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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.
Der Konstruktionsbereich ist zu einem neuen Schwerpunkt der allgemeinen Rationalisierungsbemühungen geworden. Zunehmend führt man organisatorische Hilfsmittel, technische Hilfsmittel (EDVA) und neue Konstruktionsmethoden in der Konstruktion ein. Der vorliegende Beitrag analysiert zunächst die Ursachen dieser Entwicklung und zeigt im weiteren einige heute bereits eingesetzte Hilfsmittel an Hand von Beispielen auf und diskutiert die Anwendungsmöglichkeiten.
Der Konstruktionsbereich ist zu einem neuen Schwerpunkt der allgemeinen Rationalisierungsbemühungen geworden. Zunehmend führt man organisatorische Hilfsmittel, technische Hilfsmittel (EDVA) und neue Konstruktionsmethoden in der Konstruktion ein. Der vorliegende Beitrag analysiert zunächst die Ursachen dieser Entwicklung und zeigt im weiteren einige heute bereits eingesetzte Hilfsmittel an Hand von Beispielen auf und diskutiert die Anwendungsmöglichkeiten.
Fußball oder Mathematik
(1971)
Feinbleche schweißen : die Temperaturverteilung in dünnen Stahlblechplatten beim Lichtbogenschweißen
(1971)
Die tert.-Butyloxycarbonyl-Gruppe (Boc) läßt sich mittels reiner Trifluoressigsäure nicht selektiv neben dem Benzyloxycarbonyl-Rest (Z) abspalten. Das gelingt auch nicht mit Lösungen von Trifluoressigsäure bzw. Chlorwasserstoff in organischen Lösungsmitteln. Kern-substituierte Z-Gruppen wie Z(pCl), Z(mCl) oder Z(pNO₂) sind zwar stabiler, werden aber von den obengenannten Reagenzien ebenfalls angegriffen bzw. sind nicht mehr acidolytisch abspaltbar. – Mit 70proz. wäßriger Trifluoressigsäure gelingt die Abspaltung von Boc neben Z dagegen fast selektiv; dabei werden aber Benzylester, besonders Glutaminsäure-γ-benzylester, teilweise hydrolysiert, während Methyl- sowie Äthylester nahezu beständig sind. Die Brauchbarkeit des Abspaltungsverfahrens wird anhand der schrittweise durchgeführten Synthese zweier Heptapeptid-Derivate gezeigt. – Ähnlich spezifisch gelingt die Abspaltung von Boc mit Bortrifluorid-ätherat in Eisessig; Benzylester sind gegenüber diesem Reagenz stabiler als gegen wäßrige Trifluoressigsäure. Das Bortrifluorid-Verfahren eignet sich besonders für die Abspaltung von Boc-Gruppen neben säurelabilen Thiol-Schutzgruppen (Tetrahydropyranyl- bzw. Trityl-Rest) sowie neben dem Cyclocystinyl-Rest. Die Leistungsfähigkeit der Methode wird durch die Synthese zweier Peptid-Derivate mit S-Trityl-Schutzgruppen belegt. Als Nebenreaktion ist die Acetylierung von aliphatischen Hydroxylgruppen möglich. Sie läßt sich vermeiden, wenn man die Spaltung in anderen Lösungsmitteln durchführt. Die als Modellverbindungen für Stabilitätsuntersuchungen verwendeten Nε-acylierten Lysin-Derivate werden mit dem Aminosäureanalysator quantitativ neben Lysin bestimmt.
In den letzten Jahren hat der Einsatz von graphischen Datenverarbeitungsanlagen auf dem technischen, naturwissenschaftlichen und kommerziellen Sektor immer mehr an allgemeinem Interesse und Bedeutung gewonnen. Diese Entwicklung hat neue Aspekte und Probleme in bezug auf Anwendungsmöglichkeiten, Programmierung, Datenstrukturen sowie der Hard- und Software dieser Anlagen hervorgerufen. Zur Zeit werden von verschiedenen Institutionen die Einsatzmöglichkeiten graphischer Datenverarbeitungsanlagen in den Funktionsbereichen Konstruktion und Arbeitsvorbereitung untersucht. Der folgende Beitrag zeigt eine kurze Übersicht über die verschiedenen programmiertechnischen Probleme sowie eine Auswahl von Programmbeispielen, die am Laboratorium für Werkzeugmaschinen und Betriebslehre der RWTH Aachen entwickelt wurden. Bei den Bildschirmsystemen wird zwischen zwei Arten unterschieden. Aktive Bildschirmeinheiten besitzen als äußeres Merkmal einen Lichtstift und eine Funktionstastatur zur Programmverzweigung. Passive Bildschirmeinheiten lassen demgegenüber einen Eingriff in das Programm in der oben aufgeführten Form nicht zu. Zwischen diesen extremen Formen gibt es noch eine Reihe Mischformen. Die in Aachen zur Verfügung stehende Anlage arbeitet aktiv und wird im nachfolgenden Kapitel näher beschrieben.
