Ein LIFO Branch and Bound Verfahren zur optimalen Altstoffbehälterallokation

Zusammenfassung In diesem Artikel wird auf ein Problem eingegangen, das sich im Rahmen einer abfallwirtschaftlichen Studie ergab, in der die Durchführbarkeit von Altstoffsammlungen im dichtverbauten Siedlungsgebiet untersucht wurde. Als wichtige Teilaufgabe war dabei eine platzminimale Altstoffbehälterkombination für jede Altstoffart und für jedes Haus des untersuchten Sammelgebietes zu ermitteln, wobei unter anderem die Zugänglichkeit des Behälterraumes für die Sammelmannschaft und dessen topographische Gegebenheiten zu beachten waren. Zur Lösung dieser Aufgabe, deren Formalisierung auf ein ganzzahliges LP führte, wurde ein LIFO Branch and Bound Verfahren entwickelt. Dieses wird an Hand der wesentlichen Bestandteile eines jeden Algorithmus vom Branch and Bound Typ: der Branching Strategie, der Bounding Strategie und der Search Strategie dargestellt. Der Algorithmus wurde in PL/I programmiert und hat seine Leistungsfähigkeit in zahlreichen Programmläufen unter Beweis gestellt.

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Summary In this article a problem is treated which rose in the course of a research into the suitability for reconditioning used materials. This study analyzes the feasibility of scrap collection in densily populated, urban areas. One major aspect was to provide for a space saving combination of containers for every kind of scrap and for each house of the test area, bearing in mind the constraints given by the topographical conditions of the container room and its accessibility to the collection personnel. The formulation of this problem led to an all integer program. To solve this program a LIFO branch and bound algorithm was developed. The algorithm is presented by discussing its branching strategy, its bounding strategy and its search strategy, which constitute the essential parts of each procedure of the branch and bound type. The algorithm was programmed in PL/I and proved its efficiency in numerous runs.

     

Vector fields on complex quantum groups

Using previous results we construct theq-analogues of the left invariant vector fields of the quantum enveloping algebra corresponding to the complex Lie algebras of typeA _n–1 ,B _n ,C _n , andD _n . These quantum vector fields are functionals over the complex quantum groupA. In the special caseA ₁ it is shown that this Hopf algebra coincides withU _q sl(2, ).     

Surface and bulk plasmon coupling observed in reflection electron energy loss spectra

Reflection electron energy loss spectra have been measured for a semiconductor and some metals (Si, Cu, Ag and Au). A novel procedure is presented to rigorously decompose the spectra into contributions corresponding to surface and volume excitations. The resulting distributions of energy losses in an individual surface loss are in good agreement with theory. In particular, the begrenzungs effect occurring at the boundary of a solid state plasma, i.e. the reduction of the intensity of bulk modes due to the coupling with surface modes, can be clearly observed in the retrieved energy loss distribution.     

Optimized absorption imaging of mesoscopic atomic clouds

We report on the optimization of high-intensity absorption imaging for small Bose–Einstein condensates. The imaging calibration exploits the linear scaling of the quantum projection noise with the mean number of atoms for a coherent spin state. After optimization for atomic clouds containing up to 300 atoms, we find an atom number resolution of $\varDelta_{\rm det}= 3.7$ atoms, mainly limited by photon shot noise and radiation pressure.     

Initial stages of MnAs/GaAs(0 0 1) epitaxy studied by RHEED azimuthal scans

We study the nucleation phase of molecular beam epitaxy of (hexagonal) MnAs on (cubic) GaAs (0 0 1) using reflection high-energy electron diffraction (RHEED) azimuthal scans. The nucleation proceeds from a non-reconstructed initial stage through randomly oriented small nuclei and two orientation stages to the final single-phase epitaxial orientation. The fascinatingly complex nucleation process contains elements of both Volmer-Weber and Stranski-Krastanov growth. The measurement demonstrates the potential of high-resolution RHEED techniques to assess details of the surface structure during epitaxy.     

Quadruplex CARS micro‐spectroscopy

We demonstrate a technique for simultaneous detection of coherent anti‐Stokes Raman scattering (CARS) at four vibrational frequencies, using simple passive optical elements and without spectrally resolved detection. The technique is based on pump and Stokes femtosecond pulses selectively exciting vibrational resonances through spectral focusing. By replicating the pump and Stokes pair into four pairs, each traveling through appropriate glass elements, we simultaneously excite four different vibrational frequencies. The resulting CARS is a periodic train of intensities detected by a single photomultiplier and frequency analyzed to retrieve its Fourier coefficients. We demonstrate detection of methanol and ethanol mixtures in water and quantitative determination of their concentration owing to the improved chemical selectivity of this quadruplex CARS scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Circular grating waveguide structures for intracavity generation of azimuthal polarization in a thin-disk laser

We report on the generation of beams with azimuthal polarization using resonant grating waveguide structures (GWSs) inside an Yb:YAG thin-disk laser (TDL) oscillator. Two different GWS concepts were used to select the polarization of the emitted beam. The first uses the resonant reflection principle, and the second is based on the leaky-mode approach already reported in our previous work. Up to 93 W and 103 W of output power were extracted from a TDL with an optical efficiency, η(oo), of 36.2% and 40.1% using the first and the second approaches, respectively. In both cases, a pure azimuthal polarization and a beam quality factor, M2, of about 2.2 were measured. The design, fabrication, and different experimental results, as well as the laser performances for both GWSs, are discussed in the present Letter.     

Complete spaces and zero-one measures

It is the purpose of this paper to characterize the complete spaces in the sense of [6] by measure-theoretic properties. Let (X,) be a measurable space and let be a subpaving of satisfying certain closure properties, then X is-complete iff every 0,1-valued-regular measure on is a Dirac measure. In particular, we obtain Hewitt's well-known theorem that a completely regular space X is realcompact iff every 0,1-valued Baire measure on X is a Dirac measure. The main tool for our investigations is an extension theorem for measures due to Topsoe [10].