Rozprawy doktorskie: „Integral theory”

1

Tressler, Eric. "Integral and Euclidean Ramsey theory". Diss., [La Jolla] : University of California, San Diego, 2010. http://wwwlib.umi.com/cr/ucsd/fullcit?p3404684.

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Thesis (Ph. D.)--University of California, San Diego, 2010.
Title from first page of PDF file (viewed June 15, 2010). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (leaves 42-44).

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2

Huettenmueller, Rhonda. "The Pettis Integral and Operator Theory". Thesis, University of North Texas, 2001. https://digital.library.unt.edu/ark:/67531/metadc2844/.

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Let (Ω, Σ, µ) be a finite measure space and X, a Banach space with continuous dual X*. A scalarly measurable function f: Ω→X is Dunford integrable if for each x* X*, x*f L1(µ). Define the operator Tf. X* → L1(µ) by T(x*) = x*f. Then f is Pettis integrable if and only if this operator is weak*-to-weak continuous. This paper begins with an overview of this function. Work by Robert Huff and Gunnar Stefansson on the operator Tf motivates much of this paper. Conditions that make Tf weak*-to-weak continuous are generalized to weak*-toweak continuous operators on dual spaces. For instance, if Tf is weakly compact and if there exists a separable subspace D X such that for each x* X*, x*f = x*fχDµ-a.e, then f is Pettis integrable. This nation is generalized to bounded operators T: X* → Y. To say that T is determined by D means that if x*| D = 0, then T (x*) = 0. Determining subspaces are used to help prove certain facts about operators on dual spaces. Attention is given to finding determining subspaces far a given T: X* → Y. The kernel of T and the adjoint T* of T are used to construct determining subspaces for T. For example, if T*(Y*) ∩ X is weak* dense in T*(Y*), then T is determined by T*(Y*) ∩ X. Also if ker(T) is weak* closed in X*, then the annihilator of ker(T) (in X) is the unique minimal determining subspace for T.

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3

Munsaka, Melvin Slaighter. "Some integral equations connected with statistical distribution theory". Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60056.

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This thesis looks at certain integral equations which are used to obtain statistical distributions, particularly in the multivariate case. In all, seven integral equations are considered. Two of the integral equations were introduced by Wilks (1932) and these are known as type A and type B integral equations. The other five known as type C to type G were introduced by Mathai (1984). Some statistical distributions associated with the solutions to these integral equations will also be discussed.

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Roberts, Saglinda Hallett. "The implications of integral theory on sustainable design". Thesis, Philadelphia University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1569527.

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This thesis explores Wilber's Integral Theory and DeKay's adaptation of the theory to sustainable design to discover a design process with the potential to advance the design professions toward a more holistic, restorative approach to sustainable design. The contribution and influence of architects, interior designers, and engineers on the personal and social welfare goes beyond aesthetics, visual interest, or function. The environments being designed today shape how people will live and function in the future. Integral Sustainable Design is concerned with holistically addressing the quality, equity, beauty and efficiency of the built environment. It argues that if sustainable design is to be a transformational force touching personal experience, cultural perspective, energy efficiency, and the ecosystem, it will need to become restorative.

This thesis provides an overview of the validity, feasibility and methodology of applying Integral Theory to Sustainable Design, to create a theoretical, ideological basis informing the sustainable design process. This thesis will increase awareness of integral theory by summarizing its principles and demonstrating the applicability to sustainable design and the validity to the profession as a whole. A design exercise will illustrate the difference between having a single, inherently biased view verses a comprehensive, holistic view of sustainable design. Four individual houses will be designed, each exploring one quadrant of DeKay's Integral Sustainable grid exclusively. A fifth house will synthesize all of the integral design principles. A comparison is then made to discern any difference in outcomes. All designs are based on the same client design directives, and use the same site. The comparative analysis seems to show that the integral approach can lead to an enhanced experience of nature, history, beauty with efficiency that exceeds Net Zero consumption

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5

Hertweck, Martin. "Contributions to the integral representation theory of groups". [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11103977.

