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"Through current day, only forty-three men have held the office of the President of the United States, and some have been sanctified and some reviled. This historical work addresses the careers of the first ten presidents, men who made vital contributions not only to the office of the presidency, but to the course of the fledgling nation"--Provided by publisher.
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Dr. Pinciu engaged in collaborative research with T.S. Michael from the U.S. Naval Academy focusing on visibility problems, known as art gallery (polygon interior), fortress (polygon exterior), and prison yard (polygon interior and exterior) problems. The outcome resulted in two conference presentations and an article accepted for publication, with additional presentations and another article to follow.
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When solving an algorithmic problem involving a polyhedron in R 3, it is common to start by partitioning the given polyhedron into simplier ones. The most common process is called triangulation and it refers to partitioning a polyhedron into tetrahedra in a face-to-face manner. In this paper instead of triangulations we will consider tilings by tetrahedra. In a tiling the tetrahedra are not required to be attached to each other along common faces. We will construct several polyhedra which can not be triangulated but can be tiled by tetrahedra. We will also revisit a nontriangulatable polyhedron of Rambau and a give a new proof for his theorem. Finally we will identify new families of non-tilable, and thus non-triangulable polyhedra.
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A problem posed by Vasconcelos [33] on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well. © 2011 Elsevier B.V.
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For a Noetherian local ring, we analyze conjectural relationships between the first Hilbert coefficient of a parameter ideal and the first partial Euler characteristic of its Koszul complex. Given their similar role as predictors of the Cohen-Macaulay property, we consider a direct comparison between them. For parameter ideals generated by d-sequences these numbers are related in an explicit formula. We then turn to study of families of parameter ideals that have the same Hilbert function. © 2012 Elsevier Inc.
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In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of finite co-length. Because three of the corresponding modules are Artinian, some of these relationships are very effective, with the novel approach opening up tracks to the determination of the equations and also to processes of going from homologically defined sets of equations to higher degrees ones. While not specifically directed towards the extraction of elimination equations, it will show how some of these arise naturally. © 2012 Sociedade Brasileira de Matemática.
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