In this thesis, we focus on the study of dependent arcs of acyclic orientations of graphs. Given an acyclic orientation D of G, Edelman cite{West} defined an arc to be {em dependent} if its reversal creates a cycle in D; otherwise, it is independent. Let d(D) and i(D) be the numbers of dependent arcs and independent arcs in D, respectively. And, let d_{max}(G)(d_{min}(G)) and i_{max}(G) (i_{min}(G)) be the maximum (minimum) numbers of dependent arcs and independent arcs over all acyclic orientations of G, respectively. Edelman cite{Fisher} showed that if G is connected, then d_{max}(G)=||G||-|G|+1. A graph G is said to satisfy the {em interpolation property} (or G is fully orientable) if $G$ has an acyclic orientation with exactly k dependent arcs for every k with d_{min}(G) leq k leq d_{max}(G). West established the interpolation property for complete bipartite graphs cite{West}. We obtain the minimum numbers of dependent arcs of the outerplane graphs and show that the outerplane graphs satisfy the interpolation property. Let N(G) be the set { i(D)| D is an acyclic orientation of G }. N(G) is called the independent-arc spectra of G. For complete k-partite graphs G, we obtain i_{max}(G) and discuss the independent-arc spectra for some classes. On the other hand, we consider the cover problem. A cover graph is the underlying graph of the Hasse diagram of a finite partially ordered set. The cover problem is that whether a given graph is a cover graph. It is easy to see that a graph G is a cover graph if and only if d_{min}(G)=0. We show that the generalized Mycielski graphs M_m(C_{2t+1}) of an odd cycle, Kneser graphs KG(n,k), and Schrijver graphs SG(n,k) are not cover graphs when m geq 1, t geq 1, k geq 3 and n geq 2k+2.

Reproduction de : Thèse de doctorat : Génie électrique : Toulouse, INPT : 2005. / Titre provenant de l'écran-titre. Bibliogr. 50 réf.

Thèse de doctorat : Procédés biotechnologiques et alimentaires : INPL : 2007. / Titre provenant de l'écran-titre.

Inaug.-Diss.--Basel. / Vita.

Thesis (MTech (Mechanical Engineering))--Peninsula Technikon, 2001. / Word processed copy. Summary in English. Includes bibliographical references (leaves 68-71). Also available online.

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A specially-designed plasma chamber was constructed to study the operating characteristics of a dc plasma transferred arc struck between a fluid convective cathode and a water-cooled anode. The plasmagen gas consisted of pure argon and arc lengths as high as 7 cm were studied. / The arc voltage increased markedly with arc length and with an increase in the inlet velocity of the argon flow past the cathode tip, and much less with an increase in current. The effect of the gas velocity was minor at low velocities (1 to 3 m/s) but became important at higher velocities (20 to 60 m/s). / Arc length and gas velocity were again the major factors in the distribution of the arc energy. For long arcs and at high gas velocities, the energy emitted by the arc to the wall of the chamber was dominant, while for short arcs the energy absorbed by the water-cooled anode was greater. In all cases, the fraction of the input energy absorbed by the water-cooled cathode, or leaving the system as sensible heat in the exit gas was small. At the anode, the major contribution was from electron recombination, with convection heat transfer from the plasma somewhat less. Direct radiation from the plasma to the anode surface was very small. The recombination of the electron stream occurred on a very small area of the anode ((TURN) 5 mm in diameter). In spite of the energetic water cooling, appreciable vaporization took place on that area. / Appropriate instrumentation permitted the measurement of the stagnation-pressure and pressure distribution on the anode, and that of total heat flux and radiative heat transfer. From the latter, it was estimated that the plasma temperature just above the anode was in the range 10,000 - 12,000 K. / Preliminary experiments with an anode consisting of molten copper showed that the arc root was no longer fixed, but moved around continuously. The arc was otherwise quite stable, and its operating characteristics differed little from those reported for solid anodes, in spite of the greater extent of metal vaporization.

The basic characteristics of a transferred arc argon plasma were determined. A cathode assembly suitable for transferring the electric arc to a molten metal bath or to a cooled anode was designed and constructed to produce the plasma in open air. It included provision for the injection of secondary gas into the arc column. / The measured electrical characteristics indicated that the sustained voltage depended strongly on the arc length and much less on current. The inlet gas velocity past the cathode tip was determined to be an important operating parameter, rather than the volumetric gas flowrate. / The measurement of the axial and radial profiles of temperature was effected with (+OR-) 8% accuracy by a novel diagnostic technique based on the determination of the variations in the outputs of a two-wavelength pyrometer that views a small section of the plasma, as the latter is swept rapidly by a blocking element. Temperatures up to 18,500 K were observed on the axis of the plasma column. / A sweeping microprobe was used to measure the axial and radial profiles of velocity. Velocities up to 190 m/s were recorded. The presence of a relatively colder flow surrounding the plasma column was detected. Mass and energy balances performed by taking this flow into account agreed with the measured input rates.

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