Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Automated nonlinear system modelling with multiple neural networks

This article discusses the identification of nonlinear dynamic systems using multi-layer perceptrons (MLPs). It focuses on both structure uncertainty and parameter uncertainty, which have been widely explored in the literature of nonlinear system identification. The main contribution is that an integrated analytic framework is proposed for automated neural network structure selection, parameter identification and hysteresis network switching with guaranteed neural identification performance. First, an automated network structure selection procedure is proposed within a fixed time interval for a given network construction criterion. Then, the network parameter updating algorithm is proposed with guaranteed bounded identification error. To cope with structure uncertainty, a hysteresis strategy is proposed to enable neural identifier switching with guaranteed network performance along the switching process. Both theoretic analysis and a simulation example show the efficacy of the proposed method.

Design and evaluation of tinnitus synthesis methods: From spectral to spatial matching

Purpose
This study was designed to investigate methods to help patients suffering from unilateral tinnitus synthesizing an auditory replica of their tinnitus.

Materials and methods
Two semi-automatic methods (A and B) derived from the auditory threshold of the patient and a method (C) combining a pure tone and a narrow band-pass noise centred on an adjustable frequency were devised and rated on their likeness over two test sessions. A third test evaluated the stability over time of the synthesized tinnitus replica built with method C, and its proneness to merge with the patient's tinnitus. Patients were then asked to try and control the lateralisation of this single percept through the adjustment of the tinnitus replica level.

Results
The first two tests showed that seven out of ten patients chose the tinnitus replica built with method C as their preferred one. The third test, performed on twelve patients, revealed pitch tuning was rather stable over a week interval. It showed that eight patients were able to consistently match the central frequency of the synthesized tinnitus (presented to the contralateral ear) to their own tinnitus, which leaded to a unique tinnitus percept. The lateralisation displacement was consistent across patients and revealed an average range of 29dB to obtain a full lateral shift from the ipsilateral to the contralateral side.

Conclusions
Although spectrally simpler than the semi-automatic methods, method C could replicate patients' tinnitus, to some extent. When a unique percept between synthesized tinnitus and patients' tinnitus arose, lateralisation of this percept was achieved.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Approximating the Set of Local Minima in Partial RNA Folding Landscapes

Motivation: We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

Results: The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n2D?ln?), where n is the sequence length, ? is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.

The influence of prepulse level on the 3p-3s XUV laser output from Ne-like ions of Zn, Cu and Ni

We have studied the effect of prepulses in enhancing the efficiency of generating ASE beams in soft X-ray laser plasma amplifiers based on pumping Ne-like ions, Slab targets were irradiated with a weak prepulse followed by a main plasma heating pulse of nanosecond duration, Time-integrated; time and spectrally resolved and time and angularly resolved lasing emissions on the 3p-3s (J=0-1) XUV lasing lines of Ne-like Ni, Cu and Zn at wavelengths 232 Angstrom 221 Angstrom and 212 Angstrom respectively have been monitored. Measurements were made for pre-pulse/main-pulse intensity ratios from 10(-5)-10(-1) and for pump delay times of 2 ns and 4.5 ns. Zinc is shown to exhibit a peak in output intensity at similar to 2x10(-3) pre-pulse fraction for a 4.5 ns pump delay, with a main pulse pump intensity of similar to 1.3x10(13) W cm(-2) on a 20 mm target. The Zn lasing emission had a duration of similar to 240 ps and this was insensitive to prepulse fraction. The J=0-1 XUV laser output for nickel and copper increased monotonically with prepulse fraction, with copper targets showing least sensitivity to either prepulse level or prepulse to main pulse delay. Under the conditions of the study, the pre-pulse level was observed to haveno significant influence on the output intensity of the 3p-3s (J=2-1) lines of any of the elements investigated.

THE EXPANSION HISTORY OF ALUMINUM TARGETS RELEVANT TO X-RAY LASER SCHEMES

For the first time, the technique of point projection absorption spectroscopy - which uses an intense, point source of X-rays to project and spectrally disperse an image of a plasma onto a detector- has been shown to be applicable to the study of expanding aluminium plasmas generated by approximately 80ps (2-omega) laser pulses. Massive, stripe targets of approximately 125-mu-m width and wire targets of 25-mu-m diameter have been studied. Using a PET Bragg crystal as the dispersive element, a resolving power of approximately 3500 was achieved with spatial resolution at the 5-mu-m level in frame times of the order of 80ps. Reduction of the data for times up to 150ps after the peak of the incident laser pulse produced estimates of the temperature and densities present, as a function of space and time.

