Convergence of algorithms for perturbed optimization problems

Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.     

Representation of steady-state vowels in the temporal aspects of the discharge patterns of populations of auditory-nerve fibers.

This paper is concerned with the representation of the spectra of synthesized steady-state vowels in the temporal aspects of the discharges of auditory-nerve fibers. The results are based on a study of the responses of large numbers of single auditory-nerve fibers in anesthetized cats. By presenting the same set of stimuli to all the fibers encountered in each cat, we can directly estimate the population response to those stimuli. Period histograms of the responses of each unit to the vowels were constructed. The temporal response of a fiber to each harmonic component of the stimulus is taken to be the amplitude of the corresponding component in the Fourier transform of the unit's period histogram. At low sound levels, the temporal response to each stimulus component is maximal among units with CFs near the frequency of the component (i.e., near its place). Responses to formant components are larger than responses to other stimulus components. As sound level is increased, the responses to the formants, particularly the first formant, increase near their places and spread to adjacent regions, particularly toward higher CFs. Responses to nonformant components, exept for harmonics and intermodulation products of the formants (2F1,2F2,F1 + F2, etc), are suppressed; at the highest sound levels used (approximately 80 dB SPL), temporal responses occur almost exclusively at the first two or three formants and their harmonics and intermodulation products. We describe a simple calculation which combines rate, place, and temporal information to provide a good representation of the vowels' spectra, including a clear indication of at least the first two formant frequencies. This representation is stable with changes in sound level at least up to 80 dB SPL; its stability is in sharp contrast to the behavior of the representation of the vowels' spectra in terms of discharge rate which degenerates at stimulus levels within the conversational range.     

Lineare Komplexbündel im einfach isotropen Raum

According to K. Strubecker ([5]–[8]) a three dimensional real affine space with the metric ds²=dx²+dy² is called a simply iso-tropic space J₃(1). In J₃(1) exist 41 types of bundles of linear line complexes. In this paper we study the bundles of type 1, 2-called cyclic bundle and 38-called Strubecker-bundle. For a cyclic bundle and a Strubecker-bundle we give only the fundamental theorem and one metric result, however for a cyclic bundle the metric theory is completely developed.

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Herrn o. Prof. Dr. K. Strubecker zum 80. Geburtstag gewidmet     

Über die Kurven konstanten Striktionsabstandes auf windschiefen Flächen

Ohne Zusammenfassung