The goal of this study is to assess the potential of using bench-scale fire testing to screen materials for the Steiner tunnel fire test. It is hypothesized that the chemical and physical changes made to a material to improve its fire performance in small scale fire tests will have a predictable response in the Steiner tunnel. This hypothesis is based on the observation that fire test results can, in some cases, provide insight on a material's relative fire hazard, and the assumption that the relative hazard should be consistent across scale. The ASTM E84 Steiner tunnel test provides a relative ranking of material hazard in two categories. The horizontal Flame Spread Index (FSI) is used to rank the flame hazard of a material, and the Smoke Developed Index (SDI) is used to rank the smoke hazard of a material. Two fire tests are proposed to independently assess each hazard at the bench-scale. The ASTM E1354 cone calorimeter test measures a material's open-flaming heat release rate; it is proposed that the cone calorimeter test can be used to assess a material's relative flame hazard. The ISO 5659-2 smoke density chamber test measures a material's closed-environment smoke development; it is proposed that the smoke density chamber test can be used to assess a material's relative smoke hazard. The material selected for this study is fire-retarded sprayed polyurethane foam (FRSPF) insulation. Specific details of the foam chemistry, fire retardants, and the manufacturer are confidential. Generally, the foam can be described as medium-density (approximately 2 lbs/ft³), closed-celled, and semi-rigid. The fire retardant additives are comprised of differing ratios and concentrations of phosphorous- and halogen-containing compounds. A series of 30 Steiner tunnel tests is conducted on 20 different formulations. Repeated testing is conducted on several formulations in order to assess variability in the Steiner tunnel test results. Cone calorimeter and smoke density chamber tests are conducted on a subset of those formulations, in sets of 3-5 tests per formulation. Key performance indicators are identified from each fire test, relationships between those indicators are examined, and correlations are presented where strong relationships are apparent. Empirical prediction models are proposed for FSI and SDI based on the success rate of prediction, and minimization of error between experimental (measured) and modelled (predicted) results. It is concluded that for the materials tested in this study, there is sufficient evidence of consistency in relative performance to recommend bench-scale screening tests as a cost-effective alternative to repeated Steiner tunnel testing.

The QoS Steiner Tree Problem asks for the most cost efficient way to multicast multimedia to a heterogeneous collection of users with different data consumption rates. We assume that the cost of using a link is not constant but rather depends on the maximum bandwidth routed through the link. Formally, given a graph with costs on the edges, a source node and a set of terminal nodes, each one with a bandwidth requirement, the goal is to find a Steiner tree containing the source, and the cheapest assignment of bandwidth to each of its edges so that each source-to-terminal path in the tree has bandwidth at least as large as the bandwidth required by the terminal. Our main contributions are: (1) New flow-based integer linear program formulation for the problem; (2) First implementation of 4.311 primal-dual constant factor approximation algorithm; (3) an extensive experimental study of the new heuristics and of several previously proposed algorithms.

El objetivo fundamental de este trabajo ha sido el estudio del sistema fundamental de paralelos de un cuerpo convexo (conjunto compacto y convexo) en el espacio euclídeo n-dimensional. Se ha llevado a cabo siguiendo tres líneas diferentes: el estudio del polinomio de Steiner y el polinomio alternado Steiner desde el punto de vista algebraico de sus raíces y la conjetura de Matheron; el estudio de la diferenciabilidad de las quermassintegrales asociadas al cuerpo con respecto al parámetro de definición del sistema completo de paralelos y, por último, el estudio de las quermassintegrales del cuerpo desde el punto de vista analítico proporcionado por la identificación del cuerpo convexo con su función soporte, las propiedades de ésta cuando el cuerpo es suficientemente suave y la desigualdad de Brunn-Minkowski. / The aim of this work consists on studying the full system of parallel bodies of a convex body (compact and convex set) in the n-dimensional Euclidean space. It has been carried out following three different lines of work: the study of the Steiner polynomial and the alternating Steiner polynomial from the algebraic point of view of its roots; the study of the differentiability of the quermassintegrals associated to the convex body with respect to the parameter that defines the full system of parallel bodies and finally, the study of the quermassintegrals from the analytical point of view provided by the identification of a convex body with its support function, the properties of this function when the body is smooth enough and the Brunn-Minkowski inequality

Texte remanié de: Habilitationsschrift--Theologische Fakultät--Erlangen-Nürnberg--Friedriechh-Alexander-Universität, 2000. Titre de soutenance : Die Zukunft des kosmischen Christus : theologische Analysen der Genese und Tendenzen eines modernen Christologumenons. / Bibliogr. p. 453-500. Index.

