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In-beam study of ¹⁴⁴ Gd
(1978)
Tumour cell death can be evaluated in the living mouse by externally measuring the rate of loss of tumour-bound DNA tracer. By sequentially labelling the tumour-bearing animals with ¹²⁵IUdR and ¹³¹IUdR 50 h apart, the average tumour cells at the time of the second injection are labelled by ¹²⁵IUdR and the euoxic tumour cells are specifically labelled with ¹³¹IUdR. Tumour treatment at this stage of labelling permits the observation of the reaction of euoxic cells and average tumour cells and finally yields data on hypoxic cells and thus on the oxygen enhancement ratio. This information adds to results from tumour control and growth delay.
With this technique effects were analysed of 60-Co γ-rays, cyclotron neutrons (E = 6 MeV), misonidazole (500 mg/kg body wt) and hyperthermia (42°C water-bath), or combinations of these.
Misonidazole (15 min before irradiation) altered the oxygen enhancement ratio by a factor of 1·5 for γ-rays and of 1·1 for neutrons; when evaluated from tumour-growth delay and TCD-50 misonidazole gave a dose modifying factor of 1·47 for γ-rays and of 1·2-1·3 for neutrons.
Based on percentage tumour regression 100 days after treatment, the enhancement ratio from hyperthermia (after irradiation) was 2·75 for γ-rays (at 10 Gray) and 2·2 for neutrons (at 3·2 Gray). For neutrons combined with misonidazole and hyperthermia the ratio was 2·4.
These results demonstrate that effects of neutron irradiation may be modified by electron-affinic substances and/or hyperthermia.
Side bands in ¹⁷² Hf
(1977)
In-beam study of ¹⁴⁴ Gd
(1977)
High spin states in ¹³⁶ Ce
(1975)
High spin states in ¹³⁶ Ce
(1975)
High spin states in ¹⁹¹ Au
(1975)
High spin states in ¹⁹¹ Au
(1975)
The isotopes ¹³⁰,¹³²,¹³⁴,¹³⁶ Ce are investigated by means of the reactions ¹¹⁸,¹²⁰,¹²²,¹²⁴ Sn(¹⁶O, 4n) at bombarding energies between 68 and 76 MeV. From lifetime measurements a reduction of the collective behaviour is observed with increasing neutron number. Yrast cascades of rotational structure are identified up to angular momenta I=16⁺ or I=18⁺ in ¹³⁰,¹³²,¹³⁴ Ce. These cascades show a strong “back-bending” effect. In ¹³⁶ Ce no such simple yrast cascade could be found.
Yrast states up to spin 18 have been identified in ¹³²Ce. The energies and spins of the levels suggest the existence of two fairly well-behaved collective bands. The results are compared with those obtained in the rare-earth deformed region.
Für die Approximation stetiger, 2π-periodischer Funktionen auf der reellen Achse durch trigonometrische Polynome wurde ein direkter Satz von D. Jackson 1911 [8] und die Umkehrung von S. N. Bernstein 1912 [1] bewiesen und die Ergebnisse von A. Zygmund [25] 1945 verallgemeinert. 1949 stellte M. Zamansky [25] eine Beziehung zwischen der Approximationsordnung und dem Wachstum bezϋglich n der Ableitungen der Approximationspolynome her; auf die Approximationsordnung für die Ableitungen der Funktion schloβ S. B. Steckin 1951.
Die Umkehrung des Ergebnisses von M. Zamansky bewies G. Sunouchi 1968 [21,22], womit die Aquivalenz aller Aussagen gezeigt ist.
Die Übertragung der Ergebnisse auf Approximationsoperatoren in Banachräumen stammt von K. Scherer und P. L. Butzer [3, 4], wobei gewisse Voraussetzungen an die Operatorfolge (eine verallgemeinerte Bernsteinsche Ungleichung und eine sogenannte Jacksonsche Ungleichung) gestellt werden. An die Stelle der strukturellen Eigenschaften der Funktion, die durch das Verhalten des Stetigkeitsmoduls der Funktion charakterisiert werden, treten in allgemeinen Banachräumen Eigenschaften des von J. Peetre [17] eingefϋhrten K-Funktionals.
In dieser Arbeit wird die Approximation von Funktionen, die auf der Einheitskugel Sᵏ im Rᵏ definiert sind, durch Linearkombinationen von Kugelfunktionen untersucht. Es wird für diesen Fall eine Bernstein-Ungleichung und die Jackson-Ungleichung bewiesen, wenn man die Ableitung durch den Laplace-Operator auf Sᵏ ersetzt. Damit ist der oben zitierte allgemeine Satz von Butzer-Scherer anwendbar. Weiter kann man hier an Stelle des K-Funktionals einen verallgemeinerten Stetigkeitsmodul setzen. Anschlieβend wird der Spezialfall der zonalen Funktionen und ihre Approximation durch algebraische Polynome untersucht.
Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
(1968)
Die vorliegende Arbeit untersucht das approximationstheoretische Verhalten von Summationsprozessen von Reihen von Kugelfunktionen, sogenannten Laplace-Reihen. Zunächst wird die Theorie der besten Approximation auf der Kugel, also die Erweiterung der Sätze von D. Jackson und S. Bernstein, skizziert. Nimmt man nun spezielle Verfahren zur Summation von Laplace-Reihen, dann lassen sich auch hier Sätze vom Jacksonschen und Bernsteinschen Typ beweisen. Darüber hinaus zeigen viele Verfahren ein Saturationsverhalten, d.h. es gibt eine nur vom Verfahren abhängige optimale Approximationsordnung. Das Saturationsproblem besteht nun darin, diejenige Klasse von Funktionen (Saturationsklasse) zu bestimmen, welche genau von der optimalen Ordnung approximiert werden.