A function space model approach to the rational evaluation subgroups

Let f : U → X be a map from a connected nilpotent space U to a connected rational space X. The evaluation subgroup G _*(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931–4951, 1997). In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006) is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S ¹-bundle over the n-dimensional torus is determined explicitly in the non-rational case.      

A tunable picosecond dye laser for use in dioxin analysis.

A distributed-feedback dye laser with a quenching cavity was designed and constructed for generating a tunable picosecond pulse with a narrow spectral linewidth. This nearly transform-limited pulse was succeedingly amplified by a triple-pass off-axis amplifier. The pulse duration and the spectral linewidth were 60 ps and 9.4 pm, respectively. The amplified pulse was frequency-doubled by second-harmonic generation, producing a 0.5-mJ pulse with no background emission. The potential advantage of this laser in the analysis of dioxin based on supersonic jet/resonance-enhanced multiphoton ionization/mass spectrometry is discussed.     

An improved reaction valve for flow injection analysis

Summary A new type reaction valve for flow injection analysis has been developed. In a FIA system with this valve the injected sample is once passed into a loop of the valve, thereafter the valve is rotated to the next position. Therefore, the sample is retained in the loop in a stop-state for a long time and the next sample is introduced into another loop in the next position. When the valve is rotated for one round, the stopped sample in the fist loop is again passed into the detector flow cell. Thus, an analysis, which needs a long reaction time, can be performed with this valve with high precision.

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Verbessertes Reaktionsventil für die Flie\injektionsanalyse

     

On the unstable homotopy spectral sequences

We shall study the relation between the unstable homotopy spectral sequence associated with the cell decomposition of the source space and the one associated with the Postnikov decomposition of the target space. It is proved that the Maunder's result holds for these two types of spectral sequences. This result will be exploited to study the differentials of these spectral sequences and we obtain a generalization of a theorem due to Atiyah-Hirzebruch and Dold. Making use of these spectral sequences with the convergence lemma, some results on the phantom maps and the homotopy groups of map_*(Y, X) will be proved.