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Dissertations / Theses on the topic 'Ring theory'
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1
Farina, John Dominic. "Stability properties in ring theory." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3237384.
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Thesis (Ph. D.)--University of California, San Diego, 2006.Title from first page of PDF file (viewed December 8, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 86-90).
2
Samman, M. S. "Topics in seminear-ring theory." Thesis, University of Edinburgh, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.661551.
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The idea of a seminear-ring was introduced in [8], as an algebraic system that can be constructed from a set S with two binary operations : addition + and multiplication ., such that (S, +) and (S, .) are semigroups and one distributive law is satisfied. A seminear-ring S is called distributively generated (d.g.) if S contains a multiplicative subsemigroup (T, .) of distributive elements which generates (S, +). Unlike the near-rings case for which a rich theory has already been developed, very little seems to be known about seminear-rings. The aim of this dissertation consists mainly of two goals. The first is to generalize some results which are known in the theory of near-rings. The second goal of this thesis appears mainly in the last 6 chapters in which we obtain some results about seminear-rings of endomorphisms. In chapter 1, the definitions and basic concepts about seminear-rings are given; e.g. an arbitrary seminear-ring can be embedded in a seminear-ring of the form M(S). Fröhlich [1], [2] and Meldrum [5] have given some results concerning free d.g. near-rings in a variety V. In chapter 2, we generalize some of these results to free d.g. seminear-rings and we can prove the existence of free (S,T)-semigroups on a set X in a variety V. In section 2.4, we prove a theorem which asserts that not every d.g. seminear-ring has a faithful representation. This would generalize the result which was given by Meldrum [5] for the near-ring case. Chapter 3 gives an overview of strong semilattices of near-rings and of rings. In this context we show that a strong semilattice of near-rings is a seminear-ring while a strong semilattice of rings is a near-ring. Chapter 4 is designed to be a preparatory chapter for the remaining part of the thesis. It explains the main plan which will be followed in all the last 6 chapters. It also includes some basic ideas and results which are of great use in the remaining work.
3
Merisi, Piercarlo. "Ring equivalences from Morita theory." Thesis, University of Exeter, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307287.
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Richardson, Jeremy O. "Ring-polymer approaches to instanton theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243641.
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Inspired by the success of the ring-polymer molecular dynamics (RPMD) method, we derive a transition-state-theory version (RPTST) with a dividing surface which is, in general, conical in ring-polymer space. It is explained why this conical form is a good approximation to the optimal dividing surface and therefore why centroid-based quantum transition-state theories are inaccurate for asymmetric barriers at low temperatures. The geometry of the ring-polymer transition state is found to describe a finite-difference approximation to the semi-classical instanton trajectory (a classical periodic orbit of length βħ on the inverted potential). Based on this, a new practical method for locating multidimensional instantons is proposed, by computing saddle points on the ring-polymer surface, and a derivation for the reaction rate constant based on the "ImF" premise using the ring-polymer formalism is shown to be far simpler than in previous instanton approaches based on functional determinants. The resulting expression is based only on the ring-polymer potential at the transition-state and its Hessian, and is applied to evaluate the rate in a number of polyatomic systems. We show that a free-energy version of the ImF instanton theory is related to RPTST and thereby provide an explanation for why RPMD produces accurate results for thermal reaction rates in the deep-tunnelling regime and demonstrate how it can be made more efficient and systematically improved. From this, we also explain why RPMD is seen to underestimate the rates of symmetric reactions and overestimate the rates of asymmetric reactions. We also present a ring-polymer instanton derivation of a theory for calculating tunnelling splittings leading to another new practical method, which owing to its simple form, is easily extended to determine the entire tunnelling-splitting pattern of molecular clusters with two or more degenerate wells. This method is applied to the water dimer, trimer, and octamer, and shown to be in good overall agreement with experiment and to provide a deeper understanding of the tunnelling pathways.
5
Duncan, A. J. "Two topics in commutative ring theory." Thesis, University of Edinburgh, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234124.
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Hedenlund, Alice. "Galois Theory of Commutative Ring Spectra." Thesis, KTH, Matematik (Avd.), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-183512.
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This thesis discusses Galois theory of ring spectra in the sense of John Rognes. The aim is to give a clear introduction that provides a solid foundation for further studies into the subject. We introduce ring spectra using the symmetric spectra of Hovey, Shipley and Smith, and discuss the symmetric monoidal model structure on this category. We define and give results for Galois extensions of these objects. We also give examples involving Eilenberg-Mac Lane spectra of commutative rings, topological K-theory spectra and cochain algebras of these. Galois extensions of ring spectra are compared to Ga-lois extensions of commutative rings especially relating to faithfulness, a property that is implicit in the latter, but not in the former. This is proven by looking at extensions of cochain algebras using Eilenberg-Mac Lane spectra. We end by contrasting this to cochain algebra extensions using K-theory spectra, and show that such extensions are not Galois, using methods of Baker and Richter.Denna uppsats behandlar Galoisutvidgningar av ringspektra som först introducerade av Rognes. Målet är att ge en klar introduktion för en sta-bil grund för vidare studier inom ämnet. Vi introducerar ringspektra genom att använda oss av symmetris-ka spektra utvecklade av Hovey, Shipley och Smith, och diskuterar den symmetriskt monoidiala modelstrukturen på denna kategori. Vi definierar och ger resultat för Galoisutvidgningar av dessa objekt. Vi ger också en mängd exempel, som till exempel utvidgningar av Eilenberg-Mac Lane spektra av kommutativa ringar, topologiska K-teorispektra och koked-jealgebror. Galoisutvidgningar av ringspektra jämförs med Galoisutvidgningar av kommutativa ringar, speciellt med avseende pa˚ trogenhet, en egenskap som ¨ar en inneboende egenskap hos den senare men inte i den förra. Detta visas genom att betrakta utvidgningar av kokedjealgebror av Eilenberg-Mac Lane spektra. Vi avslutar med att jämföra detta med kokedjealgebrautvidgningar av K-teorispektra och visar att sådana inte är Galois genom att använda metoder utvecklade av Baker och Richter
7
Whelan, E. A. "Symmetry conditions in ring and module theory." Thesis, University of East Anglia, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374275.