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6

Geer, Nathan. "Link invariants, quantized superalgebras and the Kontsevich integral /". view abstract or download file of text, 2004. http://wwwlib.umi.com/cr/uoregon/fullcit?p3136414.

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Thesis (Ph. D.)--University of Oregon, 2004.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 123-125). Also available for download via the World Wide Web; free to University of Oregon users.

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7

Baker, N. "Some integral identities arising in probabilistic Wiener-Hopf theory". Thesis, Swansea University, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636020.

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8

Watson, David. "Integral Clifford theory and the computation of denominator ideals". Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/33396.

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Let R be a commutative ring. To each finitely presented R-module M one can associate an ideal, Fit_R(M), called the (zeroth) Fitting ideal of M . This ideal is always contained within the R-annihilator of M . Now let R be an integrally closed complete Noetherian local ring and let Λ be a (not necessarily commutative) R-order. A. Nickel generalised the notion of the Fitting ideal, providing a definition of the Fitting invariant for finitely presented modules M over Λ. In this case, to obtain the relation between the Fitting invariant of M and the annihilator of M in the centre of Λ, one must multiply the Fitting invariant of M by a certain ideal, H(Λ), of the centre of Λ, called the denominator ideal of Λ. H. Johnston and A. Nickel have formulated several bounds for the denominator ideal and have computed the denominator ideal for certain group rings. In this thesis, we prove a local-global principle for denominator ideals. We build upon the work of H. Johnston and A. Nickel to give improved bounds for the denominator ideal of Λ assuming some structural knowledge of Λ. We also build upon the work of P. Schmid and K. Roggenkamp to determine structural information about certain group rings. Finally, we use this structural information to compute the denominator ideal of group rings R[G], where G is a p-group with commutator subgroup of order p.

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9

Ito, Yu. "Rough path theory via fractional calculus". 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199445.

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10

Bartel, Alex. "On Brauer relations and integral group representations in number theory". Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608820.

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11

Dunning, Tania Clare. "Perturbed conformal field theory, nonlinear integral equations and spectral problems". Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4329/.

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This thesis is concerned with various aspects of perturbed conformal field theory and the methods used to calculate finite-size effects of integrable quantum field theories. Nonlinear integral equations are the main tools to find the exact ground-state energy of a quantum field theory. The thermodyamic Bethe ansatz (TBA) equations are a set of examples and are known for a large number of models. However, it is also an interesting question to find exact equations describing the excited states of integrable models. The first part of this thesis uses analytical continuation in a continuous parameter to find TBA like equations describing the spin-zero excited states of the sine-Gordon model at coupling β(^2) = 16π/3. Comparisons are then made with a further type of nonlinear integral equation which also predicts the excited state energies. Relations between the two types of equation are studied using a set of functional relations recently introduced in integrable quantum field theory. A relevant perturbation of a conformal field theory results in either a massive quantum field theory such as the sine-Gordon model, or a different massless conformal field theory. The second part of this thesis investigates flows between conformal field theories using a nonlinear integral equation. New families of flows are found which exhibit a rather unexpected behaviour. The final part of this thesis begins with a review of a connection between integrable quantum field theory and properties of certain ordinary differential equations of second- and third-order. The connection is based on functional relations which appear on both sides of the correspondence; for the second-order case these are exactly the functional relations mentioned above. The results are extended to include a correspondence between n(^th) order differential equations and Bethe ansatz system of SU(n) type. A set of nonlinear integral equations are derived to check the results.

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12

Soriano, Solá Marcos. "Contributions to the integral representation theory of Iwahori-Hecke algebras". [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9866651.

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13

Pampallis, Paisley Patricia. "Towards a theory of supervision for coaching : an integral vision". Thesis, Middlesex University, 2006. http://eprints.mdx.ac.uk/22177/.

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This research project was undertaken as a response to the compelling need for coaching to firmly establish itself as a profession of the highest standing. Supervision has been a way of ensuring best practice since the beginning of the twentieth century. The practice of coaching supervision is a new field of application and has thus far drawn on supervision models imported from other helping professions, or from specific models of coaching.

