Resonance phenomena in a semi-infinite string with a periodic end

We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t^½, respectively, occur if either ω² is an eigenvalue of A or (i) ω² is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x > a (‘standing wave’).     

Extending the stochastic programming framework for the modeling of several decision makers: pricing and competition in the telecommunication sector

In a previous paper, Gouveia and Magnanti (2003) found diameter-constrained minimal spanning and Steiner tree problems to be more difficult to solve when the tree diameter D is odd. In this paper, we provide an alternate modeling approach that views problems with odd diameters as the superposition of two problems with even diameters. We show how to tighten the resulting formulation to develop a model with a stronger linear programming relaxation. The linear programming gaps for the tightened model are very small, typically less than 0.5–, and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti (2003). Moreover, the new model permits us to solve large Euclidean problem instances that are not solvable by prior approaches. Research funded in part by the Research Projects POCTI-ISFL-1-152,POSI/CPS/41459/2001 and POCTI/MAT/139/94 Research funded in part by the Singapore-MITAlliance(SMA)     

Carathéodory bounds for integer cones

We provide analogues of Carathéodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far.     

Relative Zeta Functions, Relative Determinants and Scattering Theory

We use the method of zeta function regularization to regularize the ratio det A det A ₀$ of the determinants of two elliptic self-adjoint operators A, A ₀ satisfying certain natural assumptions. This is of interest, especially, if the regularized determinants of the individual operators don't exist as, for example, in the case of elliptic operators on a noncompact manifold. Received: 15 January 1997 / Accepted: 2 July 1997     

Magnetic pigments for recording media

CrO₂ doped with 1--2 wt% Fe³⁺ on Cr⁴⁺ positions is one of the most important materials for magnetic recording in audio, data and video tapes. ⁵⁷Fe Mössbauer spectroscopy was applied to determine the level of iron doping in newly developed high coercivity CrO₂ particles. It was found that, compared with the conventional preparation process, the new particles contain increased amounts of Fe³⁺ ions in the CrO₂ crystal lattice giving rise to higher magnetocrystalline anisotropy. This is reflected in coercivities of up to over 900 Oe. All samples contain as a secondary iron-containing phase α-(Cr_1-xFe_x)₂O₃, the amount of which is higher in samples of the conventional preparation process than in those of the new BASF process. Details about the mechanism of the development of doped CrO₂ particles in both types of processes were obtained by means of Mössbauer, XRD and wet chemical investigations making possible an optimization of the new BASF process.     

Spectral properties of the Laplacian on bond-percolation graphs

Bond-percolation graphs are random subgraphs of the d-dimensional integer lattice generated by a standard bond-percolation process. The associated graph Laplacians, subject to Dirichlet or Neumann conditions at cluster boundaries, represent bounded, self-adjoint, ergodic random operators with off-diagonal disorder. They possess almost surely the non-random spectrum [0, 4d] and a self-averaging integrated density of states. The integrated density of states is shown to exhibit Lifshits tails at both spectral edges in the non-percolating phase. While the characteristic exponent of the Lifshits tail for the Dirichlet (Neumann) Laplacian at the lower (upper) spectral edge equals d/2, and thus depends on the spatial dimension, this is not the case at the upper (lower) spectral edge,where the exponent equals 1/2.