Almost free splitters

Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext_R(G,G)=0 holds. For simplicity we will call such modules splitters. Our investigation continues math.LO/9910159. In math.LO/9910159, we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In math.LO/9910159 we concentrated on splitters which are larger then the continuum and such that countable submodules are not necessarily free. The `opposite' case of aleph_1-free splitters of cardinality less or equal to aleph_1 was singled out because of basically different techniques. This is the target of the present paper. If the splitter is countable, then it must be free over some subring of the rationals by a result of Hausen. We can show that all aleph_1-free splitters of cardinality aleph_1 are free indeed

Optical Multicast Routing Under Light Splitter Constraints

During the past few years, we have observed the emergence of new applications that use multicast transmission. For a multicast routing algorithm to be applicable in optical networks, it must route data only to group members, optimize and maintain loop-free routes, and concentrate the routes on a subset of network links. For an all-optical switch to play the role of a branching router, it must be equipped with a light splitter. Light splitters are expensive equipments and therefore it will be very expensive to implement splitters on all optical switches. Optical light splitters are only implemented on some optical switches. That limited availability of light splitters raises a new problem when we want to implement multicast protocols in optical network (because usual multicast protocols make the assumption that all nodes have branching capabilities). Another issue is the knowledge of the locations of light splitters in the optical network. Nodes in the network should be able to identify the locations of light splitters scattered in the optical network so it can construct multicast trees. These problems must be resolved by implementing a multicast routing protocol that must take into consideration that not all nodes can be branching node. As a result, a new signaling process must be implemented so that light paths can be created, spanning from source to the group members

Conceptual design study of advanced acoustic composite nacelle

Conceptual nacelle designs for wide-bodied and for advanced-technology transports were studied with the objective of achieving significant reductions in community noise with minimum penalties in airplane weight, cost, and in operating expense by the application of advanced composite materials to nacelle structure and sound suppression elements. Nacelle concepts using advanced liners, annular splitters, radial splitters, translating centerbody inlets, and mixed-flow nozzles were evaluated and a preferred concept selected. A preliminary design study of the selected concept, a mixed flow nacelle with extended inlet and no splitters, was conducted and the effects on noise, direct operating cost, and return on investment determined

Active Control of Laser Wavefronts in Atom Interferometers

Wavefront aberrations are identified as a major limitation in quantum sensors. They are today the main contribution in the uncertainty budget of best cold atom interferometers based on two-photon laser beam splitters, and constitute an important limit for their long-term stability, impeding these instruments from reaching their full potential. Moreover, they will also remain a major obstacle in future experiments based on large momentum beam splitters. In this article, we tackle this issue by using a deformable mirror to control actively the laser wavefronts in atom interferometry. In particular, we demonstrate in an experimental proof of principle the efficient correction of wavefront aberrations in an atomic gravimeter