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Chin, Melanie Soo, and m. chin@cqu edu au. "Towards a Reinterpretation of the Radical Theory of Associative Rings Using Base Radical and Base Semisimple Class Constructions." Central Queensland University. Computer Science, 2004. http://library-resources.cqu.edu.au./thesis/adt-QCQU/public/adt-QCQU20050411.102928.
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This research aims to refresh and reinterpret the radical theory of associative rings using the base radical and base semisimple class constructions. It also endeavours to generalise some results about ideals of rings in terms of accessible subrings. A characterisation of accessible subrings is included. By applying the base radical and base semisimple class constructions to many of the known results in established radical theory a number of gaps are uncovered and closed, with the goal of making the theory more accessible to advanced undergraduate and graduate students and mathematicians in related fields, and to open up new areas of investigation.
After a literature review and brief reminder of algebra rudiments, the useful properties of accessible subrings and the U and S operators independent from radical class connections are described. The section on accessible subrings illustrates that replacing ideals with accessible subrings is indeed possible for a number of results and demonstrates its usefulness.
The traditional radical and semisimple class definitions are included and it is shown that the base radical and base semisimple class constructions are equivalent. Diagrams illustrating the constructions support the definitions. From then on, all radical and semisimple classes mentioned are understood to have the base radical and base semisimple class form. Subject to the constraints of this work, many known results of traditional radical theory are reinterpreted with new proofs, illustrating the potential to simplify the understanding of radical theory using the base radical and base semisimple class constructions. Along with reinterpreting known results, new results emerge giving further insight to radical theory and its intricacies. Accessible subrings and the U and S operators are integrated into the development. The duality between the base radical and base semisimple class constructions is demonstrated in earnest.
With a measure of the theory presented, the new constructions are applied to examples and concrete radicals. Context is supported by establishing the relationship between some well-known rings and the radical and related classes of interest.
The title of the thesis, Towards a Reinterpretation of the Radical Theory of Associative Rings Using Base Radical and Base Semisimple Class Constructions, reflects the understanding that reinterpreting the entirety of radical theory is beyond the scope of this work. The conclusion includes an outlook listing further research that time did not allow.
9
Stecher, Thomas. "Benchmark studies of ring polymer molecular dynamics rate theory." Thesis, University of Cambridge, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609229.
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Immormino, Nicholas A. "Clean Rings & Clean Group Rings." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1374247918.
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Attree, Nicholas Oliver. "Collisional features in Saturn's F ring." Thesis, Queen Mary, University of London, 2015. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8915.
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The role of physical collisions in shaping Saturn's F ring is explored using a mixture of dynamical theory, image analysis and computer simulations. The F ring is highly dynamic, being perturbed by the nearby moons, Prometheus and Pandora, and by a population of small bodies, whose presence is inferred by their influence on the ring, charged particle data and, occasionally, direct detection. Small-scale features, termed `mini-jets', are catalogued from images taken by the Imaging Science Subsystem of the Cassini spacecraft. More than 1000 are recorded, implying a population of 100 objects on nearby orbits, colliding with the ring at velocities of a few ms 1. Many are seen to collide several times, forming repeated structures, and must have enough physical strength, or self-gravity, to survive multiple passages through the core. Larger features, called `jets', share a similar morphology. They are likely caused by a more distant population which collide at higher velocities ( 10 ms 1) and are roughly an order of magnitude less common. Differential orbital motion causes jets to shear out over time, giving the ring its multi-stranded appearance. Jets have different orbital properties to mini-jets, probably because they result from multiple, overlapping collisions. Simulations using an N-body code show that the shape of collisional features depends heavily on the coefficient of restitution, particularly the tangential component. When both components are < 1 large objects merely sweep up small particles. Features like jets and mini-jets require large particles in both the target and impactor, as is the case for two similarly-sized aggregates colliding. A single population of aggregates is proposed, ranging from large, unconsolidated clumps, embedded in the core, through mini-jet-forming objects to the more distant, jet-forming colliders. Prometheus may be ultimately responsible for all of these features as its gravity can trigger clump formation as well as perturb particles.
12
Kuber, Amit Shekhar. "K-theory of theories of modules and algebraic varieties." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/ktheory-of-theories-of-modules-and-algebraic-varieties(5d4387d5-df36-455a-a09d-922d67b0827e).html.
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Vaughan, Stephen N. (Stephen Nick). "Some Properties of Noetherian Rings." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc501109/.
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This paper is an investigation of several basic properties of noetherian rings. Chapter I gives a brief introduction, statements of definitions, and statements of theorems without proof. Some of the main results in the study of noetherian rings are proved in Chapter II. These results include proofs of the equivalence of the maximal condition, the ascending chain condition, and that every ideal is finitely generated. Some other results are that if a ring R is noetherian, then R[x] is noetherian, and that if every prime ideal of a ring R is finitely generated, then R is noetherian.
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Edmonds, Ranthony A. C. "Factorization in polynomial rings with zero divisors." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/3248.
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Factorization theory is concerned with the decomposition of mathematical objects. Such an object could be a polynomial, a number in the set of integers, or more generally an element in a ring. A classic example of a ring is the set of integers. If we take any two integers, for example 2 and 3, we know that $2 \cdot 3=3\cdot 2$, which shows that multiplication is commutative. Thus, the integers are a commutative ring. Also, if we take any two integers, call them $a$ and $b$, and their product $a\cdot b=0$, we know that $a$ or $b$ must be $0$. Any ring that possesses this property is called an integral domain. If there exist two nonzero elements, however, whose product is zero we call such elements zero divisors. This thesis focuses on factorization in commutative rings with zero divisors.
