Subharmonische Wellen in nichtlinearen Medien

Ohne Zusammenfassung     

Quantitative Untersuchungen zum Strahlungsenergietransport in inhomogenen Plasmen

Ohne Zusammenfassung     

Zur Theorie elastisch-plastischer Wellen in dünnen Stäben

Summary The simple classical theory of elastic-plastic loading waves in thin rods due to,v. Kármán, Taylor, andRakhmatulin is generalized, according to a proposal ofMazzoleni, by taking into account the time dependent variation of the cross sectional area. Thus, an essential difference arises between tensional and compressional waves. Furthermore, the theory becomes applicable to the limiting case of ideally plastic materials which had to be excluded so far. Here, only compressional waves are possible. The ratio of the plastic and the elastic wave velocities is approximated by , whereY denotes the uniaxial yield stress andE is Young's modulus.

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Der Aufsatz stellt ein Teilergebnis des von der Deutschen Forschungsgemeinschaft (DFG) geförderten Vorhabens Li 115/2 dar.     

Über das asymptotische Verhalten thermoelastischer Wellen im R3

In [L] the author provided existence theorems for initial-boundary-value problems in thermoelasticity for unbounded domains. Continuing this work the asymptotic behaviour of solutions in R³ with respect to t → ∞ will be described in this paper.     

Stabilitätsbetrachtungen im Ljapunowschen Sinn bei rotierenden,einfach besetzten Wellen unter periodischer Belastung

Summary Stability problems of rotating shafts are usually solved by linearization without investigating the influence of nonlinearity, and in most cases persistant disturbances are not taken into account. The present paper makes a contribution to these questions. For this purpose a shaft with one disk under different boundary conditions and periodic loading is considered. If the mass of the shaft is neglected a system with two degrees of freedom has to be treated. Therefore application of Liapunov's ideas and its generalizations is possible. Stability can be determined easily by linear approximation after introducing damping forces.     

Filling in solvable groups and in lattices in semisimple groups

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all -rank one lattices in semisimple groups of -rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion constant.     

An Outlook in Teaching and Research in Mathematics in Educational Institutions

The present paper outlines some basic principles upon which an outlook in teaching and research in mathematics in educational institutions can be developed. Defining applied mathematics, the author analyses the basic topics of mathematics which permeate throughout the wider fields and diversified aspects of this branch of mathematical science.

For the institutions of learning, a course curriculum has been proposed which will gradually motivate, orient and prepare individuals through the process of learning to understand the methods and techniques, so as to apply them to physical problems. This has been illustrated in the fields of fluid dynamics and aerodynamics through the analysis of complex function theory and differential equations.

Because of the frustrating situations prevailing amongst students and teachers in the institutions of learning in the present day, a critical analysis has been made to identify the respective roles of the academicians and administrators, and with a view to improving the situation, some remedy has been suggested regarding teaching and research in educational institutions.     

Convergenza in variazione e convergenza in lunghezza

Riassunto Viene stabilita, per le trasformazioni continue di una regione piana pluriconnessa, una maggiorazione per il numero delle imagini reciproche di un insieme dik punti del piano-imagine. Dalla disuguaglianza discende una limitazione superiore per il numero dei punti ?eccezionali?, ossia aventi un numero di modelli minore a quanti ne comporterebbe l'indice topologico.

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Résumé On établit, pour les transformations continues d'une région plane à plusieurs contours, une majoration du nombre des points de l'ensemble image-inverse d'un ensemble dek points du plane-image. Il en ressort une borne supérieure pour le nombre des points exceptionnels, c'e.-à-d. ayant moins d'images inverses qu'on s'attendrait de l'indice topologique.

     

Operational research in development banking in India

The paper defines development banking as practised by major Indian commercial banks since 1969. It then goes on to discuss how OR can be useful in tackling problems of development banking. Planning, operational and organisational design problems in relation to development banking are discussed. Several case studies in each area where OR has been applied are discussed. Potential areas of application of OR in each problem class are also identified. The paper then summarizes the experiences gained so far and recommends the action to be taken for the more effective application of OR in developing economies.     

Series in multiplicative systems in Lorentz spaces

Series in multiplicative systems χ with generalized monotone coefficients are studied. Necessary and sufficient Hardy–Littlewood type conditions for the sums of such series to belong to the Lorentz space are proved. As corollaries, we establish estimates of best approximation in the system χ and Konyushkov-type theorems on the equivalence of O- and ?-relations for the weighted sums of the Fourier coefficients in the system χ and for the best approximations.