Environmental pricing of externalities from different sources of electricity generation in Chile

The rapid increase in electricity demand in Chile means a choice must be made between major investments in renewable or non-renewable sources for additional production. Current projects to develop large dams for hydropower in Chilean Patagonia impose an environmental price by damaging the natural environment. On the other hand, the increased use of fossil fuels entails an environmental price in terms of air pollution and greenhouse gas emissions contributing to climate change. This paper studies the debate on future electricity supply in Chile by investigating the preferences of households for a variety of different sources of electricity generation such as fossil fuels, large hydropower in Chilean Patagonia and other renewable energy sources. Using Double Bounded Dichotomous Choice Contingent Valuation, a novel advanced disclosure method and internal consistency test are used to elicit the willingness to pay for less environmentally damaging sources. Policy results suggest a strong preference for renewable energy sources with higher environmental prices imposed by consumers on electricity generated from fossil fuels than from large dams in Chilean Patagonia. Policy results further suggest the possibility of introducing incentives for renewable energy developments that would be supported by consumers through green tariffs or environmental premiums. Methodological findings suggest that advanced disclosure learning overcomes the problem of internal inconsistency in SB-DB estimates.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Late Quaternary glaciations in Far NE Russia; combining moraines, topography and chronology to assess regional and global glaciation synchrony

During various periods of Late Quaternary glaciation, small ice-sheets, -caps, -fields and valley glaciers, occupied the mountains and uplands of Far NE Russia (including the Verkhoyansk, Suntar-Khayata, and Chersky Mountains; the KolymaeAnyuy and Koryak Highlands; and much of the Kamchatka and Chukchi
Peninsulas). Here, the margins of former glaciers across this region are constrained through the comprehensive mapping of moraines from remote sensing data (Landsat 7 ETM+ satellite images; ASTER Global Digital Elevation Model (GDEM2); and Viewfinder Panorama DEM data). A total of 8414 moraines
are mapped, and this record is integrated with a series of published age-estimates (n = 25), considered to chronologically-constrain former ice-margin positions. Geomorphological and chronological data are compiled in a Geographic Information System (GIS) to produce ‘best estimate’ reconstructions of ice extent during the global Last Glacial Maximum (gLGM) and, to a lesser degree, during earlier phases of glaciation. The data reveal that much of Far NE Russia (~1,092,427 km2) preserves a glaciated landscape (i.e. is bounded by moraines), but there is no evidence of former ice masses having extended more than 270 km beyond mountain centres (suggesting that, during the Late Quaternary, the region has not been occupied by extensive ice sheets). During the gLGM, specifically, glaciers occupied ~253,000 km2, and rarely extended more than 50 km in length. During earlier (pre-gLGM) periods, glaciers were more extensive, though the timing of former glaciation, and the maximum Quaternary extent, appears to have been asynchronous across the region, and out-of-phase with ice-extent maxima elsewhere in the Northern Hemisphere. This glacial history is partly explained through consideration of climatic-forcing
(particularly moisture-availability, solar insolation and albedo), though topographic-controls upon the former extent and dynamics of glaciers are also considered, as are topographic-controls upon moraine deposition and preservation. Ultimately, our ability to understand the glacial and climatic history of this region is restricted when the geomorphological-record alone is considered, particularly as directly-dated glacial deposits are few, and topographic and climatic controls upon the moraine record are difficult to
distinguish.

The 'Europeanization' of Reference Groups

In this paper we address the question of the relative importance of within and between country differences in income and material deprivation in the European Union in the context of recent suggestions that insufficient attention has been paid to the latter. In particular, we respond to the argument that the 'state bounded' relative income approach obscures the significance of EU-wide reference groups. Making use of EU-SILC 2004, we have sought to quantify the magnitude of relevant within and between country differences and their relative impact. Overall, our analysis supports the view that the predominant frame of reference is a national one. The limited impact of European reference groups observed in our analysis does not require explanation in terms of the emergence of a European social stratification system. Furthermore, the significance of such comparisons depends not only on the expectations of those affected by European inequalities but on the degree of legitimacy afforded to ensuing demands. While an EU-wide income-threshold can provide information regarding progress of the Union towards greater social cohesion, its usage for this purpose does not require a strong sense of European identity. Given the current status of the European Social Model, it would seem unwise to attribute an undue degree of policy relevance to the relatively modest impact of EU-wide reference groups revealed in our analysis.