Young's inequality in trace-class operators

 If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥₁ denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality. Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003 Mathematics Subject Classification (2000): 47A63, 15A60     

Compensating intermodal dispersion in photonic crystal directional couplers

Intermodal dispersion between the supermodes of a directional coupler may induce undesirable pulse breakup in a sufficiently large device. When this happens the device will no longer exchange power between its arms, and the extinction ratio is completely canceled. It is shown that, by carefully designing the coupling area of the directional coupler, one may compensate for intermodal dispersion. The compensating device should accomplish three basic requirements: inverse intermodal dispersion, balanced coupling of each supermode, and maximum power transfer while preserving the sign of the slope of the coupling coefficient with frequency for multiplexing-demultiplexing applications. This structure is designed and optimized with a genetic algorithm.     

Poly(butylene terephthalate)/phenoxy blends: Synergistic behavior in mechanical properties

The mechanical properties of miscible poly(butylene terephthalate) (PBT)/poly (hydroxy ether of bisphenol A) (phenoxy) blends obtained by melt mixing have been studied by means of the tensile test. The crystallinity of the blends has been studied by means of DSC and density measurements. A synergistic behavior, principally in the break properties, at high PBT contents in the blends is observed. As can be seen from the torque and density data, this synergistic behavior is related with the high level of miscibility which seems to exist at high PBT contents compared with that of the high phenoxy content region.     

Observation of resonant behavior in the energy velocity of diffused light

In this Letter we demonstrate Mie resonances mediated transport of light in randomly arranged, monodisperse dielectric spheres packed at high filling fractions. By means of both static and dynamic optical experiments we show resonant behavior in the key transport parameters and, in particular, we find that the energy transport velocity, which is lower than the group velocity, also displays a resonant behavior.     

Structural phase transformations and physical properties of intercalation compounds in the Cr0.5Ti(Se1−x Tex)2 system

The atomic structure and magnetic and electric properties of the Cr_0.5TiSe₂-Cr_0.5TiTe₂ system of intercalated phases were studied in detail by gradually replacing selenium by tellurium. It was revealed that this replacement changes the crystalline structure from monoclinic in the initial compounds to hexagonal in the compounds containing various types of chalcogen atoms; this is accompanied by disordering of chromium atoms in the van der Waals gaps. The electrical resistance and magnetic characteristics vary nonmonotonically on replacement of selenium by tellurium, which is associated with a change in the degree of atomic disordering during the transition from Cr_0.5TiSe₂ to Cr_0.5TiTe₂.     

Modelling the soundscape quality of urban waterfronts by artificial neural networks

The renewal of the urban waterfronts has become a major focus of attention for politicians and decision makers in the city’s management programs. The recognition of the patterns that define the waterfronts’ identity is essential to select new strategies of intervention for the environmental recovery. In order to create adequate environments for everyday life within a sustainable development, new links between human senses, human perception and design need to be created. Within this wide approach, the landscape and the soundscape play a significant role and can become a key driving force in the implementation of the changes. New techniques have to be tested to identify the sonic and visual parameters capable to explain the specificity of a waterfront. With this purpose, an artificial neural network (ANN) was developed, and the relative importance of the input variables was evaluated. The collected database was also analysed by multiple linear regression (MLR) to compare the outcomes of both models. The urban waterfront of Naples (Italy) was chosen as case study. The results obtained show that the performance of the neural network is better than the one of the linear regression (rANN = 0.949, rMLR = 0.639). The interpretation of the relative importance method is also quite satisfactory in the ANN.     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

Neutron diffraction study of the magnetic ordering in the series R 2 BaNiO 5 (R = Rare Earth)

A neutron diffraction study, as a function of temperature, of the title compounds is presented. The whole family (space group Immm, a ≈ 3.8?, b ≈ 5.8?, c ≈ 11.3?) is structurally characterised by the presence of flattened NiO₆ octahedra that form chains along the a-axis, giving rise to a strong Ni-O-Ni antiferromagnetic interaction. Whereas for Y-compound only strong 1D correlations exist above 1.5 K, presenting the Haldane gap characteristic of 1D AF chain with integer spin, 3D AF ordering is established simultaneously for both R and Ni sublattices at temperatures depending on the rare earth size and magnetic moment. The magnetic structures of R₂BaNiO₅ ( R = Nd, Tb, Dy, Ho, Er and Tm) have been determined and refined as a function of temperature. The whole family orders with a magnetic structure characterised by the temperature-independent propagation vector = (1/2, 0, 1/2). At 1.5 K the directions of the magnetic moments differ because of the different anisotropy of the rare earth ions. Except for Tm and Yb (which does not order above 1.5 K), the magnetic moment of the R³⁺ cations are close to the free-ion value. The magnetic moment of Ni²⁺ is around 1.4 , the strong reduction with respect to the free-ion value is probably due to a combination of low-dimensional quantum effects and covalency. The thermal evolution of the magnetic structures from T _N down to 1.5 K is studied in detail. A smooth re-orientation, governed by the magnetic anisotropy of R³⁺, seems to occur below and very close to T _N in some of these compounds: the Ni moment rotates from nearly parallel to the a-axis toward the c-axis following the R moments. We demonstrate that for setting up the 3D magnetic ordering the R-R exchange interactions cannot be neglected. Received 19 July 2001