Vascular morphology by three-dimensional magnetic resonance imaging

A three-dimensional examination of blood vessels is provided using MR data from seven cases. The vascular surfaces are constructed with an algorithm that automatically follows the selected artery or vein and generates a projected three-dimensional gradient shaded image. Fast 3DFT pulse sequences were optimized to enhance the time-of-flight contrast of the intravascular region. By increasing the surface threshold value in a three-dimensional head study, the flesh of a patient's face was peeled away to demonstrate the superfacial temporal artery. Gated cardiac images show the great vessels and cardiac chambers. A three-dimensional view of the aorta shows an irregular surface in the vicinity of an adrenal tumor. 3D MR exams provide a non-invasive technique for assessing vascular morphology in a clinical setting.     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

What are We Developing? A Case Study of a College Mathematics Program

Over one‐third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses.