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.

Differential expression and distribution of syndecan-1 and-2 in periodontal wound healing of the rat

Cell-surface proteoglycans participate in several biological functions including interactions with adhesion molecules, growth factors and a variety of other effector molecules. Accordingly, these molecules play a central role in various aspects of cell-cell and cell-matrix interactions. To investigate the expression and distribution of the cell surface proteoglycans, syndecan-1 and -2, during periodontal wound healing, immunohistochemical analyses were carried out using monoclonal antibodies against syndecan-1, or -2 core proteins. Both syndecan-1 and -2 were expressed and distributed differentially at various stages of early inflammatory cell infiltration, granulation tissue formation, and tissue remodeling in periodontal wound healing. Expression of syndecan-1 was noted in inflammatory cells within and around the fibrin clots during the earliest stages of inflammatory cell infiltration. During granulation tissue formation it was noted in fibroblast-like cells and newly formed blood vessels. Syndecan-1 was not seen in newly formed bone or cementum matrix at any of the time periods studied. Syndecan-1 expression was generally less during the late stages of wound healing but was markedly expressed in cells that were close to the repairing junctional epithelium. In contrast, syndecan-2 expression and distribution was not evident at the early stages of inflammatory cell infiltration. During the formation of granulation tissue and subsequent tissue remodeling, syndecan-2 was expressed extracellularly in the newly formed fibrils which were oriented toward the root surface. Syndecan-2 was found to be significantly expressed on cells that were close to the root surface and within the matrix of repaired cementum covering root dentin as well as at the alveolar bone edge. These findings indicate that syndecan-1 and -2 may have distinctive functions during wound healing of the periodontium. The appearance of syndecan-1 may involve both cell-cell and cell-matrix interactions, while syndecan-2 showed a predilection to associate with cell-matrix interactions during hard tissue formation.

Investigation of electrical conductivity as a function of dopant-ion radius in the systems Zr0.75Ce0.08M0.17O1.92 (M=Nd, Sm, Gd, Dy, Ho, Y, Er, Yb, Sc)

Electrical conductivity versus dopant ionic radius studies in zirconia- and ceria-based, solid oxide fuel cell (SOFC) electrolyte systems have shown that oxygen-ion conductivity is highest when the host and dopant ions are similar in size [J. Am. Ceram. Soc. 48 (1965) 286; Solid State Ionics 37 (1989) 67; Solid State Ionics 5 (1981) 547]. Under these conditions, it is thought that the conduction paths within the crystal lattice become less distorted [Solid State Ionics 8 (1983) 201]. In this study, binary ZrO2-M2O3 unit cells were expanded, via the partial substitution of Ce+4 for Zr+4 into the lattice, in an attempt to identify new, ternary, zirconia/ceria-based electrolyte systems with enhanced electrical conductivity. The compositions Zr0.75Ce0.08M0.17O1.92 (M = Nd, Sm, Gd, Dy, Ho, Y, Yb, Sc) were prepared using traditional solid state techniques. Bulk phase characterisation and precise lattice parameter measurements were performed with X-ray diffraction techniques. Four-probe DC conductivity measurements between 400 and 900 degreesC showed that the dopant-ion radius influenced electrical conductivity. The conductivity versus dopant-ion radius trends previously observed in zirconia-based, binary systems are clearly apparent in the ternary systems investigated in this study. The addition of ceria was found to have a negative influence on the electrical conductivity over the temperature range 400-900 degreesC. It is suggested that distortion of the oxygen-ion conduction path by the presence of the larger M+3 and Ce+4 species (relative to Zr+4) is the reason for the decreasing electrical conductivity as a function of increasing dopant size and ceria addition, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.

