The Four Isomeric 1,3,5-Undecatrienes. Synthesis and configurational assignment

The four geometrical isomers of 1,3,5-undecatriene, 1a–d have been prepared (stereospecifically and non-stereospecifically), using either (1) the Wittig reaction, (2) thermal sigmatropic hydrogen shifts, (3) partial reduction of triple bonds by zinc, or (4) organocopper reagents. The thermal behaviour of the four 1,3,5-undecatrienes has been investigated and the products formed have been characterized. The spectra of 1a–d, and of related compounds, have been discussed in order to corroborate their configurational assignment.     

Automatische amperometrische Bestimmung von Calcium und Magnesium durch komplexometrische Titration

Zusammenfassung Eine Methode wurde entwickelt, um Calcium und Magnesium in natürlichen Wässern bei pH 10 an einer Tl₂O₃-Anode unter Verwendung von ÄDTA und ÄGTA als Titrationsmittel zu bestimmen. Die dabei verwendete Apparatur eignet sich gut für Serienbestimmungen, da die Zugabe des Titrationsmittels und die Aufzeichnung des Kurvenverlaufs automatisch erfolgen. Die Auswertung wird graphisch durchgeführt.

---

Automatic amperometer determination of calcium and magnesium through complexometric titration

Summary A method has been developed for the determination of calcium and magnesium in natural waters at pH 10 on a Tl₂O₃-anode with employment of EDTA and EGTA as titration agents. The apparatus used is well suited to series determinations, because the addition of the titration agent and the recording of the course of the curve are done automatically. The evaluation is conducted graphically.

     

The Pyruvate Dehydrogenase Multienzyme Complex

The three enzymes pyruvate dehydrogenase, dihydrolipoamide transacetylase, and dihydrolipoamide dehydrogenase constitute the pyruvate dehydrogenase multienzyme complex of E. coli; in mammals the complex also contains a kinase and a phosphatase. Multienzyme complexes are structural, functional, and regulatory units enabling the organism to operate more economically than with single enzymes. The pyruvate dehydrogenase multienzyme complex may stand at the switch-point between energy metabolism and gluconeogenesis.     

Construction of the distribution functions of the oh radicals in the H2-O2 flame

In the present paper the construction of the distribution functions for OH radicals in the H₂-O₂ flame is dealt with. The construction is based on the fact stated in [1] that there are two groups of OH radicals in the flame. It is shown here that the method for temperature determination used in [1] can be considered as the first approximation only. According to this fact the method of determining the parameters of the flame (temperature etc.) solving system of equations for line intensities is presented here. In practice it is possible under certain conditions, discussed here, to use an improved method in order to determine the flame parameters and distribution functions of OH radicals. Also the reduction of the temperatures of the cold group of OH radicals based on above mentioned improved method is discussed here. The values of the temperature of the cold group of OH radicals to be reduced are taken from [1].     

Invariant Manifolds in Dissipative Dynamical Systems

Invariant manifolds like tori, spheres and cylinders play an important part in dynamical systems. In engineering, tori correspond with the important phenomenon of multi-frequency oscillations. Normal hyperbolicity guarantees the robustness of these manifolds but in many applications weaker forms of hyperbolicity present more realistic cases and interesting phenomena. We will review the theory and present a number of examples using normalization-averaging techniques.Dedicated to nonlinear scientist Ale Tondl on his 80th birthdayMathematics Subject Classifications (2000) 34C30, 34C20.