Summierbarkeit der geometrischen Reihe auf vorgeschriebenen Mengen

In this paper we are concerned with the summability of the geometric series by matrix methods. We prove the following theorem: Suppose M_o:={z:|z|<1}, M₁, M₂, is a collection of countably many Lebesgue measureable, disjoint sets. For k=1,2, let f_k be a prescribed function, analytic on . Then there exists a triangular matrix , such that the V-transform {_n(z)} of the geometric series has the following properties: {_n(z)} converges compactly to on M_o; for k=1,2, there are sets B_k, such that has Lebesgue-measure zero and _n(z)f_k(z) for zB_k; if there is a set B^*, such that B^*M^* has Lebesgue-measure zero and {_n(z)} diverges for zB^*.     

Two questions in diophantine approximation

The first question is about a possible variation on Dirichlet's approximation theorem for linear forms x+y+z, wherex,y are restricted topositive integers. The second question, which turns out to be related to the first, is about approximation to elements in a power series fieldk((t ^–1)) by solutions of first order linear differential equationsx+y+z=0, wherex,y,z are polynomials int. Dedicated to Prof. Dr. E. Hlawka on the occasion of his 60th birthday     

Non-stationary waiting times in a closed exponential tandem queue

A closed exponential tandem queue in which every customer has to be served by two servers is considered. Given the numbers of customers lined up at each of the two servers, we derive the probability distributions of the waiting time of any customer until his second service is completed, and of the total busy time of the system.     

A characterization of subgroups of the orthogonal group

LetG be a subgroup of the general linear group GL_n(K), where charK 2. Put Kⁿ =V. AssumeG is generated by the setS of all elements inG for which dimV( – 1) = 1, and suppose ²=1_V for each inS. If {V(–1)¦S} contains a simplex, if – 1_V G, and if inG is a product of dim v(–1) elements inS wheneverV(–1) is not contained in the kernel of–1, thenG is a subgroup of an orthogonal group.This research was supported in part by NSERC Canada grant A7251.To Helmut Mäurer on his 60th birthday     

Optofluidic droplet router

This contribution presents an optofluidic droplet router which is able to route and steer microdroplets using optically induced forces created solely by the bulk photovoltaic effect on a nonlinear substrate. The combination of microfluidic tools with the properties of a photorefractive crystal allows for the generation of dielectrophoretic forces that can be either repulsive, leading to virtual barriers, or attractive, creating virtual rails. The sign of these forces is solely determined by the electrical properties of the liquid medium under investigation. Moreover, the induced structures on the bottom of the microfluidic channel are optically reconfigurable, so that the same device can easily be adopted for different purposes. Appropriate droplet‐generating devices are fabricated by UV illumination of SU‐8 and polydimethylsiloxane replica molding of the master structures. The bottom of the channels is formed by an iron‐doped lithium niobate crystal, whose internal electric fields are induced by structured illumination patterns and exert dielectrophoretic forces on droplets in the microfluidic section.

     

Two-color cross-correlation of fs-laser pulses by two-photon induced photoconductivity for near and far field optical measurements

Two-color two-photon induced photoconductivity in a GaAsP diffusion type photodiode is demonstrated by measuring femtosecond cross-correlation functions for widely separated wavelength pairs of 775 and 1300 nm. Results are obtained for a range of tunable wavelengths and average powers of the incident lasers by measuring the two-photon induced photocurrent as a function of the optical delay between the pulses. The temporal autocorrelation of femtosecond laser pulses in the near-field of a small diameter aluminum coated optical fiber tip is also obtained with the same photodiode method for single colors.     

Ground-state complex formation of perylene with pyromellitic dianhydride studied by static fluorescence quenching

The association of complex formation with static quenching in CT systems was investigated. Evaluation of the data made evident that the inner filter effect must be allowed for. Time-resolved and temperature-dependent stationary measurements of fluorescence led to the separation of dynamic and static quenching components. The static quenching constant is discussed with respect to the equilibrium constant of complex formation determined by absorption spectroscopy.