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14

McCabe, Andrew Peter. "Proportional-integral-plus control of nonlinear systems". Thesis, Lancaster University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289039.

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15

Aberegg, Keith R. "Electromagnetic scattering using the integral equation-asymptotic phase method". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/14860.

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16

Dawson, Dan Paul. "Concerning Integral Approximations of Bounded Finitely Additive Set Functions". Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc332650/.

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The purpose of this paper is to generalize a theorem that characterizes absolute continuity of bounded finitely additive set functions in the form of an integral approximation. We show that his integral exists if the condition of absolute continuity is removed.

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17

Spura, Thomas [Verfasser]. "Ab initio path integral molecular dynamics : theory and applications / Thomas Spura". Paderborn : Universitätsbibliothek, 2015. http://d-nb.info/1078666504/34.

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18

Cruz, Flaviani Cristina da Silva [UNESP]. "Interpolação integral e estimadores de densidade". Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/154120.

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Esta dissertação objetiva-se ao estudo analítico de técnicas de interpolação integral – fundamentadas na teoria de distribuição, também conhecida como teoria de funções generalizadas – e suas aplicações a reconstrução de imagens formadas por partículas (noise image) e à forma anisotrópica das equações da hidrodinâmica com partículas suavizadas, no inglês smoothed particle hydrodynamics, bem conhecida como SPH. A aplicação a processamento de imagens é um caso particular da técnica de interpolação utilizada em SPH. A imagem original é fragmentada na forma de partículas (em duas dimensões), aleatoriamente colhidas dos píxeis da imagem original, cuja densidade de probabilidade é proporcional à escala de cinza de cada píxel vizinho. Então é feita uma reconstrução da imagem através de interpolação anisotrópica, evidenciando que detalhes estruturais do contexto original são mais bem recuperados do que a correspondente técnica isotrópica. Apesar de não realizarmos diretamente simulações de mecânica dos fluidos neste trabalho, o que é proposto aqui é uma revisão das equações fundamentais da técnica de simulação SPH para o caso anisotrópico. As interpolações apresentadas neste trabalho foram feitas a partir de um núcleo normalizado de suavização, definido na forma de uma função regulada por partes, conhecida como cubic-B-spline, que é de classe analítica C2.
This mastered dissertation aims at the analytical study of integral interpolation techniques – based on the theory of distribution, also known as generalized function theory – and its applications the reconstruction of images formed by particles (noise image) and the anisotropic form of the fundamental equations of smoothed particle hydrodynamics, well known as SPH. The application to image processing is a particular case of the interpolation technique used in SPH. The original image is fragmented in the form of particles (in two dimensions), randomly drawn from the píxels of the original image, whose density is proportional to the gray scale of each neighboring píxel. Then a reconstruction of the image is made through anisotropic interpolation, evidencing that structural details of the original context are better recovered than the corresponding isotropic technique. Although we do not directly perform fluid mechanics simulations in this work, what is proposed here is a review of the fundamental equations of the SPH simulation technique for the anisotropic case. The interpolations presented in this work were made from a normalized smoothing kernel, defined as cubic-B-spline, which is of analytic class C2.

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19

Hakk, Kristiina. "Approximation methods for weakly singular integral equations with discontinuous coefficients /". Online version, 2004. http://dspace.utlib.ee/dspace/bitstream/10062/588/5/Hakk.pdf.

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20

Timonin, Mikhail. "Axiomatizations of the Choquet integral on general decision spaces". Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/24864.

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We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set X = X1 Xn. Previous characterizations of the Choquet integral have been given for the particular cases X = Y n and X = Rn. However, this makes the results inapplicable to problems in many fields of decision theory, such as multicriteria decision analysis (MCDA), state-dependent utility (SD-DUU), and social choice. For example, in multicriteria decision analysis the elements of X are interpreted as alternatives, characterized by criteria taking values from the sets Xi. Obviously, the identicalness or even commensurateness of criteria cannot be assumed a priori. Despite this theoretical gap, the Choquet integral model is quite popular in the MCDA community and is widely used in applied and theoretical works. In fact, the absence of a sufficiently general axiomatic treatment of the Choquet integral has been recognized several times in the decision-theoretic literature. In our work we aim to provide missing results { we construct the axiomatization based on a novel axiomatic system and study its uniqueness properties. Also, we extend our construction to various particular cases of the Choquet integral and analyse the constraints of the earlier characterizations. Finally, we discuss in detail the implications of our results for the applications of the Choquet integral as a model of decision making.

