Decompositions of finite projective planes

We consider decompositions of finite projective planes into copies of a particular structure. Our main theorem provides a connection between the existence of a proper projective subplane and the existence of a decomposition into sets of collinear points. Based on this result, we develop a connection between the existence of a projective subplane in a plane II and that of a hitting set in the dual of II.

New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D^-_k and D⁺_k inequalities (see Grötschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW ₂ inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.

When planes fall out of the sky : the war body on screen

I can’t keep my eyes off the war body, even though in the repeated seeing of it I feel nauseous: implicated in, and affected by, its painful coming into being. In this age of the War on Terror, wherever I look, wherever I am directed to look by the all-seeing “vision machines” that “illuminate” our identities (Virilio 1994, 70), the body of the soldier, terrorist, hostage, and victim come into troubling view. These war bodies are real in the ontological and phenomenological sense; they are also metaphoric, simulated, and discursive. In this chapter I will define and explore the complex ways in which these three articulating axis—war, in its militaristic and ideological sense; the screen, in all its multifaceted forms and contexts; and the body, individual and social—conjoin and synthesize, disintegrate and dislocate, in a phantasmagoric but simultaneously desperately real collision of power, desire, and control. My main contention will be that the war body on screen is a “sickening” creation that we have desired into being, so that we may feel, better understand, and be taken over by its terror. This terror of living ultimately helps ensure our docility, a docility required by the late capitalist nation-state; it also reconnect us to our bodies in profoundly moving and potentially challenging ways.

Variant selection and intervariant crystallographic planes distribution in martensite in a Ti-6Al-4V alloy

The transformation texture was studied in a Ti-6Al-4V alloy for two microstructures produced through different phase transformation mechanisms (i.e. diffusional vs. displacive). Both microstructures revealed qualitatively similar crystallographic texture characteristics, having two main texture components with Euler angles of (90°, 90°, 0°) and (90°, 30°, 0°). However, the overall α texture strength was considerably weaker in the martensitic structure (i.e. displacive mechanism) compared with the α + β microstructure produced through slow cooling (i.e. diffusional mechanism). The intervariant boundary distribution in martensite mostly revealed five misorientations associated with the Burgers orientation relationship. The five-parameter boundary analysis also showed a very strong interface plane orientation texture, with interfaces terminated mostly on the prismatic planes {hki0}, when misorientation was ignored. The highest intervariant boundary populations belonged to the 63.26°/[10 553 ] and 60°/[112 0] misorientations, with length fractions of 0.38 and 0.3, respectively. The former was terminated on (41 3 0), and the latter was a symmetric tilt boundary, terminated on (1 011). The intervariant plane distribution in martensite was determined more by the constraints of the phase transformation than by the relative interface energies.

Ships, planes and automobiles – the perils and pluses of place - making in an outer Melbourne suburb

Building a new suburb is increasingly seen as creating a “place” as well as a set of houses and neighbourhoods. Developers view “place-making” as a way to differentiate one estate from another and to capture a market segment; planners see the practice as the basis of good master planning. Local governments too support the concept to give residents a sense of pride and identity. While usually seen as a contemporary exercise, imprinted on the blank slate of greenfield sites, the experience of at least one outer suburb suggests that place-making is as much historical as contemporary and may be both a welcome element of a community and a focus of disaffection. The example of Point Cook in Melbourne’s west offers a range of iconic “places” – historical and contemporary markers of identity and difference – which have formed both the basis of local pride but also tension. Thus the RAAF base, Point Cook Homestead and Werribee Mansion long pre-dated the expansion of the city but they have been embraced as centres of pride, historical achievement and as tourist attractions. In contrast, a massive pirate-ship playground built in the centre of a park by a developer as a marker of difference and centre of community attraction was widely appreciated before being burned to the ground! This paper will report on a sample of resident experiences of place-making in outer suburban Melbourne which highlights some of the local complexities of place-making.