Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size. (c) 2007 Elsevier B.V. All rights reserved.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

The effect of monocular and binocular cataract blur on postural stability among older adults

Purpose: First-eye cataract surgery can reduce the rate of falls among older adults, yet the effect of second-eye surgery on the rate of falling remains unclear. The present study investigated the effect of monocular and binocular simulated cataract blur on postural stability among older adults. Methods: Postural stability was assessed on 34 healthy older adults (mean 68.2 years, SD 3.5) with normal vision, using a portable force platform (BT4, HUR Labs, Finland) which collected data on centre of pressure (COP) displacement. Stability was assessed on firm and foam surfaces under four binocular viewing conditions using Vistech filters to simulate cataract blur: [1] best-corrected vision both eyes; [2] blur over non-dominant eye, [3] blur over dominant eye and [4] blur over both eyes. Binocular logMAR visual acuity, Pelli-Robson contrast sensitivity and stereoacuity were also measured under these viewing conditions and ocular dominance measured using the hole-in-card test. Generalized estimating equations with an exchangeable correlation structure examined the effect of the surface and vision conditions on postural stability. Results: Visual acuity and contrast sensitivity were significantly reduced under monocular and binocular cataract blur compared to normal viewing. All blur conditions resulted in loss of stereoacuity. Binocular cataract blur significantly reduced postural stability compared to normal vision on the firm (COP path length; p=0.013) and foam surface (anterior-posterior COP RMS, COP path length and COP area; p<0.01). However, no significant differences in postural stability were found between the monocular blur conditions compared to normal vision, or between the dominant and non-dominant monocular blur conditions on either the firm or foam surfaces. Conclusions: Findings indicate that binocular blur significantly impairs postural stability, and suggests that improvements in postural stability may justify first-eye cataract surgery, particularly during somatosensory disruption. Postural stability was not significantly impaired in the monocular cataract blur conditions compared to the normal vision condition, nor was there any effect of ocular dominance on postural stability in the presence of monocular cataract blur.

Impacts of different wind power generators on power system small signal and transient stability

With the ever-increasing penetration level of wind power, the impacts of wind power on the power system are becoming more and more significant. Hence, it is necessary to systematically examine its impacts on the small signal stability and transient stability in order to find out countermeasures. As such, a comprehensive study is carried out to compare the dynamic performances of power system respectively with three widely-used power generators. First, the dynamic models are described for three types of wind power generators, i. e. the squirrel cage induction generator (SCIG), doubly fed induction generator (DFIG) and permanent magnet generator (PMG). Then, the impacts of these wind power generators on the small signal stability and transient stability are compared with that of a substituted synchronous generator (SG) in the WSCC three-machine nine-bus system by the eigenvalue analysis and dynamic time-domain simulations. Simulation results show that the impacts of different wind power generators are different under small and large disturbances.

Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Can measures of limb loading and dynamic stability during the squat maneuver provide an index of early functional recovery following unilateral total hip arthroplasty?

Objective: To investigate limb loading and dynamic stability during squatting in the early functional recovery of total hip arthroplasty (THA) patients. Design: Cohort study Setting: Inpatient rehabilitation clinic. Participants: A random sample of 61 THA patients (34♂/27♀; 62±9 yrs, 77±14 kg, 174±9 cm) was assessed twice, 13.2±3.8 days (PRE) and 26.6±3.3 days post-surgery (POST), and compared with a healthy reference group (REF) (22♂/16♀; 47±12yrs; 78±20kg; 175±10cm). Interventions: THA patients received two weeks of standard in-patient rehabilitation. Main Outcome Measure(s): Inter-limb vertical force distribution and dynamic stability during the squat maneuver, as defined by the root mean square (RMS) of the center of pressure in antero-posterior and medio-lateral directions, of operated (OP) and non-operated (NON)limbs. Self-reported function was assessed via FFb-H-OA 2.0 questionnaire. Results: At PRE, unloading of the OP limb was 15.8% greater (P<.001, d=1.070) and antero-posterior and medio-lateral center of pressure RMS were 30-34% higher in THA than REF P<.05). Unloading was reduced by 12.8% towards a more equal distribution from PRE to POST (P<.001, d=0.874). Although medio-lateral stability improved between PRE and POST (OP: 14.8%, P=.024, d=0.397; NON: 13.1%, P=.015, d=0.321), antero-posterior stability was not significantly different. Self-reported physical function improved by 15.8% (P<.001, d=0.965). Conclusion(s): THA patients unload the OP limb and are dynamically more unstable during squatting in the early rehabilitation phase following total hip replacement than healthy adults. Although loading symmetry and medio-lateral stability improved to the level of healthy adults with rehabilitation, antero-posterior stability remained impaired. Measures of dynamic stability and load symmetry during squatting provide quantitative information that can be used to clinically monitor early functional recovery from THA.