Habilitation à diriger des recherches : Informatique : Rennes 1 : 2008. / Bibliogr. p. 137-163.

No description available.

In the Directed Steiner Tree problem, we are given a directed graph G = (V,E) with edge costs, a root vertex r ∈ V, and a terminal set X ⊆ V . The goal is to find the cheapest subset of edges that contains an r-t path for every terminal t ∈ X. The only known polylogarithmic approximations for Directed Steiner Tree run in quasi-polynomial time and the best polynomial time approximations only achieve a guarantee of O(|X|^ε) for any constant ε > 0. Furthermore, the integrality gap of a natural LP relaxation can be as bad as Ω(√|X|).  We demonstrate that l rounds of the Sherali-Adams hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in l-layered graphs from Ω( k) to O(l · log k) where k is the number of terminals. This is an improvement over Rothvoss’ result that 2l rounds of the considerably stronger Lasserre SDP hierarchy reduce the integrality gap of a similar formulation to O(l · log k). We also observe that Directed Steiner Tree instances with 3 layers of edges have only an O(logk) integrality gap bound in the standard LP relaxation, complementing the fact that the gap can be as large as Ω(√k) in graphs with 4 layers. Finally, we consider quasi-bipartite instances of Directed Steiner Tree meaning no edge in E connects two Steiner nodes V − (X ∪ {r}). By a simple reduction from Set Cover, it is still NP-hard to approximate quasi-bipartite instances within a ratio better than O(log|X|). We present a polynomial-time O(log |X|)-approximation for quasi-bipartite instances of Directed Steiner Tree. Our approach also bounds the integrality gap of the natural LP relaxation by the same quantity. A novel feature of our algorithm is that it is based on the primal-dual framework, which typically does not result in good approximations for network design problems in directed graphs.

The goal of this study is to assess the potential of using bench-scale fire testing to screen materials for the Steiner tunnel fire test. It is hypothesized that the chemical and physical changes made to a material to improve its fire performance in small scale fire tests will have a predictable response in the Steiner tunnel. This hypothesis is based on the observation that fire test results can, in some cases, provide insight on a material's relative fire hazard, and the assumption that the relative hazard should be consistent across scale. The ASTM E84 Steiner tunnel test provides a relative ranking of material hazard in two categories. The horizontal Flame Spread Index (FSI) is used to rank the flame hazard of a material, and the Smoke Developed Index (SDI) is used to rank the smoke hazard of a material. Two fire tests are proposed to independently assess each hazard at the bench-scale. The ASTM E1354 cone calorimeter test measures a material's open-flaming heat release rate; it is proposed that the cone calorimeter test can be used to assess a material's relative flame hazard. The ISO 5659-2 smoke density chamber test measures a material's closed-environment smoke development; it is proposed that the smoke density chamber test can be used to assess a material's relative smoke hazard. The material selected for this study is fire-retarded sprayed polyurethane foam (FRSPF) insulation. Specific details of the foam chemistry, fire retardants, and the manufacturer are confidential. Generally, the foam can be described as medium-density (approximately 2 lbs/ft³), closed-celled, and semi-rigid. The fire retardant additives are comprised of differing ratios and concentrations of phosphorous- and halogen-containing compounds. A series of 30 Steiner tunnel tests is conducted on 20 different formulations. Repeated testing is conducted on several formulations in order to assess variability in the Steiner tunnel test results. Cone calorimeter and smoke density chamber tests are conducted on a subset of those formulations, in sets of 3-5 tests per formulation. Key performance indicators are identified from each fire test, relationships between those indicators are examined, and correlations are presented where strong relationships are apparent. Empirical prediction models are proposed for FSI and SDI based on the success rate of prediction, and minimization of error between experimental (measured) and modelled (predicted) results. It is concluded that for the materials tested in this study, there is sufficient evidence of consistency in relative performance to recommend bench-scale screening tests as a cost-effective alternative to repeated Steiner tunnel testing.

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 2045. Adviser: T. Jiang.

Proefschrift--Letteren--Amsterdam, 1986.