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.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (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.

Analysis of the sequence and expression of a second putative acetylcholinesterase cDNA from organophosphate-susceptible and organophosphate-resistant cattle ticks

The cattle tick, Boophilus microplus, is a major pest of cattle in Australia, Central and South America, and parts of Africa and Asia. Control of ticks with organophosphates (OPs) and carbamates, which target acetylcholinesterases (AChE), led to evolution of resistance to these pesticides. Alleles at the locus studied here, AChE2, from OP-susceptible female ticks from Australia and Mexico differed at 46 of 1689 nucleotide positions (20 putative amino acid differences) whereas alleles from three strains of OP-resistant ticks from Australia differed with the allele from the Australian susceptible ticks at six to 13 nucleotide positions (three to six putative amino acid differences). However, the role, if any, of these polymorphisms in the OP-resistance phenotype is unknown. Certainly none of the polymorphisms correspond to sites in ACK that are involved in catalysis or binding of acetylcholine in other organisms. Both of the AChE loci of B. microplus, AChE1 and AChE2, are apparently expressed in synganglia; AChE1 is also expressed in salivary glands and ovaries, in OP-susceptible and OP-resistant ticks. This seems to contradict studies of enzyme kinetics, which indicated that only one form of AChE was present in the synganglia, the site of the action of OPs, in this species of tick. (C) 2002 Elsevier Science Ltd. All rights reserved.

Productivity growth in pre-1990 Mongolian agriculture: Spiralling disaster or emerging success?

The reasons for the spectacular collapse of so many centrally-planned economies are a source of ongoing debate. In this paper, we use detailed farm-level data to measure total factor productivity (TFP) changes in Mongolian grain and potato farming during the 14-year period immediately preceding the 1990 economic reforms. We measure TFP growth using stochastic frontier analysis (SFA) and data envelopment analysis (DEA) methods. Our results indicate quite poor overall performance, with an average annual TFP change of - 1.7% in grain and 0.8% in potatoes, over the 14-year period. However, the pattern of TFP growth changed substantially during this period, with TFP growth exceeding 7% per year in the latter half of this period. This suggests that the new policies of improved education, greater management autonomy, and improved incentives, which were introduced in final two planning periods in the 1980s, were beginning to have a significant influence upon the performance of Mongolian crop farming. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Hydrofluoric acid pre-treatment for improving 13C CPMAS NMR spectral quality of forest soils in south-east Queensland, Australia

Hydrofluoric acid (HF) was used to pre-treat forest soils of south-east Queensland for assessing the effectiveness of iron (Fe) removal, carbon (C) composition using C-13 cross-polarisation (CP) with magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) before and after the HF pre-treatment, and the improvement of C-13 CPMAS NMR spectra. Soil samples were collected from 4 experimental sites of different soil types, harvest residue management or prescribed burning, and tree species. More than 86% of Fe was in all soil types removed by the HF treatment. The C-13 NMR spectral quality was improved with increased resolution, especially in the alkyl C and O-alkyl C regions, and reduced NMR run-time (1-5 h per sample compared with >20 h per sample without the pre-treatment). The C composition appeared to alter slightly after the pre-treatment, but this might be largely due to improved spectrometer conditions and increased resolution leading to more accurate NMR spectral integration. Organic C recovery after HF pre-treatment varied with soil types and forest management, and soluble soil organic matter (SOM) could be lost during the pre-treatment. The Fourier Transform-Infrared (FT-IR) spectra of HF extracts indicated the preferential removal of carboxylic C groups during the pre-treatment, but this could also be due to adsorbed water on the mineral matter. The NMR spectra revealed some changes in C composition and quality due to residue management and decomposition. Overall, the HF treatment was a useful pre-treatment for obtaining semi-quantitative C-13 CPMAS NMR spectra of subtropical Australian forest soils.

