Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Comparison of algal and fish sources on the oxidative stability of poultry meat and its enrichment with omega-3 polyunsaturated fatty acids

Human consumption of long-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) is below recommendations, and enriching chicken meat (by incorporating LC n-3 PUFA into broiler diets) is a viable means of increasing consumption. Fish oil is the most common LC n-3 PUFA supplement used but is unsustainable and reduces the oxidative stability of the meat. The objective of this experiment was to compare fresh fish oil (FFO) with fish oil encapsulated (EFO) in a gelatin matrix (to maintain its oxidative stability) and algal biomass at a low (LAG, 11), medium (MAG, 22), or high (HAG, 33 g/kg of diet) level of inclusion. The C22:6n-3 contents of the FFO, EFO, and MAG diets were equal. A control (CON) diet using blended vegetable oil was also made. As-hatched 1-d-old Ross 308 broilers (144) were reared (21 d) on a common starter diet then allocated to treatment pens (4 pens per treatment, 6 birds per pen) and fed treatment diets for 21 d before being slaughtered. Breast and leg meat was analyzed (per pen) for fatty acids, and cooked samples (2 pens per treatment) were analyzed for volatile aldehydes. Concentrations (mg/100 g of meat) of C20:5n-3, C22:5n-3, and C22:6n-3 were (respectively) CON: 4, 15, 24; FFO: 31, 46, 129; EFO: 18, 27, 122; LAG: 9, 19, 111; MAG: 6, 16, 147; and HAG: 9, 14, 187 (SEM: 2.4, 3.6, 13.1) in breast meat and CON: 4, 12, 9; FFO: 58, 56, 132; EFO: 63, 49, 153; LAG: 13, 14, 101; MAG: 11, 15, 102; HAG: 37, 37, 203 (SEM: 7.8, 6.7, 14.4) in leg meat. Cooked EFO and HAG leg meat was more oxidized (5.2 mg of hexanal/kg of meat) than the other meats (mean 2.2 mg/kg, SEM 0.63). It is concluded that algal biomass is as effective as fish oil at enriching broiler diets with C22:6 LC n-3 PUFA, and at equal C22:6n-3 contents, there is no significant difference between these 2 supplements on the oxidative stability of the meat that is produced.

Reduced-order modelling of a high-voltage oscillatory impulse generator

The design of high-voltage equipment encompasses the study of oscillatory surges caused by transients such as those produced by switching. By obtaining a model, the response of which reconstructs that observed in the actual system, simulation studies and critical tests can be carried out on the model rather than on the equipment itself. In this paper, methods for the construction of simplified models are described and it is shown how the use of a complex model does not necessarily result in superior response pattern reconstruction.

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.

Real-time expert system for fault location on high voltage underground distribution cables

To ensure minimum loss of system security and revenue it is essential that faults on underground cable systems be located and repaired rapidly. Currently in the UK, the impulse current method is used to prelocate faults, prior to using acoustic methods to pinpoint the fault location. The impulse current method is heavily dependent on the engineer's knowledge and experience in recognising/interpreting the transient waveforms produced by the fault. The development of a prototype real-time expert system aid for the prelocation of cable faults is described. Results from the prototype demonstrate the feasibility and benefits of the expert system as an aid for the diagnosis and location of faults on underground cable systems.

The effect of the year of wheat variety release on productivity and stability of performance on two organic and two non-organic farms

Nineteen wheat cultivars, released from 1934 to 2000, were grown at two organic and two non-organic sites in each of 3 years. Assessments included grain yield, grain protein concentration, protein yield, disease incidence and green leaf area. The superiority of each cultivar (the sum of the squares of the differences between its mean in each environment and the mean of the best cultivar there, divided by twice the number of environments; CS) was calculated for yield, grain protein concentration and protein yield, and ranked in each environment. The yield and grain protein concentration CS were more closely correlated with cultivar release date at the non-organic sites than at organic sites. This difference may be attributed to higher yield levels with larger differences among cultivars at the non-organic sites, rather than to improved stability (i.e. similar ranks) across sites. The significant difference in the correlation of protein yield CS and cultivar age between organic and non-organic sites would support evidence that the ability to take up mineral nitrogen (N) compared to soil N has been a component of the selection conditions of more modern cultivars (released after 1989). This is supported by assessment of green leaf area (GLA), where more modern cultivars in the non-organic systems had greater late-season GLA, a trend that was not identified in organic conditions. This effect could explain the poor correlation between age and protein yield CS in organic compared to non-organic conditions where modern cultivars are selected to benefit from later nitrogen (N) availability which includes the spring nitrogen applications tailored to coincide with peak crop demand. Under organic management, N release is largely based on the breakdown of fertility-building crops incorporated (ploughed-in) in the previous autumn. The release of nutrients from these residues is dependent on the soil conditions, which includes temperature and microbial populations, in addition to the potential leaching effect of high winter rainfall in the UK. In organic cereal crops, early resource capture is a major advantage for maximizing the utilization of nutrients from residue breakdown. It is concluded that selection of cultivars under conditions of high agrochemical inputs selects for cultivars that yield well under maximal conditions in terms of nutrient availability and pest, disease and weed control. The selection conditions for breeding have a tendency to select cultivars which perform relatively better in non-organic compared to organic systems.

