Mango stem-end rot (Botryosphaeria dothidea) disease control by partial-pressure infiltration of fungicides

The in vitro efficacy of several fungicides against Botryosphaeria dothidea (syn. Dothiorella dominicana) and their in vivo efficacy in controlling mango cv. Kensington Pride stem-end rot on partial-pressure infiltration v. dip treatment of green mature fruit was evaluated. In vitro sensitivity of B. dothidea to Benlate (benomyl), Sportak (prochloraz) and Scala (pyrimethanil) at 10 dilutions of the manufacturer's recommended rate was first determined at typical cold (13degreesC) and shelf (23degreesC) storage temperatures. The effectiveness of partial-pressure infiltration and conventional hot (52degreesC) or cold (26degreesC) dipping of fruit after harvest was then evaluated using the commercially recommended rate for each fungicide. In vitro, Benlate and Sportak prevented the growth of B. dothidea at both storage temperatures and at all concentrations, while Scala partially controlled growth of the pathogen. Benlate was the most effective fungicide for stem-end rot control. Sportak and Scala resulted in stem-end rot control when applied by partial-pressure infiltration, but not as dips. Partial-pressure infiltration holds promise for enhancing the efficacy of otherwise less effective but alternative fungicides for control of stem-end rot diseases.

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.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

A conjecture on small embeddings of partial Steiner triple systems

A well-known, and unresolved, conjecture states that every partial Steiner triple system of order u can be embedded in a Steiner triple system of order v for all v equivalent to 1 or 3 (mod 6), v greater than or equal to 2u + 1. However, some partial Steiner triple systems of order u can be embedded in Steiner triple systems of order v < 2u + 1. A more general conjecture that considers these small embeddings is presented and verified for some cases. (C) 2002 Wiley Periodicals, Inc.

A Case Study of Partial Agenesis of the Corpus Callosum: Audiological Implications

This case study presents four and a half years of audiological observations, testing and aural habilitation of a female child with a partial agenesis of the corpus callosum (ACC). The ACC was diagnosed by MRI scan performed at 6 months of age to eliminate neurological causes for the developmental delay. This child was also born with a cleft palate and was diagnosed with Robinow Syndrome at 3 years and 3 months of age. The audiological results showed an improvement in hearing thresholds over the 4-year period. The child’s ophthalmologist also reported an improvement in visual skills over time. The most interesting aspect of the child’s hearing was the discrepancy between the monaural and the binaural results. That is, when assessed binaurally she often presented with a mild to moderate mixed loss and, when assessed monaurally, she showed a moderate to severe mixed loss for the right ear and a severe mixed loss for the left ear. Over time, the discrepancy between the monaural and binaural results changed. When assessed binaurally, the loss decreased to normal low frequency hearing sloping to a mild high frequency loss. When assessed monaurally, the most recent results showed a mild loss for the right ear and a moderate loss for the left ear. This discrepancy between binaural and monaural results was evident for both aided and unaided tests. For the most recent thresholds, the binaural results were consistent with the right monaural thresholds for the first time over the four and a half years. Parental reports of the child’s hearing were consistent with the binaural clinical results. This case indicates the need for audiologists to (1) carefully monitor the hearing of children with ACC, (2) obtain monaural and binaural hearing and aided thresholds results, and (3) compare these children’s functional abilities with the objective test results obtained. This case does question whether hearing aids are appropriate for children with ACC. If hearing aids are deemed to be appropriate, then hearing aids with compression characteristics should be considered.

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.

Supersymmetric t-J Gaudin models and KZ equations

Supersymmetric t-J Gaudin models with open boundary conditions are investigated by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the boundary Gaudin systems are derived, and used to construct and solve the KZ equations associated with sl (2\1)((1)) superalgebra.

Partial automation of database processing of simulation outputs from L-systems models of plant morphogenesis

Models of plant architecture allow us to explore how genotype environment interactions effect the development of plant phenotypes. Such models generate masses of data organised in complex hierarchies. This paper presents a generic system for creating and automatically populating a relational database from data generated by the widely used L-system approach to modelling plant morphogenesis. Techniques from compiler technology are applied to generate attributes (new fields) in the database, to simplify query development for the recursively-structured branching relationship. Use of biological terminology in an interactive query builder contributes towards making the system biologist-friendly. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

Perp-systems and partial geometries

A perp-system R(r) is a maximal set of r-dimensional subspaces of PG(N,q) equipped with a polarity rho, such that the tangent space of an element of R(r) does not intersect any element of R(r). We prove that a perp-system yields partial geometries, strongly regular graphs, two-weight codes, maximal arcs and k-ovoids. We also give some examples, one of them yielding a new pg(8,20,2).

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.

Modelling the activated sludge flocculation process combining laser light diffraction particle sizing and population balance modelling (PBM)

A technique based on laser light diffraction is shown to be successful in collecting on-line experimental data. Time series of floc size distributions (FSD) under different shear rates (G) and calcium additions were collected. The steady state mass mean diameter decreased with increasing shear rate G and increased when calcium additions exceeded 8 mg/l. A so-called population balance model (PBM) was used to describe the experimental data, This kind of model describes both aggregation and breakage through birth and death terms. A discretised PBM was used since analytical solutions of the integro-partial differential equations are non-existing. Despite the complexity of the model, only 2 parameters need to be estimated: the aggregation rate and the breakage rate. The model seems, however, to lack flexibility. Also, the description of the floc size distribution (FSD) in time is not accurate.