In this work we extend the theory of factorization in commutative rings to polynomial rings with zero divisors. For a commutative ring $R$ with identity and its polynomial extension $R[X]$ the following questions are considered: if one of these rings has a certain factorization property, does the other? If not, what conditions must be in place for the answer to be yes? If there are no suitable conditions, are there counterexamples that demonstrate a polynomial ring can possess one factorization property and not another? Examples are given with respect to the properties of atomicity and ACCP. The central result is a comprehensive characterization of when $R[X]$ is a unique factorization ring.
15
Reid, Adam. "Quantum tunnelling splittings in water clusters, from ring-polymer instanton theory." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709028.
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Corwin, Stephen P. "Representation theory of the diagram An over the ring k[[x]]." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/50001.
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Fix R = k[[x]]. Let Qn be the category whose objects are ((M₁,...,Mn),(f₁,...,fn-1)) where each Mi is a free R-module and fi:Mi⟶Mi+1 for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let βn be the full subcategory of Ωn in which each map fi is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ωn⟶βn. If X is an object of βn, we say that X diagonalizes if X is isomorphic to a direct sum of objects ((M₁,...,Mn),(f₁,...,fn-1)) in which each Mi is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of βn, and which fails only in case X is not diagonalizable.
Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable.Ph. D.
incomplete_metadata
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Adhikari, S. Prashanth. "Torsion in the homology of the general linear group for a ring of algebraic integers /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5770.
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Mariaule, Nathanaël. "On the decidability of the p-adic exponential ring." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/on-the-decidability-of-the-padic-exponential-ring(fc75a490-aa93-4b5e-b017-e71849c2a675).html.
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Let Zp be the ring of p-adic integers and Ep be the map x-->exp(px) where exp denotes the exponential map determined by the usual power series. It defines an exponential ring (Zp, + , . , 0, 1, Ep). The goal of the thesis is to study the model theory of this structure. In particular, we are interested by the question of the decidability of this theory. The main theorem of the thesis is: Theorem: If the p-adic Schanuel's conjecture is true, then the theory of (Zp, + , . , 0, 1, Ep) is decidable. The proof involves: 1- A result of effective model-completeness (chapters 3 and 4): If F is a family of restricted analytic functions (i.e. power series with coefficients in the valuation ring and convergent on Zp) closed under decomposition functions and such that the set of terms in the language LF= (+, . , 0, 1, f; f in F) is closed under derivation, then we prove that the theory of Zp in the language LF is model-complete. And furthermore, if each term of LF has an effective Weierstrass bound, then the model-completeness is effective. 2- A resolution of the decision problem for existential formulas (assuming Schanuel's conjecture) in chapter 5. We also consider the problem of the decidability of the structure (Op, + , . , 0, 1, |, E_p) where Op denotes the valuation ring of Cp. We give a positive answer to this question assuming the p-adic Schanuel's conjecture.
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Roh, Chung-Hee. "Electron transport through double quantum dots in an Aharonov-Bohm ring." Muncie, Ind. : Ball State University, 2008. http://cardinalscholar.bsu.edu/382.
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Al-Hazmi, Husain S. "A Study of CS and Σ-CS Rings and Modules." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1121268376.
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Fulghesu, Damiano. "On the Chow ring of the stack of rational nodal curves." Doctoral thesis, Scuola Normale Superiore, 2005. http://hdl.handle.net/11384/85710.
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From the introduction: In this thesis we start investigating the intersection theory of the
Artin stack M0 of nodal curves of genus 0, following a suggestion of
Rahul Pandharipande.
Intersection theory on moduli spaces of stable curves has a not
so long, but very intense history. It started at the beginning of the
’80’s with Mumford’s paper [Mum2], where he laid the foundations
and carried out the first calculations. Many people have contributed
to the theory after this (such as Witten and Kontsevich), building an
imposing structure.
The foundations of intersection theory on Deligne-Mumford stacks
have been developed by Gillet and Vistoli. The first step towards an
intersection theory on general Artin stacks (like those that arise from
looking at unstable curves) was the equivariant intersection theory that
Edidin and Graham developed, following an idea of Totaro. Their
theory associates a commutative graded Chow ring A (M) with every
smooth quotient stack M of finite type over a field.
Unfortunately many stacks of geometric interest are not known to
be quotient stacks (the general question of when a stack is a quotient
stack is not well understood). Later, A. Kresch developed an intersection
theory for general Artin stacks; in particular, he associates a Chow
ring A (M) with every smooth Artin stack M locally of finite type over
a field, provided some technical conditions hold, which are satisfied in
particular for stacks of pointed nodal curves of fixed genus.
Since there is not yet a theory of Chow rings of such stacks that
extends the theory of stacks of stable curves, there does not seem to be
much else to do than look at specific examples: and the first example
is the stack M0 of nodal connected curves of genus 0. However, even
this case turns out to be extremely complicated.
In this thesis we compute the rational Chow ring of the open substack
M 3
0 consisting of nodal curves of genus 0 with at most 3 nodes:
it is a Q-algebra with 10 generators and 11 relations.
The techniques that we use, and the problems that we encounter,
are discussed below.
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Crawford, Simon Philip. "Singularities of noncommutative surfaces." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31543.
