On the Determination of the Degree of a Polynomial

Starting from a method suggested by T.W. Anderson (1971) stagewise rejective test procedures for determining the-degree of a polynomial are proposed. Accounting for the special structure of the problem, Holm's (1979) individual significance levels can be improved. If the critical limits for the individual tests of the simultaneous test procedure are chosen in an appropriate dependence on the sample size, the test procedure provides a weakly consistent estimate of the correct order of polynomial. The corresponding theorem is proved for a general procedure for determining the correct subset of a finite number of model parameters

A variational growth approach to topology optimization

In this contribution we present an overview of our work on a novel approach to topology optimization based on growth processes [1, 2, 3]. A compliance parameter to describe the spatial distribution of mass is introduced. It serves as an internal variable for which an associated evolution equation is derived using Hamilton’s principle. The well-known problem of checkerboarding is faced with energy regularization techniques. Numerical examples are given for demonstration purposes

Non-equilibrium dynamics of a system with Quantum Frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.Comment: 22 pages, 9 figure

Raman scattering from a superconductivity-induced bound state in MgB2MgB_2

It is shown that the sharp peak in the $E_{2g}$ Raman spectrum of superconducting $MgB_2$ is due to a bound state caused by the electron-phonon coupling. Our theory explains why this peak appears only in the spectra with $E_{2g}$ symmetry and only in the $\sigma$ but not $\pi$ bands. The properties of the bound state and the Raman spectrum are investigated, also in the presence of impurity scattering.Comment: 4 pages, 4 figures, will appear in PR

Statistical Analysis of "Structural Change" - An Annotated Bibliography

Within the framework of the Economic Structural Change Program, a cooperative research activity of IIASA and the University of Bonn, FRG, a project is carried out on "Statistical and Econometric Identification of Structural Change"; the project involves studies on the formal aspects of the analysis of structural changes. On the one hand, they include statistical methods to detect non-constancies, such as stability tests, detection criteria, etc., and on the other hand, methods which are suitable for models which incorporate nonconstancy of the parameters, such as estimation techniques for time-varying parameters, adaptive methods, etc. The present paper provides a documentation of the state of the art in the form of a bibliography

Excitation intensity dependence of photoluminescence spectra of SiGe quantum dots grown on prepatterned Si substrates: Evidence for biexcitonic transition

The pumping intensity (I) dependence of the photoluminescence (PL) spectra of perfectly laterally two-dimensionally ordered SiGe quantum dots on Si(001) substrates was studied. The PL results from recombinations of holes localized in the SiGe quantum dots and electrons localized due to the strain field in the surrounding Si matrix. The analysis of the spectra revealed several distinct bands, attributed to phonon-assisted recombination and no-phonon recombination of the excitonic ground state and of the excited excitonic states, which all exhibit a linear I dependence of the PL intensity. At approximately I>3W/cm^2, additional bands with a nearly quadratic I dependence appear in the PL spectra, resulting from biexcitonic transitions. These emerging PL contributions shift the composite no-phonon PL band of the SiGe quantum dots to higher energies. The experimentally obtained energies of the no-phonon transitions are in good agreement with the exciton and biexciton energies calculated using the envelope function approximation and the configuration interaction method

The Pairing Mechanism in HTSC investigated by Electronic Raman Scattering

By means of electronic Raman scattering we investigated the symmetry of the energy gap Delta(k), its temperature dependence and its variation with doping of well characterized Bi2Sr2CaCu2O8+delta single crystals. The oxygen content delta was varied between the under- and the overdoped regime by subsequently annealing the same single crystal in Ar and O2, respectively. The symmetry analysis of the polarized electronic Raman scattering is consistent with a d_x^2-y^2-wave symmetry of the energy gap in both regimes. The gap ratio 2Delta_max/k_BT_c and its temperature dependence changes with doping similar to predictions of theories based on paramagnon coupling.Comment: 3 pages, LaTeX, 2 ps figures available on request to [email protected]