Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate gl(2\2) current superalgebra at general level k. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented. (C) 2003 Elsevier B.V. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

The modeling of turbulent reactive flows based on multiple mapping conditioning

A new modeling approach-multiple mapping conditioning (MMC)-is introduced to treat mixing and reaction in turbulent flows. The model combines the advantages of the probability density function and the conditional moment closure methods and is based on a certain generalization of the mapping closure concept. An equivalent stochastic formulation of the MMC model is given. The validity of the closuring hypothesis of the model is demonstrated by a comparison with direct numerical simulation results for the three-stream mixing problem. (C) 2003 American Institute of Physics.

An electromagnetic-field method modeling of a radial line planar antenna with coupling probes

This communications describes an electromagnetic model of a radial line planar antenna consisting of a radial guide with one central probe and many peripheral probes arranged in concentric circles feeding an array of antenna elements such as patches or wire curls. The model takes into account interactions between the coupling probes while assuming isolation of radiating elements. Based on this model, computer programs are developed to determine equivalent circuit parameters of the feed network and the radiation pattern of the radial line planar antenna. Comparisons are made between the present model and the two-probe model developed earlier by other researchers.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

A rapid method for determining recent sunscreen use in field studies

The role of sunscreens in preventing skin cancer and melanoma is the focus of ongoing research. Currently, there is no objective measure which can be used in field studies to determine whether a person has applied sunscreen to their skin, and researchers must use indirect assessments such as questionnaires. We sought to develop a rapid, non-invasive method for identifying sunscreen on the skin for use in epidemiological studies. Our basic method is to swab the skin, elute any residues which have been adsorbed onto the swab by rinsing in ethanol, and submit the eluted washings for spectrophotometric analysis. In a controlled study, we applied 0.1 ml of sunscreen to a 50 cm(2) grid on both forearms of 21 volunteers. Each forearm was allocated one of 10 different sunscreen brands. The skin was swabbed after intervals of 20 min, 1 h, 2 h and 4 h. In a field study conducted among 12 children aged 2-4 years attending a child care centre, sunscreen was applied to the faces of half the children. Swabs were then taken from the face and back of all children without knowledge of sunscreen status. In the controlled study, sunscreen was clearly detectable up to 2 h after application for all brands containing organic sunscreen, and marginally detectable at 4 h. In the field study, this method correctly identified all children with and without sunscreen. We conclude that spectrophotometric analysis of skin swabs can reliably detect the presence of sunscreen on the skin for up to 2 It after application. (C) 2002 Elsevier Science B.V. All rights reserved.

Field evaluation of a sentinel mosquito (Diptera : culicidae) trap system to detect Japanese encephalitis in remote Australia

Incursions of Japanese encephalitis (JE) virus into northern Queensland are currently monitored using sentinel pigs. However, the maintenance of these pigs is expensive, and because pigs are the major amplifying hosts of the virus, they may contribute to JE transmission. Therefore, we evaluated a mosquito-based detection system to potentially replace the sentinel pigs. Single, inactivated JE-infected Culex annulirostris Skuse and C. sitiens Wiedemann were placed into pools of uninfected mosquitoes that were housed in a Mosquito Magnet Pro (MM) trap set under wet season field conditions in Cairns, Queensland for 0, 7, or 14 d. JE viral RNA was detected (cycling threshold [CT] = 40) in 11/ 12, 10/14, and 2/5 pools containing 200, 1,000, and 5,000 mosquitoes, respectively, using a TaqMan real-time reverse transcription-polymerase chain reaction (RT-PCR). The ability to detect virus was not affected by the length of time pools were maintained under field conditions, although the CT score tended to increase with field exposure time. Furthermore, JE viral RNA was detected in three pools of 1,000 mosquitoes collected from Badu Island using a MM trap. These results indicated that a mosquito trap system employing self-powered traps, such as the MosquitoMagnet, and a real-time PCR system, could be used to monitor for JE in remote areas.

Estimation of body fatness from body mass index and bioelectrical impedance: comparison of New Zealand European, Maori and Pacific Island children

Objective: To compare percentage body fat (%BF) for a given body mass index (BMI) among New Zealand European, Maori and Pacific Island children. To develop prediction equations based on bioimpedance measurements for the estimation of fat-free mass (FFM) appropriate to children in these three ethnic groups. Design: Cross-sectional study. Purposive sampling of schoolchildren aimed at recruiting three children of each sex and ethnicity for each year of age. Double cross-validation of FFM prediction equations developed by multiple regression. Setting: Local schools in Auckland. Subjects: Healthy European, Maori and Pacific Island children (n = 172, 83 M, 89 F, mean age 9.4 +/- 2.8(s. d.), range 5 - 14 y). Measurements: Height, weight, age, sex and ethnicity were recorded. FFM was derived from measurements of total body water by deuterium dilution and resistance and reactance were measured by bioimpedance analysis. Results: For fixed BMI, the Maori and Pacific Island girls averaged 3.7% lower % BF than European girls. For boys a similar relation was not found since BMI did not significantly influence % BF of European boys ( P = 0.18). Based on bioimpedance measurements a single prediction equation was developed for all children: FFM (kg) = 0.622 height (cm)(2)/ resistance +0.234 weight (kg)+1.166, R-2 = 0.96, s. e. e. = 2.44 kg. Ethnicity, age and sex were not significant predictors. Conclusions: A robust equation for estimation of FFM in New Zealand European, Maori and Pacific Island children in the 5 - 14 y age range that is more suitable than BMI for the determination of body fatness in field studies has been developed. Sponsorship: Maurice and Phyllis Paykel Trust, Auckland University of Technology Contestable Grants Fund and the Ministry of Health.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may he one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time.-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.

Calculation of electric fields induced by body and head motion in high-field MRI

In modern magnetic resonance imaging (MRI), patients are exposed to strong, nonuniform static magnetic fields outside the central imaging region, in which the movement of the body may be able to induce electric currents in tissues which could be possibly harmful. This paper presents theoretical investigations into the spatial distribution of induced electric fields and currents in the patient when moving into the MRI scanner and also for head motion at various positions in the magnet. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic, full-body, male model. 3D field profiles from an actively shielded 4T magnet system are used and the body model projected through the field profile with a range of velocities. The simulation shows that it possible to induce electric fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The results are extrapolated to very high field strengths and tabulated data shows the expected induced currents and fields with both movement velocity and field strength. (C) 2003 Elsevier Science (USA). All rights reserved.

Multilayer transverse gradient coil design

In small, cylindrical gradient coils consisting of a single layer of wires, the limiting factor in achieving large magnetic field gradients is the rapid increase in coil resistance with efficiency. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, mathematical expressions have been developed that allow the design of multilayer coils. These expressions have previously been applied to the design of a four-layer z-gradient coil. As a further development, the equations have now been modified to allow the design of multilayer transverse gradient coils. The variation in coil performance with the number of layers employed has been investigated for coils of a size suitable for use in NMR microscopy, and the effect of constructing the coil using wires or cuts in a continuous conducting surface has also been assessed. We find that at fixed resistance a small wire-wound two-layer coil offers an increase in efficiency of a factor of about 1.5 compared with a single-layer coil. In addition, a two-layer coil of 10-mm inner diameter has been designed and built. This coil had an efficiency of 0.41 Tm-1 A(-1), a resistance of 0.96 +/- 0.01 Omega, and an inductance of 22.3 +/- 0.2 muH. The coil produces a gradient that deviates from linearity by less than 5% over a central cylindrical region of interest of height and length 6.2 mm. (C) 2003 Wiley Periodicals, Inc.