Mathematical methods for spatially cohesive reserve design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.

Specific orofacial problems experienced by musicians

Background: Patients who play musical instruments (especially wind and stringed instruments) and vocalists are prone to particular types of orofacial problems. Some problems are caused by playing and some are the result of dental treatment. This paper proposes to give an insight into these problems and practical guidance to general practice dentists. Method: Information in this paper is gathered from studies published in dental, music and occupational health journals, and from discussions with career musicians and music teachers. Results: Orthodontic problems, soft tissue trauma, focal dystonia, denture retention, herpes labialis, dry mouth and temporomandibular joint (TMJ) disorders were identified as orofacial problems of career musicians. Options available for prevention and palliative treatment as well as instrument selection are suggested to overcome these problems. Conclusions: Career musicians express reluctance to attend dentists who are not sensitive to their specific needs. General practitioner dentists who understand how the instruments impact on the orofacial structures and are aware of potential problems faced by musicians are able to offer preventive advice and supportive treatment to these patients, especially those in the early stages of their career.

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.

Interval training program optimization in highly trained endurance cyclists

Purpose: The purpose of this study was to examine the influence of three different high-intensity interval training (HIT) regimens on endurance performance in highly trained endurance athletes. Methods: Before, and after 2 and 4 wk of training, 38 cyclists and triathletes (mean +/- SD; age = 25 +/- 6 yr; mass = 75 +/- 7 kg; (V)over dot O-2peak = 64.5 +/- 5.2 mL.kg(-1).min(-1)) performed: 1) a progressive cycle test to measure peak oxygen consumption ((V)over dotO(2peak)) and peak aerobic power output (PPO), 2) a time to exhaustion test (T-max) at their (V)over dotO(2peak) power output (P-max), as well as 3) a 40-kin time-trial (TT40). Subjects were matched and assigned to one of four training groups (G(1), N = 8, 8 X 60% T-max P-max, 1:2 work:recovery ratio; G(2), N = 9, 8 X 60% T-max at P-max, recovery at 65% HRmax; G(3), N = 10, 12 X 30 s at 175% PPO, 4.5-min recovery; G(CON), N = 11). In addition to G(1) G(2), and G(3) performing HIT twice per week, all athletes maintained their regular low-intensity training throughout the experimental period. Results: All HIT groups improved TT40 performance (+4.4 to +5.8%) and PPO (+3.0 to +6.2%) significantly more than G(CON) (-0.9 to + 1.1 %; P < 0.05). Furthermore, G(1) (+5.4%) and G(2) (+8.1%) improved their (V)over dot O-2peak significantly more than G(CON) (+ 1.0%; P < 0.05). Conclusion: The present study has shown that when HIT incorporates P-max as the interval intensity and 60% of T-max as the interval duration, already highly trained cyclists can significantly improve their 40-km time trial performance. Moreover, the present data confirm prior research, in that repeated supramaximal HIT can significantly improve 40-km time trial performance.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

A genetic algorithm/method of moments approach to the optimization of an RF coil for MRI applications - Theoretical considerations - Abstract

A Combined Genetic Algorithm and Method of Moments design methods is presented for the design of unusual near-field antennas for use in Magnetic Resonance Imaging systems. The method is successfully applied to the design of an asymmetric coil structure for use at 190MHz and demonstrates excellent radiofrequency field homogeneity.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.