Frequency of convergence and accommodative disorders in a clinical population of Mashhad, Iran

Purpose To investigate the frequency of convergence and accommodation anomalies in an optometric clinical setting in Mashhad, Iran, and to determine tests with highest accuracy in diagnosing these anomalies. Methods From 261 patients who came to the optometric clinics of Mashhad University of Medical Sciences during a month, 83 of them were included in the study based on the inclusion criteria. Near point of convergence (NPC), near and distance heterophoria, monocular and binocular accommodative facility (MAF and BAF, respectively), lag of accommodation, positive and negative fusional vergences (PFV and NFV, respectively), AC/A ratio, relative accommodation, and amplitude of accommodation (AA) were measured to diagnose the convergence and accommodation anomalies. The results were also compared between symptomatic and asymptomatic patients. The accuracy of these tests was explored using sensitivity (S), specificity (Sp), and positive and negative likelihood ratios (LR+, LR−). Results Mean age of the patients was 21.3 ± 3.5 years and 14.5% of them had specific binocular and accommodative symptoms. Convergence and accommodative anomalies were found in 19.3% of the patients; accommodative excess (4.8%) and convergence insufficiency (3.6%) were the most common accommodative and convergence disorders, respectively. Symptomatic patients showed lower values for BAF (p = .003), MAF (p = .001), as well as AA (p = .001) compared with asymptomatic patients. Moreover, BAF (S = 75%, Sp = 62%) and MAF (S = 62%, Sp = 89%) were the most accurate tests for detecting accommodative and convergence disorders in terms of both sensitivity and specificity. Conclusions Convergence and accommodative anomalies are the most common binocular disorders in optometric patients. Including tests of monocular and binocular accommodative facility in routine eye examinations as accurate tests to diagnose these anomalies requires further investigation.

Endurance exercise and DNA stability: Is there a link to duration and intensity?

It is commonly accepted that regular moderate intensity physical activity reduces the risk of developing many diseases. Counter intuitively, however, evidence also exists for oxidative stress resulting from acute and strenuous exercise. Enhanced formation of reactive oxygen and nitrogen species may lead to oxidatively modified lipids, proteins and nucleic acids and possibly disease. Currently, only a few studies have investigated the influence of exercise on DNA stability and damage with conflicting results, small study groups and the use of different sample matrices or methods and result units. This is the first review to address the effect of exercise of various intensities and durations on DNA stability, focusing on human population studies. Furthermore, this article describes the principles and limitations of commonly used methods for the assessment of oxidatively modified DNA and DNA stability. This review is structured according to the type of exercise conducted (field or laboratory based) and the intensity performed (i.e. competitive ultra/endurance exercise or maximal tests until exhaustion). The findings presented here suggest that competitive ultra-endurance exercise (>4h) does not induce persistent DNA damage. However, when considering the effects of endurance exercise (<4h), no clear conclusions could be drawn. Laboratory studies have shown equivocal results (increased or no oxidative stress) after endurance or exhaustive exercise. To clarify which components of exercise participation (i.e. duration, intensity and training status of subjects) have an impact on DNA stability and damage, additional carefully designed studies combining the measurement of DNA damage, gene expression and DNA repair mechanisms before, during and after exercise of differing intensities and durations are required.

Critical review on the stability of illicit drugs in sewers and wastewater samples

