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.

---

---

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.     

Introducing technology in algebra in Hong Kong: addressing issues in learning

A review of recent studies in Hong Kong suggests that possible problems in secondary school algebra may be due to the procedural paradigm orientation in the curriculum and the conventional style of teaching in the classroom which do not provide sufficient opportunities for students to develop conceptual understanding. Based on the works of a number of projects in the West, it is hypothesized that the introduction of technology in lessons which embody a cognitive model in their design and delivery will provide a viable alternative for enhancing algebraic thinking. The key features of the cognitive model are concrete preparation, cognitive conflict, construction, metacognition and bridging, imbedded in a ‘mediation’ style of teaching. These features are exemplified by detailed accounts of classroom episodes from a Hong Kong lesson supported by the use of graphics calculators. Results indicate that while the approach places particular demands on teachers (a tension between a transmission style of teaching and mediating) there is real potential for supporting more dynamic student constructions.     

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.     

二值回归模型中自变量误差的处理

In this paper the binary regression model, in which the response Y is binary, i.e. Y takes the value 0 or 1 only, is considered. The conditional probability P{Y=1|X=x} is assumed to be of the form G(a₀+a₁x), where x is the measurement of the factor, a= (a₀,a₁)′ is the vector of the unknown parameter being estimated and G(a) = (1+e^a)^-1. The measurement x is assu-med to be contaminated when the value of x is out of certain limit. M-estimation is employed to estimate the unknown a of the model. In this paper, the consistent M-estimation is proved to be asymptotically normal and the optimal M-equation is obtained. Finally, a computation method is introduced to solve the M-equation and to get the optimal solution.