Let S be a subset of diagonal entries of an n × n complex matrix A. When the members of S have a common value which is equal to an eigenvalue of A, then S is a critical diagonal set of A. The existence of such a set is equivalent to the matrix Ã, obtained from A by setting its diagonal entries equal to zero, having an s × t zero submatrix with s + t ≥ n + 1. If S is a minimal critical diagonal ...

2 has nonzero entries only on its diagonal and first superdiagonal ) Compute orthogonal matrices P and Q such that Σ = P BQ is diagonal and nonnegat i 2 2 2 T 2 ive. The diagonal entries σ of Σ are the singular values of A . We will take them to be sorted in decreasing order: σ ≥ σ . The columns of Q= Q Q are the right singular vec i i + 1 1 2 t 1 2 ors, and the columns of P= P P are the left s...

In this study, the effects of three different viscous damper configurations, chevron, diagonal and toggle, as well as brace stiffness on the performance of brace-viscous damper system in various steel frams under different earthquake records were investigated. A finite element software, ANSYS, is exploited to develop the numerical models. To verify the numerical simulations, their results were ...

The fully homomorphic symmetric encryption scheme MORE encrypts keys by conjugation with a random invertible matrix over an RSA modulus. We provide a two known-ciphertexts cryptanalysis recovering a linear dependence among the two encrypted keys. 1. The FHE scheme MORE In their paper [1], Kipnis and Hibshoosh propose, among other things, to use the following type of fully homomorphic encryption...