On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

Structures and negative thermal expansion properties of the one-dimensional cyanides, CuCN, AgCN and AuCN

The behaviour of the lattice parameters of HTCuCN (high-temperature form), AgCN and AuCN have been investigated as a function of temperature over the temperature range 90–490 K. All materials show one-dimensional negative thermal expansion (NTE) along the ––(M––CN)–– chain direction c (ac(HT-CuCN) ¼32.1 10–6 K1, ac(AgCN)¼23.910–6 K1 and ac(AuCN) ¼9.3106 K1 over the temperature range 90–490 K). The origin of this behaviour has been studied using RMC modelling of Bragg and total neutron diffraction data from AgCN and AuCN at 10 and 300 K. These analyses yield details of the local motions within the chains responsible for NTE. The low-temperature form of CuCN, LT-CuCN, has been studied using single-crystal X-ray diffraction. In this form of CuCN, wavelike distortions of the ––(Cu––CN)–– chains occur in the static structure, which are reminiscent of the motions seen in the RMC modelling of AgCN and AuCN, which are responsible for the NTE behaviour.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Stability of solutions of linear difference equations with periodic coefficients

This paper represents the last technical contribution of Professor Patrick Parks before his untimely death in February 1995. The remaining authors of the paper, which was subsequently completed, wish to dedicate the article to Patrick. A frequency criterion for the stability of solutions of linear difference equations with periodic coefficients is established. The stability criterion is based on a consideration of the behaviour of a frequency hodograph with respect to the origin of coordinates in the complex plane. The formulation of this criterion does not depend on the order of the difference equation.

Minimum jerk trajectory control for rehabilitation and haptic applications

Smooth trajectories are essential for safe interaction in between human and a haptic interface. Different methods and strategies have been introduced to create such smooth trajectories. This paper studies the creation of human-like movements in haptic interfaces, based on the study of human arm motion. These motions are intended to retrain the upper limb movements of patients that lose manipulation functions following stroke. We present a model that uses higher degree polynomials to define a trajectory and control the robot arm to achieve minimum jerk movements. It also studies different methods that can be driven from polynomials to create more realistic human-like movements for therapeutic purposes.

Explaining deviations from NAV in UK property companies: rationality and sentimentality

One of the most vexing issues for analysts and managers of property companies across Europe has been the existence and persistence of deviations of Net Asset Values of property companies from their market capitalisation. The issue has clear links to similar discounts and premiums in closed-end funds. The closed end fund puzzle is regarded as an important unsolved problem in financial economics undermining theories of market efficiency and the Law of One Price. Consequently, it has generated a huge body of research. Although it can be tempting to focus on the particular inefficiencies of real estate markets in attempting to explain deviations from NAV, the closed end fund discount puzzle indicates that divergences between underlying asset values and market capitalisation are not a ‘pure’ real estate phenomenon. When examining potential explanations, two recurring factors stand out in the closed end fund literature as often undermining the economic rationale for a discount – the existence of premiums and cross-sectional and periodic fluctuations in the level of discount/premium. These need to be borne in mind when considering potential explanations for real estate markets. There are two approaches to investigating the discount to net asset value in closed-end funds: the ‘rational’ approach and the ‘noise trader’ or ‘sentiment’ approach. The ‘rational’ approach hypothesizes the discount to net asset value as being the result of company specific factors relating to such factors as management quality, tax liability and the type of stocks held by the fund. Despite the intuitive appeal of the ‘rational’ approach to closed-end fund discounts the studies have not successfully explained the variance in closed-end fund discounts or why the discount to net asset value in closed-end funds varies so much over time. The variation over time in the average sector discount is not only a feature of closed-end funds but also property companies. This paper analyses changes in the deviations from NAV for UK property companies between 2000 and 2003. The paper present a new way to study the phenomenon ‘cleaning’ the gearing effect by introducing a new way of calculating the discount itself. We call it “ungeared discount”. It is calculated by assuming that a firm issues new equity to repurchase outstanding debt without any variation on asset side. In this way discount does not depend on an accounting effect and the analysis should better explain the effect of other independent variables.

Valuation accuracy: reconciling the timing of the valuation and sale

Carsberg (2002) suggested that the periodic valuation accuracy studies undertaken by, amongst others, IPD/Drivers Jonas (2003) should be undertaken every year and be sponsored by the RICS, which acts as the self-regulating body for valuations in the UK. This paper does not address the wider issues concerning the nature of properties which are sold and whether the sale prices are influenced by prior valuations, but considers solely the technical issues concerning the timing of the valuation and sales data. This study uses valuations and sales data from the Investment Property Databank UK Monthly Index to attempt to identify the date that sale data is divulged to valuers. This information will inform accuracy studies that use a cut-off date as to the closeness of valuations to sales completion date as a yardstick for excluding data from the analysis. It will also, assuming valuers are informed quickly of any agreed sales, help to determine the actual sale agreed date rather than the completion date, which includes a period of due diligence between when the sale is agreed and its completion. Valuations should be updated to this date, rather than the formal completion date, if a reliable measure of valuation accuracy is to be determined. An accuracy study is then undertaken using a variety of updating periods and the differences between the results are examined. The paper concludes that the sale only becomes known to valuers in the month prior to the sale taking place and that this assumes either that sales due diligence procedures are shortening or valuers are not told quickly of agreed sale prices. Studies that adopt a four-month cut-off date for any valuations compared to sales completion dates are over cautious, and this could be reduced to two months without compromising the data.

