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.

Enhanced vector competence of Aedes aegypti (Diptera : Culicidae) from the torres strait compared with mainland Australia for dengue 2 and 4 viruses

Australian Aedes aegypti (L.) mosquitoes colonized from the Torres Strait and three mainland localities (Charters Towers, Townsville, and Cairns) were fed on blood suspensions containing dengue virus type 2 (DEN-2) or dengue virus type 4 (DEN-4). Variation was found in oral susceptibility to DEN-2 (59-99% infection) and DEN-4 (28-79% infection) among Ae. aegypti assayed for virus at 8, 12, 16, or 20 d after ingestion of infected blood. Torres Strait Ae. aegypti were the most susceptible to DEN-2 and were significantly more efficient in transmission to capillary tube at 16 d (76% transmission) than mainland Ae. aegypti populations (20-28% transmission). Torres Strait Ae. aegypti were also the most susceptible to DEN-4, although transmission did not vary significantly from mainland populations at 16 d (12% compared with 0-4%) or 20 d (16% compared with 4-16%). Disseminated infection (i.e., leg infection) with either DEN-2 or DEN-4 was not an accurate predictor of transmission potential. This study demonstrates differences among Australian Ae. aegypti populations in vector competence for DEN-2 and DEN-4. Torres Strait Ae. aegypti were more frequently infected and able to transmit DEN-2 at higher rates than mainland populations. These data indicate that the Torres Strait region is potentially more receptive to dengue transmission than mainland localities, a finding discussed with respect to past outbreaks.

Vector competence of Australian mosquitoes (Diptera : Culicidae) for Japanese encephalitis virus

Australian mosquitoes were evaluated for their ability to become infected with and transmit a Torres Strait strain of Japanese encephalitis virus. Mosquitoes, which were obtained from either laboratory colonies and collected using Centers for Disease Control and Prevention light traps baited with CO2 and octenol or reared from larvae, were infected by feeding on a blood/sucrose solution containing 10(4.5+/-0.1) porcine stable-equine kidney (PS-EK) tissue culture infectious dose(50)/ mosquito of the TS3306 virus strain. After 14 d, infection and transmission rates of 100% and 81%, respectively, were obtained for a southeast Queensland strain of Culex annulirostris Skuse, and 93% and 61%, respectively, for a far north Queensland strain. After 13 or more days, infection and transmission rates of > 90% and greater than or equal to 50%, respectively, were obtained for southeast Queensland strains of Culex sitiens Wiedemann and Culex quinquefasciatus Say, and a far north Queensland strain of Culex gelidus Theobald. Although infection rates were > 55%, only 17% of Ochlerotatus vigilax (Skuse) and no Cx. quinquefasciatus, collected from far north Queensland, transmitted virus. North Queensland strains of Aedes aegypti L., Ochlerotatus kochi (Donitz), and Verrallina funerea (Theobald) were relatively refractory to infection. Vertical transmission was not detected among 673 F, progeny of Oc. vigilax. Results of the current vector competence study, coupled with high field isolation rates, host feeding patterns and widespread distribution, confirm the status of Cx. annulirostris as the major vector of Japanese encephalitis virus in northern Australia. The relative roles of other species in potential Japanese encephalitis virus transmission cycles in northern Australia are discussed.

Winding patterns for actively shielded shim coils with asymmetric target-fields

A method is presented for calculating the currents and winding patterns required to design independent zonal and tesseral shim coils for magnetic resonance imaging. Both actively shielded and unshielded configurations are considered, and the region of interest can be located asymmetrically with respect to the coil's length. Streamline, target-field and Fourier-series methods are utilized. The desired target-field is specified at two cylindrical radii, on and inside a circular conducting cylinder of length 2L and radius a. The specification is over some asymmetric portion pL < z < qL of the coil's length (-1 < p < q < 1). Arbitrary functions are used in the outer sections, -L < z < pL and qL < z < L, to ensure continuity of the magnetic field across the entire length of the coil. The entire field is then periodically extended as a half-range cosine Fourier series about either end of the coil. The resultant Fourier coefficients are then substituted into the Fourier-series expressions for the internal and external magnetic fields, and current densities and stream functions on both the primary coil and shield. A contour plot of the stream function directly gives the required coil winding patterns. Spherical harmonic analysis and shielding analysis on field calculations from a ZX shim coil indicate that example designs and theory are well matched.

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.

Influence of magnetically-induced E-fields on cardiac electric activity during MRI: A modeling study

In modern magnetic resonance imaging (MRI), patients are exposed to strong, time-varying gradient magnetic fields that may be able to induce electric fields (E-fields)/currents in tissues approaching the level of physiological significance. In this work we present theoretical investigations into induced E-fields in the thorax, and evaluate their potential influence on cardiac electric activity under the assumption that the sites of maximum E-field correspond to the myocardial stimulation threshold (an abnormal circumstance). Whole-body cylindrical and planar gradient coils were included in the model. The calculations of the induced fields are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic, whole-body model. The potential for cardiac stimulation was evaluated using an electrical model of the heart. Twelve-lead electrocardiogram (ECG) signals were simulated and inspected for arrhythmias caused by the applied fields for both healthy and diseased hearts. The simulations show that the shape of the thorax and the conductive paths significantly influence induced E-fields. In healthy patients, these fields are not sufficient to elicit serious arrhythmias with the use of contemporary gradient sets. However, raising the strength and number of repeated switching episodes of gradients, as is certainly possible in local chest gradient sets, could expose patients to increased risk. For patients with cardiac disease, the risk factors are elevated. By the use of this model, the sensitivity of cardiac pathologies, such as abnormal conductive pathways, to the induced fields generated by an MRI sequence can be investigated. (C) 2003 Wiley-Liss, Inc.

Instrumentation used to measure residential magnetic fields and currents

The equipment used to measure magnetic fields and, electric currents in residences is described. The instrumentation consisted of current transformers, magnetic field probes and locally designed and, built signal conditioning modules. The data acquisition system was capable of unattended recording for extended time periods. The complete system was calibrated to verify its response to known physical inputs. (C) 2003 ISA-The Instrumentation Automation Society.