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The primary objects of study in this thesis are noncommutative surfaces; that is, noncommutative noetherian domains of GK dimension 2. Frequently these rings will also be singular, in the sense that they have infinite global dimension. Very little is known about singularities of noncommutative rings, particularly those which are not finite over their centre. In this thesis, we are able to give a precise description of the singularities of a few families of examples. In many examples, we lay the foundations of noncommutative singularity theory by giving a precise description of the singularities of the fundamental examples of noncommutative surfaces. We draw comparisons with the fundamental examples of commutative surface singularities, called Kleinian singularities, which arise from the action of a finite subgroup of SL(2; k) acting on a polynomial ring. The main tool we use to study the singularities of noncommutative surfaces is the singularity category, first introduced by Buchweitz in [Buc86]. This takes a (possibly noncommutative) ring R and produces a triangulated category Dsg(R) which provides a measure of "how singular" R is. Roughly speaking, the size of this category reflects how bad the singularity is; in particular, Dsg(R) is trivial if and only if R has finite global dimension. In [CBH98], Crawley-Boevey-Holland introduced a family of noncommutative rings which can be thought of as deformations of the coordinate ring of a Kleinian singularity. We give a precise description of the singularity categories of these deformations, and show that their singularities can be thought of as unions of (commutative) Kleinian singularities. In particular, our results show that deforming a singularity in this setting makes it no worse. Another family of noncommutative surfaces were introduced by Rogalski-Sierra-Stafford in [RSS15b]. The authors showed that these rings share a number of ring-theoretic properties with deformations of type A Kleinian singularities. We apply our techniques to show that the "least singular" example has an A1 singularity, and conjecture that other examples exhibit similar behaviour. In [CKWZ16a], Chan-Kirkman-Walton-Zhang gave a definition for a quantum version of Kleinian singularities. These require the data of a two-dimensional AS regular algebra A and a finite group G acting on A with trivial homological determinant. We extend a number of results in [CBH98] to the setting of quantum Kleinian singularities. More precisely, we show that one can construct deformations of the skew group rings A#G and the invariant rings AG, and then determine some of their ring-theoretic properties. These results allow us to give a precise description of the singularity categories of quantum Kleinian singularities, which often have very different behaviour to their non-quantum analogues.
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Wulff, Christopher Peter Reinhard [Verfasser], and Bernhard [Akademischer Betreuer] Hanke. "Ring structures in coarse K-theory / Christopher Peter Reinhard Wulff. Betreuer: Bernhard Hanke." Augsburg : Universität Augsburg, 2015. http://d-nb.info/1077705832/34.
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Biondi, Franco, and Fares Qeadan. "A Theory-Driven Approach To Tree-Ring Standardization: Defining The Biological Trend From Expected Basal Area Increment." Tree-Ring Society, 2008. http://hdl.handle.net/10150/622585.
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One of the main elements of dendrochronological standardization is removing the biological
trend, i.e. the progressive decline of ring width along a cross-sectional radius that is caused by the corresponding increase in stem size and tree age over time. The ‘‘conservative’’ option for removing this biological trend is to fit a modified negative exponential curve (or a straight line with slope ≤ 0) to the ring-width measurements. This method is based on the assumption that, especially for open-grown and/or shade-intolerant species, annual growth rate of mature trees fluctuates around a specific level, expressed by a constant ring width. Because this method has numerical and conceptual drawbacks, we propose an alternative approach based on the assumption that constant growth is expressed by a constant basal area increment distributed over a growing surface. From this starting point, we derive a mathematical expression for the biological trend of ring width, which can be easily calculated and used for dendrochronological standardization. The proposed C-method is compared to other standardization techniques, including Regional Curve Standardization (RCS), of tree-ring width from ponderosa pines (Pinus ponderosa Douglas ex P.Lawson & C.Lawson) located at the Gus Pearson Natural Area (GPNA) in northern Arizona, USA. Master ring-index chronologies built from ring area, RCS, and C-method reproduced stand-wide patterns of tree growth at the GPNA, whereas other standardization options, including the ‘‘conservative’’ one, failed to do so. In addition, the C-method has the advantage of calculating an expected growth curve for each tree, whereas RCS is based on applying the same growth curve to all trees. In conclusion, the C-method replaces the purely empirical ‘‘conservative’’ option with a theory based approach, which is applicable to individual ring-width measurement series, does not require fitting a growth curve using nonlinear regression, and can be rigorously tested for improving tree-ring records of environmental changes.
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Sato, Takashi. "The T-equivariant Integral Cohomology Ring of F4/T." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199076.
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McGovern, Patrick Joseph. "A three ring circus: The disciplining and commodification of political science." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280726.
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The purpose of this dissertation is to examine the impact of economic rationality upon the practice of political theory within the discipline of political science and its relationship with the larger modern political context in which they are embedded. This work addresses an interest in tying together the rise of economic rationality and the rise methodism within political theory with the decline of "epic" political theory and civil society. I argue here that the decline of civil society is tied in part to the commodification of political knowledge within the modern university system, and that the modern university system and its practices are inundated by market rationality and discourse. This is expressed in the practice of political theorists "capturing" the idea of the public and commodifying it through the peer-review journal process; the "public" becomes the medium through which political theory and science identifies itself as a discipline and its practitioners professionally. The public is not privy to understanding itself as a public and is cut off from its own intellectual means of coming to grips with its own identity. Notions and ideas about the public are "methodized" and "disciplined" and are traded among political scientists and theorists more out of private professional concern than concern for serving public interests or democratic ideals and values. The purpose of political science and theory is the analysis of power in all its dimensions. I argue that political theory's position to comment on the nature of power is itself compromised by the dominance of market rationality and methodism. Political theory's critical distance from the methodism of political science has been narrowed by the rise in the importance of the peer-reviewed article for "professional development." In order for political theory to engage the expansive, critical position of epic political theory, and thus public interest, it must address the issue and problems presented by peer-review, the nature of "progress" in the social sciences and come to engage an ethic of responsibility to democracy.
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Xu, Tianyuan. "On the Subregular J-ring of Coxeter Systems." Thesis, University of Oregon, 2017. http://hdl.handle.net/1794/22741.
