The vectorial extension of the Ribaucour transformation for the Lamé equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an exam...

A Clifford algebra model for Möbius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of “discrete Ribaucour con...

A Cliiord algebra model for MM obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced , and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of \discrete Ribaucour c...

The effect of perspective transformation on transfer of face training was investigated in a yes/no recognition task using face stimuli with 42 degrees, 10 degrees, or no perspective convergence. A strong dependence of recognition performance on the magnitude of perspective transformation was found, with large perspective changes such as from 42 degrees at learning to orthogonal at test producin...

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...

Quantum information theory is used to analyze various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The efficiency of the transformation of non-orthogonal states into orthogonal ones is discussed.

The importance of geometric moment (GM) invariants first received research attention when Hu [1] introduced them in his study. As they capture global features have been widely used in applications such as object classification, image and shape analysis and edge detection [2-8]. However, since GMs are non-orthogonal, a set of continuous orthogonal moments including Zernike and Legendre moments w...

There is a famous construction of orthogonal arrays by R.C. Bose (1947). The construction uses linear transformations over a finite field. We generalize this to use non-linear transformation instead of linear and a subset of vector space as their domains. We show here constructions of orthogonal and balanced arrays which are generated by a set of quadratic function.