Isotrope Unterräume rationaler quadratischer Formen

Ohne ZusammenfassungDiese Arbeit wurde während eines Aufenthaltes von Schmidt in der Bundesrepublik Deutschland als Preisträger der Alexander von Humboldt-Stiftung geschrieben.     

Magnetic properties of mechanically alloyed Co–Ti powder

An amorphous phase containing traces of non-transformed Co and Ti powders was obtained by mechanical alloying nominal compositions of Co₆₇Ti₃₃ and Co₅₀Ti₅₀ in a high-energy ball-mill. These alloys were prepared from elemental powders of Co and Ti. The heat treatment of Co₆₇Ti₃₃ at 573, 873 and 1173 K crystallized nanoparticles of Co₂Ti and Co₃Ti compounds, while the same treatments conducted on Co₅₀Ti₅₀ resulted in the formation of Co₂Ti and CoTi nanoparticles. The saturation magnetizations reached a maximum value in the amorphous state and they decreased when the temperatures of the heat treatment rose. Demagnetizing interparticle interaction effects were estimated through hysteresis loops and initial magnetization curves using the Fourier technique.     

Propagation of mesons in asymmetric nuclear matter in a density-dependent coupling model

We study the propagation of the light mesons σ,ω,ρ, and a₀(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in β-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean-field approximation are investigated. Received: 16 October 2001 / Accepted: 10 January 2002     

Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

On the maximum cardinality search lower bound for treewidth

The Maximum Cardinality Search (MCS) algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbours becomes visited. A maximum cardinality search ordering (MCS-ordering) of a graph is an ordering of the vertices that can be generated by the MCS algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighbours of v that are before v in the ordering. The visited degree of an MCS-ordering ψ of G is the maximum visited degree over all vertices v in ψ. The maximum visited degree over all MCS-orderings of graph G is called its maximum visited degree. Lucena [A new lower bound for tree-width using maximum cardinality search, SIAM J. Discrete Math. 16 (2003) 345-353] showed that the treewidth of a graph G is at least its maximum visited degree.We show that the maximum visited degree is of size O(logn) for planar graphs, and give examples of planar graphs G with maximum visited degree k with O(k!) vertices, for all k∈N. Given a graph G, it is NP-complete to determine if its maximum visited degree is at least k, for any fixed k?7. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P=NP. Variants of the problem are also shown to be NP-complete.In this paper, we also propose some heuristics for the problem, and report on an experimental analysis of them. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications.     

On Lattices of Uniformities

We study lattice theoretical properties of lattices of uniformities such as modularity, distributive laws and the existence of (relative) complements. For this the concepts of permutable uniformities (see Definition 3.1) and independent uniformities (see Definition 4.1) are important. Moreover, we show that e.g. the lattice of all lattice uniformities on a lattice L is a closed sublattice of the lattice of all uniformities on L.     

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.     

Group-valued measures on coarse-grained quantum logics

In [3] it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later ([9]) this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.     

Characteristics of Nd：GdVO4 Laser with Different Nd-Doping Concentrations

We report the properties of a compact diode-pumped continuous-wave Nd：GdV04 laser with a linear cavity and different Nd-doped laser crystals. In a 0.2at.% Nd-doped Nd：GdVO4 laser, 1.54 W output laser power is achieved at 912nm wavelength with a slope efficiency of 24.8% at an absorbed pump power of 9.4W. With 0.3at.% Nd-doping concentration, we can obtain the either single-wavelength emission at 1064nm or 912nm or the dual-wavelength emission at 1064nm and 912nm by controlling the incident pump power. From an incident pump power of 11.6 W, the 1064nm emission between ^4Fa/2 and ^4I11/2 is suppressed completely by the 912nm emission between ^4Fa/2 and ^4I9/2. We obtain 670 mW output of the 912nm single-wavelength laser emission with a slope efficiency of 5.5% by taking an incident pump power of 18.4 W. Using a Nd：GdV04 laser with 0.4at.% Nd-doping concentration, we obtain either the single-wavelength emission at 1064nm or the dual-wavelength emission at both 1064nm and 912nm by increasing the incident pump power. We observe a strong competition process in the dualavelength laser.