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.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

How to unravel and solve soil fertility problems

This book provides a way for farmers in developing countries to benefit from scientific knowledge on plant nutrition and soil fertility. Specifically, it will help farmers recognise and deal with shortages or excesses of chemical elements.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

The excitatory behavioral and antianalgesic pharmacology of normorphine-3-glucuronide after intracerebroventricular administration to rats

In the adult male Sprague-Dawley rat, a species commonly used to study tolerance to the antinociceptive effects of morphine, approximate to 10% of the morphine dose is metabolized to normorphine-3-glucuronide (NM3G). In contrast, NM3G is a relatively minor metabolite of morphine in human urine reportedly accounting for approximate to 1% of the morphine dose. To date, the pharmacology of NM3G has been poorly characterized. Therefore, our studies were designed to determine whether the intrinsic pharmacology of NM3G is similar to that of morphine-3-glucuronide (M3G), the major metabolite of morphine, which has been shown to be a potent central nervous system (CNS) excitant and to attenuate the intrinsic antinociceptive effects of morphine in rats. The CNS excitatory potency of NM3G was found to be approximately half that of M3G, inducing convulsions in rats at intracerebroventricular (i.c.v.) doses of greater than or equal to 16.8 nmol. When administered before morphine (70 nmol i.c.v.), NM3G (8.9 nmol i.c.v.) attenuated antinociception for up to 2 hr, but when administered after morphine, no significant attenuation of morphine antinociception was observed. Thus, after i.c.v. administration, NM3G like M3G, is a potent CNS excitant and antianalgesic in the rat. NM3G may therefore play a role in the development of tolerance to the antinociceptive effects of morphine in the rat as has been proposed previously for M3G.

Incorporating cognitive-behavioral therapy with occupational therapy: A comparative study with patients with low back pain

This paper reports on the implementation of a psychoeducational program utilizing cognitive-behavioral principles. The efficacy of this psychoeducational treatment program in modifying dysfunctional attitudes in patients with chronic low back pain was examined using a two-group pretest posttest design with a follow-lip at 3 months Thirty patients (average age = 44.37 SD = 13.71) participated in the study, with 15 in the psychoeducational treatment group and 15 in the placebo control group. These two conditions were added on to an existing eclectic inpatient pain management program. After assessment on the IPAM (The Integrated Psychosocial Assessment Model), scores were reduced to multivariate composite scores on the factors of illness behavior depressed and negative cognitions, and acute pain strategies. Results of a group x time repeated measures analysis of variance for the three pain factors revealed a significant main effect for group (F(23,1) = 5.00 p < .04), tempered by a significant interaction between group and rime on the 'depressed and negative' pain factor (F(23,1) = 4.77 p < .04). Patients in the treatment group improved significantly over time and significantly more than the placebo control group patients at posttreatment. Results provide support for the program in increasing patients' feelings of control over their pain and the use of positive coping strategies, while reducing perceived helplessness, depression, disability, and pain intensity.

Solution of adsorption problems involving steep moving profiles

The moving finite element collocation method proposed by Kill et al. (1995) Chem. Engng Sci. 51 (4), 2793-2799 for solution of problems with steep gradients is further developed to solve transient problems arising in the field of adsorption. The technique is applied to a model of adsorption in solids with bidisperse pore structures. Numerical solutions were found to match the analytical solution when it exists (i.e. when the adsorption isotherm is linear). The method is simple yet sufficiently accurate for use in adsorption problems, where global collocation methods fail. (C) 1998 Elsevier Science Ltd. All rights reserved.

Effects of interventions in health care settings on physical activity or cardiorespiratory fitness

Introduction: This paper reviews studies of physical activity interventions in health care settings to determine effects on physical activity and/or fitness and characteristics of successful interventions. Methods: Studies testing interventions to promote physical activity in health care settings for primary prevention (patients without disease) and secondary prevention (patients with cardiovascular disease [CVD]) were identified by computerized search methods and reference lists of reviews and articles. Inclusion criteria included assignment to intervention and control groups, physical activity or cardiorespiratory fitness outcome measures, and, for the secondary prevention studies, measurement 12 or more months after randomization. The number of studies with statistically significant effects was determined overall as well as for studies testing interventions with various characteristics. Results: Twelve studies of primary prevention were identified, seven of which were randomized. Three of four randomized studies with short-term measurement (4 weeks to 3 months after randomization), and two of five randomized studies with long-term measurement (6 months after randomization) achieved significant effects on physical activity. Twenty-four randomized studies of CVD secondary prevention were identified; 13 achieved significant effects on activity and/or fitness at twelve or more months. Studies with measurement at two time points showed decaying effects over time, particularly if the intervention were discontinued. Successful interventions contained multiple contacts, behavioral approaches, supervised exercise, provision of equipment, and/or continuing intervention. Many studies had methodologic problems such as low follow-up rates. Conclusion: Interventions in health care settings can increase physical activity for both primary and secondary prevention. Long-term effects are more likely with continuing intervention and multiple intervention components such as supervised exercise, provision of equipment, and behavioral approaches. Recommendations for additional research are given.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Brain region-specific studies of the excitatory behavioral effects of morphine-3-glucuronide

This study was designed to determine in rats whether morphine-3-glucuronide (M3G) produces its neuro-excitatory effects most potently in the ventral hippocampus (as has been reported previously for subanalgesic doses of opioid peptides). Guide cannulae were implanted into one of seven regions of the rat brain: lateral ventricle; ventral, CA1 and CA2-CA3 regions of the hippocampus; amygdala; striatum or cortex. After a 7 day recovery period, rats received intracerebral injections of (i) M3G (1.1 or 11 nmol) (ii) DADLE ([D-Ala(2),D-Leu(5)]enkephalin), (45 nmol, positive controls) or (iii) vehicle (deionised water), and behavioral excitation was quantified over 80 min. High-dose M3G (11 nmol) evoked behavioral excitation in all brain regions but the onset, severity and duration of these effects varied considerably among brain regions. By contrast, low-dose M3G (1.1 nmol) evoked excitatory behaviors only when administered into the ventral hippocampus and the amygdala, with the most potent effects being observed in the ventral hippocampus. Prior administration of the nonselective opioid antagonists, naloxone and beta-funaltrexamine into the ventral hippocampus, markedly attenuated low-dose M3G's excitatory effects but did not significantly alter levels of excitation evoked by high-dose M3G. Naloxone given 10 min after M3G (1.1 or 11 nmol) did not significantly attenuate behavioral excitation. Thus, M3G's excitatory behavioral effects occur most potently in the ventral hippocampus as reported previously for subanalgesic doses of opioid peptides, and appear to be mediated through at least two mechanisms, one possibly involving excitatory opioid receptors and the other, non-opioid receptors.