tensor valuations that are -equivariant, although the method of proof cannot be adapted

Integral geometry of complex space forms

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and complex euclidean space. In particular, we compute the family of kinematic formulas for invariant valuations and invariant curvature measures in these spaces. In addition to new and more efficient framings of the tube formulas of Gray and the kinematic formulas of Shifrin, this approach yields a new formula expressing the volumes of the tubes about a totally real submanifold in terms of its intrinsic Riemannian structure. We also show by direct calculation that the Lipschitz-Killing valuations stabilize the subspace of invariant angular curvature measures, suggesting the possibility that a similar phenomenon holds for all Riemannian manifolds. We conclude with a number of open questions and conjectures.Comment: 68 pages; minor change

Spread Spectrum Audio Watermarking Using Vector Space Projections

Efficient watermarking techniques guarantee inaudibility and robustness against signal degradation. Spread spectrum watermarking technique makes it harder for unauthorized adversary to detect the position of the embedded watermark in the carrier file, because the watermark bits are spread in the carrier medium. Unfortunately, there is a high possibility that synchronization of the watermark bits and carrier bits will go out of phase. This will lead to watermark detection problem in the carrier bit sequence. In this paper, we propose a vector space projections approach on spread spectrum audio watermarking technique, in order to presents both the watermark bits and carrier bits as vectors. Similarities of watermark vector to a carrier vector are resolve by the normalized dot product of the cosine of angle between them for embedding. After embedding and extraction by the technique, signal processing methods in the form of attacks were applied. Our approach proved robust when compared with other audio watermarking techniques. This technique gives good results and was found to be robust on performance test