Linear optimization aims at maximizing, or minimizing, a linear objective function over a feasible region defined by a finite number of linear constrains. For several well-studied problems such as maxcut, all the vertices of the feasible region are integral, that is, with integer-valued coordinates. The diameter of the feasible region is the diameter of the edge-graph formed by the vertices and the edges of the feasible region. This diameter is a lower bound for the worst-case behaviour for the widely used pivot-based simplex methods to solve linear optimization instances. A lattice (d,k)-polytope is the convex hull of a set of points whose coordinates are integer ranging from 0 to k. This dissertation provides new insights into the determination of the largest possible diameter δ(d,k) over all possible lattice (d,k)-polytopes. An enhanced algorithm to determine δ(d,k) is introduced to compute previously intractable instances. The key improvements are achieved by introducing a novel branching that exploits convexity and combinatorial properties, and by using a linear optimization formulation to significantly reduce the search space. In particular we determine the value for δ(3,7). / Thesis / Doctor of Philosophy (PhD)

A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. In this paper we characterize the diameter-2-critical graphs with no induced path on five vertices. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph of order n is at most n2/4 and that the extremal graphs are the complete bipartite graphs with partite sets whose cardinality differs by at most one. We use an association with total domination to prove that if G is a diameter-2-critical graph with no induced path P5, then G is triangle-free. As a consequence, we observe that the Murty-Simon Conjecture is true for P5-free, diameter-2-critical graphs by Turán's Theorem. Finally we characterize these graphs by characterizing their complements.

A graph is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. Let G be a diameter-2-critical graph of order n. Murty and Simon conjectured that the number of edges in G is at most ⌊n 2/4⌋ and that the extremal graphs are the complete bipartite graphs K ⌊n/2⌋,⌊n/2⌉. Fan [Discrete Math. 67 (1987), 235-240] proved the conjecture for n ≤ 24 and for n = 26, while Füredi [J. Graph Theory 16 (1992), 81-98] proved the conjecture for n > n 0 where n 0 is a tower of 2's of height about 1014. The conjecture has yet to be proven for other values of n. Let Δ denote the maximum degree of G. We prove the following maximum degree theorems for diameter-2-critical graphs. If Δ ≥ 0.7 n, then the Murty-Simon Conjecture is true. If n ≥ 2000 and Δ ≥ 0.6789 n, then the Murty-Simon Conjecture is true.

A graph G is diameter-2-critical if its diameter is two and the deletion of any edge increases the diameter. The complete graph on four vertices minus one edge is called a diamond, and a diamond-free graph has no induced diamond subgraph. In this paper we use an association with total domination to characterize the diameter-2-critical graphs whose complements are diamond-free. Murty and Simon conjectured that the number of edges in a diameter-2-critical graph G of order n is at most ⌊ n24⌋ and that the extremal graphs are the complete bipartite graphs K⌊ n2⌋n2⌉. As a consequence of our characterization, we prove the Murty-Simon conjecture for graphs whose complements are diamond-free.

Drilling and blasting are seen as sub-systems of size reducing operations in mining. To have better design parameters for economical excavation of mineral production and fragmentation, the comminution and fragmentation operations need to be studied and optimized independently, as well as together, to create optimized use of energy and cost-effective operation. When there is a change in drillhole diameter or fragmentation specification, changes in the blast design parameters are required affecting the cost of a drilling and blasting operation. A model was developed to calculate blast design parameters and costs on the basis of the required 80% fragment size needed for crusher operation. The model is based on previously developed fragmentation models, found in the literature. The model examines the effect of drilling diameter on blasting requirements to achieve certain fragmentation targets and calculates blast design parameters and costs for a range of diameters from 75 to 350 mm. To examine the effectiveness of this model, two different 80% passing sizes of fragments have been considered. It was shown that cost optimization occurs at an intermediate diameter, since there are opposing trends of the effect of diameter on powder factor and accessories needed. To achieve a certain fragmentation target, the total cost of drilling and blasting shows a clear trend allowing an optimum selection of diameter. The selected diameter also allows the examination of the suitability of the drill machine under the given geological and operational conditions of the drilling site. / Thesis (Master, Mining Engineering) -- Queen's University, 2009-03-27 07:34:33.787

No description available.