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Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke
algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study
a subalgebra J_C of J corresponding to the subregular cell C of W . We prove a
factorization theorem that allows us to compute products in J_C without inputs
from Kazhdan-Lusztig theory, then discuss two applications of this result. First, we
describe J_C in terms of the Coxeter diagram of (W, S) in the case (W, S) is simply-
laced, and deduce more connections between the diagram and J_C in some other
cases. Second, we prove that for certain specific Coxeter systems, some subalgebras
of J_C are free fusion rings, thereby connecting the algebras to compact quantum
groups arising in operator algebra theory.
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Palmer, Prem. "Structure, Energetics and Reactions of Bisketenes: An Ab Initio and Density Functional Theory Study." Thesis, University of North Texas, 1997. https://digital.library.unt.edu/ark:/67531/metadc501272/.
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The effect of varying substituents on structure and energies of bisketenes was studied using ab initio methods. Effect of substituents on ring closing reaction of bisketenes to the corresponding cyclobutenediones was also studied using ab initio methods. One or two of the following substituents were used to study the effect of varying substituents: BH2, CH3, NH2, OH, F, AlH2, SiH3, PH2, SH, Cl. Studies were done at the Hartree-Fock (HF), Møller-Plesset (MP2), and Density Functional Theory (B3LYP) levels of theory using the 6-31G* basis set.
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Suzuki, Jiro, Atsushi Takano, Tetsuo Deguchi, and Yushu Matsushita. "Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory." American Institute of Physics, 2009. http://hdl.handle.net/2237/14168.
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Roman, Cosmin Stefan. "Baer and quasi-baer modules." The Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=osu1092676774.
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Hasse, Erik Gregory. "Lowest terms in commutative rings." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6433.
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Putting fractions in lowest terms is a common problem for basic algebra courses, but it is rarely discussed in abstract algebra. In a 1990 paper, D.D. Anderson, D.F. Anderson, and M. Zafrullah published a paper called Factorization in Integral Domains, which summarized the results concerning different factorization properties in domains. In it, they defined an LT domain as one where every fraction is equal to a fraction in lowest terms. That is, for any x/y in the field of fractions of D, there is some a/b with x/y=a/b and the greatest common divisor of a and b is 1. In addition, R. Gilmer included a brief exercise concerning lowest terms over a domain in his book Multiplicative Ideal Theory.
In this thesis, we expand upon those definitions. First, in Chapter 2 we make a distinction between putting a fraction in lowest terms and reducing it to lowest terms. In the first case, we simply require the existence of an equal fraction which is in lowest terms, while the second requires an element which divides both the numerator and the denominator to reach lowest terms. We also define essentially unique lowest terms, which requires a fraction to have only one lowest terms representation up to unit multiples. We prove that a reduced lowest terms domain is equivalent to a weak GCD domain, and that a domain which is both a reduced lowest terms domain and a unique lowest terms domain is equivalent to a GCD domain. We also provide an example showing that not every domain is a lowest terms domain as well as an example showing that putting a fraction in lowest terms is a strictly weaker condition than reducing it to lowest terms.
Next, in Chapter 3 we discuss how lowest terms in a domain interacts with the polynomial ring. We prove that if D[T] is a unique lowest terms domain, then D must be a GCD domain. We also provide an alternative approach to some of the earlier results using the group of divisibility.
So far, all fractions have been representatives of the field of fractions of a domain. However, in Chapter 4 we examine fractions in other localizations of a domain. We define a necessary and sufficient condition on the multiplicatively closed set, and then examine how this relates to existing properties of multiplicatively closed sets.
Finally, in Chapter 5 we briefly examine lowest terms in rings with zero divisors. Because many properties of GCDs do not hold in such rings, this proved difficult. However, we were able to prove some results from Chapter 2 in this more general case.
32
Perkins, Abigail C. "Electron spin-polarization via Zeeman and Aharonov-Bohm effects in a double quantum dot ring." CardinalScholar 1.0, 2009. http://liblink.bsu.edu/uhtbin/catkey/1540705.
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A nanoscale Aharonov-Bohm (AB) ring with a quantum dot (QD) embedded in each arm is investigated analytically to provide electron transmission characteristics. A parallel magnetic field provides Zeeman splitting of the QD energy levels. Combined Zeeman energy level splitting and AB-effects occur with a perpendicular field. In our device, the AB-ring interferometer, Zeeman splitting of the QD energy levels creates regions of parameter space in which the electron transmission is highly spin-polarized. In addition to Zeeman splitting caused by a parallel magnetic field, combined Zeeman energy level splitting and AB-interference effects occur with a perpendicular field. The weighted spin-polarization function is calculated and presented as a function of magnetic field and electron energy. Due to a unique parameter regime in which the AB-oscillations show extreme sharpening [1], the electron transmission can be tuned to produce spin-polarized currents which can be switched and controlled by small changes of external fields.Introduction -- AB-oscillations and resonances in a double quantum dot ring -- Results for combined Zeeman and AB effects -- Spin-polarization.
Department of Physics and Astronomy
33
Matuska, Vit. "Five-membered sulfur-nitrogen ring compounds." Thesis, St Andrews, 2009. http://hdl.handle.net/10023/828.
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Pinnawala, Nimalsiri, and nimalsiri pinnawala@rmit edu au. "Properties of Trace Maps and their Applications to Coding Theory." RMIT University. Mathematical and Geospatial Sciences, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080515.121603.
