Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Long-run growth effects of taxation in a non-scale growth model with innovation

In previous studies, taxing income or consumption hinders long-run growth. Incorporating saving and leisure into the non-scale Schumpeterian model of [Journal of Political Economy 107 (1999) 715-730], we show that the usual growth effects of taxing consumption and labor income do not exist. (C) 2002 Elsevier Science B.V. All rights reserved.

Growth of a Bose-Einstein condensate: a detailed comparison of theory and experiment

We extend the earlier model of condensate growth of Davis et at (Davis M J, Gardiner C W and Ballagh R J 2000 Phys. Rev. A 62 063608) to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by Kohl et al (Kohl M, Davis M J, Gardiner C W, Hansch T and Esslinger T 2001 Preprint cond-mat/0106642) who study the formation of a rubidium Bose-Einstein condensate for a range of evaporative cooling parameters. We find that, in the regime where our model is valid, the theoretical curves agree with all the experimental data with no fitting parameters. However, for the slowest cooling of the gas the theoretical curve deviates significantly from the experimental curves. It is possible that this discrepancy may be related to the formation of a quasicondensate.

Constitutive expression of a phenylalanine ammonia-lyase gene from Stylosanthes humilis in transgenic tobacco leads to enhanced disease resistance but impaired plant growth

Transgenic tobacco plants expressing a phenylalanine ammonia-lyase cDNA (ShPAL), isolated from Stylosanthes humilis, under the control of the 35S promoter of the cauliflower mosaic virus were produced to test the effect of high level PAL expression on disease resistance. The transgenic plants showed up to eightfold PAL activity and were slowed in growth and flowering relative to non-transgenic controls which have segregated out the transgene. The expression of the ShPAL transgene and elevated PAL levels were correlated and stably inherited. In T-1 and T-2 tobacco plants with increased PAL activity, lesion expansion was significantly reduced by up to 55% on stems inoculated with the Oomycete pathogen Phytophthora parasitica pv. nicotianae, Lesion area was significantly reduced by up to 50% on leaves inoculated with the fungal pathogen Cercospora nicotianae. This study provides further evidence that PAL has a role in plant defence. (C) 2002 Elsevier Science Ltd. All rights reserved.

The effects of temperature on the growth, survival and biomass of different families of juvenile Penaeus japonicus Bate

Variation in the growth, survival and change in total biomass (termed biomass increase) of different families of juvenile Penaeus japonicus was investigated over a range of temperatures in controlled laboratory experiments. In the first experiment, the effects of temperature on six families of juveniles were examined over a broad range of temperatures (24 to 30 degreesC). In the second experiment, the effects of temperature on six more families of juveniles were examined over a narrower range of temperatures (27.5 to 31.2 degreesC). Over the broad temperature range, mean growth and biomass increase were highest at 27 degreesC and mean survival was highest at 24 degreesC. Mean growth was lowest at 24 degreesC, whilst survival and biomass increase were lowest at 30 degreesC. However, there was a significant interaction between family and temperature, with some families tolerating a broader range of temperatures than others. As a result, the ranking of families in relation to growth, survival and biomass increase changed at each temperature. This effect was more pronounced for survival than for growth. Over the narrower range, temperature significantly affected growth, survival and biomass increase, but there was no significant interaction between family and temperature. Growth, survival and biomass increase were significantly lower at 31.2 than at 27.5 and 29.2 degreesC. These results suggest that if grow-out conditions for P. japonicus vary by more than a few degrees, interactions between family and temperature could affect the efficiency of selection. The results also suggest that the family x temperature interaction may have a more pronounced effect on survival than on growth. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Controlling the complex Lorenz equations by modulation

We demonstrate that a system obeying the complex Lorenz equations in the deep chaotic regime can be controlled to periodic behavior by applying a modulation to the pump parameter. For arbitrary modulation frequency and amplitude there is no obvious simplification of the dynamics. However, we find that there are numerous windows where the chaotic system has been controlled to different periodic behaviors. The widths of these windows in parameter space are narrow, and the positions are related to the ratio of the modulation frequency of the pump to the average pulsation frequency of the output variable. These results are in good agreement with observations previously made in a far-infrared laser system.

Interacting roles of myofibroblasts, apoptosis and fibrogenic growth factors in the pathogenesis of renal tubulo-interstitial fibrosis

The interrelationship between myofibroblasts and fibrogenic growth factors in the pathogenesis of renal fibrosis is poorly defined. A temporal and spatial analysis of myofibroblasts, their proliferation and death, and presence of transforming growth factor-beta1 (TGF-beta1) and platelet-derived growth factor-B (PDGF-B) was carried out in an established rodent model in which chronic renal scarring and fibrosis occurs after healed renal papillary necrosis (RPN), similar to that seen with analgesic nephropathy. Treated and control groups (N = 6 and 4, respectively) were compared at 2, 4, 8 and 12 weeks. A positive relationship was found between presence of tubulo-interstitial myofibroblasts and development of fibrosis. Apoptotic myofibroblasts were identified in the interstitium and their incidence peaked 2 weeks after treatment. Levels of interstitial cell apoptosis and fibrosis were negatively correlated over time (r = -0.57, p < 0.01 ), suggesting that as apoptosis progressively failed to limit myofibroblast numbers, fibrosis increased. In comparison with the diminishing apoptosis in the interstitium, the tubular epithelium had progressively increasing levels of apoptosis over time, indicative of developing atrophy of nephrons. TGF-beta1 protein expression had a close spatial and temporal association with fibrosis and myofibroblasts, whilst PDGF-B appeared to have a closer link with populations of other chronic inflammatory cells such as infiltrating lymphocytes. Peritubular myofibroblasts were often seen near apoptotic cells in the tubular epithelium, suggestive of a paracrine toxic effect of factor/s secreted by the myofibroblasts. In vitro , TGF-beta1 was found to be toxic to renal tubular epithelial cells. These findings suggest an interaction between myofibroblasts, their deletion by apoptosis, and the presence of the fibrogenic growth factor TGF-beta1 in renal fibrosis, whereby apoptotic deletion of myofibroblasts could act as a controlling factor in progression of fibrosis.