We study satellites of Legendrian knots in R and their relation to the Chekanov–Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in R and augmentations of its DGA by showing that the DGA has finite-dimensional representations if and only if there exist certain rulings of satellites of the knot. We...

The Americans with Disabilities Act (ADA) was signed into law nearly a decade ago. The ADA is designed to protect persons with disabilities from discrimination in nearly every aspect of American life. This article focuses on a number of recent court rulings that help to clarify important components of the ADA. It is critical for health and human services professionals to be aware of these recen...

A non-linear differential equation is analyzed to determine the geodesic curves on ruled surfaces with time-like rulings inR31. When it is assumed that curvature and torsion of the base curve and components with respect to Frenet’s frame of time-like straight-line are constants, for a special integration constant, it appears that the resulting non-linear differential equation can be integrated ...

In this article, we research on the correspondences between the geometry of del Pezzo surfaces Sr and the geometry of Gosset polytopes (r−4)21. We study skew a-lines(a ≤ r), exceptional systems and rulings, and we explain their correspondences to (a− 1)-simplexes, (r − 1)-simplexes and (r − 1)-crosspolytopes in (r − 4)21. And we apply these correspondences to the monoidal transform for lines an...

one of the significant legal-theological rule, which has drawn little attention in legal texts, is the rule of “not reprimanding a person for another person’s sin and the unaccountability of the person for other people’s action,” which is expressed as part of āya 164 of sūrat al-an‘ām, ﴾no bearer shall bear another's burden﴿. according to this rule, which includes both matters of this world and...

justice rule is among the legal rules that have less dealt with. application of this rule is based on achievement of justice as an attribute for legal rulings. some jurists have no regarded human beings to be capable of comprehending the legal rulings as just and have subjected it to the legislator’s view. thus, using this rule in inference of legal issues and extending it to jurisprudence has ...

The extent and existence of defensive medicine in the face of medical malpractice liability pressure is a perennial subject of both policy and academic debate. In this paper, I investigate the impact of a series of court rulings in Taiwan that increased physicians’ liability risks, and a subsequent amendment to the law that reversed the courts’ rulings, on physicians’ test-ordering behavior and...