We study the rank of a general tensor u in a tensor product space H1 ⊗ · · · ⊗ Hk. The rank of u is the minimal number p of pure states v1, · · · , vp such that u is a linear combination of the vj ’s. This rank is an algebraic measure of the degree of entanglement of u. Motivated by quantum computation, we completely describe the rank of an arbitrary tensor in (C) and give normal forms for tens...

The total number of 542 patients with colorectal cancer surgery have been analyzed in order to estimate the effect of receiving transfusion local recurrences, and the disease free - survival. It should be examined whether there are changes in general immunity indicators which would be connected with perioperative transfusion. A significant connection has been found between local recurrences and...

In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analisis of the possible saturated fusion systems in terms of the outer automorphism group ant the proper F -radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-...

Abstract We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged isotropic laws. As an application, we central limit theorem in quantum unique ergodicity (QUE): is, show quadratic forms deterministic matrix A on bulk eigenvectors have approximately Gaussian fluctuation. For spectrum, generalise our previous r...

a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...