A characterization of network representable polymatroids

Meggido [1974] showed that the maximum flow through sets of sources in a multiple sink flow network is a polymatroidal function. Recently, Federgruen and Groenevelt [1985], [1986] have considered polymatroids that can be represented by a multiple source flow network and have improved the runnung time of an important scheduling application.We give a characterization of network representability and relate representable polymatroids to the theory of gammoids.

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Zusammenfassung Meggido [1974] hat gezeigt, daß ein maximaler Fluß durch ein Netzwerk mit mehrfachen Senken eine polymatroidale Funktion beschreibt. Federgruen und Groenvelt [1985], [1986] haben kürzlich solche Polymatroide betrachtet, die durch Flüsse in derartigen Netzwerken repräsentiert werden können und haben so die Laufzeit einer wichtigen Schedulinganwendung verbessern können.Wir geben eine Charakterisierung von Funktionen, die durch derartige Netzflußnetzwerke realisierbar sind. Dabei stellen wir eine Verbindung her zwischen Repräsentierbarkeit und Gammoidtheorie.

     

Ordered micro/mesoporous composite prepared as thin films

A new synthesis method for preparation of thin films and powders consisting of zeolite beta nanocrystals embedded in ordered mesoporous silica matrix is described. The final structures possessing bimodal porosity, i.e., high degree of mesophase order and spatially defined microporous zeolite nanocrystals are obtained via simultaneous solvent evaporation of preformed silica/surfactant/ethanol/nanosized zeolite beta assemblies. The films were characterized with grazing-incident diffraction (GID), nitrogen sorption based on gravimetric measurements with quartz crystal microbalance (QCM) devices, and transmission electron microscopy (TEM). It is shown that the incorporation of beta nanocrystals in the mesoporous silica matrix and the mesophase order itself can be controlled through the variation of the fractional amounts of the zeolite nanoparticles and silica/surfactant solutions. The HR-TEM measurements showed that the nanosized Beta microporous crystals are separated and at the same time connected through an ordered mesostructured matrix.     

Gold electroless reduction in nanosized channels of thiol-modified SBA-15 material

A new procedure for the preparation of high aspect ratio Au nanowires utilizing gold electroless reduction in the hexagonally ordered, thiol-modified nanosized channels of the SBA-15 material is reported. Two different Au precursors were adsorbed onto pedant thiol groups, covalently bonded to the mesoporous silica surface, and used as seeds to grow extended Au nanostructures by treatment in Au electroless reduction bath. It is shown that the dimensions and the assembly of the Au seeds are important parameters for the subsequent electroless reduction process. The [AuCl4]- ions complexed to the TOAB molecules assembled on the thiol-modified mesoporous surface of the SBA-15 material are suitable precursors for the subsequent gold electroless reduction. The resulting structures are several micrometer long Au nanowires with uniform diameters of about 5 nm, having large single-crystalline domains. The TEM results clearly show that the growth of the Au nanowires is templated by the channel structure of the SBA-15 material.     

Synthesis and characterization of the open-framework barium bisphosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O

Following the strategy of using polyfunctional phosphonic acids for the synthesis of open-framework metal phosphonates, the phosphonocarboxylic acid (H2O3PCH2)2NCH2C6H4COOH was used in the hydrothermal synthesis of new Ba phosphonates. Its decomposition led to the first open-framework barium phosphonate [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O. The synthesis was also successfully performed using iminobis(methylphosphonic acid), (H2O3PCH2)2NH, as a starting material, and the synthesis was optimized to obtain as a pure material. The reaction setup as well as the pH are the dominant parameters, and only a diffusion-controlled reaction led to the desired compound. The crystal structure was solved from single-crystal data: monoclinic; C2/c; a=2328.7(2), b=1359.95(7), and c=718.62(6) pm; beta=98.732(10) degrees ; V=2249.5(3)x10(6) pm3; Z=4; R1=0.036; and wR2=0.072 (all data). The structure of [Ba3(O3PCH2NH2CH2PO3)2(H2O)4].3H2O is built up from BaO8 and BaO10 polyhedra forming BaO chains and layers, respectively. These are connected to a three-dimensional metal-oxygen-metal framework with the iminobis(methylphosphonic acid) formally coating the inner walls of the pores. The one-dimensional pores (3.6x4 A) are filled with H2O molecules that can be thermally removed. Thermogravimetric investigations and temperature-dependent X-ray powder diffraction demonstrate the stability of the crystal structure up to 240 degrees C. The uptake of N,N-dimethylformamide and H2O by dehydrated samples is demonstrated. Furthermore, IR, Raman, and 31P magic-angle-spinning NMR data are also presented.     

The thermal contact problem in nano- and micro-scale photothermal measurements

Thermal contact resistance between two solids is discussed with regard to its influence on the measurements of temperature and thermo-physical parameters in micro- and nano-structures. Two important applications are considered: thin film coatings on substrates and local measurements with a nano-probe in scanning thermal microscopy. The mechanical contact of a copper layer on carbon is measured by adhesion strength experiments and correlated to the thermal transport across the interface deduced from infrared radiometric measurements. A novel quantity the thermal wave contrast is introduced which takes into account the interface resistance and modifications of the coating and substrates at the interface. With regard to scanning thermal microscopy the contact resistance problem is discussed for 3ω-measurements in the active mode and for temperature measurements in the passive mode. It is shown that the thermo-elastic response can offer a means to avoid the influence of the thermal contact resistance on local temperature measurements.     

Photothermal and micro-thermal characterization of metal coated diamond crystallites

Photoacoustic effect and scanning near field microscopy have been applied to characterise the thermal properties of diamond crystallites which were coated by a Cu film, a Cr-film and a Cr-Cu film. The Cu-coated diamond exhibits a considerable thermal barrier at the Cu-diamond interface which had disappeared for the crystallites with a thin bond Cr-layer between diamond and Cu. The local inspection of the thermal conductivity with a thermal nano-probe operated in the 3ω-mode reveals slight local variations of the thermal conductivity of the Cr-coated crystallite.