# University of Iowa Department of Mathematics

Overview
Works: 74 works in 75 publications in 1 language and 79 library holdings QA171,
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Most widely held works about University of Iowa

Most widely held works by University of Iowa
Decision problems in group theory by Andrzej Włodzimierz Mostowski( Book )

1 edition published in 1969 in English and held by 3 WorldCat member libraries worldwide

The report is primarily an exposition of current material on the presentation of groups with particular attention given to the word problem and to algorithms for effective computations. (Author)
Geometry in motion in the manuscripts of Leonardo da Vinci by Matilde Macagno( Book )

1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide

Factorization in integral domains without identity by Jonathan Preisser( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

Springer varieties from a topological perspective by Heather Michelle Russell( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

Generalizations of GCD-domains and related topics by Rebecca Lynn Lewin( )

2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide

GCD-domains are an important class of integral domains from classical ideal theory. In a GCD-domain, the intersection of any two principal ideals is principal. This property can be generalized in several different ways. A domain for which the intersection of any two invertible ideals is invertible is called a generalized GCD-domain (GGCD-domain). If for elements $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $a\sp n R\ \cap\ b\sp n R$ principal, we say $R$ is an almost GCD-domain (AGCD-domain). Combining these two definitions, we get an almost generalized GCD-domain (AGGCD-domain)--for $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $a\sp n R \cap b\sp n R$ invertible. Anderson and Zafrullah began the study of the first two of these generalizations. They showed that the integral closure of an AGCD-domain is also an AGCD-domain. We show that, in general, an overring of an AGCD-domain need not be an AGCD-domain. Certain special types of overrings do, however, inherit the property. Among these, it is shown, are localizations and LCM-stable overrings. A similar result holds for the AGGCD-domains. Relationships between these classes of domains and the classical domains of ring theory are investigated. Wealso investigate how adding the property that $R$ is Noetherian affects an AGCD- or AGGCD-domain. It is shown that a Noetherian AGCD-domain is almost weakly factorial, that is, $R$ = $\cap R\sb P$, where $P$ ranges over all rank one primes of $R$, has finite character and $R$ has torsion t-class group. Similarly, it is shown that a Noetherian AGGCD-domain is weakly Krull, that is, $R$ = $\cap R\sb P$, where $P$ ranges over all rank one primes of $R$, has finite character. Finally, we consider two additional generalizations defined using the ideal $I\sb n$, where $I\sb n$ = $\{i\sp n\ \vert\ i \in I\}$. A domain $R$ is called a nearly GCD-domain or NGCD-domain (respectively nearly generalized GCD-domain or NGGCD-domain) if for $a, b \in R - \{0\}$, there is an $n$ = $n(a, b)$ with $\lbrack (a, b)\sb n\rbrack \sb t$ principal (respectively invertible)
Conjugate diameters Apollonius of Perga and Eutocius of Ascalon by Colin Bryan Powell McKinney( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions
Universal deformation rings of modules over self -injective algebras by Jose Alberto Velez Marulanda( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

The Milnor fiber associated to an arrangement of hyperplanes by Kristopher John Williams( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

Let f be a non-constant, homogeneous, complex polynomial in n variables. We may associate to f a fibration with typical fiber F known as the Milnor fiber. For regular and isolated singular points of f at the origin, the topology of the Milnor fiber is well-understood. However, much less is known about the topology in the case of non-isolated singular points. In this thesis we analyze the Milnor fiber associated to a hyperplane arrangement, ie, f is a reduced, homogeneous polynomial with degree one irreducible components in n variables. If n> 2 then the origin will be a non-isolated singular point. In particular, we use the fundamental group of the complement of the arrangement in order to construct a regular CW-complex that is homotopy equivalent to the Milnor fiber. Combining this construction with some local combinatorics of the arrangement, we generalize some known results on the upper bounds for the first betti number of the Milnor fiber. For several classes of arrangements we show that the first homology group of the Milnor fiber is torsion free. In the final section, we use methods that depend on the embedding of the arrangement in the complex projective plane (ie not necessarily combinatorial data) in order to analyze arrangements to which the known results on arrangements do not apply
Extension of positive definite functions by Robert Niedzialomski( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Positive denite functions play an important role in many aspects of pure and applied mathematics. They are of interest in probability theory, stochastic processes, representation theory, harmonic analysis, complex analysis, approximation theory, information theory, and machine learning. We will give many examples of positive denite functions and positive denite kernels to, at least partially, validate the above statement. The approach to introduce positive defnite functions, that we take here, is to look at them as a subcollection of the collection of positive definite kernels. In this way, we naturally arrive at the notion of a reproducing kernel Hilbert space. The study and the construction of the reproducing kernel Hilbert space associated to a positive defnite kernel will be of great importance for us
Equivariant cohomology and local invariants of Hessenberg varieties by Erik Andrew Insko( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

