In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K_n</em> must be a triangle (for <em>n</em> &ge; 3). We prove that, for the larger class of pseudolinear drawings, the outer face must be a triangle. The other main result is the next step toward Guy's Conjecture that the crossing number of <em>K_n</em> is $(1/4)[n/2][(n-1)/2][(n-2)/2][(n-3)/2]$. We show that the conjecture is true for <em>n</em> = 11,12; previously the conjecture was known to be true for <em>n</em> &le; 10. We also prove several minor results.

In this thesis we prove two main results. The Triangle Conjecture asserts that the convex hull of any optimal rectilinear drawing of <em>K_n</em> must be a triangle (for <em>n</em> &ge; 3). We prove that, for the larger class of pseudolinear drawings, the outer face must be a triangle. The other main result is the next step toward Guy's Conjecture that the crossing number of <em>K_n</em> is $(1/4)[n/2][(n-1)/2][(n-2)/2][(n-3)/2]$. We show that the conjecture is true for <em>n</em> = 11,12; previously the conjecture was known to be true for <em>n</em> &le; 10. We also prove several minor results.

The crossing number of a graph is the minimum number of pairwise crossings of edges among all planar drawings of the graph. A graph G is k-crossing critical if it has crossing number k and any proper subgraph of G has a crossing number less than k. The set of 1-crossing critical graphs is is determined by Kuratowski’s Theorem to be {K5, K3,3}. Work has been done to approach the problem of classifying all 2-crossing critical graphs. The graph V2n is a cycle on 2n vertices with n intersecting chords. The only remaining graphs to find in the classification of 2-crossing critical graphs are those that are 3-connected with a V8 minor but no V10 minor. This paper seeks to fill some of this gap by defining and completely describing a class of graphs called fully covered. In addition, we examine other ways in which graphs may be 2-crossing critical. This discussion classifies all known examples of 3-connected, 2-crossing critical graphs with a V8 minor but no V10 minor.

Caryl Phillips’s novel Crossing the River deals with European colonialism and the consequences of it. Crossing the River is a novel which embraces characters from colonized cultures as well as characters from colonizing cultures. Following a timeline that begins in 1752 and ends in 1963, the novel shows slavery in progress as well as what transpires in the aftermath of slavery        In this essay I will argue that Caryl Phillips demonstrates the complexity of colonialism and slavery in his novel Crossing the River; he approaches the two concepts from different perspectives and shows us that colonialism and slavery are complicated concepts. Caryl Phillips uses narrative to demonstrate the negative sides of colonialism and slavery, to show that the negative aspects of the two concepts can affect not only the colonized people but also the colonizing people.        Colonialism, in its traditional sense, is present in some of the novel’s episodes but slavery, in different forms, appears in all episodes. Nevertheless, all episodes in Crossing the River have a common origin; which Phillips reminds us about by using the relationship between plot and story. Diversity is an important theme in the novel. From a narrative perspective, Crossing the River has a diversity of narrators who tell their stories as well as other persons’ stories. There are female narrators as well as male ones; some narrators are known while other narrators are unknown. The ways the episodes are told are diversified. Some of the episodes follow a chronological line (“The Pagan Coast” and “Crossing the River”) while other episodes jump back and forth in time (“West” and “Somewhere in England”). The forms of narration are diversified, not only between the individual episodes but also within some of the episodes. Crossing the River plays with diversity in several layers. The structure of the novel is as diversified as the number of narrators, a diversity of ways of dealing with the main themes results in a diversity of fates for Phillips’s characters. Caryl Phillips combines structure with content to demonstrate that colonialism and slavery are problematic concepts: the negative consequences of the two concepts can, in different ways and in different degrees, affect colonized people as well as those responsible for colonialism.

The main purpose of this thesis is to detect pedestrian crossing by static and dynamic image processing. This technique can help the blind and the disabled people to find the pedestrian crossing and walk through it safely. Until now there is no research about detecting pedestrian crossing in Taiwan. Therefore, this article applies the algorithm of Bipolarity feature in an image-based technique. In this thesis, the Bipolarity is regarded as the main feature in detecting pedestrian crossing. At first, it uses the features of pedestrian crossing, the black road surface is painted with constant-width periodic white stripes. After computation, the analysis and comparison in an image of intensity distribution is obtained. And the background will be eliminated. Secondly, Connected Component Labeling is used to extract the most similar region, and the marked region will be detected by the image. Finally, this thesis will detect whether the crossing exist or not in the marked region and measure the length of crossing. In dynamic model, the real-time image processing technique combines with wheelchair robot in order to walk through pedestrian crossing automatically, and image processing technique provides real-time offset and angle of displacement for the wheelchair robot to control and reach the destination. In this thesis, the image processing is in PC-base, and it receives the information by using a digital camera to record the real scene of pedestrian crossing. Keywords:pedestrian crossing , image processing, wheelchair robot

The purpose of this thesis is to investigate radio systems for the protection of vehicles and grade crossings. The protection function used with wireless communication, associated with grade crossings (the vehicles), uses the radio propagation to dispatch message (data) from the radio facilities to the vehicles when the emergency button is pushed to enable the operator to assess the emergency situation in advance. The rule for static and non-static measurements of the radio system, concerned with the crossing, is able to offer an improved spectrum assignment tool. All measurement data was derived from measurements performed for the trains of The Taiwan Railway Administration. The results are compared with the European Norm and China National Standard. Thus, the electromagnetic interferences due to trains can be analyzed. In order to estimate the radio propagation distances, we particularize the several modes of radio propagation in detail, and use the Lagrange method to analyze and determine the distance.

By examining the range of stances that white characters in Hollywood films are represented as taking in relation to blackness, this dissertation considers the question of how language becomes ideologically linked to categories of race through linguistic representations. Through an analysis of 59 films (1979-2008) from multiple genres, this study focuses on the linguistic practices of the characters that contribute to larger semiotic practices performed by discernible social types. The first linguistic practice, crossing, plays on the stereotype of the inauthentic, white male, who tries to gain coolness through linguistic representations of African Americans. The second practice, passing, conjures images of blackface because in addition to using linguistic representations of African Americans, the passing characters darken their skin. By demonstrating complex links between language and social meanings such as ideologies about authenticity, identity and racial and gendered stereotypes, these films use linguistic features along with other visual and physical semiotic displays to both construct and comment on black and white authenticity. Specifically, crossing was found to comment on disseminated images of the young, white male as lacking a particular type of masculinity and sexuality and overcompensating for them by imitating widely circulating images of the hypermasculine, hypersexual and hyperphysical black male. In addition, it commented on the tendency to read this linguistic practice as inauthentic. Therefore, the social meaning of the white linguistic representations of African Americans used when crossing was found to be related to authenticity or who had the right to use ethnically-marked linguistic features. On the other hand, passing was argued to communicate the ideologies that some whites may have of African Americans, particularly African American men. The linguistic resources utilized in these performances are not used to form identity, but for humor and to distance the character from being read as traditional minstrelsy. By highlighting some of the linguistic strategies that speakers in Hollywood use to (re)produce not only indexical links between linguistic forms and racialized stereotypes but also ideologies about racial authenticity, this dissertation provides an empirical study of some of the semiotic practices that involve the re-indexicalization of minority vernacular resources by members of the majority. / text

We defined a new type of open Gromov-Witten invariants on hyperK\"aher manifolds with holomorphic / Mathematics

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Studies on chromosomal segregation in higher organisms have established a definite relationship between crossing-over and nondisjunction -- the two appear to be inversely correlated. Most of the experiments performed involve segregation from inversion and translocation heterozygotes. [...]