Differential requirements for COPI coats in formation of replication complexes among three genera of Picornaviridae

Picornavirus RNA replication requires the formation of replication complexes (RCs). consisting of virus-induced vesicles associated with viral nonstructural proteins and RNA. Brefeldin A (BFA) has been shown to strongly inhibit RNA replication of poliovirus but not of encephalomyocarditis virus (EMCV). Here, we demonstrate that the replication of parechovirus 1 (ParV1) is partly resistant to BFA, whereas echovirus 11 (EV11) replication is strongly inhibited. Since BFA inhibits COPI-dependent steps in endoplasmic reticulum (ER)-Golgi transport, we tested a hypothesis that different picornaviruses may have differential requirements for COPI in the formation of their RCs. Using immunofluorescence and cryo-immunoelectron microscopy we examined the association of a COPI component, beta-COP, with the RCs of EMCV, ParV1, and EV11 EMCV RCs did not contain beta-COP. In contrast, beta-COP appeared to be specifically distributed to the RCs of EV11 In ParV1-infected cells beta-COP was largely dispersed throughout the cytoplasm, with some being present in the RCs. These results suggest that there are differences in the involvement of COPI in the formation of the RCs of various picornaviruses, corresponding to their differential sensitivity to BFA. EMCV RCs are likely to be formed immediately after vesicle budding from the ER, prior to COPI association with membranes. ParV1 RCs are formed from COPI-containing membranes but COPI is unlikely to be directly involved in their formation, whereas formation of EV11 RCs appears to be dependent on COPI association with membranes.

Cash, customers, and care: The experience and meaning of differential payment for high care places in aged care facilities

The introduction of new asset/income tested charges for high care residents was the 1997-98 Commonwealth government policy response to concerns about financing residential aged care. This in-depth study of residents, families, staff and managers in three aged care facilities explores issues of equity, access and empowerment arising when some residents pay more for the same level of care and amenity. The study reports little evidence of financial contributions affecting access to high care places and the delivery of care, the potential for differential access to amenities such as single rooms linked to the extra payments, and no evidence of a sense of empowerment linked to payment of the new charges. The complexity of current financial arrangements, access to appropriate financial advice at the time of entry, and the potential for an informal two tier system in relation to the allocation Of amenities are identified as developing policy issues.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Lead stimulus modality change and the attentional modulation of the acoustic and electrical blink reflex

Two experiments investigated the effects of the sensory modality of the lead and of the blink-eliciting stimulus during lead stimulus modality change on blink modulation at lead intervals of 2500 and 3500 ins. Participants were presented with acoustic, visual, or tactile change stimuli after habituation training with lead stimuli from the same or a different sensory modality. In Experiment 1, latency and magnitude of the acoustic blink were facilitated during a change to acoustic or visual lead stimuli, but not during a change to tactile lead stimuli. After habituation to acoustic lead stimuli, blink magnitude was smaller during tactile change stimuli than during habituation stimuli. The latter finding was replicated in Experiment 2 in which blink was elicited by electrical stimulation of the trigeminal nerve. The consistency of the findings across different combinations of lead stimulus and blink-eliciting stimulus modalities does not support a modality-specific account of attentional blink modulation. Rather, blink modulation during generalized orienting reflects modality non-specific processes, although modulation may not always be found during tactile lead stimuli. (C) 2002 Elsevier Science B.V. All rights reserved.

Quadriceps concentric and eccentric exercise 1: Changes in contractile and electrical activity following eccentric and concentric exercise

The purpose of this study was to determine whether or not losses of strength or endurance following eccentric and concentric exercise are associated with reduced excitation. The effects of eccentric and concentric work on maximal voluntary isometric contraction (MVC) and surface electromyogram (EMG) of the quadriceps were studied in 10 healthy male subjects following bench-stepping for 20 min with a constant leading leg. Prior to stepping and at 0, 0.25, 0.50, 0.75, 1, 3. 24 and 48 h afterwards the subjects performed a 30 s leg extension MVC with each leg during which the isometric force and the root mean square voltage of the EMG were recorded. In the eccentrically exercised muscles (ECC), MVC0-3 (force during the first 3 s of contraction) fen immediately after the bench-stepping exercise to 88 +/- 2% (mean SE) of the pre-exercise value and remained significantly lower than the concentrically exercised muscles (p < 0.05). The muscle weakness in the ECC could not be attributed to central fatigue as surface EMG amplitude at MVC0-3 increased during the recovery period. Muscle weakness after eccentric exercise appears to be due to contractile failure, which is not associated with a reduction in excitation as assessed by surface EMG. Muscular fatigue over 30 s did not change in the two muscle groups after exercise (p = 0.79), indicating that the ECC were weaker but not more fatiguable after exercise.

