On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Modal Extraction for Wind Turbines using Moving Window Subspace Identification

This paper proposes a method for wind turbine mode identification using the multivariable output error statespace (MOESP) identification algorithm. The paper incorporates a fast moving window QR decomposition and propagator method from array signal processing, yielding a moving window subspace identification algorithm. The algorithm assumes that the system order is known as a priori and remains constant during identification. For the purpose of extracting modal information for turbines modelled as a linear parameter varying (LPV) system, the algorithm is applicable since a nonlinear system can be approximated as a piecewise time invariant system in consecutive data windows. The algorithm is exemplified using numerical simulations which show that the moving window algorithm can track the modal information. The paper also demonstrates that the low computational burden of the algorithm, compared to conventional batch subspace identification, has significant implications for online implementation.

Radiocarbon peat chronologies and environmental change

Raised bog peat deposits form important archives for reconstructing past changes in climate. Precise and reliable age models are of vital importance for interpreting such archives. We propose enhanced, Markov chain Monte Carlo based methods for obtaining age models from radiocarbon-dated peat cores, based on the assumption of piecewise linear accumulation. Included are automatic choice of sections, a measure of the goodness of fit and outlier downweighting. The approach is illustrated by using a peat core from the Netherlands.

Rasch Analysis of the Daily Living Tasks Dependent on Vision (DLTV)

PURPOSE. To examine internal consistency, refine the response scale, and obtain a linear scoring system for the visual function instrument, the Daily Living Tasks Dependent on Vision (DLTV). METHODS. Data were available from 186 participants with a clinical diagnosis of AMD who completed the 22-item DLTV (DLTV-22) according to four-point ordinal response scale. An independent group of 386 participants with AMD were administered a reduced version of the DLTV with 11 items (DLTV-11), according to a five-point response scale. Rasch analysis was performed on both datasets and used to generate item statistics for measure order, response odds ratios per item and per person, and infit and outfit mean square statistics. The Rasch output from the DLTV-22 was examined to identify redundant items and for factorial validity and person item measure separation reliabilities. RESULTS. The average rating for the DLTV-22 changed monotonically with the magnitude of the latent person trait. The expected versus observed average measures were extremely close, with step calibrations evenly separated for the four-point ordinal scale. In the case of the DLTV-11, step calibrations were not as evenly separated, suggesting that the five-point scale should be reduced to either a four- or three-point scale. Five items in the DLTV-22 were removed, and all 17 remaining items had good infit and outfit mean squares. PCA with residuals from Rasch analysis identified two domains containing 7 and 10 items each. The domains had high person separation reliabilities (0.86 and 0.77 for domains 1 and 2, respectively) and item measure reliabilities (0.99 and 0.98 for domains 1 and 2, respectively). CONCLUSIONS. With the improved internal consistency, establishment of the accuracy and precision of the rating scale for the DLTV and the establishment of a valid domain structure we believe that it constitutes a useful instrument for assessing visual function in older adults with age-related macular degeneration.

Vortex-induced vibrations of a rigid cylinder on elastic supports with endstops. Part 1: Experimental Results

This paper describes an experimental investigation into the effect of restricting the vortex-induced vibrations of a spring-mounted rigid cylinder by means of stiff mechanical endstops. Cases of both asymmetric and symmetric restraint are investigated. Results show that limiting the amplitude of the vibrations strongly affects the dynamics of the cylinder, particularly when the offset is small. Fluid-structure interaction is profoundly affected, and the well-known modes of vortex shedding observed with a linear elastic system are modified or absent. There is no evidence of lock-in, and the dominant impact frequency corresponds to a constant Strouhal number of 0.18. The presence of an endstop on one side of the motion can lead to large increases in displacements in the opposite direction. Attention is also given to the nature of the developing chaotic motion, and to impact velocities, which in single-sided impacts approach the maximum velocity of a cylinder with linear compliance undergoing VIV at lock-in. With symmetrical endstops, impact velocities were about one-half of this. Lift coefficients are computed from an analysis of the cylinder’s motion between impacts.

A-level Mathematics Options – Views of Secondary-level Teachers

The A-level Mathematics qualification is based on a compulsory set of pure maths modules and a selection of applied maths modules with the pure maths representing two thirds of the assessment. The applied maths section includes mechanics, statistics and (sometimes) decision maths. A combination of mechanics and statistics tends to be the most popular choice by far. The current study aims to understand how maths teachers in secondary education make decisions regarding the curriculum options and offers useful insight to those currently designing the new A-level specifications.

Semi-structured interviews were conducted with A-level maths teachers representing 27 grammar schools across Northern Ireland. Teachers were generally in agreement regarding the importance of pure maths and the balance between pure and applied within the A-level maths curriculum. A wide variety of opinions existed concerning the applied options. While many believe that the basic mechanics-statistics (M1-S1) combination is most accessible, it was also noted that the M1-M2 combination fits neatly alongside A-level physics. Lack of resources, timetabling constraints and competition with other subjects in the curriculum hinder uptake of A-level Further Maths.

