Some of these curves are considered in a rather incidental way in the writings of Poincare.** However, the full concept of pseudo closed trajectories does not seem to have been discussed explicitly heretofore. We assume that all of the variables in the equations (1) are real, that the functions X and Y are continuous in an open connected region R in the xy-plane, that these functions satisfy Li...

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they ...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

In this work, we employ quantitative methods from the realm of statistics and machine learning to develop novel methodologies for author attribution and textual analysis. In particular, we develop techniques and software suitable for applications to Classical study, and we illustrate the efficacy of our approach in several interesting open questions in the field. We apply our numerical analysis...

The previous chapter reviewed three traditions of genre studies, namely, the new rhetoric, systemic functional and ESP perspectives on genre. While new rhetoric genre analyses focus on the interrelation between text and context and SFL genre studies stress the linguistic analysis of text, ESP approaches to genre take an approach that is some way between these two. This chapter extends the discu...

The paper begins with a brief overview of sense and sense-making with reference to cohesion, coherence and intertextuality. Based on a word-by-word close analysis, it charts the semantic coherence of a classical Chinese poem, Ye Yu Ji Bei by Li Shangyin, followed by a mapping of the text’s metaphorical coherence in terms of ontological metaphors. Using the poem as a case example, the paper exam...

Visualizing the book of the future, one might consider multi-modal integrations, non-linear reading strategies, Internet distribution, and customizable configurations to suit different user/reader profiles. In the first part of this paper, we discuss such concepts critically. The second part deals with a more profound aspect of electronic documents, one which could modify the very act of readin...