In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial “torsion-type” invariant which refines the PR-metric introduced in [Fa] and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler ...

In this paper, we propose a least-squares regression method [2] with unitary constraints with applications to classification and recognition. To do this, we employ a kernel to map the input instances to a feature space on a sphere. In a similar fashion, we view the labels associated with the training data as points which have been mapped onto a Stiefel manifold using random rotations. In this m...

Multiple antennas at transmitter and receiver can be used to improve communication efficiency by canceling channel noises using the correlated information among the signals transmitted from different antennas. In this paper, a novel approach is proposed for this problem for another interesting case where multiple symbols are used to make the best use of the multiple antenna channel. Such an iss...

We consider the dynamics of three point masses, where we assume that the mass of the third body is so small that it does not affect the motion of the primaries. In the framework of the restricted three–body problem, we investigate the collisional trajectories, which correspond to a singularity of the equations of motion. We investigate the regularizing techniques known as Levi–Civita, Kustaanhe...

In this note we announce an extension of these theorems to the setting of Stiefel manifolds and matrix space. Our work makes it possible to construct holomorphic discrete series representations for the real symplectic group by decomposing a tensor product of certain projective representations introduced earlier by Shale and Weil. (See Weil [11] and also Shalika [10].) Proofs of the results anno...