Oxygen-distribution imaging with a novel two-tracer laser-induced fluorescence technique

We introduce a new technique for imaging oxygen concentrations in fuel/air mixtures that takes advantage of the different responses of toluene and 3-pentanone to collisional quenching by molecular oxygen. Since laser-induced fluorescence signals from both tracers upon excitation at 248 nm are spectrally well separated, simultaneous detection is possible. The technique is first applied to instantaneous imaging in turbulent mixing processes of interacting seeded air and nitrogen flows. Received: 1 August 2001 / Revised version: 29 October 2001 / Published online: 29 November 2001     

The influence of the salt concentration on the aggregation behavior of viscoelastic detergents

The influence of excess NaCl on the properties of viscoelastic detergent solutions of Cetypyridiniumsalicylate (CPySal) has been studied by static and dynamic light scattering, electric birefringence and rheological measurements. It is obeserved that the rodlike micelles of length L which are present in these solutions and which are responsible for their elastic properties grow in length with the increase of the NaCl concentration. As long as the rods are shorter than their mean distance, their length can be determined from the rheological and electric birefringence measurements. For very small shear fields these solutions behave as Newtonian fluids. The viscosity of the solution increases strongly when the rods begin to overlap. Solutions with overlapping rods are elastic. It is postulated from the results that the cmc_II (the critical concentration above which rods are present) and the length L of the rods are partially determined by the intermicellar interaction energy. It is furthermore postulated that this intermicellar interaction energy has an influence on the polydispersity of the rods and seems to make the rods relatively monodisperse.     

Studies on main - chain liquid - crystalline model oligomers of defined length and structure

Oligomers of defined sequence and structure modelling main chain LC polymers were prepared a) by solution synthesis; b) by a novel liquid phase synthesis using two monomethoxy-poly (ethylene glycol) supports. Benzyl- and tert.butyl-groups were used as orthogonal pair of protecting groups for route a), and also as compatible anchor groups for carriers in route b). Depending on chain structure and end groups, at least ca. 3 mesogenic elements are required to allow for LC phase transitions. The phase behaviour of oligomers with free carboxylic ends can be explained by their association tendency.     

Die exakte OC- und ASN-Funktion eines sequentiellen Quotiententests im Falle der Exponentialverteilung

Zusammenfassung M. Raghavachari hat 1965 die Operationscharakteristik (OC-Funktion) und den Erwartungswert für den Stichprobenumfang (ASN-Funktion) eines sequentiellen Quotiententests für die einfache Exponentialverteilung unter einschneidenden Einschränkungen bezüglich der StopschrankenA undB durch Auswertung iterierter Integrale exakt angegeben. In der vorliegenden Arbeit werden über die Lösung zweier Integralgleichungen für beliebige SchrankenA undB die OC- und die ASN-Funktion exakt berechnet.

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Summary In 1965M. Raghavachari calculated the operating characteristic and the expected sample size of a sequential probability ratio test for the simple exponential distribution for a very special choice of the stopping boundsA andB. In the present paper these two functions are given by solving two integral equations for any choice ofA andB.

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Vorgel. v.:H. Söhngen.     

On properties of the iterative maximum likelihood reconstruction method

In this paper, we continue our investigations⁶ on the iterative maximum likelihood reconstruction method applied to a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Equations of this type often occur in connection with the determination of density functions from measured data. There are certain relations between the directed Kullback–Leibler divergence and the iterative maximum likelihood reconstruction method some of which were already observed by other authors. Using these relations, further properties of the iterative scheme are shown and, in particular, a new short and elementary proof of convergence of the iterative method is given for the discrete case. Numerical examples have already been given in References 6. Here, an example is considered which can be worked out analytically and which demonstrates fundamental properties of the algorithm.     

Beliefs and engagement structures: behind the affective dimension of mathematical learning

Beliefs influencing students’ mathematical learning and problem solving are structured and intertwined with larger affective and cognitive structures. This theoretical article explores a psychological concept we term an engagement structure, with which beliefs are intertwined. Engagement structures are idealized, hypothetical constructs, analogous in many ways to cognitive structures. They describe complex “in the moment” affective and social interactions as students work on conceptually challenging mathematics. We present engagement structures in a self-contained way, paying special attention to their theoretical justification and relation to other constructs. We suggest how beliefs are characteristically woven into their fabric and influence their activation. The research is based on continuing studies of middle school students in inner-city classrooms in the USA.