Model inter-comparison between statistical and dynamic model assessments of the long-term stability of blanket peat in Great Britain (1940-2099)

We compared output from 3 dynamic process-based models (DMs: ECOSSE, MILLENNIA and the Durham Carbon Model) and 9 bioclimatic envelope models (BCEMs; including BBOG ensemble and PEATSTASH) ranging from simple threshold to semi-process-based models. Model simulations were run at 4 British peatland sites using historical climate data and climate projections under a medium (A1B) emissions scenario from the 11-RCM (regional climate model) ensemble underpinning UKCP09. The models showed that blanket peatlands are vulnerable to projected climate change; however, predictions varied between models as well as between sites. All BCEMs predicted a shift from presence to absence of a climate associated with blanket peat, where the sites with the lowest total annual precipitation were closest to the presence/absence threshold. DMs showed a more variable response. ECOSSE predicted a decline in net C sink and shift to net C source by the end of this century. The Durham Carbon Model predicted a smaller decline in the net C sink strength, but no shift to net C source. MILLENNIA predicted a slight overall increase in the net C sink. In contrast to the BCEM projections, the DMs predicted that the sites with coolest temperatures and greatest total annual precipitation showed the largest change in carbon sinks. In this model inter-comparison, the greatest variation in model output in response to climate change projections was not between the BCEMs and DMs but between the DMs themselves, because of different approaches to modelling soil organic matter pools and decomposition amongst other processes. The difference in the sign of the response has major implications for future climate feedbacks, climate policy and peatland management. Enhanced data collection, in particular monitoring peatland response to current change, would significantly improve model development and projections of future change.

Interpretation bias and anxiety in childhood: stability, specificity and longitudinal associations

Background: Biases in the interpretation of ambiguous material are central to cognitive models of anxiety; however, understanding of the association between interpretation and anxiety in childhood is limited. To address this, a prospective investigation of the stability and specificity of anxious cognitions and anxiety and the relationship between these factors was conducted. Method: Sixty-five children (10–11 years) from a community sample completed measures of self-reported anxiety, depression, and conduct problems, and responded to ambiguous stories at three time points over one-year. Results: Individual differences in biases in interpretation of ambiguity (specifically “anticipated distress” and “threat interpretation”) were stable over time. Furthermore, anticipated distress and threat interpretation were specifically associated with anxiety symptoms. Distress anticipation predicted change in anxiety symptoms over time. In contrast, anxiety scores predicted change in threat interpretation over time. Conclusions: The results suggest that different cognitive constructs may show different longitudinal links with anxiety. These preliminary findings extend research and theory on anxious cognitions and their link with anxiety in children, and suggest that these cognitive processes may be valuable targets for assessment and intervention.

Stability of pollination services decreases with isolation from natural areas despite honey bee visits

Sustainable agricultural landscapes by definition provide high magnitude and stability of ecosystem services, biodiversity and crop productivity. However, few studies have considered landscape effects on the stability of ecosystem services. We tested whether isolation from florally diverse natural and semi-natural areas reduces the spatial and temporal stability of flower-visitor richness and pollination services in crop fields. We synthesised data from 29 studies with contrasting biomes, crop species and pollinator communities. Stability of flower-visitor richness, visitation rate (all insects except honey bees) and fruit set all decreased with distance from natural areas. At 1 km from adjacent natural areas, spatial stability decreased by 25, 16 and 9% for richness, visitation and fruit set, respectively, while temporal stability decreased by 39% for richness and 13% for visitation. Mean richness, visitation and fruit set also decreased with isolation, by 34, 27 and 16% at 1 km respectively. In contrast, honey bee visitation did not change with isolation and represented > 25% of crop visits in 21 studies. Therefore, wild pollinators are relevant for crop productivity and stability even when honey bees are abundant. Policies to preserve and restore natural areas in agricultural landscapes should enhance levels and reliability of pollination services.

Novel margin management to enhance Auchenorrhyncha biodiversity in intensive grasslands

Agricultural intensification, including changes in cutting, grazing and fertilizer regimes, has led to declines in UK and NW European grassland biodiversity. We aimed to develop field margin management practices that would support invertebrate diversity and abundance on intensively managed grassland farms, focusing on planthoppers and leafhoppers (Auchenorrhyncha). Replicated across four farms in south-west England, we manipulated conventional management practices (inorganic fertilizer, cutting frequency and height, and aftermath grazing) to create seven treatments along a gradient of decreasing management intensity and increasing sward architectural complexity. Auchenorrhyncha were sampled annually between 2003 and 2005. Auchenorrhyncha abundance and species richness was highest in the most extensively managed treatments. Abundance was lowest with frequent cutting, while species richness was lowest where cattle grazing occurred. Unexpectedly, application of inorganic fertilizer had no effect on Auchenorrhyncha abundance or species richness. Management options that enhance invertebrate diversity, while allowing the remainder of the field to be managed conventionally, represent a potentially important conservation tool for many lowland improved grasslands. Extensification of conventional management in field margin areas of such grasslands are likely to benefit this numerically dominant component of grassland invertebrate fauna. These management practices have the potential to be incorporated into existing UK and European agri-environment schemes.