Nilpotent Hessenberg varieties are a family of subvarieties of the flag variety, which include the Springer varieties, the Peterson variety, and the whole flag variety. In this thesis I give a geometric proof that the cohomology of the flag variety surjects onto the cohomology of the Peterson variety; I provide a combinatorial criterion for determing the singular loci of a large family of regular nilpotent Hessenberg varieties; and I describe the equivariant cohomology of any regular nilpotent Hessenberg variety whose cohomology is generated by its degree two classes
Extremal sextic truncated moment problems by Seonguk Yoo( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

Inverse problems naturally occur in many branches of science and mathematics. An inverse problem entails finding the values of one or more parameters using the values obtained from observed data. A typical example of an inverse problem is the inversion of the Radon transform. Here a function (for example of two variables) is deduced from its integrals along all possible lines. This problem is intimately connected with image reconstruction for X-ray computerized tomography. Moment problems are a special class of inverse problems. While the classical theory of moments dates back to the beginning of the 20th century, the systematic study of truncated moment problems began only a few years ago. In this dissertation we will first survey the elementary theory of truncated moment problems, and then focus on those problems with cubic column relations
Applications of deformation rigidity theory in Von Neumann algebras by Bogdan Teodor Udrea( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

This work contains some structural results for von Neumann algebras arising from measure preserving actions by direct products of groups on probability spaces. The technology and the methods we use are a continuation of those used by Chifan and Sinclair in [10]. By employing these methods, we obtain new examples of strongly solid factors as well as von Neumann algebras with unique or no Cartan subalgebra. We show for instance that every II 1 factor associated with a weakly amenable group in the class S of Ozawa is strongly solid [59]. We also obtain a product version of this result: any maximal abelian *-subalgebra of any II 1 factor associated with a finite direct product of weakly amenable groups in the class S of Ozawa has an amenable normalizing algebra. Finally, pairing some of these results with Ioana's cocycle superrigidity theorem [36], we prove that compact actions by finite products of lattices in Sp(n, 1), n ≥ 2, are virtually W*-superrigid. The results presented here are joint work with Ionut Chifan and Thomas Sinclair. They constitute the substance of an article [11] which has already been submitted for publication
A biological application for the oriented skein relation by Candice Renee Price( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

The study of DNA knots and links are of great interest to molecular biologists as they are present in many cellular process. The variety of experimentally observed DNA knots and links makes separating and categorizing these molecules a critical issue. Thus, knowing the knot Floer homology will provide restrictions on knotted and linked products of protein action. We give a summary of the combinatorial version of knot Floer homology from known work, providing a worked out example. The thesis ends with reviewing knot Floer homology properties of three particular sub-families of biologically relevant links known as (2, p)- torus links, clasp knots and 3-strand pretzel links
C1,[alpha] regularity for boundaries with prescribed mean curvature by Stephen William Welch( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

In this study we provide a new proof of C1,[alpha] boundary regularity for finite perimeter sets with flat boundary which are local minimizers of a variational mean curvature formula. Our proof is provided for curvature term H [is a member of] L[superscript infinity] [Omega]. The proof is a generalization of Cafarelli and Córdoba's method, and combines techniques from geometric measure theory and the theory of viscosity solutions which have been developed in the last 50 years. We rely on the delicate interplay between the global nature of sets which are variational minimizers of a given functional, and the pointwise local nature of comparison surfaces which satisfy certain PDE. As a heuristic, in our proof we can consider the curvature as an error term which is estimated and controlled at each point of the calculation
Operations on infinite x infinite matrices and their use in dynamics and spectral theory by Corissa Marie Goertzen( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Extensions of Hilbert modules over tensor algebras by Andrew Koichi Greene( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

