Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) 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 of Lakshmikantham et al.

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.

The anodic dissolution of magnesium in chloride and sulphate solutions

The electrochemical behaviour of magnesium was studied in representative chloride and sulphate solutions including NaCl, Na2SO4, NaOH and their mixed solutions, HCl, and H2SO4: (1) by measuring electrochemical polarisation curves, (2) by using electrochemical impedance spectroscopy (EIS), and (3) by simultaneous measurement of hydrogen gas evolution and measurement of magnesium dissolution rates using inductively coupled plasma atomic emission spectrophotometry (ICPEAS). These experiments showed that a partially protective surface film played an important role in the dissolution of magnesium in chloride and sulphate solutions. Furthermore, the experimental data were consistent with the involvement of the intermediate species Mg+ in magnesium dissolution at film imperfections or on a film-free surface. At such sites, magnesium first oxidised electrochemically to the intermediate species Mg+, and then the intermediate species chemically reacted with water to produce hydrogen and Mg2+. The presence of Cl- ions increased the film free area, and accelerated the electrochemical reaction rate from magnesium metal to Mg+. (C) 1997 Elsevier Science Ltd.

Behavior and interactions of children in cooperative groups in lower and middle elementary grades

The study investigated the behaviors and interactions of children in structured and unstructured groups as they worked together on a 6-week social studies activity each term for 3 school terms. Two hundred and twelve children in Grade 1 and 184 children in Grade 3 participated in the study. Stratified random assignment occurred so that each gender-balanced group consisted of 1 high-, 2 medium-, and 1 low-ability student. The results show that the children in the structured groups were consistently more cooperative and they provided more elaborated and nonelaborated help than did their peers in the unstructured groups. The children in the structured groups in Grade 3 obtained higher reading and learning outcome scores than their peers in the unstructured groups.

Onset of sheath extension and duration of lamina extension are major determinants of the response of maize lamina length to plant density

Background and Aims Plants regulate their architecture strongly in response to density, and there is evidence that this involves changes in the duration of leaf extension. This questions the approximation, central in crop models, that development follows a fixed thermal time schedule. The aim of this research is to investigate, using maize as a model, how the kinetics of extension of grass leaves change with density, and to propose directions for inclusion of this regulation in plant models. • Methods Periodic dissection of plants allowed the establishment of the kinetics of lamina and sheath extension for two contrasting sowing densities. The temperature of the growing zone was measured with thermocouples. Two-phase (exponential plus linear) models were fitted to the data, allowing analysis of the timing of the phase changes of extension, and the extension rate of sheaths and blades during both phases. • Key Results The duration of lamina extension dictated the variation in lamina length between treatments. The lower phytomers were longer at high density, with delayed onset of sheath extension allowing more time for the lamina to extend. In the upper phytomers—which were shorter at high density—the laminae had a lower relative extension rate (RER) in the exponential phase and delayed onset of linear extension, and less time available for extension since early sheath extension was not delayed. • Conclusions The relative timing of the onset of fast extension of the lamina with that of sheath development is the main determinant of the response of lamina length to density. Evidence is presented that the contrasting behaviour of lower and upper phytomers is related to differing regulation of sheath ontogeny before and after panicle initiation. A conceptual model is proposed to explain how the observed asynchrony between lamina and sheath development is regulated.

Efficiently computing weighted proximity relationships in spatial databases

Spatial data mining recently emerges from a number of real applications, such as real-estate marketing, urban planning, weather forecasting, medical image analysis, road traffic accident analysis, etc. It demands for efficient solutions for many new, expensive, and complicated problems. In this paper, we investigate the problem of evaluating the top k distinguished “features” for a “cluster” based on weighted proximity relationships between the cluster and features. We measure proximity in an average fashion to address possible nonuniform data distribution in a cluster. Combining a standard multi-step paradigm with new lower and upper proximity bounds, we presented an efficient algorithm to solve the problem. The algorithm is implemented in several different modes. Our experiment results not only give a comparison among them but also illustrate the efficiency of the algorithm.

Abdominal muscle recruitment during a range of voluntary exercises

Various exercises are used to retrain the abdominal muscles in the management of low back pain and other musculoskeletal disorders. However. few studies have directly investigated the activity of all the abdominal muscles or the recruitment of regions of the abdominal muscles during these manoeuvres. This study examined the activity of different regions of transversus abdominis (TrA), obliquus internus (OI) and externus abdominis (OE), and rectus abdominis (RA), and movement of lumbar spine, pelvis and abdomen during inward movement of the lower abdominal wall, abdominal bracing, pelvic tilting, and inward movement of the lower and upper abdominal wall. Inward movement of the lower abdominal wall in supine produced greater activity of TrA compared to OI. OE and RA. During posterior pelvic tilting. middle OI was most active and with abdominal bracing. OE was predominately recruited. Regions of TrA were recruited differentially and in inverse relationship between lumbopelvic motion and TrA electromyography (EMG) was found. This study indicates that inward movement of the abdominal wall in supine produces the most independent activity of TrA relative to the other abdominal muscle, recruitment varies between regions of TrA, and observation of abdominal and lumbopelvic motion may assist in evalation of exercise performance. (c) 2004 Elsevier Ltd. All rights reserved.

