In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace TP of initial opinions (where P is the influence matrix) that ensure consensu...

It is a well-known fact that while reducing a symmetric matrix into a similar tridiagonal one, the already tridiagonal matrix in the partially reduced matrix has as eigenvalues the Lanczos-Ritz values (see e.g. [Golub G. and Van Loan C.] ). This behavior is also shared by the reduction algorithm which transforms symmetric matrices via orthogonal similarity transformations to semiseparable form ...

Travelling wave solutions to the vortex filament flow generated by elastica produce surfaces in R that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the Bäcklund transformation for constant tors...

Travelling wave solutions to the vortex lament ow generated by elastica produce surfaces in R 3 that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classiied in the special cases where the helices are all congruent or are all generated by a single screw motion. The rst case yields a new characterization for the BB acklund transformation for constant torsion...

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems-interior and exterior orientation of sensors-to a common, known in both systems, point. Each of the systems is t...

Usually bilingual word vectors are trained “online”. Mikolov et al. (2013a) showed they can also be found “offline”; whereby two pre-trained embeddings are aligned with a linear transformation, using dictionaries compiled from expert knowledge. In this work, we prove that the linear transformation between two spaces should be orthogonal. This transformation can be obtained using the singular va...

In this paper we introduce a novel methodology to transmit the origin to the center of a polygon in a molecule structure such that the special axis be perpendicular to the plane containing the polygon. The mathematical calculation are described completely and the algorithm will be showed as a computer program.

Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbita...