Graphical Linking of MO Multicenter Bond Index and VB Structures. II- 5-c Rings and 6-c Heterocyclic Rings

Through the graphical method proposed, it is possible to create a link between an MO multicenter bond index and VB structures. The value of the index depends on the order of the atoms involved, if there are more than three. For 5-c rings, three basic structures are required; the eventually different values are 12. Unlike the 6-c case, it may happen that different pairs of basic structures are used to build the same polygon. For the 6-c rings, including heteroatoms, the original degeneracy of benzene splits, leading eventually to 60 different I_ring values.     

On measuring birefringences and dichroisms using Fabry–Pérot cavities

When measuring very small ellipticities or rotations induced on a polarized beam of light, Fabry–Pérot cavities are often used to increase the number of passes within the region of interest. In this paper we show that due to the intrinsic birefringence of the reflective surface of the cavity mirrors, a cross talk between dichroism and ellipticity is induced. We also show how such a cross talk may be measured and kept under control by means of an adequate phase locking scheme of the laser to the cavity.PACS 75.30.Gw; 07.60.Fs; 42.25.-p; 42.62.-b     

Effective Borel degrees of some topological functions

The focus of this paper is the incomputability of some topological functions (with respect to certain representations) using the tools of Borel computability theory, as introduced by V. Brattka in [3] and [4]. First, we analyze some basic topological functions on closed subsets of ?ⁿ , like closure, border, intersection, and derivative, and we prove for such functions results of Σ⁰₂‐completeness and Σ⁰₃‐completeness in the effective Borel hierarchy. Then, following [13], we re‐consider two well‐known topological results: the lemmas of Urysohn and Urysohn‐Tietze for generic metric spaces (for the latter we refer to the proof given by Dieudonné). Both lemmas define Σ⁰₂‐computable functions which in some cases are even Σ⁰₂‐complete. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computing the asymptotic worst-case of bin packing lower bounds

This paper addresses the issue of computing the asymptotic worst-case of lower bounds for the Bin Packing Problem. We introduce a general result that allows to bound the asymptotic worst-case performance of any lower bound for the problem and to derive for the first time the asymptotic worst-case of the well-known bound L₃ by Martello and Toth. We also show that the general result allows to easily derive the asymptotic worst-case of several lower bounds proposed in the literature.     

Strategies for detecting fraudulent claims in the automobile insurance industry

Some property and casualty insurers use automated detection systems to help to decide whether or not to investigate claims suspected of fraud. Claim screening systems benefit from the coded experience of previously investigated claims. The embedded detection models typically consist of scoring devices relating fraud indicators to some measure of suspicion of fraud. In practice these scoring models often focus on minimizing the error rate rather than on the cost of (mis)classification. We show that focusing on cost is a profitable approach. We analyse the effects of taking into account information on damages and audit costs early on in the screening process. We discuss several scenarios using real-life data. The findings suggest that with claim amount information available at screening time detection rules can be accommodated to increase expected profits. Our results show the value of cost-sensitive claim fraud screening and provide guidance on how to render this strategy operational.     

A concrete procedure for obtaining sharp reconstructions of unsharp observables in finite-dimensional quantum mechanics

We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined.     

System linearization via feedback: A control engineering perspective

The possibility of using feedback to achieve or to enhance system linearity is well known to control engineers since decades ago. A few major breakthroughs, made possible by the application of differential geometric tools to control theoretic issues, have revamped a new interest in all facets of the problem, including the search, the analysis and the computation of suitable approximate solutions. In the present paper, recent developments and new trends in the field are shortly reviewed, with special attention paid to some research issues currently addressed by the authors. Though primarily meant for learned mathematically oriented readers, the presentation focuses on ideas and concepts more than on their most general and mathematically rigorous formulations. On the other hand, it does not assume familiarity with advanced control theory nor modern control technology.