This report defines the rank complement of a diagonalizable matrix (i.e. a matrix which can be brought to a diagonal form by means of a change of basis) as the interchange of the range and the null space. Given a diagonalizable matrix A there is in general no unique matrix Ac which has a range equal to the null space of A and a null space equal to the range of A, only matrices of full rank have...

ing this paper new factorization techniques for computation of the Operational Space Mass Matrix (A) and its inverse (A-l) are developed. Starting with a new factorization of the inverse of mass matrix (M-l) in the form of Schur Complement as M-l = G’ %)TsI-lB, where d and 8 are block tridlagonal matrices and G is a tridiagonal matrix, similar factorization for A and A-i are derived. Specifical...

Given a 3-manifold M , there are generically infinitely many manifold which covers M . However, if we are restricted to the category of knot complements, the situation is quite different. It can be shown (see Lemma 1 and bellow) that if the complement E(K) of a knot K is n-fold covered by some knot complement, then the covering is cyclic, and K admits a cyclic surgery, i.e. a Dehn surgery such ...

We would like to give a brief review concerning liquid-liquid equilibrium in binary liquid mixtures under absolute negative pressure. Although negative pressure states are metastable ones, they can be maintained long enough to make phase equilibrium measurements. Several phenomena concerning liquid-liquid equilibrium can be seen only – or can be seen better – under negative pressure; these are ...

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