The return to schooling: Estimates from a sample of young Australian twins

This study uses a sample of young Australian twins to examine whether the findings reported in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp.1157-73] and [Miller, P.W., Mulvey, C and Martin, N., (1994). 'What Do Twins Studies Tell Us About the Economic Returns to Education?: A Comparison of Australian and US Findings', Western Australian Labour Market Research Centre Discussion Paper 94/4] are robust to choice of sample and dependent variable. The economic return to schooling in Australia is between 5 and 7 percent when account is taken of genetic and family effects using either fixed-effects models or the selection effects model of Ashenfelter and Krueger. Given the similarity of the findings in this and in related studies, it would appear that the models applied by [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73] are robust. Moreover, viewing the OLS and IV estimators as lower and upper bounds in the manner of [Black, Dan A., Berger, Mark C., and Scott, Frank C., (2000). 'Bounding Parameter Estimates with Nonclassical Measurement Error', Journal of the American Statistical Association, Vol. 95, No.451, pp.739-748], it is shown that the bounds on the return to schooling in Australia are much tighter than in [Ashenfelter, Orley and Krueger, Alan, (1994). 'Estimates of the Economic Return to Schooling from a New Sample of Twins', American Economic Review, Vol. 84, No. 5, pp. 1157-73], and the return is bounded at a much lower level than in the US. (c) 2005 Elsevier B.V. All rights reserved.

Using cohort studies to estimate mortality among injecting drug users that is not attributable to AIDS

Background: Injecting drug use (IDU) and associated mortality appear to be increasing in many parts of the world. IDU is an important factor in HIV transmission. In estimating AIDS mortality attributable to IDU, it is important to take account of premature mortality rates from other causes to ensure that AIDS related mortality among injecting drug users (IDUs) is not overestimated. The current review provides estimates of the excess non-AIDS mortality among IDUs. Method: Searches were conducted with Medline, PsycINFO, and the Web of Science. The authors also searched reference lists of identified papers and an earlier literature review by English et al (1995). Crude. mortality rates (CMRs) were derived from data on the number of deaths, period of follow UP, and number of participants. In estimating the all-cause mortality, two rates were calculated: one that included all cohort studies identified in the search, and one that only included studies that reported on AIDS deaths in their cohort. This provided lower and upper mortality rates, respectively. Results: The current paper derived weighted mortality rates based upon cohort studies that included 179 885 participants, 1 219 422 person-years of observation, and 16 593 deaths. The weighted crude AIDS mortality rate from studies that reported AIDS deaths was approximately 0.78% per annum. The median estimated non-AIDS mortality rate was 1.08% per annum. Conclusions: Illicit drug users have a greatly increased risk of premature death and mortality due to AIDS forms a significant part of that increased risk; it is, however, only part of that risk. Future work needs to examine mortality rates among IDUs in developing countries, and collect data on the relation between HIV and increased mortality due to all causes among this group.

Low back pain patients demonstrate increased hip extensor muscle activity during standardized submaximal rotation efforts

Study Design. A comparative study of trunk and hip extensor muscle recruitment patterns in 2 subject groups. Objective. To examine for changes in recruitment of the hip and back extensor muscles during low level isometric trunk rotation efforts in chronic low back pain (CLBP) subjects by comparison with matched asymptomatic control subjects. Summary of Background Data. Anatomic and biomechanical models have provided evidence that muscles attaching to the thoracolumbar fascia (TLF) are important for providing stabilization to the lumbopelvic region during trunk rotation. This has guided rehabilitation programs. The muscles that link diagonally to the posterior layer of the TLF have not previously been examined individually and compared during low-level trunk rotation efforts in CLBP patients and matched controls. Methods. Thirty CLBP patients and 30 matched controls were assessed using surface electromyography (EMG) as they performed low-level isometric rotation efforts while standing upright. Muscles studied included latissimus dorsi, erector spinae, upper and lower gluteus maximus, and biceps femoris. Subjects performed the rotation exertion with various levels of external trunk support, related to different functional tasks. Results. EMG results demonstrated that subjects with CLBP had significantly higher levels of recruitment for the lower and upper gluteus maximus (P < 0.05), hamstrings (P < 0.05), and erector spinae muscles (P < 0.05) during rotation to the left compared with the control subjects. Conclusion. This study provided evidence of increased muscle recruitment in CLBP patients when performing a standardized trunk rotation task. These results may have implications for the design of therapeutic exercise programs for CLBP patients.

Surface k-NN query processing

A k-NN query finds the k nearest-neighbors of a given point from a point database. When it is sufficient to measure object distance using the Euclidian distance, the key to efficient k-NN query processing is to fetch and check the distances of a minimum number of points from the database. For many applications, such as vehicle movement along road networks or rover and animal movement along terrain surfaces, the distance is only meaningful when it is along a valid movement path. For this type of k-NN queries, the focus of efficient query processing is to minimize the cost of computing distances using the environment data (such as the road network data and the terrain data), which can be several orders of magnitude larger than that of the point data. Efficient processing of k-NN queries based on the Euclidian distance or the road network distance has been investigated extensively in the past. In this paper, we investigate the problem of surface k-NN query processing, where the distance is calculated from the shortest path along a terrain surface. This problem is very challenging, as the terrain data can be very large and the computational cost of finding shortest paths is very high. We propose an efficient solution based on multiresolution terrain models. Our approach eliminates the need of costly process of finding shortest paths by ranking objects using estimated lower and upper bounds of distance on multiresolution terrain models.

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.