Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

where B is a real matrix with m rows and n columns, x ranges over the set of row vectors with m components, all non-negative and adding up to one, y ranges over the corresponding set of «-component column vectors, and the pay-off, (x2?, y), indicates the inner product of the two vectors xB and y. One device which may simplify a game computation is that of "dominance" or "majorization" [vNM, p. ...

We investigate representations of the Z22-graded extension osp(1|2), which is spectrum generating algebra recently introduced version superconformal mechanics. The main result a classification irreducible lowest weight modules osp(1|2). This done via introduction Verma and its maximal invariant submodule generated by singular vectors. Explicit formulas all vectors are also presented.

We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter ...

This note treats the problem of stabilization of linear systems by static output feedback using the concept of (C,A, B)-invariant subspaces. The work provides a new characterization of Output Stabilizable (C,A,B)invariant subspaces through two coupled quadratic stabilization conditions. An equivalence is shown between the existence of a solution to this set of conditions and the possibility to ...

Bistatic SAR uses transmitter and receiver flying distinct platforms. There are two main configuration types. Time invariant configuration: velocity vectors are identical and parallel to the ground. Thus, equidistance lines and lines of equal radial velocity are translated along the trajectory as time grows. Non time invariant configuration: velocity vectors are not equal. There are two princip...

in this paper, a new method is presented for the detection of defects in random textures. in the training stage, the feature vectors of the normal textures’ images are extracted by using the optimal response of gabor wavelet filters, and their probability density is estimated by means of the gaussian mixture model (gmm). in the testing stage, similar to the previous stage,at  first, the feature...

This paper studies how redundant data affect maximizing of weighted distances of vectors in a set of vectors. To maximize distances differential evolution is used, because the problem does not have analytical solution and is complex. This paper at first describes suppressing of redundant data mathematically and then it checks this theoretical result in two experiments practically. As a result i...

We study Sp2n(R)-invariant functionals on the spaces of smooth vectors in Speh representations of GL2n(R). For even n we give expressions for such invariant functionals using an explicit realization of the space of smooth vectors in the Speh representations. Furthermore, we show that the functional we construct is, up to a constant, the unique functional on the Speh representation which is inva...

For a system of M coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of...