Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

In situ electron paramagnetic resonance (EPR) study of surface oxygen species on Au/ZnO catalyst for low-temperature carbon monoxide oxidation

Some paramagnetic superoxide ions detectable by electron paramagnetic resonance (EPR) can be generated on Au/ZnO catalyst by oxygen adsorption at room temperature as well as at 553 K. In both the cases, the O-2(-) ions are present on the catalyst surface. The disappearance of the O-2(-) signal by the introduction of carbon monoxide over the catalyst surface implies that the O-2(-) ions are either the active oxygen species or the precursors of the active oxygen species. The CO3- species produced are also detected by EPR. (C) 2001 Elsevier Science B.V. All rights reserved.

A novel target-field method for finite-length magnetic resonance shim coils: I. Zonal shims

This paper presents a new approach for the design of genuinely finite-length shim and gradient coils, intended for use in magnetic resonance imaging equipment. A cylindrical target region is located asymmetrically, at an arbitrary position within a coil of finite length. A desired target field is specified on the surface of that region, and a method is given that enables winding patterns on the surface of the coil to be designed, to produce the desired field at the inner target region. The method uses a minimization technique combined with regularization, to find the current density on the surface of the coil. The method is illustrated for linear, quadratic and cubic magnetic target fields located asymmetrically within a finite-length coil.

Asymmetric zonal shim coils for magnetic resonance applications

A method is presented for the systematic design of asymmetric zonal shim coils for magnetic resonance applications. Fourier-series methods are used to represent the magnetic field inside and outside a circular cylinder of length 2L and radius a. The current density on the cylinder is also represented using Fourier series. Any desired field can be specified in advance on the cylinder's radius, over some nonsymmetric portion pL

On a possible mechanism for peripheral nerve stimulation during magnetic resonance imaging scans

When patients undergo a magnetic resonance imaging scan, they are subject to both strong static and temporal magnetic fields. The temporal fields are designed to vary at each point in the region being imaged. This is achieved by the use of gradient coils. However, when the gradient coils are switched very rapidly, the strongly time-varying magnetic fields produced can be responsible for stimulating nerves in the peripheral regions of the body. This paper gives a somewhat novel explanation for this phenomenon. The physical mechanism suggested is supported by an illustrative theoretical calculation.

The stochastic design of force-minimized compact magnets for high-field magnetic resonance imaging applications

New designs for force-minimized compact high-field clinical MRI magnets are described. The design method is a modified simulated annealing (SA) procedure which includes Maxwell forces in the error function to be minimized. This permits an automated force reduction in the magnet designs while controlling the overall dimensions of the system. As SA optimization requires many iterations to achieve a final design, it is important that each iteration in the procedure is rapid. We have therefore developed a rapid force calculation algorithm. Novel designs for short 3- and 4-T clinical MRI systems are presented in which force reduction has been invoked. The final designs provide large homogeneous regions and reduced stray fields in remarkable short magnets. A shielded 4-T design that is approximately 30% shorter than current designs is presented. This novel magnet generates a full 50-cm diameter homogeneous region.

A segmentation-based and partial-volume-compensated method for an accurate measurement of lateral ventricular volumes on T-1-weighted magnetic resonance images

Lateral ventricular volumes based on segmented brain MR images can be significantly underestimated if partial volume effects are not considered. This is because a group of voxels in the neighborhood of lateral ventricles is often mis-classified as gray matter voxels due to partial volume effects. This group of voxels is actually a mixture of ventricular cerebro-spinal fluid and the white matter and therefore, a portion of it should be included as part of the lateral ventricular structure. In this note, we describe an automated method for the measurement of lateral ventricular volumes on segmented brain MR images. Image segmentation was carried in combination of intensity correction and thresholding. The method is featured with a procedure for addressing mis-classified voxels in the surrounding of lateral ventricles. A detailed analysis showed that lateral ventricular volumes could be underestimated by 10 to 30% depending upon the size of the lateral ventricular structure, if mis-classified voxels were not included. Validation of the method was done through comparison with the averaged manually traced volumes. Finally, the merit of the method is demonstrated in the evaluation of the rate of lateral ventricular enlargement. (C) 2001 Elsevier Science Inc. All rights reserved.

Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

Current density mapping approach for design of clinical magnetic resonance imaging magnets

Novel current density mapping (CDM) schemes are developed for the design of new actively shielded, clinical magnetic resonance imaging (MRI) magnets. This is an extended inverse method in which the entire potential solution space for the superconductors has been considered, rather than single current density layers. The solution provides an insight into the required superconducting coil pattern for a desired magnet configuration. This information is then used as an initial set of parameters for the magnet structure, and a previously developed hybrid numerical optimization technique is used to obtain the final geometry of the magnet. The CDM scheme is applied to the design of compact symmetric, asymmetric, and open architecture 1.0-1.5 T MRI magnet systems of novel geometry and utility. A new symmetric 1.0-T system that is just I m in length with a full 50-cm diameter of the active, or sensitive, volume (DSV) is detailed, as well as an asymmetric system in which a 50-cm DSV begins just 14 cm from the end of the coil structure. Finally a 1.0-T open magnet system with a full 50-cm DSV is presented. These new designs provide clinically useful homogeneous regions and have appropriately restricted stray fields but, in some of the designs, the DSV is much closer to the end of the magnet system than in conventional designs. These new designs have the potential to reduce patient claustrophobia and improve physician access to patients undergoing scans. (C) 2002 Wiley Periodicals, Inc.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Impact of malocclusion and orthognathic reconstruction surgery on resonance and articulatory function: an examination of variability in five cases

Articulatory patterns and nasal resonance were assessed before and 6 months after orthognathic reconstruction surgery in five patients with dentofacial deformities. Perceptual and physiological assessments showed disorders of nasality and articulatory function preoperatively, two patients being hyponasal, and one hypernasal. Four patients had mild articulatory deficits, and four had reduced maximal lip or tongue pressures. Operation resulted in different patterns of change. Nasality deteriorated in three patients and articulatory precision and intelligibility improved in only one patient and showed no change in the other four. Operation improved interlabial pressures in three patients, while its impact on tongue pressures varied, being improved in one case, deteriorating in one, and remaining unchanged in the other three. The variability in the results highlights the need for routine assessment of speech and resonance before and after orthognathic reconstruction. (C) 2002 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Science Ltd. All rights reserved.