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In this thesis we study the application of trace maps over Galois fields and Galois rings in the construction of non-binary linear and non-linear codes and mutually unbiased bases. Properties of the trace map over the Galois fields and Galois rings has been used very successfully in the construction of cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and consequently to construct linear codes over integers modulo prime and prime powers. These results provide motivation to extend this work to construct codes over integers modulo . The prime factorization of integers paved the way to focus our attention on the direct product of Galois rings and Galois fields of the same degree. We define a new map over the direct product of Galois rings and Galois fields by using the usual trace maps. We study the fundamental properties of the this map and notice that these are very similar to that of the trace map over Galois rings and Galois fields. As such this map called the trace-like map and is used to construct cocyclic Butson Hadamard matrices and consequently to construct linear codes over integers modulo . We notice that the codes construct in this way over the integers modulo 6 is simplex code of type . A further generalization of the trace-like map called the weighted-trace map is defined over the direct product of Galois rings and Galois fields of different degrees. We use the weighted-trace map to construct some non-linear codes and mutually unbiased bases of odd integer dimensions. Further more we study the distribution of over the Galois fields of degree 2 and use it to construct 2-dimensional, two-weight, self-orthogonal codes and constant weight codes over integers modulo prime.
35
Phillips, Laura Rose. "Some structures interpretable in the ring of continuous semi-algebraic functions on a curve." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/some-structures-interpretable-in-the-ring-of-continuous-semialgebraic-functions-on-a-curve(f5a52f43-1bf2-42da-85c0-22847a35dcfc).html.
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Julius, Hayden. "Nonstandard solutions of linear preserver problems." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1626101272174819.
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Wesslén, Carl-Johan. "Many-Body effects in Semiconductor Nanostructures." Licentiate thesis, Stockholms universitet, Fysikum, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-102344.
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Low dimensional semiconductor structures are modeled using techniques from the field of many-body atomic physics. B-splines are used to create a one-particle basis, used to solve the more complex many-body problems. Details on methods such as the Configuration Interaction (CI), Many-Body Perturbation Theory (MBPT) and Coupled Cluster (CC) are discussed. Results from the CC singles and doubles method are compared to other high-precision methods for the circular harmonic oscillator quantum dot. The results show a good agreement for the energy of many-body states of up to 12 electrons. Properties of elliptical quantum dots, circular quantum dots, quantum rings and concentric quantum rings are all reviewed. The effects of tilted external magnetic fields applied to the elliptical dot are discussed, and the energy splitting between the lowest singlet and triplet states is explored for varying geometrical properties. Results are compared to experimental energy splittings for the same system containing 2 electrons.
38
Conner, Andrew Brondos 1981. "A(infinity)-structures, generalized Koszul properties, and combinatorial topology." Thesis, University of Oregon, 2011. http://hdl.handle.net/1794/11559.
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x, 68 p. : ill. (some col.)Motivated by the Adams spectral sequence for computing stable homotopy groups, Priddy defined a class of algebras called Koszul algebras with nice homological properties. Many important algebras arising naturally in mathematics are Koszul, and the Koszul property is often tied to important structure in the settings which produced the algebras. However, the strong defining conditions for a Koszul algebra imply that such algebras must be quadratic. A very natural generalization of Koszul algebras called K 2 algebras was recently introduced by Cassidy and Shelton. Unlike other generalizations of the Koszul property, the class of K 2 algebras is closed under many standard operations in ring theory. The class of K 2 algebras includes Artin-Schelter regular algebras of global dimension 4 on three linear generators as well as graded complete intersections. Our work comprises two distinct projects. Each project was motivated by an aspect of the theory of Koszul algebras which we regard as sufficiently powerful or fundamental to warrant an interpretation for K 2 algebras. A very useful theorem due to Backelin and Fröberg states that if A is a Koszul algebra and I is a quadratic ideal of A which is Koszul as a left A -module, then the factor algebra A/I is a Koszul algebra. We prove that if A is Koszul algebra and A I is a K 2 module, then A/I is a K 2 algebra provided A/I acts trivially on Ext A ( A/I,k ). As an application of our theorem, we show that the class of sequentially Cohen-Macaulay Stanley-Reisner rings are K 2 algebras and we give examples that suggest the class of K 2 Stanley-Reisner rings is actually much larger. Another important recent development in ring theory is the use of A ∞ -algebras. One can characterize Koszul algebras as those graded algebras whose Yoneda algebra admits only trivial A ∞ -structure. We show that, in contrast to the situation for Koszul algebras, vanishing of higher A ∞ -structure on the Yoneda algebra of a K 2 algebra need not be determined in any obvious way by the degrees of defining relations. We also demonstrate that obvious patterns of vanishing among higher multiplications cannot detect the K 2 property. This dissertation includes previously unpublished co-authored material.
Committee in charge: Dr. Brad Shelton, Chair; Dr. Victor Ostrik, Member; Dr. Nicholas Proudfoot, Member; Dr. Arkady Vaintrob, Member; Dr. David Boush, Outside Member
39
Chasen, Lee A. "The cohomology rings of classical Brauer tree algebras." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/38572.
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Steward, Michael. "Extending the Skolem Property." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492517341492202.
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Clark, Duncan. "An operad structure for the Goodwillie derivatives of the identity functor in structured ring spectra." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu161702647643754.
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Xantcha, Qimh. "The Theory of Polynomial Functors." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-45943.
