Triostin A Derived Cyclopeptide as Architectural Template for the Alignment of Four Recognition Units

The DNA bisintercalator triostin A is structurally based on a disulfide-bridged depsipeptide scaffold that provides preorganization of two quinoxaline units in 10.5 Å distance. Triostin A analogues are synthesized with nucleobase recognition units replacing the quinoxalines and containing two additional recognition units in between. Thus, four nucleobase recognition units are organized on a rigid template, well suited for DNA double strand interactions. The new tetra-nucleobase binders are synthesized as aza-TANDEM derivatives lacking the N-methylation of triostin A and based on a cyclopeptide backbone. Synthesis of two tetra-nucleobase aza-TANDEM derivatives is established, DNA interaction analyzed by microscale thermophoresis, cytotoxic activity studied and a nucleobase sequence dependent self-aggregation investigated by mass spectrometry.     

Numerical solution of a nonlinear parabolic control problem by a reduced SQP method

We consider a control problem for a nonlinear diffusion equation with boundary input that occurs when heating ceramic products in a kiln. We interpret this control problem as a constrained optimization problem, and we develop a reduced SQP method that presents for this problem a new and efficient approach of its numerical solution. As opposed to Newton's method for the unconstrained problem, where at each iteration the state must be computed from a set of nonlinear equations,in the proposed algorithm only the linearized state equations need to be solved. Furthermore, by use of a secant update formula, the calculation of exact second derivatives is avoided. In this way the algorithm achieves a substantial decrease in the total cost compared to the implementation of Newton's method in [2]. Our method is practicable with regard to storage requirements, and by choosing an appropriate representation for the null space of the Jacobian of the constraints we are able to exploit the sparsity pattern of the Jacobian in the course of the iteration. We conclude with a presentation of numerical examples that demonstrate the fast two-step superlinear convergence behavior of the method.     

Rates of convergence for adaptive Newton methods

We consider Newton-type methods for constrained optimization problems in infinite-dimensional spaces, where at each iteration the first and second derivatives and the feasible set are approximated. The approximations can change at each iteration and conditions are given under which linear and superlinear rates of convergence of the iterates to the optimal point hold. Several applications are discussed.     

Nachweis und Bestimmung von Zuckerarten

Ohne Zusammenfassung     

A pointwise quasi-Newton method for unconstrained optimal control problems

Summary For a class of unconstrained optimal control problems we propose a quasi-Newton method that exploits the structure of the problem. We define a new type of superlinear convergence for sequences in function spaces and prove superlinear convergence of the iterates generated by the quasi-Newton method in this sense.This author supported by NSF grants # DMS-8300841 and # DMS-8500844     

Parabolische Schiebzykliden des einfach isotropen Raumes

Ohne ZusammenfassungMeinem verehrten Kollegen, Herrn O. Prof. Dr. Dr. H. Brauner zum 60. Geburtstag gewidmet.     

Response to Rodrigues and Rosa on the twin paradox

This paper responds briefly to the criticism of Rodrigues and Rosa on my earlier analysis of the twin paradox. The main point that I have emphasized (and that the authors have not refuted, either logically or mathematically) is the error in directly identifying anabstract measure relative to a reference frame [and its transformations to all other possible reference frames in which the laws of nature are to be compared (such as temporal and spatial measures)], with aphysical extension and duration of a material body.     

59Co nuclear magnetic resonance study in GdCo2Si2 compound

The spin echo NMR spectra of⁵⁹Co for GdCo₂Si₂ are reported. A weak negative hyperfine field on Co nuclei was found in magnetically ordered state of the compound. The splitting of resonance lines in external magnetic field indicates on antiferromagnetic structure of Gd moments lying in thea-a plane with energetic minima in [100] and [110] directions as in GdFe₂Si₂ and GdNi₂Si₂.