The shortest lengths and the enclosure method for time dependent problems

In this paper, we discuss the role of the shortest distance in time-dependent enclosure method for the inverse problems when the inclusions are embedded in a non-layered or two-layered medium. Furthermore, the regularity assumptions for the boundaries of the inclusions are relaxed.Comment: 21cpage

ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR THE LAPLACE EQUATION WITH A LARGE SPECTRAL PARAMETER AND THE INHOMOGENEOUS ROBIN TYPE CONDITIONS

Reduced problems are elliptic problems with a large parameter (as the spectral parameter) given by the Laplace transform of time dependent problems. In this paper, asymptotic behavior of the solutions of the reduced problem for the classical heat equation in bounded domains with the inhomogeneous Robin type conditions is discussed. The boundary of the domain consists of two disjoint surfaces, outside one and inside one. When there are inhomogeneous Robin type data at both boundaries, it is shown that asymptotics of the value of the solution with respect to the large parameter at a given point inside the domain is closely connected to the distance from the point to the both boundaries. It is also shown that if the inside boundary is strictly convex and the data therein vanish, then the asymptotics is different from the previous one. The method for the proof employs a representation of the solution via single layer potentials. It is based on some non trivial estimates on the integral kernels of related integral equations which are previously established and used in studying an inverse problem for the heat equation via the enclosure method

Erasing the Color Line: The Racial Formation of Creoles of Color and the Public School Integration Movement in New Orleans, 1867-1880

This thesis examines the public school racial integration movement of Creoles of color, a francophone interracial group in New Orleans, from 1867 to 1880. During Reconstruction, Creoles of color succeeded in desegregating about one-third of the city public schools. This thesis argues that the integration campaign of Creoles of color was an attempt to maintain their in-between identity--being neither fully whites nor fully blacks and being both Creoles and Americans--and an effort to erase the color line by improving the social status of black Americans to equal that of white Americans. Creoles of color forged desegregation by manipulating their ambiguous ethno-racial heritage and by negotiating with white radical Republicans, white New Orleanians and Anglophone blacks. Focusing on the political, legal and grass-root struggles of Creoles of color, this thesis reveals that they challenged segregation as it symbolized the emergence of biracial hierarchy in post-Civil War New Orleans.Master of Art