Evaluation of various pre-treatments for the dehydration of banana and selection of suitable drying models

The thin-layer drying behaviour of bananas in a beat pump dehumidifier dryer was examined. Four pre-treatments (blanching, chilling, freezing and combined blanching and freezing) were applied to the bananas, which were dried at 50 degreesC with an air velocity of 3.1 m s(-1) and with the relative humidity of the inlet air of 10-35%. Three drying models, the simple model, the two-term exponential model and the Page model were examined. All models were evaluated using three statistical measures, correlation coefficient, root means square error, and mean absolute percent error. Moisture diffusivity was calculated based on the diffusion equation for an infinite cylindrical shape using the slope method. The rate of drying was higher for the pre-treatments involving freezing. The sample which was blanched only did not show any improvement in drying rate. In fact, a longer drying time resulted due to water absorption during blanching. There was no change in the rate for the chilled sample compared with the control. While all models closely fitted the drying data, the simple model showed greatest deviation from the experimental results. The two-term exponential model was found to be the best model for describing the drying curves of bananas because its parameters represent better the physical characteristics of the drying process. Moisture diffusivities of bananas were in the range 4.3-13.2 x 10(-10) m(2)s(-1). (C) 2002 Published by Elsevier Science Ltd.

Second primary oesophageal cancer following radiation for breast cancer

The management of 12 women who presented with a second primary oesophageal cancer following radiotherapy for breast cancer was reviewed. It was concluded that nine cases fitted the classical description of a radiation-induced malignancy. Most cases were successfully managed with combined modality therapy in spite of their previous radiotherapy. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

MR image-based measurement of rates of change in volumes of brain structures. Part 1: Method and validation

A detailed analysis procedure is described for evaluating rates of volumetric change in brain structures based on structural magnetic resonance (MR) images. In this procedure, a series of image processing tools have been employed to address the problems encountered in measuring rates of change based on structural MR images. These tools include an algorithm for intensity non-uniforniity correction, a robust algorithm for three-dimensional image registration with sub-voxel precision and an algorithm for brain tissue segmentation. However, a unique feature in the procedure is the use of a fractional volume model that has been developed to provide a quantitative measure for the partial volume effect. With this model, the fractional constituent tissue volumes are evaluated for voxels at the tissue boundary that manifest partial volume effect, thus allowing tissue boundaries be defined at a sub-voxel level and in an automated fashion. Validation studies are presented on key algorithms including segmentation and registration. An overall assessment of the method is provided through the evaluation of the rates of brain atrophy in a group of normal elderly subjects for which the rate of brain atrophy due to normal aging is predictably small. An application of the method is given in Part 11 where the rates of brain atrophy in various brain regions are studied in relation to normal aging and Alzheimer's disease. (C) 2002 Elsevier Science Inc. All rights reserved.

MR image-based measurement of rates of change in volumes of brain structures. Part II: Application to a study of Alzheimer's disease and normal aging

We present global and regional rates of brain atrophy measured on serially acquired T1-weighted brain MR images for a group of Alzheimer's disease (AD) patients and age-matched normal control (NC) subjects using the analysis procedure described in Part I. Three rates of brain atrophy: the rate of atrophy in the cerebrum, the rate of lateral ventricular enlargement and the rate of atrophy in the region of temporal lobes, were evaluated for 14 AD patients and 14 age-matched NC subjects. All three rates showed significant differences between the two groups, However, the greatest separation of the two groups was obtained when the regional rates were combined. This application has demonstrated that rates of brain atrophy, especially in specific regions of the brain, based on MR images can provide sensitive measures for evaluating the progression of AD. These measures will be useful for the evaluation of therapeutic effects of novel therapies for AD. (C) 2002 Elsevier Science Inc. All rights reserved.

Fetal Growth Spurt and Pregestational Diabetic Pregnancy

OBJECTIVE - To assess the timing of fetal growth spurt among pre-existing diabetic pregnancies (types 1 and 2) and its relationship with diabetic control. To correlate fetal growth acceleration with factors that might influence fetal growth. RESEARCH DESIGN AND METHODS - This retrospective study involved all pregestational diabetic pregnancies delivered at a tertiary obstetric hospital in Australia between 1 January 1994 and 31 December 1999. Pregnancies with major congenital fetal anomalies, multiple pregnancies, small-for-gestational-age pregnancies (90th centile for gestation) were compared with babies with normal birth weights. RESULTS- A total of 101 diabetic pregnancies were included. Diabetic mothers, who had LGA babies, had significantly higher prepregnancy body weight and BMI (P < 0.05). There were no differences in maternal age or parity among the two groups. There were also no differences in the first-, second-, and third-trimester HbA(1c) levels between the two groups. The abdominal circumference z-scores were significantly higher for LGA babies from 18 weeks and thereafter. The differences increased progressively as the gestation advanced. Maximum difference was noted in the third trimester (30-38 weeks). CONCLUSIONS - Fetal growth acceleration in LGA fetuses of diabetic mothers starts in the second trimester, from as early as 18 weeks. In this study, glucose control did not appear to have a direct effect on the incidence of LGA babies, and such observation might result from the effects of other confounding factors.

