Neuartige HF-angeregte Plasmaquellen fuer Atmosphaerendruck. Teilvorhaben: Grundlegende Untersuchungen zum Einsatz der Mie-Ellipsometrie zur Partikeldiagnostik Abschlussbericht

SIGLEAvailable from TIB Hannover: DtF QN1(97,43) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Bildung und Forschung, Berlin (Germany)DEGerman

Inductive counting below LOGSPACE

We apply inductive counting to nondeterministic branching programs and prove that complementation on this model can be done without increasing the width of the branching programs too much. This shows that for an arbitrary space bound s(n), the class of languages accepted by nonuniform nondeterministic O(s(n)) space bounded Turing machines is closed under complementation. We obtain for arbitrary space bounds s(n) that the alternation hierarchy of nonuniform O(s(n)) space bounded Turing machines collapses to its first level. This improves the previously known result of Immermann and Szelepcsenyi to space bounds of order o(logn) in the nonuniform setting. This reveals a strong difference to the relations between the corresponding uniform complexity classes, since very recently it has been proved that in the uniform case the alternating space hierarchy does not collapse for sublogarithmic space bounds. (orig.)Available from TIB Hannover: RR 1843(94-12) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Proximal methods in view of interior-point-strategies

The paper deals with regularized penalty-barrier methods for ill-posed convex programming problems. The approach suggested combines a generalized proximal algorithm developed in (5) with an interior-point-strategy, using barrier function. In the spirit of a proximal algorithm we consider interior-point-methods in which on each step a strongly convex function has to be minimized and the prox-term can be scaled by a variable scaling factor (cf. formula (3)). In the first part of the paper convergence of the regularized penalty method is studied for an axiomatically given class of penalty functions (Theorem 1). The technique used here differs essentially from those in other papers, where usually a uniform approximation of the original problem is performed. According to the results obtained a wide class of penalty functions, in particular, penalties of logarithmic and exponential type (cf. formulas (40) and (41)), can be applied in order to design special algorithms. In the second part rate of convergence is investigated. Conditions ensuring linear convergence w.r.t. the objective values (Theorem 3) as well as w.r.t. the iterates (Theorem 4) are established. (orig.)Available from TIB Hannover: RR 1843(95-18) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman