Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> http://www.scielo.cl/rss.php?pid=0716-091720030002&lang=en vol. 22 num. 2 lang. en <![CDATA[SciELO Logo]]> http://www.scielo.cl/img/en/fbpelogp.gif http://www.scielo.cl <![CDATA[<B>GENERALIZATION OF THE SECOND TRACE FORM OF CENTRAL SIMPLE ALGEBRAS IN CHARACTERISTIC TWO</B>]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200001&lng=en&nrm=iso&tlng=en Let F be a field with characteristic two. We generalize the second trace form for central simple algebras with odd degree over F. We determine the second trace form and the Arf invariant and Clifford invariant for tensor products of central simple algebras <![CDATA[A COMMUTATOR RIGIDITY FOR FUNCTION GROUPS AND TORELLI’S THEOREM]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200002&lng=en&nrm=iso&tlng=en We show that a non-elementary finitely generated torsion-free func-tion group is uniquely determined by its commutator subgroup. In this way, we obtain a generalization of the results obtained in [2], [3] and [8]. This is well related to Torelli’s theorem for closed Riemann sur-faces.For a general non-elementary torsion-free Kleinian group the above rigidity property still unknown <![CDATA[DIAGONALS AND EIGENVALUES OF SUMS OF HERMITIAN MATRICES: EXTREME CASES]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200003&lng=en&nrm=iso&tlng=en There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through con-gruences of the form UAU*+ V BV *; where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equal-ities are examined here <![CDATA[ORLICZ - PETTIS THEOREMS FOR MULTIPLIER CONVERGENT OPERATOR VALUED SERIES]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200004&lng=en&nrm=iso&tlng=en There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through con-gruences of the form UAU*+ V BV *; where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equal-ities are examined here <![CDATA[NON - AUTONOMOUS INHOMOGENEOUS BOUNDARY CAUCHY PROBLEMS AND RETARDED EQUATIONS]]> http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000200005&lng=en&nrm=iso&tlng=en In this paper we prove the existence and the uniqueness of the clas-sical solution of non-autonomous inhomogeneous boundary Cauchy problems, and that this solution is given by a variation of constants formula. This result is applied to show the existence of solutions of a retarded equation