Browsing Mathematics by Issue Date
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Qualitative stability properties of matrices
(1985)A matrix A is sign stable if some matrix with the same sign pattern of positive, negative, and zero entries has all eigenvalues with negative real parts. It is potentially stable if it is not sign unstable. The system A x ... 
Convergence and approximation for primaldual methods in largescale optimization
(1990)Largescale problems in convex optimization often can be reformulated in primaldual (minimax) representations having special decomposition properties. Approximation of the resulting highdimensional problems by restriction ... 
Markov partitions for hyperbolic toral automorphisms
(1992)The study of the dynamical properties of hyperbolic toral automorphisms is simplified when the automorphisms are represented as shifts of finite type. The conventional method used to represent such an automorphism symbolically ... 
Stable processes with opposing drifts
(1996)A strong Markov process, $W\sp0$, is constructed by a natural linking together of two independent stable processes of type ($\alpha,\ \beta\sb1$) and ($\alpha,\ \beta\sb2$). The drift for a stable process X of type ($\alpha,\ ... 
The nonexistence of certain free prop extensions and capitulation in a family of dihedral extensions of Q
(1996)$\doubz\sbsp{p}{d}$extensions are a natural way to extend Iwasawa's theory of $\doubz\sb{p}$extensions. A further extension would be to look at free prop extensions which though nonabelian, can be studied by looking at ... 
Essential spanning forests and electric networks in groups
(1997)Let $\Gamma$ be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of $\Gamma ,$ have no cycles, and no finite connected components are called essential spanning forests. The set ${\cal ... 
On the mod 2 general linear group homology of totally real number rings
(1997)We study the mod 2 homology of the general linear group of rings of integers in totally real number fields. In particular, for certain such rings R, we construct a space JKR and show that the mod 2 homology of JKR is a ... 
An electrodynamic inverse problem in chiral media
(1998)We consider the inverse problem of determining the electromagnetic material parameters of a body from information obtainable only at the boundary of the body; such information comes in the form of a boundary map which we ... 
Noninterior pathfollowing methods for complementarity problems
(1998)Because of its excellent numerical performance, noninterior path following methods (also called smoothing methods) have become an important class of methods for solving complementarity problems. However, no rate of ... 
Nonholonomic EulerPoincaré equations and stability in Chaplygin's sphere
(2000)A method of reducing several classes of nonholonomic mechanical systems that are defined on semidirect products of Lie groups is developed. The method reduces the Lagranged'Alembert principle to obtain a reduced constrained ... 
Convexity, convergence and feedback in optimal control
(2000)The results of this thesis are oriented towards the study of convex problems of optimal control in the extended piecewise linearquadratic format. Such format greatly extends the classical linearquadratic regulator problem ... 
Selmer groups for elliptic curves with isogenies of prime degree
(2003)The MordellWeil theorem states that the points of an elliptic curve defined over a number field form a finitely generated, abelian group. The rank of this group, generally referred to as the rank of the elliptic curve, ... 
Strichartz estimates for wave equations with coefficients of Sobolev regularity
(2005)Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for ... 
On singularities of generic projection hypersurfaces
(2006)The present work studies singularities of hypersurfaces arising from generic projections of smooth projective varieties, in the context of Du Bois and semi log canonical singularities. It is demonstrated that Du Bois ... 
Problems in computational algebra and integer programming
(2007)This thesis is a compendium of several projects that span the gap between commutative algebra and geometric combinatorics: one in tropical geometry, one in computational algebra, and two in discrete geometry and integer ... 
The topology of graph homomorphisms
(2007)In this thesis we consider topological aspects of graph homomorphisms. Our main object of study is the Hom complex of graphs, a space first introduced by Lovasz to obtain lower bounds on chromatic number, and more recently ... 
Inverse transport with angularly averaged measurements
(2008)The inverse problem in radiative transfer is considered. The measurement setup involves controlling incoming radiation at the boundary of a convex domain in Rn and measuring the outgoing radiation in an attempt to ... 
Wild Automorphisms and Abelian Varieties
(2010)An automorphism $\sigma$ of a projective variety $X$ is said to be \textit{wild} if $\sigma(Y)\neq Y$ for every nonempty subvariety $Y\subsetneq X$. In MR2227726 Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that ... 
Connections Between Lanczos Iteration and Orthogonal Polynomials
(20100110)In this thesis we examine the connections between orthogonal polynomials and the Lanczos algorithm for tridiagonalizing a Hermitian matrix. The Lanczos algorithm provides an easy way to calculate and to estimate the ... 
A TensorTriangulated Approach to Derived Categories of NonNoetherian Rings
(20120913)We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between ...