The web graph of a tourism system

The website network of a tourism destination is examined. Network theoretic metrics are used to gauge the static and dynamic characteristics of the webspace. The topology of the network is found partly similar to the one exhibited by similar systems. However, some differences are found, mainly due to the relatively poor connectivity and clusterisation of the network. These results are interpreted by considering the formation mechanisms and the connotation of the linkages between websites. Clustering and assortativity coefficients are proposed as quantitative estimations of the degree of collaboration and cooperation among destination stakeholders.     

Classical and quantum self amplified spontaneous emission in a high gain free electron laser

We describe the quantum theory and the photon statistics of self amplified spontaneous emission (SASE) in a high gain free electron laser (FEL) using Glauber's quantum theory of coherence. We generalize a previous theory by taking into account many-mode effects and the initiation process resulting from classical shot noise, quantum noise, an injected coherent field and coherent bunching. In particular, we define the concept of quantum SASE which is appropriate when the initial quantum fluctuations dominate over the classical shot noise. We also discuss the conditions for the observation. Quantum SASE is a new quantum phenomenon in which the single electron uncertainty fluctuations of the conjugate variables position and momentum produce exponential amplification of the vacuum field.     

Effect of carbon nanotubes on phase transitions of nematic liquid crystals

Phase diagrams of multi-wall carbon nanotube (MWNT)/nematic liquid crystal (E7) and buckminsterfullerene (C₆₀-I _h)/nematic liquid crystal (E7) binary systems have been investigated by means of polarizing optical microscopy and differential scanning calorimetry. It was found that the isotropic-nematic phase transition temperature (T _NI) of the liquid crystal component was enhanced by the incorporation of MWNT within a small composition gap. A chimney-type phase diagram can be identified in the MWNT/E7 mixture over a narrow range of ∼0.1-0.2% MWNT concentration. Upon substituting the nanotubes with isotropic fillers such as fullerene, the (C₆₀-I _h)/E7 blend showed no discernible change of T _NI in the same concentration range of the chimney of the MWNT/E7 mixture, suggesting a significant contribution of anisotropy (or the aspect ratio) of the nanotubes to the entropy of the system containing liquid crystal molecules. This enhanced T _NI phenomenon may be attributed to anisotropic alignment of liquid crystal molecules along the carbon nanotube bundles.     

An efficient catalytic system for cyclocarbonylation of terpenes into lactones

Three different kinds of representative monoterpenic alcohol are involved in the palladium‐catalysed cyclocarbonylation reaction. Lactone formation is shown to occur when cyclic ( 1 ), tertiary ( 3 ) and primary allylic alcohol ( 7 ) functions are reacted, in the presence of CO with [HPd(SnCl₃)L₂] as the active catalytic species. Good yields and selectivities can easily be reached for isopulegol ( 1 ), and dihydromyrcenol ( 3 ). However, more modest results are obtained for the functionalization of geraniol into the original lactone ( 9 ). This lactone can be largely favoured by using a basic chelating diphosphine ligand such as 1,4‐bis(diphenylphosphino)butane. Copyright © 2005 John Wiley & Sons, Ltd.     

Mean oscillation of functions and the Paley-Wiener space

The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown. Acknowledgements and Notes. Supported in part by NSF grants DMS 9303363 and DMS 9623251.     

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.     

Canonical Quantum Gravity on the Space of Vassiliev Invariants

I review some recent results on canonicalquantum gravity in the spin network representation. Aset of ambient isotopy spin network invariants isintroduced. These invariants are the natural extensionto spin networks of the Vassiliev invariants. Itis shown that this set is loop differentiable in thesense of distributions. The quantum gravity constraintsare written in terms of loop derivatives. It is explicitly shown that Vassiliev invariantssolve the diffeomorphism constraint. The regularizedAshtekar Hamiltonian constraint is studied, and itsaction on valence-four Vassiliev invariantsdiscussed.     

A note on forced vibrations of a clamped rectangular plate

Simple polynomial approximations and Galerkin's method are used to determine the response of a thin, elastic, rectangular plate clamped along the boundary and subjected to sinusoidal excitation. It also is shown that a one-term polynomial solution yields good accuracy in the case of a rectangular plate with simply supported edges.     

A Bayes sensitivity analysis when using the beta distribution as aprior

Results that illustrate the determination of the parameters of a beta prior distribution when either the mean and one percentile or two percentiles are given are presented. Further results show how sensitive the parameters of the beta prior are to errors in the given values. The sensitivity of the probability distribution of the reliability of a system to errors in either the given mean and percentile or the given percentiles of the component beta priors is studied. Included in the study are several systems, ranging from simple ones that occur as subsystems of real systems up to a real type of system consisting of 74 components