Transversality and intersection theory / Sard’s theorem, topological analysis approach Introduction The concept of transversality deals with the intersection of two objects; in several ways, one may consider it the reverse of tangency. For transversality to occur between two sub- manifolds, their tangential spaces at every intersection point need to extend across the ambient manifold’s tangent space. Transversality, invariably, particularly fails in case of tangency between two sub- manifolds. However, a more

Gender is a complex concept that varies across cultures and time periods (Butler, 1990). It encompasses a range of biological, psychological, social, and cultural factors that shape individuals' perceptions, beliefs, and behaviors based on perceived sex (West & Zimmerman, 2009). Gender cultural analysis examines how cultural norms, values, and expectations influence the construction of gender roles and identities, as well as their implications for power relations and social inequalities (Connell,

Dark Ages The author of this report is asked to answer to a number of questions relating to the Dark Ages. Specifically, the author is asked to define what "Dark Ages" means. Second, the author is asked to ask how this society unwittingly paved the way for a preservation of literature and art from the classical era. In particular, the author is asked to identify how Ireland was instrumental in this

Theoretically, CLIL draws on research that situates the integration of language and content as the relationship between form and meaning. An understanding of the theory and practice related to the content-based classroom is essential to the present study. In this section of the chapter, I outline the underlying theory and rationale commonly cited as a basis for CLIL, review empirical research that has evaluated CLIL in the classroom, and

race and racial inequality are structured in the United States of America. It explains the concepts of oppression and privilege, describing ways in which various social institutions (educational system, the media, the economy, politics and the state, criminal justice system, etc.) intersect to construct categories of difference in society. It concludes with a policy suggestions that would help to decrease racial and ethnic inequality in U.S. society. Institutional Structures and

), [he knows] that media companies are responsive to pressure when it is sustained, sophisticated and well executed," he fails to offer any concrete examples of this kind of pressure or how it might actually be applied (Schechter, 2003, p. 242). He does propose "a Media and Democracy Act, an omnibus bill that could be a way of showing how all of these issues are connected," but he does not