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Polynomial functors were introduced by Professors Eilenberg and Mac Lane in 1954, who used them to study certain homology rings. Strict polynomial functors were invented by Professors Friedlander and Suslin in 1997, in order to develop the theory of group schemes. The first real investigation of their intrinsic properties was performed in 1988, when Professor Pirashvili showed that polynomial functors are equivalent to modules over a certain ring. A similar study was conducted on strict polynomial functors in 2003 by Dr. Salomonsson in his doctoral thesis. A radically different method of attack was initiated by Dr. Dreckman and Professors Pirashvili, Franjou, and Baues in the year 2000. Their approach was to combinatorially encode polynomial functors, and utilised for this purpose the category of sets and surjections. Dr. Salomonsson would later repeat the feat for strict polynomial functors, employing instead the category of multi-sets. This thesis proposes the following: 1:o. To generalise the notion of polynomial functor to more general base rings than Z, so that it smoothly agree with the existing definition of strict polynomial functor, allowing for easy comparison. This results in the definition of numerical functors. 2:o. To make an extensive study of numerical maps of modules, to see how they fit into Professor Roby's framework of strict polynomial maps. 3:o. To conduct a survey of numerical rings. 4:o. To develop the theories of numerical and strict polynomial functors so that they run in parallel. 5:o. To show how also numerical functors may be interpreted as modules over a certain ring. 6:o. To expound the theory of mazes, which will be seen to vastly generalise the category of surjections employed by Professor Pirashvili et al., since they turn out to encode, not only polynomial or numerical functors, but all module functors over any base ring. 7:o. To simplify Dr. Salomonsson's construction involving multi-sets, making it more amenable to a comparison with mazes. 8:o. To prove comparison theorems interrelating numerical and strict polynomial functors. 9:o. And, finally, to indicate how polynomial functors may be used to extend the operad concept.
43
Macfarlane, Andrew Ian. "Reporting structures: Category theory, algebraic and topological properties." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/132394/1/Andrew_Macfarlane_Thesis.pdf.
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This thesis treats the logic of operations and governance of a large corporation as a single abstract mathematical object that expresses the web of dependencies and the coordinating hierarchies of corporate logic. The thesis initiates a study of the logic of high-level descriptions and the evolutionary dynamics of reporting structures. It provides a new way for an enterprise to investigate and characterise its own complex logic.
44
Mbirika, Abukuse III. "Analysis of symmetric function ideals: towards a combinatorial description of the cohomology ring of Hessenberg varieties." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/708.
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Symmetric functions arise in many areas of mathematics including combinatorics, topology and algebraic geometry. Using ideals of symmetric functions, we tie these three branches together. This thesis generalizes work of Garsia and Procesi in 1992 that gave a quotient ring presentation for the cohomology ring of Springer varieties.
Let R be the polynomial ring Ζ[x1,…,xn]. We present two different ideals in R. Both are parametrized by a Hessenberg function h, namely a nondecreasing function that satisfies h(i) ≥ i for all i. The first ideal, which we call Ih, is generated by modified elementary symmetric functions. The ideal I_h generalizes the work of Tanisaki who gave a combinatorial description of the ideal used in Garsia and Procesi's quotient ring. Like the Tanisaki ideal, the generating set for Ih is redundant. We give a minimal generating set for this ideal. The second ideal, which we call Jh, is generated by modified complete symmetric functions. The generators of this ideal form a Gröbner basis, which is a useful property. Using the Gröbner basis for Jh, we identify a basis for the quotient R/Jh.
We introduce a partial ordering on the Hessenberg functions, and in turn we discover nice nesting properties in both families of ideals. When h>h', we have Ih ⊂ Ih' and Jh ⊂ Jh'. We prove that Ih equals Jh when h is maximal. Since Ih is the ideal generated by the elementary symmetric functions when h is maximal, the generating set for Jh forms a Gröbner basis for the elementary symmetric functions. Moreover, the quotient R/Jh gives another description of the cohomology ring of the full flag variety.
The generators of the ring R/Jh are in bijective correspondence with the Betti numbers of certain Hessenberg varieties. These varieties are a two-parameter generalization of Springer varieties, parametrized by a nilpotent operator X and a Hessenberg function h. These varieties were introduced in 1992 by De Mari, Procesi and Shayman. We provide evidence that as h varies, the quotient R/Jh may be a presentation for the cohomology ring of a subclass of Hessenberg varieties called regular nilpotent varieties.
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Johnson, William T. G. "Synthesis of precursors of a highly pyramidalized alkene and ab initio calculations on methylenecyclopropane, cyclopropene, and 1,3-diradicals /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/11586.
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Lorenzon, Emmanuel. "Sponsored Search and Sequential Auctions : Three Essays in Auction Theory." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0357/document.
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Cette thèse regroupe trois essais en théorie des enchères. Le chapitre 1 introduit de ladélégation dans le mécanisme d’enchère GSP. Dans un jeu impliquant des transferts monétaires et unepolitique de rémunération mise en place par une agence, un équilibre collusif efficace est atteint.Nousproposons une caractérisation du profil d’enchères collusif implémentable dans un jeu de positions `a troisjoueurs et deux positions. Le chapitre 2 considère des ventes séquentielles d’un objet `a deux acheteurs: l’unconnaît son évaluation privée tandis que l’autre non. Les acheteurs ont une demande multi-unitaire et lesévaluations privées entre unit´es sont parfaitement corrélées. Un équilibre asymétrique existe dans lequelle joueur non-informé adopte une stratégie agressive tandis que le joueur informé joue de manière prudente.Le comportement du joueur non-informé est justifié par l’opportunité d’acquérir de l’informationgratuitement. Cette dynamique induit une décroissance des prix entre les ventes. Le chapitre 3, introduitun jeu de décision séquentielle dans la première enchère. Un équilibre séparateur existe dans lequel lejoueur informé est agressif lorsqu’il est le premier `a jouer impliquant une stratégie de non-participationde la part de son concurrent non-informé. A l’inverse, ce dernier adopte une attitude plus prudentelorsqu’il est le premier `a joueur. Un équilibre mélangeant dans lequel le joueur informé cache son informationprivée ne peut exister que si le joueur non-informé adopte une stratégie de non-participationThis thesis is a collection of three essays in theoretical auction analysis. Chapter 1 considersbid delegation in the GSP auction mechanism. In a game involving side-contracts and a compensationpolicy set by an agency, the first-best collusive outcome is achieved. We offer a characterization of the implementablebid profiles for the two-position game with three players. Chapter 2 considers the sequentialsale of an object to two buyers: one knows his private information and the other buyer does not. Buyershave a multi-unit demand and private valuations for each unit are perfectly correlated. An asymmetricequilibrium exists when the uninformed player adopts an aggressive bidding strategy. Conversely, hisinformed opponent behaves more conservatively by using bid shading. The bidding behaviour of theuninformed bidder is driven by the opportunity to learn his private valuation for free. This dynamic is atthe root of the decline in the equilibrium price across both sales. In chapter 3, information is observableduring the first-stage auction in a sequential-move game in which the first-mover bidder is observed byhis opponent. A separating equilibrium exists in which the informed bidder bids aggressively when he isthe first-mover which entails a non-participation strategy from his uninformed competitor. Conversely,the latter adopts a conservative behaviour when he is the first-mover. A pooling equilibrium in which theinformed bidder blurs his valuation can only exist if his uninformed opponent adopts a non-participatingstrategy
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Metzner, Norman. "Twistor theory of higher-dimensional black holes." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:0c275046-2d6f-4860-9bb3-5d5e5048cd5a.
