A photochemical route for efficient cyclopeptide formation with a minimum of protection and activation chemistry

An elaborated protocol is described which allows the efficient transformation of di-, tri-, and tetrapeptides into cyclopeptides with a minimum of protection and activation chemistry using the photoinduced electron transfer initiated decarboxylation of N-phthaloyl peptides resulting in C-C coupling between the initially formed carbon radicals.     

Approaching supramolecular functionality

Functional molecules require a high degree of complexity which is difficult to achieve by covalent synthesis. This article discusses supramolecular approaches to the creation of larger architectures through noncovalent bonds, self-assembly, and template strategies. It highlights selected examples for the structural and conformational control of function and attempts to identify difficulties and challenges which may arise in future.     

On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and Monte-Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected. Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number generators with Dickson polynomials.     

Strong field quantum path control using attosecond pulse trains

We show that attosecond pulse trains have a natural application in the control of strong field processes. In combination with an intense infrared laser field, the pulse train can be used to microscopically select a single quantum path contribution to a process that would otherwise consist of several interfering components. We present calculations that demonstrate this by manipulating the time-frequency properties of high order harmonics at the single atom level. This quantum path selection can also be used to define a high resolution attosecond clock.     

Stress functions and internal stresses in linear three-dimensional anisotropic elasticity

A stress function method is presented in order to give a general solution of the incompatibility problem of three-dimensional linear anisotropic elasticity theory. A relation between the internal stress tensor in terms of derivatives of a sixth-order stress function tensor will be derived. Using this formulation the so far open problem of the representation of the second-order stress function tensor by the fourth-order stress function tensor in anisotropic elasticity theory is solved in general.     

Scattering theory for Stark Hamiltonians

We give an introduction to the spectral and scattering theory for Schr?dinger operators. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians.     

Size Measurement of Very Small Spherical Particles by Mie Scattering Imaging (MSI)

The Mie Scattering Imaging method (MSI) gathers out‐of‐focus images of dispersed spherical particles present in a laser light sheet and extracts the individual particle diameter from these images. The general idea of the method has been around for more than a decade and a number of papers has dealt with it over recent years. Our work focuses on small particle sizes from 20 μm down to 2 μm, a range which has not been tackled so far although it is of great importance in particle systems. We present an optical set‐up with a special arrangement of camera lenses that allows to work in this range. An evaluation algorithm based on correlation of the experimental optical information with theoretical Mie scattering was found to give the most accurate results for particle sizing. Besides accuracy measurements on solid spheres the versatility of the method is demonstrated by an example of transient droplet growth between 2–7 μm.