Für viele Zwecke ist es nützlich, von einem technischen System ein mathematisches Modell zu haben. Für Systeme, die sich durch eine Verzögerung höherer Ordnung mit oder ohne Ausgleich beschreiben lassen, wird ein Identifizierungsverfahren vorgestellt, das aus gemessenen Zeitfunktionen die Bestimmung einer Übertragungsfunktion ermöglicht. Die Systeme werden dabei durch Testsignale erregt. Die Modellkoeffizienten werden dann mit Hilfe eines Integrationsverfahrens aus dem Testsignal und der Antwort des Systems auf dieses Testsignal bestimmt. Ein praktisches Beispiel zeigt die Leistungsfähigkeit des Verfahrens.
Die technischen und wirtschaftlichen Anforderungen, die heutzutage an moderne Maschinen, Geräte und Apparate gestellt werden, steigen ständig. Immer häufiger sehen sich die Konstrukteure gezwungen, geforderte Funktionen mit Hilfe zugekaufter Normeinzelteile, Bauelemente und Funktionsgruppen zu erfüllen. Bei dieser Entwicklung vergrößert sich die Zahl der von den Spezialherstellern angebotenen Zukaufteile überproportional, in gleichem Maße geht dem Anwender die Übersicht über das Zukaufteilespektrum verloren. Zunächst wird in diesem Bericht diese Entwicklung anhand einer im allgemeinen Maschinenbau durchgeführten Befragung aufgezeigt. Anschließend soll darauf aufbauend ein Ordnungssystem vorgestellt werden, welches jedem Unternehmen wieder eine Übersicht über das am Markt angebotene Zukaufteilespektrum ermöglicht.
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.
Es wird die Synthese der Sequenz A 6–9 des Schafinsulins in der geschützten Form Boc-Cys-Cys-Ala-Gly-OBuᵗ (5) sowie das Verhalten dieses monomeren cyclischen Cystinpeptidderivates gegenüber den in der Peptidchemie gebräuchlichen Reagenzien Bortrifluorid/Eisessig, Triäthylamin und Hydrazinhydrat beschrieben.
Stellungen : 9 Texte, 9 Zeichnungen / [Texte] Dieter Boeminghaus ; [Zeichnungen] Ulf Hegewald
(1973)
Es wird von Gleichungen ausgegangen, mit denen die Modellkoeffizienten von Regelstrecken mit Ausgleich aus der gemessenen Sprungantwort ermittelt werden können. Die Übertragungsfunktion der Regelstrecke hat einen konstanten Zähler und ein Nennerpolynom. Unter der Annahme, daß die ideale und exakte Sprungantwort des Systems durch ein stochastisches Signal gestört wird, wird untersucht, wie die Fehler der ermittelten Modellkoeffizienten von Kennwerten des Störsignals und von der Meßzeit für die Sprungantwort abhängen. Durch eine Simulation auf dem Digitalrechner wurden die Ergebnisse kontrolliert. Es zeigt sich, daß durch eine Filterung der gestörten Sprungantwort über einen Tiefpaß keine Verbesserung der Analyseergebnisse erreicht werden kann, da das Identifizierungsverfahren eine glättende Eigenschaft hat.
Photoabsorption of alloys of Al with transition metals V, Fe, Ni and Cu and Pr near the Al L₂,₃-edge
(1974)
The onset of Al 2p transitions of VAl₃, FeAl, NiAl, NiAl₃, CuAl₂, PrAl₂ and the disordered alloys V-Al (16 at % Al, 28%, 41%), Fe-Al (11%) is shifted up to 1.1 eV. New pronounced structure develops close to the onset which for NiAl agrees with a density of states calculation by Connolly and Johnson.
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.