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The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions is the lack of a higher-dimensional equivalent of the Ernst poten- tial. This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the rod structure, other asymptotic data, and the requirement of a regular axis. Examples in five dimensions are studied and necessary tools are developed, in particular rules for the transition between different adaptations of the patching matrix and rules for the elimination of conical singularities.
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Yasar, Orten Pinar. "Numerical Analysis, Design And Two Port Equivalent Circuit Models For Split Ring Resonator Arrays." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12611620/index.pdf.
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Split ring resonator (SRR) is a metamaterial structure which displays negative permeability values over a relatively small bandwidth around its magnetic resonance frequency. Unit SRR cells and arrays have been used in various novel applications including the design of miniaturized microwave devices and antennas. When the SRR arrays are combined with the arrays of conducting wires, left handed materials can be constructed with the unusual property of having negative valued effective refractive indices.
In this thesis, unit cells and arrays of single-ring multiple-split type SRR structures are numerically analyzed by using Ansoft&rsquos HFSS software that is based on the finite elements method (FEM). Some of these structures are constructed over low-loss dielectric substrates and their complex scattering parameters are measured to verify the numerical simulation results. The major purpose of this study has been to establish equivalent circuit models to estimate the behavior of SRR structures in a simple and computationally efficient manner. For this purpose, individual single ring SRR cells with multiple splits are modeled by appropriate two-port RLC resonant circuits paying special attention to conductor and dielectric loss effects. Results obtained from these models are compared with the results of HFSS simulations which use either PEC/PMC (perfect electric conductor/perfect magnetic conductor) type or perfectly matched layer (PML) type boundary conditions. Interactions between the elements of SRR arrays such as the mutual inductance and capacitance effects as well as additional dielectric losses are also modeled by proper two-port equivalent circuits to describe the overall array behavior and to compute the associated transmission spectrum by simple MATLAB codes. Results of numerical HFSS simulations, equivalent circuit model computations and measurements are shown to be in good agreement.
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Perera, Simon. "Grothendieck rings of theories of modules." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/grothendieck-rings-of-theories-of-modules(897cbbd9-77b6-47fb-8cf8-d15c7432e61b).html.
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We consider right modules over a ring, as models of a first order theory. We explorethe definable sets and the definable bijections between them. We employ the notionsof Euler characteristic and Grothendieck ring for a first order structure, introduced byJ. Krajicek and T. Scanlon in [24]. The Grothendieck ring is an algebraic structurethat captures certain properties of a model and its category of definable sets.If M is a module over a product of rings A and B, then M has a decomposition into a direct sum of an A-module and a B-module. Theorem 3.5.1 states that then the Grothendieck ring of M is the tensor product of the Grothendieck rings of the summands.Theorem 4.3.1 states that the Grothendieck ring of every infinite module over afield or skew field is isomorphic to Z[X].Proposition 5.2.4 states that for an elementary extension of models of anytheory, the elementary embedding induces an embedding of the corresponding Grothendieck rings. Theorem 5.3.1 is that for an elementary embedding of modules, we have the stronger result that the embedding induces an isomorphism of Grothendieck rings.We define a model-theoretic Grothendieck ring of the category Mod-R and explorethe relationship between this ring and the Grothendieck rings of general right R-modules. The category of pp-imaginaries, shown by K. Burke in [7] to be equivalentto the subcategory of finitely presented functors in (mod-R; Ab), provides a functorial approach to studying the generators of theGrothendieck rings of R-modules. It is shown in Theorem 6.3.5 that whenever R andS are Morita equivalent rings, the rings Grothendieck rings of the module categories Mod-R and Mod-S are isomorphic.Combining results from previous chapters, we derive Theorem 7.2.1 saying that theGrothendieck ring of any module over a semisimple ring is isomorphic to a polynomialring Z[X1,...,Xn] for some n.
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Sauer, Jacob A. "Cold Atom Manipulation for Quantum Computing and Control." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4809.
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Devices that exploit the properties of quantum mechanics for their operation can offer unique advantages over their classical counterparts. Interference of matter waves can be used to
dramatically increase the rotational sensitivity of gyroscopes. Complete control of the quantum evolution of a system could produce a new powerful computational device known as a quantum computer. Research into these technologies offers a deeper
understanding of quantum mechanics as well as exciting new insights into many other areas of science. Currently, a limiting factor in many quantum devices using neutral atoms is accurate motional control over the atoms. This thesis describes two recent advancements in neutral atom motional control using both magnetic and electromagnetic confining fields. Part I reports on the demonstration of the first storage ring for neutral atoms. This storage ring may one day provide the basis for the world's most
sensitive gyroscope. Part II describes the optical delivery of neutral atoms into the mode of a high-finesse cavity for applications in quantum computing and communication.