Wastewater-based epidemiology (WBE) applies advanced analytical methods to quantify drug residues in wastewater with the aim to estimate illicit drug use at the population level. Transformation processes during transport in sewers (chemical and biological reactors) and storage of wastewater samples before analysis are expected to change concentrations of different drugs to varying degrees. Ignoring transformation for drugs with low to medium stability will lead to an unknown degree of systematic under- or overestimation of drug use, which should be avoided. This review aims to summarize the current knowledge related to the stability of commonly investigated drugs and, furthermore, suggest a more effective approach to future experiments. From over 100 WBE studies, around 50 mentioned the importance of stability and 24 included tests in wastewater. Most focused on in-sample stability (i.e., sample preparation, preservation and storage) and some extrapolated to in-sewer stability (i.e., during transport in real sewers). While consistent results were reported for rather stable compounds (e.g., MDMA and methamphetamine), a varying range of stability under different or similar conditions was observed for other compounds (e.g., cocaine, amphetamine and morphine). Wastewater composition can vary considerably over time, and different conditions prevail in different sewer systems. In summary, this indicates that more systematic studies are needed to: i) cover the range of possible conditions in sewers and ii) compare results more objectively. To facilitate the latter, we propose a set of parameters that should be reported for in-sewer stability experiments. Finally, a best practice of sample collection, preservation, and preparation before analysis is suggested in order to minimize transformation during these steps.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

Effect of residual stresses and metallographic stability on the over all performance of integral diaphragm material

The integral diaphragm pressure transducer consists of a diaphragm machined from precipitation hardened martensitic (APX4) steel. Its performance is quite significant as it depends upon various factors such as mechanical properties including induced residual stress levels, metallurgical and physical parameters due to different stages of processing involved. Hence, the measurement and analysis of residual stress becomes very important from the point of in-service assessment of a component. In the present work, the stress measurements have been done using the X-ray diffraction (XRD) technique, which is a non-destructive test (NDT). This method is more reliable and widely used compared to the other NDT techniques. The metallurgical aspects have been studied by adopting the conventional metallographic practices including examination of microstructure using light microscope. The dimensional measurements have been carried out using dimensional gauge. The results of the present investigation reveals that the diaphragm material after undergoing series of realization processes has yielded good amount of retained austenite in it. Also, the presence of higher compressive stresses induced in the transducer results in non-linearity, zero shift and dimensional instability. The problem of higher retained austenite content and higher compressive stress have been overcome by adopting a new realization process involving machining and cold and hot stabilization soak which has brought down the retained austenite content to about 5–6% and acceptable level of compressive stress in the range −100 to −150 MPa with fine tempered martensitic phase structure and good dimensional stability. The new realization process seems to be quite effective in terms of controlling retained austenite content, residual stress, metallurgical phase as well as dimensional stability and this may result in minimum zero shift of the diaphragm system.

Optimal reactive power dispatch based on voltage stability criteria in a large power system with AC/DC and FACTs devices

An algorithm for optimal allocation of reactive power in AC/DC system using FACTs devices, with an objective of improving the voltage profile and also voltage stability of the system has been presented. The technique attempts to utilize fully the reactive power sources in the system to improve the voltage stability and profile as well as meeting the reactive power requirements at the AC-DC terminals to facilitate the smooth operation of DC links. The method involves successive solution of steady-state power flows and optimization of reactive power control variables with Unified Power Flow Controller (UPFC) using linear programming technique. The proposed method has been tested on a real life equivalent 96-bus AC and a two terminal DC system under normal and contingency conditions.

Producing interactivity : Does media convergence promote interactivity and audience participation?

This study investigates the process of producing interactivity in a converged media environment. The study asks whether more media convergence equals more interactivity. The research object is approached through semi-structured interviews of prominent decision makers within the Finnish media. The main focus of the study are the three big ones of the traditional media, radio, television and the printing press, and their ability to adapt to the changing environment. The study develops theoretical models for the analysis of interactive features and convergence. Case-studies are formed from the interview data and they are evaluated against the models. As a result the cases arc plotted and compared on a four-fold table. The cases are Radio Rock, NRJ, Biu Brother, Television Chat, Olivia and Sanoma News. It is found out that the theoretical models can accurately forecast the results of the case studies. The models are also able to distinguish different aspects of both interactivity and convergence so that a case, which at a first glance seems not to be very interactive is in the end found out to receive second highest scores on the analysis. The highest scores are received by Big Brother and Sanoma News. Through the theory and the analysis of the research data it is found out that the concepts of interactivity and convergence arc intimately intertwined and very hard in many cases to separate from each other. Hence the answer to the main question of this study is yes, convergence does promote interactivity and audience participation. The main theoretical background for the analysis of interactivity follows the work of Came Fleeter, Spiro Kiousis and Sally McMillan. Heeler's six-dimensional definition of interactivity is used as the basis for operationalizing interactivity. The actor-network theory is used as the main theoretical framework to analyze convergence. The definition and operationalization of the actor-network theory into a model of convergence follows the work of Michel Callon. Bruno Latour and especially John Law and Felix Stalder.

Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.