E-optimal designs for polynomial spline regression

We give the E-optimal approximate designs for mean (sub-) parameters in d-th degree totally positive polynomial spline regression with prescribed knots over an arbitrary compact real interval. Based on a duality between E- and scalar optimality, the optimal design is found to be supported by the extrema of the Chebyshev (i.e., equi-oscillating) spline, with corresponding weights given in terms of certain Lagrange interpolation splines. In particular, for d-th degree polynomial regression, parameterized w.r.t. a totally positive basis (e.g. the Bernstein polynomials), we obtain the solution to the E-optimal design problem, where, contrary to the ordinary monomial setup, no restrictions on the size and location of the regression interval or on the particular system of parameters of interest are required. (orig.)Available from TIB Hannover: RR 4487(1997,16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Cutting planes from a mixed integer Farkas Lemma

SIGLEAvailable from TIB Hannover: RR 4487(2002,23) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A note on perturbations of stochastic matrices

SIGLEAvailable from TIB Hannover: RR 4487(2000,6) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Das 'Verdopplungsproblem' des SOCRATES - unterrichtsmethodisch betrachtet

Available from TIB Hannover: RR 4487(1997,26) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Isomorphism for digraphs and sequences of shop scheduling problems

The computational complexity of the graph isomorphism problem is still unknown. We consider Cartesian products K_nXK_m of two complete graphs K_n and K_m. An acyclic orientation of such a Cartesian product is called a sequence graph because it has an application in production scheduling. It can be shown that the graph isomorphism problem on the class of these acyclic digraphs is solvable in polynomial time. We give numbers of non-isomorphic sequence graphs for small n and m. The orientation on the cliques of a sequence graph can be interpreted as job orders and machine orders of a shop scheduling problem with a complete operation set. (orig.)Available from TIB Hannover: RR 4487(1996,21) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

Isomorphism for digraphs and sequences of shop scheduling problems

The computational complexity of the graph isomorphism problem is still unknown. We consider Cartesian products K_nXK_m of two complete graphs K_n and K_m. An acyclic orientation of such a Cartesian product is called a sequence graph because it has an application in production scheduling. It can be shown that the graph isomorphism problem on the class of these acyclic digraphs is solvable in polynomial time. We give numbers of non-isomorphic sequence graphs for small n and m. The orientation on the cliques of a sequence graph can be interpreted as job orders and machine orders of a shop scheduling problem with a complete operation set. (orig.)Available from TIB Hannover: RR 4487(1996,21) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

On the Durfee size of Kronecker products of characters of the symmetric group and its double covers

SIGLEAvailable from TIB Hannover: RR 4487(2003,36) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Heights of spin characters in characteristic 2

Based on our earlier description of the distribution into 2-blocks of the spin characters of the covering groups of symmetric groups we compute the heights of such characters in the blocks containing them. We also give a complete set of labels for the spin characters of minimal height in a 2-block. Another related topic treated here is the determination of the minimal power of 2 dividing a spin character degree and the explicit description of the labels of spin characters with this minimal power of 2 in their degree. Also, an upper bound for the heights of spin characters in 2-blocks is derived, and the labels of spin characters attaining this bound are described. As an application of our results we show that the 2-blocks of the covering groups of symmetric groups provide further evidence for some important representation theoretical conjectures. (orig.)Available from TIB Hannover: RR 4487(1994,34) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Branching of modular representations of the alternating groups

Based on Kleshchev's branching theorems for the p-modular irreducible representations of the symmetric group and on the recent proof of the Mullineux Conjecture, we investigate in this article the corresponding branching problem for the p-modular irreducible representations of the alternating group A_n. We obtain information on the socle of the restrictions of such A_n-respresentations to A_n_-_1 as well as on the multiplicities of certain composition factors; furthermore, irreducible A_n-representations with irreducible restrictions to A_n_-_1 are studied. (orig.)Available from TIB Hannover: RR 4487(1997,33) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A note on Cartan matrices for symmetric groups

SIGLEAvailable from TIB Hannover: RR 4487(2001,19) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman