New limits on neutrino non-unitary mixings based on prescribed singular values

Singular values are used to construct physically admissible 3-dimensional mix- ing matrices characterized as contractions. Depending on the number of singular values strictly less than one, the space of the 3-dimensional mixing matrices can be split into four disjoint subsets, which accordingly corresponds to the minimal number of additional, non-standard neutrinos. We show in numerical analysis that taking into account present experimental precision and fits to different neutrino mass splitting schemes, it is not pos- sible to distinguish, on the level of 3-dimensional mixing matrices, between two and three extra neutrino states. It means that in 3+2 and 3+3 neutrino mixing scenarios, using the so-called α parametrization, ranges of non-unitary mixings are the same. However, on the level of a complete unitary 3+1 neutrino mixing matrix, using the dilation procedure and the Cosine-Sine decomposition, we were able to shrink bounds for the \light-heavy" mixing matrix elements. For instance, in the so-called seesaw mass scheme, a new upper limit on jUe4j is about two times stringent than before and equals 0.021. For all considered mass schemes the lowest bounds are also obtained for all mixings, i.e. |Ue4|, |Uμ4|, |Uτ4|. New results obtained in this work are based on analysis of neutrino mixing matrices obtained from the global fits at the 95% CL

A structured approach to design-for-frequency problems using the Cayley-Hamilton theorem

Abstract An inverse eigenvalue problem approach to system design is considered. The Cayley-Hamilton theorem is developed for the general case involving the generalized eigenvalue vibration problem. Since many solutions exist for a desired frequency spectrum, a discussion of the required design information and suggestions for including structural constraints are given. An algorithm for solving the inverse eigenvalue design problem using the generalized Cayley-Hamilton theorem is proposed. A method for solving partially described systems is also specified. The Cayley-Hamilton theorem algorithm is shown to be a good design tool for solving inverse eigenvalue problems of mechanical and structural systems

A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values

The Weyl-Horn theorem characterizes a relationship between the eigenvalues and the singular values of an arbitrary matrix. Based on that characterization, a fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values. Beside being theoretically interesting, the technique could be employed to create test matrices with desired spectral features. Numerical experiment shows this algorithm is quite efficient and robust