Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

A characterization of exterior lines of certain sets of points in PG (2, q)

Let A and B be disjoint sets of points in PG(2, q) the Desarguesian projective plane of order q, with |A|q, |B|=q+1, such that each line through a point of A meets B (just once). Then B is a line.     

Reibungsdämpfung durch Scheuerleisten: Ein praxisgerechtes Auslegungskonzept

Übersicht Die Fugen zusammengesetzter Bauteile sind einerseits für eine nachteilige Steifigkeitsminderung verantwortlich, tragen aber andererseits durch Reibungsvorgänge wesentlich zum Dämpfungsvermögen einer Konstruktion bei. Merkliche Reibungsdämpfung ohne gleichzeitigen Steifigkeitsverlust bewirken zusätzliche Fugen, die durch Anbringen sogenannter Scheuerleisten entstehen. Der Autor stellt ein Näherungsverfahren zur dämpfungsoptimalen Auslegung von Scheuerleisten vor. Ausgehend von der zu dämpfenden Schwingungsform liefert dieses Verfahren Kriterien für eine günstige Scheuerleistenanordnung, geeignete Leistenabmessungen und als wichtigstes Ergebnis eine dämpfungsoptimale Fugenpressung, die zu maximaler Energiedissipation führt. Schließlich kann das zu erwartende Dämpfungsmaß berechnet und damit das Ergebnis einer vorgesehenen Dämpfungsmaßnahme abgeschätzt werden.

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Damping by friction ledges: a practical design concept

Summary On the one hand, mating surfaces of structures are responsible for a reduction of stiffness, on the other hand relative motion produces friction, which contributes considerably to the damping. Noticeable friction damping without simultaneous stiffness reduction can be achieved by adding further mating surfaces. Such interfaces are realized by fastening additional elements (e.g. beamlike) onto the structure. An analytic approximation method for these so-called friction ledges is described in this paper. Initiating from the mode shape to be damped the procedure yields criteria for the suitable positioning and design of the ledges. Most important of all is the damping optimized interface pressure, that leads to maximum energy dissipation. Finally, the expected damping rate can be computed, and therefore the result of the proposed measure assessed.

     

Asymptotic expansions for dynamic programming recursions with general nonnegative matrices

This paper is concerned with the study of the asymptotic behavior of dynamic programming recursions of the form $$x(n + 1) = \mathop {\max }\limits_{P \in \mathcal{K}} Px(n), n = 0,1,2,...,$$ where ? denotes a set of matrices, generated by all possible interchanges of corresponding rows, taken from a fixed finite set of nonnegative square matrices. These recursions arise in a number of well-known and frequently studied problems, e.g. in the theory of controlled Markov chains, Leontief substitution systems, controlled branching processes, etc. Results concerning the asymptotic behavior ofx(n), forn→∞, are established in terms of the maximal spectral radius, the maximal index, and a set of generalized eigenvectors. A key role in the analysis is played by a geometric convergence result for value iteration in undiscounted multichain Markov decision processes. A new proof of this result is also presented.     

Two-photon absorption and energy band structure of orthorhombic Hg2Cl2 crystals

Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg₂Cl₂ crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg₂Cl₂ is proposed regarding Hg₂Cl₂ crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg₂Cl₂ crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement.     

Consistency of field equations in “Self-Creation” cosmologies

It is pointed out that the field equations in one of Barber's two self-creation cosmologies are not only in disagreement with experiment, but are actually inconsistent, in general. The construction of consistent general relativistic field equations involving field variables, such as, without invoking Lagrangian techniques, requires careful checking that sufficient functional freedom has been provided so as to produce a consistent set of equations.     

Dual pairs and representations of scattering amplitudes

A procedure for constructing scattering amplitudes for production processes that is exactly unitary, preserves the bosonic character of the many-particle states, and is invariant with respect to an underlying symmetry group is given. Two simple models, dealing with isospin internal symmetry and the two-dimensional Euclidean space group are presented which illustrate how scattering amplitudes can be represented as matrix elements of groups whose action commutes with the action of the invariance group on the relevant Fock space.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.Work supported in part by the Department of Energy.     

Multiparticle excitations in142Nd

An (α, 2nγ) in-beam study of excited states in 142Nd revealed 27 new levels on top of the 6⁺ isomer. Nanosecond lifetimes were found for two levels. The measured excitation energies were compared with spherical shell-model predictions obtained from suitably truncated model spaces.     

Computermodelling of Fluorescent Lamp Plasmas

• 1 A computer model is designed in which the lamp voltage is obtained by solving the equations of the operating circuit.
• 2 The lamp resistance is determined by using hydrodynamic equations for the lamp plasma with following conditions:
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