Non-ideal Circumstances Research Articles

Solving for non-ideal conditions in two-dimensional Fourier transform magnetic resonance imaging using a generalised inverse transform

Magnetic resonance imaging uses real and complex forms of the Fourier transform and to a lesser degree the Radon transform and their appropriate inverses. Under ideal conditions, these solutions are fast and optimal in the sense of signal-to-noise ratio (S/N). In practice, though, the phase of the signal may not be ideal so that the effective forward transform is no longer a Fourier transform. Using the inverse Fourier transform would then result in an image with artifacts. In this paper the generalised matrix inverse problem is addressed for such non-ideal conditions. Solutions are obtained for the following non-ideal circumstances: non-uniform sampling; imaging in the presence of motion; deconvolution of T2 effects; resolution enhancement; one-sided data reconstruction. The method is applicable to other deviant models as well. The goal is to maintain some specified property of the image, such as resolution, with minimal production of artifacts. A concomitant loss in S/N is inevitable for such trade-offs, but is often not a serious problem compared with the artifacts themselves.

Justice and Charity

The distinction between justice and charity is thought to be fundamental in ethical theory. Yet remarkably little has been done to develop the distinction systematically or to articulate the role it is to play in ethical theory. Four theses about the difference between justice and charity are widely held and rarely argued for: (1) Duties ofjustice (with the exception of those which correspond to special rights generated by promising or special relationships or reciprocal group undertakings that generate obligations of fair play) are exclusively negative duties (duties to refrain from certain actions); duties of charity are generally positive duties (duties to render aid). (2) Duties of justice may be enforced; duties of charity may not. (3) Duties of justice are perfect duties; duties of charity are imperfect. (Perfect duties are determinate both with regard to the content of what is required and with regard to the identity of the individual who is the object of the duty; duties of charity are indeterminate in both senses: the kind and amount of aid, as well as the choice of a recipient are left to the discretion of the benefactor.) (4) Justice is a matter of rights; charity is not (duties of justice have correlative rights; duties of charity do not), and what is one's right is owed to one, the lack of which gives one justified grounds for complaint that one has been wronged. It is far from clear how claims 1-4 are supposed to be related to one another. Although all four purport to characterize differences between justice and charity, we shall see that not all are equally plausible candidates for answering the question, What makes something a duty of charity rather than a duty of justice, and vice versa? Moreover, it will become clear that some of these claims are thought to be derivable from the others, although the connecting assumptions are often either not made explicit or not argued for. By analyzing theses 1-4 and by articulating and assessing the grounds for asserting them, I shall explore the distinction between justice and

Angular relation and energy dependence of Andreev reflection.

Andreev reflection at an interface between an Ag single crystal and a Pb film is studied by an electron-focusing experiment. Quasiparticles are observed to be reflected within a cone with an angle approx. =10/sup -4/ rad centered about the incident direction. The energy dependence of Andreev reflection is found to be consistent with theory. In spite of the nonideal circumstances during the Pb deposition, the probability for Andreev reflection approaches that of a perfect interface.