Ideals Generated by Principal Minors.

Let X be a square matrix of indeterminates. Let K[X] denote the polynomial ring in those indeterminates over an algebraically closed field, K. A minor is principal means it is defined by the same row and column indices. We prove various statements about ideals generated by principal minors of a fixed size t. When t=2 the resulting quotient ring is a normal complete intersection domain. When t>2 we break the problem into cases by intersecting with the locally closed variety of rank r matrices. We show when r=n for any t, there is a K-automorphism of that maps the ideal generated by size t principal minors to the ideal generated by size n-t principal minors, inducing an isomorphism on the respectively defined schemes. When t=r we factor a matrix in the algebraic set as the product of its row space matrix, an invertible size t matrix, and its column space matrix. We show that for the analysis of components it is enough to consider irreducible algebraic sets in the product of two Grassmannians, Grass(t,n). For t=r we also observe the connection between such decompositions and matroid theory.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108987/1/wheeles_1.pd

Damping of the woodwind instrument reed material Arundo donax L

The viscoelastic properties (E', G', tanΦ, δ) of Arundo donax (AD) and a polypropylene-beech fiber composite (PPC) were measured from RT to 580K for various frequencies and strains. E' of AD varies between 5250-6250MPa depending on ageing at RT while E'(RT)=2250MPa of PPC is signifcantly lower. E' of the AD is higher than E' of PPC in the whole investigated temperature range with the exception of AD after a heat treatment up to 575K. Damping spectra exhibit peaks around 340K (Q=234kJ/mol) and 415K for the PPC related to relaxations in the crystalline part of polypropylene and the relaxation at melting temperature. For AD damping peaks were found at 350K (Q=320kJ/mol) related to the glass-rubber transition of lignin, at 420K due to a reorganization in the amorphous phase of lignin, at 480K related to micro-Brownian motions in the non-crystalline region of cell-wall polymers and reduction of the crystallinity of cellulose, and at 570K due to the polymeric compounds of wood and/or a decomposition of lignin. The course of E' and tanΦ of AD and PPC is comparable from 20-200Hz, whereas tanΦ of AD is lower than tanΦ of PPC while E' of AD is higher than E' of PPC.Fil: Weidenfeller, Bernd. Technische Universitat Clausthal; AlemaniaFil: Lambri, Osvaldo Agustin F.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Bonifacich, Federico Guillermo. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Arlic, Uwe. Technische Universitat Clausthal; AlemaniaFil: Gargicevich, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

Constructions of Large Graphs on Surfaces

We consider the degree/diameter problem for graphs embedded in a surface, namely, given a surface $\Sigma$ and integers $\Delta$ and $k$, determine the maximum order $N(\Delta,k,\Sigma)$ of a graph embeddable in $\Sigma$ with maximum degree $\Delta$ and diameter $k$. We introduce a number of constructions which produce many new largest known planar and toroidal graphs. We record all these graphs in the available tables of largest known graphs. Given a surface $\Sigma$ of Euler genus $g$ and an odd diameter $k$, the current best asymptotic lower bound for $N(\Delta,k,\Sigma)$ is given by $$\sqrt{\frac{3}{8}g}\Delta^{\lfloor k/2\rfloor}.$$ Our constructions produce new graphs of order \begin{cases}6\Delta^{\lfloor k/2\rfloor}& \text{if $\Sigma$ is the Klein bottle}\\ \(\frac{7}{2}+\sqrt{6g+\frac{1}{4}}\)\Delta^{\lfloor k/2\rfloor}& \text{otherwise,}\end{cases} thus improving the former value by a factor of 4.Comment: 15 pages, 7 figure

Metacognitive self-reflectivity moderates the relationship between distress tolerance and empathy in schizophrenia

Deficits in empathy seen in schizophrenia are thought to play a major role in the social dysfunction seen in the disorder. However, little work has investigated potential determinants of empathic deficits. This study aimed to fill that gap by examining the effects of two variables on empathy – distress tolerance and metacognitive self-reflectivity. Fifty-four people with schizophrenia-spectrum disorders receiving services at an urban VA or community mental health center were assessed for empathy, metacognition, and distress tolerance. Bivariate correlations and moderation methods were used to ascertain associations amongst these variables and examine interactions. Results revealed that, against hypotheses, empathy was not related at the bivariate level to either distress tolerance or metacognitive self-reflectivity. However, consistent with hypotheses, moderation analyses revealed that participants with higher self-reflectivity showed no relationship between distress tolerance and empathy, while those with lower self-reflectivity showed a relationship such that reduced ability to tolerate distress predicted reduced empathy. Taken together, results of this study suggest that lack of distress tolerance can negatively affect empathy in people with schizophrenia with lesser capacity for metacognitive self-reflection; thus, fostering self-reflectivity may help overcome that negative impact. Future work is needed investigating the impact of metacognitively-tailored interventions on empathy in this population

The canonical fractional Galois ideal at s=0

The Stickelberger elements attached to an abelian extension of number fields conjecturally participate, under certain conditions, in annihilator relations involving higher algebraic K-groups. In [Victor P. Snaith, Stark's conjecture and new Stickelberger phenomena, Canad. J. Math. 58 (2) (2006) 419--448], Snaith introduces canonical Galois modules hoped to appear in annihilator relations generalising and improving those involving Stickelberger elements. In this paper we study the first of these modules, corresponding to the classical Stickelberger element, and prove a connection with the Stark units in a special case.Comment: 22 page