Das Transportsystem BANDIT zur Messung von Halbwertszeiten kurzlebiger, neutronenarmer Isotope
(1974)
Andere Primärenergiequellen
(1974)
Optical constants from the far infrared to the X-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al₂O₃
(1975)
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)
Non-nuclear and non-fossil energy resources and their possibilities for future power generation
(1975)
It must be stressed that the assessment of the exploitation possibilities of the energy resources discussed in this paper requires further studies. With this proviso, the situation can be provisionally summarised as follows: The total potential of known geothermal steam sources is only 64 GW. Geothermal energy could therefore only make a significant contribution to covering the worldwide power needs if we succeed in exploiting dry geothermal reservoirs. Exploitation of tidal energy is limited to a few geographically favourable locations. The power generation potential at these locations is only about 64 GW. An important drawback of tidal power is discontinuous power generation. Large scale exploitation of wind, wave and glacier energy, and of ocean heat, requires solution of a number of technological problems. The environmental effects of exploitation of these energy resources are to some extent of a qualitatively different nature from those of operation of fossil-fuel-fired and of nuclear power plants. The scanty knowledge in this area often results in these effects being underestimated. In any case, however, it would be deliberately misleading to postulate that any form of power generation is possible without some detrimental effects on the environment. It may be stated in conclusion that, owing to their small potential or to the as yet insufficiently advanced technological development, none of the energy resources discussed in this paper can make a significant contribution to the solution of middle-term energy supply problems, i.e., to a rapid replacement of mineral oil and natural gas.
Die Darstellung der N-[2-(p-Biphenylyl)isopropyloxycarbonyl]-Derivate (Bpoc-Derivate) des Cysteins unter Verwendung der Thiolschutzgruppen Tetrahydropyranyl (Thp) für 1, Diphenylmethyl (Dpm) für 2, Trityl (Trt) für 3 und S-tert.-Butyl (SBut) für 4 sowie die Synthese von aktivierten Estern der Bpoc-Derivate des Glycins (5), Isoleucins (6) und Prolins (7) werden beschrieben. An einem Beispiel wird die Möglichkeit aufgezeigt, die Bpoc-Gruppe über das Bpoc-Azid nachträglich in den Peptidverband einzuführen.
Die Synthese der Sequenzen A2—21 (13) und A1—21 (15) der Schafinsulin-A-Kette als monomere cyclische Dicystinpeptidderivate wird beschrieben. Die intrachenaren Cystinbrücken A6—7 und A 11 —20 vermitteln die Löslichkeit dieser Derivate in Dimethylformamid und ermöglichen erstmalig die Reindarstellung vollgeschützter Insulin-A-Kettenderivate. Die während der Synthese eingesetzten Schutzgruppen lassen sich mittels Trifluoressigsäure und 2-Mercaptoäthanol quantitativ entfernen.
Wilhelm Schürmann
(1976)
Geboren 1946, lebt und arbeitet in Aachen. Studium der Chemie an der Technischen Hochschule Aachen. Danach als freiberuflicher Photograph tätig für verschiedene Tageszeitungen. Seit 1972 Lehrer für Photographie am Reiff Museum der TH-Aachen, Institut für Architektur. Seit 1973 Dozent für Photographie an der Volkshochschule Aachen. Ende 1973 Gründung der Galerie Lichttropfen in Aachen. Organisator zahlreicher Ausstellungen historischer und zeitgenössischer Photographie im In- und Ausland.
The absorption coefficient of VAI3, FeAI, NiAI, NiAl2, CuAI2, PrAl2, and of disordered V–AI (16 at% AI, 28%, 41%) and Fe–AI (11%) alloys has been measured in the region of the M₂,₃ absorption of the transition metals and the Labsorption of AI. The strong changes of the AI spectrum in the region of the 100 eV maximum upon alloying are explained as another evidence of the EXAFS (extended X-ray absorption fine structure) nature of these structures. The broad, prominent absorption peaks from the 3p excitations in V and Fe and from the 4d excitations in Pr are influenced only little on allyoing and thus appear to be of atomic origin. The fine structure at the onset of the Pr 4d transitions is identical in the metal and the alloy but differs from that of Pr oxide. The only M₂,₃ edge which is detectably shifted is that of Ni (up to 2.1 eV), whereas the onset of the AI L₂,₃ edge is shifted in all the alloys (up to 1.1 eV). The shifts are interpreted in accordance with X-ray fluorescence and nuclear resonance measurements as changes of the density of states in the valence band of the alloys.