Almost automorphic symbolic minimal sets without unique ergodicity

Given a metrizable monothetic groupG with generatorg and a suitable closed nowhere dense subsetC of positive Haar measure, we associate a natural compact metric space whose points are almost automorphic symbolic minimal sets. It is then shown that those minimal sets which have positive topological entropy and fail to be uniquely ergodic form a esidual set. The example due to P. Julius [2] of a Toeplitz sequence of positive entropy which, is uniquely ergodic shows that the “residual” conclusion is sharp.     

The one dimensional Compartmentalised Knapsack Problem: A case study

The Compartmentalised Knapsack Problem (CKP) is similar to the ordinary Knapsack Problem except that items to be packed belong to separate classes, and items can only be packed, in knapsack compartments, amongst items in their own class. This paper addresses a case study in the cutting of steel rolls in which the CKP arises. The rolls are cut in two-phases: the first phase produces sub-rolls (compartments) which are, after reducing the thickness, cut in a second phase to produce ribbons (a class consists of ordered items with the same thickness). Finally, two methods of solving CKP are presented, and these are used to generate columns in the classical linear optimisation model of Gilmore and Gomory. Results of computational experiments are presented.     

Using a Conic Formulation for Finding Steiner Minimal Trees

We present a new mathematical programming formulation for the Steiner minimal tree problem. We relax the integrality constraints on this formulation and transform the resulting problem (which is convex, but not everywhere differentiable) into a standard convex programming problem in conic form. We consider an efficient computation of an ε-optimal solution for this latter problem using an interior-point algorithm.     

Periodic Solutions of a Nonlinear Evolution Problem

In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.     

Recent Advances of Multi-Channel Transmission in Metro Access Networks

We discuss the concept of coarse wavelength-division multiplexing (CWDM) for metro networks. After reviewing the requirements on components such as lasers and fiber, we propose different architectures for a flexible upgrade of existing CWDM systems.     

An experimental comparison of the focused beamformer and the inverse method for the characterisation of acoustic sources in ideal and non-ideal acoustic environments

The current availability and affordability of multi-microphone array systems has awakened a strong interest in sound source location and characterisation in many fields of experimental acoustics and noise control. Although the theory behind the design of such arrays has been known for some time, the algorithms used to process the microphone signals are the subject of on-going research and development. The beamformer algorithm is well-known and relatively simple to implement. It is useful for ‘scanning’ an area to find the position of sound sources but has limited ability to characterise fully the spatial distribution of the strength of an acoustic source. The inverse method, on the other hand, requires prior information regarding the position of sources or an appropriate discretisation of the source strength distribution. The method is more difficult to implement but can yield more useful source characterisation data. This paper presents a comparison between the two methods based on experimental data. The results show that, in the presence of more than one source, the beamformer cannot yield reliable estimates of the source strength of individual sources since the output from the beamformer is shown to be dependent upon the degree of correlation between multiple sources as well as the source strengths themselves. The inverse method, on the other hand, is shown to yield reliable estimates of source strength when more than one source is present, regardless of the correlation between the sources, although the results presented here are restricted to the case of a relatively small number of sources. It is clearly demonstrated, both theoretically and through carefully controlled experiments, that either method can be used effectively under reverberant conditions through the use of measured Green functions in place of the simple geometrically-derived free-space values of the Green function. This greatly improves the possibility for the successful use of these methods in many important industrial applications.