A fixed geometry hybrid thrust bearing is investigated with three different supply orifice diameters. The test rig uses a face-to-face thrust bearing design, with the test bearing acting as the rotor loading mechanism. A hydraulic shaker applies the static axial load, which is reacted by a second thrust bearing. The rotor is supported radially by two water-lubricated fluid film journal bearings and is attached to a 30,600 rpm motor via a high speed coupling with very low axial stiffness. Thrust bearings with three different orifice diameters (1.63, 1.80, and 1.93 mm) are tested for a range of supply pressures, fluid film thicknesses, and rotational speeds. The water-lubricated test bearings have eight pockets, with feed orifices located centrally in each pocket. Experimental results are comparted to predictions found using bulk flow model HYDROTHRUST. Analysis of the data reveals generally good agreements between predictions and measurements. Thrust-bearing inlet supply and inner radius flow rates all decreased with decreasing orifice diameters and bearing axial clearances. In most cases, the bearings with larger orifice diameters exhibit higher recess pressure ratios, operating clearances, and flow rates. The largest orifice diameter configuration does not display higher recess pressure ratios or operating clearances at high speeds for some supply pressures, but it does continue to require additional lubricant flow rate compared to the smaller orifice bearings. In these cases, the results are not reflected in predictions, which otherwise correlate very well with experimental measurements. Estimations of static loading axial stiffness are obtained using experimental results. An optimum hybrid thrust bearing orifice diameter will depend on the conditions of individual applications. Larger orifices generally provide larger operating clearances and higher stiffnesses, but also require higher flow rates. For most applications, a compromise of bearing performance parameters will be desired. The test results and comparisons presented will aid in sizing orifice diameters for future hybrid thrust bearing designs.

<p>AAA-protokoll är ett protokoll som hanterar uppkopplingsförfrågningar och bokför använda resurser hos användare för att senare kunna ta betalt. Det kan användas för mer än detta så som att erbjuda uppkoppling till trådlösa nätverk. AAA-protokoll erbjuder en centraliserad punkt för administration av uppkopplingshantering och nätverksåtkomst.RADIUS-protokollet är det mest använda AAA-protokollet i världen på grund av sin flexibilitet och öppna standarder. Protokollet innehåller dock en del brister mot funktionalitet och säkerhet, så som att protokollet är svagt mot man-i-mitten-attacker. Diameter är uppföljaren till RADIUS och är det bättre av dem båda. Arbetet går igenom, med fokus på säkerhet och funktionalitet, ifall Diameter rättar till de brister som finns i RADIUS och samtidigt om Diameter är ett protokoll för framtiden.Resultatet som presenteras är att Diameter förbättrar nästan alla de brister som uppdagats mot säkerhet och funktionalitet i RADIUS. De mest kritiska bristerna med RADIUS är dess skalbarhet och dess brist på trafikstockningskontroll i större organisationers nätverk. RADIUS-protokollet lämpar sig inte för större organisationer.Framtiden för Diameter är att anses som ljus. Diameter har rätt uppbackning från organisationer och marknaden i helhet för att bli det nästa stora AAA-protokollet. Diameter har även fått protokollet IMS anpassat efter sig och på så sett visar marknaden stort förtroende för Diameter-protokollet.</p>

Det finns ett stort intresse för exoter inom skogsbruket och i denna rapport behandlas klippgran (Abies laciocarpa) och Contorta (Pinus contorta). Vid undersökningen av dessa trädsorter jämfördes diameter och höjdtillväxt med gran (Picea abies) och björk (Betula pubescens). Mätningarna utfördes på lokaler i Strömsunds kommun i Jämtlands län vid Näxåsen (Strömsund) och runt Jorm i Frostviken på SCA:s marker

Essa dissertação aborda o estudo teórico, experimental e computacional de algumas configurações usuais para derivações de pequeno diâmetro, interligadas a uma tubulação principal, sujeitas à vibração. O estudo de vibração, induzida por diversos fatores, foi a base teórica utilizada para a previsão de esforços máximos admissíveis e garantia da confiabilidade das tubulações. A confecção dos corpos-de-prova buscou a reprodução de condições típicas de uso em instalações de petróleo e gás, visando uma comparação de desempenho para as diferentes condições de montagem. Também foi realizada uma etapa de avaliação computacional, usando o programa Triflex para verificação da frequência natural e rigidez do conjunto montado. As análises de deslocamentos e esforços através dos dados obtidos pela instrumentação das peças soldadas e resultados do programa ANSYS apresentaram resultados importantes, enfatizando a resistência mecânica de determinadas configurações de menor comprimento ou com reforço vinculado à tubulação principal, as quais podem ser utilizadas em projetos de tubulações, melhorando a confiabilidade das instalações. / This dissertation adresses the theoretical, experimental and computational study of some usual settings for small diameter pipe, connected to a main pipe, subject to vibration. The study of vibration induced by several factors was the theoretical basis used for predicting maximum permissible efforts and ensuring the reliability of pipes. The creation of the specimens sought to reproduce typical use conditions in the oil and gas factories aimed at comparative performance for different installation conditions. It was also performed a computational evaluation stage using software Triflex to check the natural frequency and rigidity of the mounted assembly. The displacement analysis and effort for parts by informations obtained with instrumentation of welded pipes and results of ANSYS software presented important results, emphasizing the mechanical strength of certain settings with smaller length or with reinforcement linked to a main pipe which can be used in pipe projects, improving the reliability of the facilities.