<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

Measure of Ordering in Statistical Systems

In this paper, we introduce a phenomenological measure of ordering in statistical systems. Using this characteristic, we construct a formal model of a system evolving according to the law of steepest ascent as the control parameter increases.     

Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001     

A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.     

Electron-level dynamics in the presence of impurities and the Ruijsenaars-Schneider model

The dynamic equations for the energy level of a finite system with impurities are shown to be equivalent to the rational Ruijsenaars-Schneider system. The action, which is simultaneously the generating function of the Bäcklund canonical transformation for this system, is calculated. Various variants of statistical averaging of the energy-level distribution are discussed.     

Local effect of electric and magnetic fields on the position of an attached shock in a supersonic diffuser

Effective ways for controlling shock wave configurations by means of external actions are sought. One such way is a local effect of electric and magnetic fields. In this paper, the local effect of external fields is implemented by current localization in a limited region of a diffuser. The experiment is carried out in a diffuser providing the complete internal compression of the gas with a Mach number at the inlet M=4.3. As a working medium, a xenon plasma is used. The plasma flow is formed in a shock tube equipped with an accelerating nozzle. Two ways of current localization are tested. In the first one, the diffuser inlet is a short channel of Faraday generator type. In this case, the ponderomotive force basically decelerates or accelerates the flow depending on the direction of the electric field. In the second way, the current flows through a narrow near-wall region between adjacent electrodes. In this case, the ponderomotive force compresses or expands the gas. In both cases, it is shown that the angle of an attached shock due to MHD interaction can be both decreased and increased. The central problem with the MHD control of shock waves is near-electrode and near-wall phenomena.     

Photo-orientation at liquid crystal—polymer interfaces

It is suggested that liquid crystal—polymer interfaces are coupled systems, in which the components mutually influence the orientational state of each other. The photo-orientation process at liquid crystal-polymer interfaces provides a striking example of such a coupling. Experiments show that the anisotropic structure generated by polarised light at a polymer surface is strongly affected by the phase of the liquid crystal covering the polymer. Photo-orientation is significantly more efficient when the liquid crystal is in the isotropic phase than when it exhibits orientational order. The observations are interpreted by assuming that in the smectic and nematic phases the liquid crystal stabilises to a large extent polymer chain-segments aligned parallel to the director, while it blocks the photo-induced formation of chain-segments in the perpendicular direction. Other situations, in which the coupling between the liquid crystal and the polymer can be important, are also discussed briefly.     

Phonon scattering from the boundaries of small crystals embedded in a dielectric porous-glass matrix

The thermal conductivity of porous glass with randomly distributed connecting pores ～70 Å in size (glass porosity ～25%), as well as of a porous glass + NaCl composite, was measured in the temperature range 5–300 K. NaCl filled one fourth of the pores in the composite. The experimental results on the composite thermal conductivity can be accounted for only by assuming that phonons scatter from the boundaries of NaCl nanocrystals embedded in channels of the porous glass.