Teachers are very conscious of the need to obtain high grades to benefit both their pupils and the school’s reputation. The move to a linear assessment system in England while Northern Ireland retains the modular system is likely to cause some schools to review their choice of exam board although there is disagreement as to whether a modular or linear system is more advantageous for pupils. The upcoming change in the specification offers an opportunity to refresh the assessment also and reduce the number of leading questions. However, teachers note that there are serious issues with GCSE maths and these have implications for A-level.

Thin-shell instability in collisionless plasma

Thin-shell instability is one process which can generate entangled structures in astrophysical plasma on collisional (fluid) scales. It is driven by a spatially varying imbalance between the ram pressure of the inflowing upstream plasma and the downstream's thermal pressure at a nonplanar shock. Here we show by means of a particle-in-cell simulation that an analog process can destabilize a thin shell formed by two interpenetrating, unmagnetized, and collisionless plasma clouds. The amplitude of the shell's spatial modulation grows and saturates after about ten inverse proton plasma frequencies, when the shell consists of connected piecewise linear patches.

The effects of transients on photospheric and chromospheric power distributions

We have observed a quiet Sun region with the Swedish 1-meter Solar Telescope (SST) equipped with CRISP Imaging SpectroPolarimeter. High-resolution, high-cadence, H-alpha line scanning images were taken to observe different layers of the solar atmosphere from the photosphere to upper chromosphere. We study the distribution of power in different period-bands at different heights. Power maps of the upper photosphere and the lower chromosphere show suppressed power surrounding the magnetic-network elements, known as "magnetic shadows". These also show enhanced power close to the photosphere, traditionally referred to as"power halos". The interaction between acoustic waves and inclined magnetic fields is generally believed to be responsible for these two effects. In this study we explore if small-scale transients can influence the distribution of power at different heights. We show that the presence of transients, like mottles, Rapid Blueshifted Excursions (RBEs) and Rapid Redshifted Excursions (RREs), can strongly influence the power-maps. The short and finite lifetime of these events strongly affects all powermaps, potentially influencing the observed power distribution. We show that Doppler-shifted transients like RBEs and RREs that occur ubiquitously, can have a dominant effect on the formation ofthe power halos in the quiet Sun. For magnetic shadows, transients like mottles do not seem to have a significant effect in the power suppression around 3 minutes and wave interaction may play a key role here. Our high cadence observations reveal that flows, waves and shocks manifest in presence of magnetic fields to form a non-linear magnetohydrodynamic system.

Differential expression of components of the cardiomyocyte adrenomedullin/intermedin receptor system following blood pressure reduction in nitric oxide-deficient hypertension.

Adrenomedullin (AM) and intermedin (IMD; adrenomedulln-2) are vasodilator peptides related to calcitonin gene-related peptide (CGRP). The actions of these peptides are mediated by the calcitonin receptor-like receptor (CLR) in association with one of three receptor activity-modifying proteins. CGRP is selective for CLR/receptor activity modifying protein (RAMP)1, AM for CLR/RAMP2 and -3, and IMD acts at both CGRP and AM receptors. In a model of pressure overload induced by inhibition of nitric-oxide synthase, up-regulation of AM was observed previously in cardiomyocytes demonstrating a hypertrophic phenotype. The current objective was to examine the effects of blood pressure reduction on cardiomyocyte expression of AM and IMD and their receptor components. Nomega-nitro-L-arginine methyl ester (L-NAME) (35 mg/kg/day) was administered to rats for 8 weeks, with or without concurrent administration of hydralazine (50 mg/kg/day) and hydrochlorothiazide (7.5 mg/kg/day). In left ventricular cardiomyocytes from L-NAME-treated rats, increases (-fold) in mRNA expression were 1.6 (preproAM), 8.4 (preproIMD), 3.4 (CLR), 4.1 (RAMP1), 2.8 (RAMP2), and 4.4 (RAMP3). Hydralazine/hydrochlorothiazide normalized systolic blood pressure (BP) and abolished mRNA up-regulation of hypertrophic markers sk-alpha-actin and BNP and of preproAM, CLR, RAMP2, and RAMP3 but did not normalize cardiomyocyte width nor preproIMD or RAMP1 mRNA expression. The robust increase in IMD expression indicates an important role for this peptide in the cardiac pathology of this model but, unlike AM, IMD is not associated with pressure overload upon the myocardium. The concordance of IMD and RAMP1 up-regulation indicates a CGRP-type receptor action; considering also a lack of response to BP reduction, IMD may, like CGRP, have an anti-ischemic function.

Model selection approaches for non-linear system identification: a review

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

Iterative Multiuser Detection and Decoding for DS-CDMA System With Space-Time Linear Dispersion

This paper considers a Q-ary orthogonal direct-sequence code-division multiple-access (DS-CDMA) system with high-rate space-time linear dispersion codes (LDCs) in time-varying Rayleigh fading multiple-input-multiple-output (MIMO) channels. We propose a joint multiuser detection, LDC decoding, Q-ary demodulation, and channel-decoding algorithm and apply the turbo processing principle to improve system performance in an iterative fashion. The proposed iterative scheme demonstrates faster convergence and superior performance compared with the V-BLAST-based DS-CDMA system and is shown to approach the single-user performance bound. We also show that the CDMA system is able to exploit the time diversity offered by the LDCS in rapid-fading channels.