Routine ultrasound screening in diabetic pregnancies

Objectives To assess the detection rate of congenital fetal malformations and specific problems related to routine ultrasound screening in women with pre-existing diabetes. Methods A retrospective study was carried out to assess the performance of routine ultrasound screening in women with pre-existing diabetes (Types 1 and 2) within a tertiary institution. The incidence, type and risk factors for congenital fetal malformations were determined. The detection rate of fetal anomalies for diabetic women was compared with that for the low-risk population. Factors affecting these detection rates were evaluated. Results During the study period, 12 169 low-risk pregnant women and 130 women with pre-existing diabetes had routine ultrasound screening performed within the institution. A total of 10 major anomalies (7.7%) and three minor anomalies (2.3%) were present in the fetuses of the diabetic women. Central nervous system and cardiovascular system anomalies accounted for 60% of the major anomalies. Peri-conceptional hemoglobin A 1 c of more than 9% was associated with a high prevalence of major anomalies (14311000). Women who had fetuses with major anomalies bad a significantly higher incidence of obesity (78% vs. 37%; P < 0.05). Ultrasound examination of these diabetic pregnancies showed high incidences of suboptimal image quality (37%), incomplete examinations, and repeat examinations (17%). Compared to the 'low-risk' non-diabetic population from the same institution, the relative risk for a major congenital anomaly among the diabetic women was 5.9-fold higher (95% confidence interval, 2.9-11.9). The detection rate for major fetal anomalies was significantly lower for diabetic women (30% vs. 73%; P < 0.01), and the mean body mass index for the diabetic group was significantly higher (29 vs. 23 kg/m(2); P < 0.001). Conclusion The incidence of congenital anomalies is higher in diabetic pregnancies. Unfortunately, the detection rate for fetal anomalies by antenatal ultrasound scan was significantly, worse than that for the low-risk population. This is likely to be related to the maternal body habitus and unsatisfactory examinations. Methods to overcome these difficulties are discussed.

Risk factors for non-haemorrhagic stroke in patients with coronary heart disease and the effect of lipid-modifying therapy with pravastatin

Objective To determine the relative importance of recognised risk factors for non-haemorrhagic stroke, including serum cholesterol and the effect of cholesterol-lowering therapy, on the occurrence of non-haemorrhagic stroke in patients enrolled in the LIPID (Long-term Intervention with Pravastatin in Ischaemic Disease) study. Design The LIPID study was a placebo-controlled, double-blind trial of the efficacy on coronary heart disease mortality of pravastatin therapy over 6 years in 9014 patients with previous acute coronary syndromes and baseline total cholesterol of 4-7 mmol/l. Following identification of patients who had suffered non-haemorrhagic stroke, a pre-specified secondary end point, multivariate Cox regression was used to determine risk in the total population. Time-to-event analysis was used to determine the effect of pravastatin therapy on the rate of non-haemorrhagic stroke. Results There were 388 non-haemorrhagic strokes in 350 patients. Factors conferring risk of future non-haemorrhagic stroke were age, atrial fibrillation, prior stroke, diabetes, hypertension, systolic blood pressure, cigarette smoking, body mass index, male sex and creatinine clearance. Baseline lipids did not predict non-haemorrhagic stroke. Treatment with pravastatin reduced non-haemorrhagic stroke by 23% (P= 0.016) when considered alone, and 21% (P= 0.024) after adjustment for other risk factors. Conclusions The study confirmed the variety of risk factors for non-haemorrhagic stroke. From the risk predictors, a simple prognostic index was created for nonhaemorrhagic stroke to identify a group of patients at high risk. Treatment with pravastatin resulted in significant additional benefit after allowance for risk factors. (C) 2002 Lippincott Williams Wilkins.