The analogous statement for tensor algebras is deduced as a corollary. In the final chapter, a brief survey of non-abelian category theory is provided. Extensions of completely bounded Hilbert modules over operator algebras are defined. Theorems asserting the projectivity of isometric modules and injectivity of coisometric modules by Carlson, Clark, Foias, and Williams in 1995 are generalized to the noncommutative setting of tensor algebras using commutant lifting. A result of Popesecu in 1996 for noncommutative disc algebras is also covered in the general framework of this thesis
Reduced [tau]n-factorizations in Z and [tau]n-factorizations in N by Alina Anca Florescu( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

In this dissertation we expand on the study of [tau]n-factorizations or generalized integer factorizations introduced by D.D. Anderson and A. Frazier and examined by S. Hamon. ... This work serves to compare the [tau]n-factorizations of the integers with the reduced [tau]n-factorizations in Z and the [tau]n-factorizations in N. One of the main goals is to explore how the Fundamental Theorem of Arithmetic extends to these generalized factorizations. Results regarding the [tau]n-factorizations in Z have been discussed by S. Hamon. Using different methods based on group theory we explore similar results about the reduced [tau]n-factorizations in Z and the [tau]n-factorizations in N. In other words, we identify the few values of n for which every integer can be expressed as a product of the irreducible elements related to these factorizations and indicate when one can do so uniquely
The geometry and topology of wide ribbons by Susan Cecile Brooks( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Intuitively, a ribbon is a topological and geometric surface that has a fixed width. In the 1960s and 1970s, Calugareanu, White, and Fuller each independently proved a relationship between the geometry and topology of thin ribbons. This result has been applied in mathematical biology when analyzing properties of DNA strands. Although ribbons of small width have been studied extensively, it appears as though little to no research has be completed regarding ribbons of large width. In general, suppose K is a smoothly embedded knot in R 3 . Given an arclength parametrization of K, denoted by gamma(s), and given a smooth, smoothly-closed, unit vector field u(s) with the property that u'(s) is not equal to 0 for any s in the domain, we may define a ribbon of generalized width r 0 associated to gamma and u as the set of all points gamma(s) + ru(s) for all s in the domain and for all r in [0,r 0 ]. These wide ribbons are likely to have self-intersections. In this thesis, we analyze how the knot type of the outer ribbon edge relates to that of the original knot K and the embedded resolutions of the unit vector field u as the width increases indefinitely. If the outer ribbon edge is embedded for large widths, we prove that the knot type of the outer ribbon edge is one of only finitely many possibilities. Furthermore, the possible set of finitely many knot types is completely determinable from u, independent of gamma. However, the particular knot type in general depends on gamma. The occurrence of stabilized knot types for large widths is generic; we show that the set of pairs (gamma, u) for which the outer ribbon edge stabilizes for large widths (as a subset of all such pairs (gamma, u) is open and dense in the C 1 topology. Finally, we provide an algorithm for constructing a ribbon of constant generalized width between any two given knot types K 1 and K 2 . We conclude by providing concrete examples
Two varieties of tunnel number subadditivity by Trenton Frederick Schirmer( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

Knot theory and 3-manifold topology are closely intertwined, and few invariants stand so firmly in the intersection of these two subjects as the tunnel number of a knot, denoted t(K). We describe two very general constructions that result in knot and link pairs which are subbaditive with respect to tunnel number under connect sum. Our constructions encompass all previously known examples and introduce many new ones. As an application we describe a class of knots K in the 3-sphere such that, for every manifold M obtained from an integral Dehn filling of E(K), g(E(K))>g(M)
Generalized factorization in commutative rings with zero-divisors by Christopher Park Mooney( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

The study of factorization in integral domains has a long history. Unique factorization domains, like the integers, have been studied extensively for many years. More recently, mathematicians have turned their attention to generalizations of this such as Dedekind domains or other domains which have weaker factorization properties. Many authors have sought to generalize the notion of factorization in domains. One particular method which has encapsulated many of the generalizations into a single study is that of tau-factorization, studied extensively by A. Frazier and D.D. Anderson. Another generalization comes in the form of studying factorization in rings with zero-divisors. Factorization gets quite complicated when zero-divisors are present due to the existence of several types of associate relations as well as several choices about what to consider the irreducible elements. In this thesis, we investigate several methods for extending the theory of tau-factorization into rings with zero-divisors

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University of Iowa. Dept. of Mathematics

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English (25)