Appraiser behaviour and appraisal smoothing: some qualitative and quantitative evidence

There is a substantial literature which suggests that appraisals are smoothed and lag the true level of prices. This study combines a qualitative interview survey of the leading fund manager/owners in the UK and their appraisers with a empirical study of the number of appraisals which change each month within the IPD Monthly Index. The paper concentrates on how the appraisal process operates for commercial property performance measurement purposes. The survey interviews suggest that periodic appraisal services are consolidating in fewer firms and, within these major firms, appraisers adopt different approaches to changing appraisals on a period by period basis, with some wanting hard transaction evidence while others act on "softer' signals. The survey also indicates a seasonal effect with greater effort and information being applied to annual and quarterly appraisals than monthly. The analysis of the appraisals within the Investment Property Databank Monthly Index confirms this effect with around 5% more appraisals being moved at each quarter day than the other months. January and August have significantly less appraisal changes than other months.

Evidence for the chaotic origin of Northern Annular Mode variability

Exponential spectra are found to characterize variability of the Northern Annular Mode (NAM) for periods less than 36 days. This corresponds to the observed rounding of the autocorrelation function at lags of a few days. The characteristic persistence timescales during winter and summer is found to be ∼5 days for these high frequencies. Beyond periods of 36 days the characteristic decorrelation timescale is ∼20 days during winter and ∼6 days in summer. We conclude that the NAM cannot be described by autoregressive models for high frequencies; the spectra are more consistent with low-order chaos. We also propose that the NAM exhibits regime behaviour, however the nature of this has yet to be identified.

Periodic time series modeling of environmental proxy records with guaranteed positive growth rate estimation

Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I

Fruit and vegetables, and the role they have played in determining the EU’s aggregate measurement of support

In its periodic declarations of domestic support to the WTO, the EU has progressively reduced its amber-box declarations in line with its changing system of farm support. Surprisingly, however, in 2007/08 it managed to more than halve its amber box compared with that of the previous year, easily achieving the reduction targets being touted in the Doha Round. This was largely due to a change in the calculations for fresh fruits and vegetables. These had been linked to the entry price system, which was not affected by the 2008 fruit and vegetables reform. Why the EU chose to make this change during the ongoing Doha Round negotiations remains unclear.

Appraiser behaviour and appraisal smoothing: some qualitative and quantitative evidence

There is a substantial literature which suggests that appraisals are smoothed and lag the true level of prices. This study combines a qualitative interview survey of the leading fund manager/owners in the UK and their appraisers with a empirical study of the number of appraisals which change each month within the IPD Monthly Index. The paper concentrates on how the appraisal process operates for commercial real estate performance measurement purposes. The survey interviews suggest that periodic appraisal services are consolidating in fewer firms and, within these major firms, appraisers adopt different approaches to changing appraisals on a period by period basis, with some wanting hard transaction evidence while others act on ‘softer’ signals. The survey also indicates a seasonal effect with greater effort and information being applied to annual and quarterly appraisals than monthly. The analysis of the appraisals within the IPD Monthly Index confirms this effect with around 5% more appraisals being moved at each quarter day than the other months. More November appraisals change than expected and this suggests that the increased information flows for the December end year appraisals are flowing through into earlier appraisals, especially as client/appraiser draft appraisal meetings for the December appraisals, a regular occurrence in the UK, can occur in November. January illustrates significantly less activity than other months, a seasonal effect after the exertions of the December appraisals.

Frontiers and borderlands in Imperial perspectives: exploring Rome’s Egyptian frontier

Archaeological research has addressed imperial frontiers for more than a century. Romanists, in particular, have engaged in exploring frontiers from economic, militaristic, political, and (more recently) social vantages. This article suggests that we also consider the dialogue between space and social perception to understand imperial borderland developments. In addition to formulating new theoretical approaches to frontiers, this contribution represents the first comprehensive overview of both the documentary sources and the archaeological material found in Egypt's Great Oasis during the Roman period (ca. 30 B.C.E. to the sixth century C.E.). A holistic analysis of these sources reveals that Egypt's Great Oasis, which consisted of two separate but linked oases, served as a conceptual, physical, and human buffer zone for the Roman empire. This buffer zone protected the "ordered" Nile Valley inhabitants from the "chaotic" desert nomads, who lived just beyond the oases. This conclusion suggests that nomads required specific imperial frontier policies and that these policies may have been ideological as well as economic and militaristic.