1. Introduction. Let A be a topological space, F be a metrizable space, and C be the collection of continuous functions on X into Y. We shall be interested in two topologies on C. The compact-open or k-topology. Given compact subset K of X and open subset W of F, denote by (K, W) the collection of functions fEC such that fiK)E W. The assembly of finite intersections of sets iK, W) forms a base ...

We compare the effectiveness of uniform versus non-uniform waveband switching under the dual cost metrics of switching requirements and fiber capacity. We consider a star topology and begin by characterizing the optimal performance frontier achievable under no restrictions on waveband sizing, and provide algorithms employing non-uniform waveband sizing that approach or achieve this optimum. We ...

We establish a large deviation principle for chordal SLE\(_\kappa\) parametrized by capacity, as the parameter \(\kappa \to 0+\), in topology generated uniform convergence on compact intervals of positive real line. The rate function is shown to equal Loewner energy curve. This strengthens recent result Peltola and Wang who obtained analogous statement using Hausdorff topology.

Topology Control (TC) has been established as an efficient technique for improving the properties of wireless multi-hop networks. In this paper we first analyze the impact of non-uniform node placement on the effectiveness of traditional and well established topology control approaches that preserve connectivity with high probability, thus revealing and demonstrating their inefficiency in prope...

This paper considers the problem of Routing and Wavelength Assignment (RWA) in optical passive star networks with non-uniform traffic load. The problem can be considered as designing a logical topology over an optical passive star physical topology with a given non-uniform traffic. The approach uses the bipartite graphs and the concept of Time and Wavelength Division Multiplexing (TWDM) embeddi...

In this paper, we present a large deviation principle for partial sums processes indexed by the half line, which is particularly suited to queueing applications. The large deviation principle is established in a topology that is finer than the topology of uniform convergence on compacts and in which the queueing map is continuous. Consequently, a large deviation principle for steady-state queue...

Let X be a locally connected, b-compact metric space and E a closed subset of X. Let G be the space of all continuous real-valued functions defined on some closed subsets of E. We prove the equivalence of the τ aw and τ K topologies on G, where τ aw is the so called Attouch-Wets topology, defined in terms of uniform convergence of distance functionals, and τ K is the topology of Kuratowski conv...