Polarised infrared and differential scanning calorimetry studies on oriented vinyl pipe materials

The molecular orientation in a conventionally extruded PVC pipe, a uniaxially oriented PVC pipe and a biaxially oriented PVC pipe has been studied via Infrared dichroism. The degree of order or crystallinity has also been studied by Differential Scanning Calorimetry and also via Infrared Spectroscopy. The fundamental structural difference between the conventional and oriented pipes was that polymer chains were preferentially aligning in the hoop direction for oriented pipes whereas they were fairly isotropic in the conventional pipe with a slight preferential alignment in the axial direction. Analysis of the C-Cl stretching mode indicated that the uniaxially oriented pipe had much higher alignment of the C-Cl bond in the axial direction than the biaxial pipe, which correlates with higher fracture toughness for circumferential cracking in the biaxial pipe. Both DSC and Infrared spectroscopy detected little change in the crystallinity or order in the oriented pipes compared to the conventionally extruded pipes. (C) 2002 Kluwer Academic Publishers.

Differential regulation of twitching motility and elastase production by Vfr in Pseudomonas aeruginosa

Vfr, a homolog of Escherichia coli cyclic AMP (cAMP) receptor protein, has been shown to regulate quorum sensing, exotoxin A production, and regA transcription in Pseudomonas aeruginosa. We identified a twitching motility-defective mutant that carries a transposon insertion in vfr and confirmed that vfr is required for twitching motility by construction of an independent allelic deletion-replacement mutant of vfr that exhibited the same phenotype, as well as by the restoration of normal twitching motility by complementation of these mutants with wild-type vfr. Vfr-null mutants exhibited severely reduced twitching motility with barely detectable levels of type IV pili, as well as loss of elastase production and altered pyocyanin production. We also identified reduced-twitching variants of quorum-sensing mutants (PAK lasl::Tc) with a spontaneous deletion in vfr (S. A. Beatson, C. B. Whitchurch, A. B. T. Semmler, and J. S. Mattick, J. Bacteriol., 184:3598-3604,2002), the net result of which was the loss of five residues (EQERS) from the putative cAMP-binding pocket or Vfr. This allele (VfrDeltaEQERS) was capable of restoring elastase and pyocyanin production to wild-type levels in vfr-null mutants but not their defects in twitching motility. Furthermore, structural analysis of Vfr and VfrDeltaEQERS in relation to E. coli CRP suggests that Vfr is capable of binding both cAMP and cyclic GMP whereas VfrDeltaEQERS is only capable of responding to cAMP. We suggest that Vfr controls twitching motility and quorum sensing via independent pathways in response to these different signals, bound by the same cyclic nucleotide monophosphate-binding pocket.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

The differential role of alcohol expectancies, drinking refusal self-efficacy and coping resources in predicting alcohol consumption in community and clinical samples

This study explored the relationship between coping, alcohol expectancies and drinking refusal self-efficacy in predicting drinking behaviour in both community and clinical samples. These variables were found to have differential effects in their association with frequency and volume of alcohol consumption across the two samples. Generally, drinking refusal self-efficacy was a more salient factor in relation to frequency and volume of community drinking, while coping and expectancies were more strongly associated with frequency of drinking sessions by problem drinkers. The interaction between expectancies and drinking refusal self-efficacy was related to volume of consumption in both groups, while coping and expectancies interacted in their association with frequency in the clinical group. The findings are discussed with regard to the different patterns of cognitive variables governing the decision to drink and the amount consumed in each drinking session, which may differentiate community and problem drinkers.