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21

Edwards, Mark Gerard. "An integral metatheory for organisational transformation". University of Western Australia. Faculty of Business, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0145.

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This thesis proposes a metatheory for the study of organisational transformation. A metatheory is a coherent conceptual system that analyses and accommodates the insights of other theory. In a time of rapidly changing organisational, societal and global environments there is a strong imperative for developing integrative conceptual frameworks that contribute to our understanding and explanation of transformational change. Like other areas of social science, the field of organisational transformation is made up of a multitude of diverse theories that offer useful and valid insights into aspects of transformational phenomena. These theories come from many different theoretical schools and research paradigms and they employ a wide range of explanatory concepts. There are however, no overarching theoretical frameworks specifically developed from metatheory building techniques that might give an overall coherency to the field. Consequently, there is no way of deciding on the relative conceptual merits of particular theories and there is often little justification for adopting one theory over another to explore some aspect of organisational transformation. To fill this gap, this thesis uses conceptual research methods to i) review extant literature, ii) develop a metatheory for organisational transformation and iii) apply this metatheory to the exemplar topic of organisational sustainability. The initial chapters introduce the topics of organisational transformation and metatheory building and provide a rationale for an overarching approach to radical organisational change. Following this, a method for metatheory building is developed and its application in this study is described. A rationale for the sampling procedure and organisational of data is also presented. The metatheory building method involves the use of conceptual theme analysis for identifying the core themes theorists use in describing and explaining organisational transformation. In subsequent chapters, core themes are analysed using the techniques of bridging and bracketing to derive a number of conceptual lenses. These lenses, and the relationships between them, form the central components for the integral metatheory. Having identified and described the basic set of conceptual lenses for transformation, the exemplar topic of organisational sustainability is used to show how the metatheory can be applied to a specific area of research. The final chapter evaluates the integral metatheory with some commonly used criteria for judging the results of conceptual research. A brief evaluation of the chief metatheoretical resource used in the study, i.e., AQAL metatheory, is also carried out. This thesis endeavours to contribute to the field of organisational, transformational and sustainability studies by i) developing a metatheoretical framework for the study of radical organisational change, ii) offering a comprehensive review of paradigms and theories of organisational transformation and their core explanatory concepts, and iii) proposing a more detailed metatheory building method which can make a significant contribution to the conceptual development of many fields within organisational studies.

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22

Bachmann, Michael. "Path integral methods in quantum statistics, quantum field theory and membrane physics". [S.l.] : [s.n.], 2001. http://www.diss.fu-berlin.de/2001/106/index.html.

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23

Ghaempanah, Mahsa [Verfasser], i Torsten [Akademischer Betreuer] Enßlin. "Information Field Theory with INTEGRAL/SPI data / Mahsa Ghaempanah ; Betreuer: Torsten Enßlin". München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/113058741X/34.

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24

Gusakova, Anna [Verfasser]. "Application of Probability Methods in Number Theory and Integral Geometry / Anna Gusakova". Bielefeld : Universitätsbibliothek Bielefeld, 2018. http://d-nb.info/1174670371/34.

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25

Nixon, Steven Paul. "Theory and applications of the multiwavelets for compression of boundary integral operators". Thesis, University of Salford, 2004. http://usir.salford.ac.uk/2035/.

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In general the numerical solution of boundary integral equations leads to full coefficient matrices. The discrete system can be solved in O(N2) operations by iterative solvers of the Conjugate Gradient type. Therefore, we are interested in fast methods such as fast multipole and wavelets, that reduce the computational cost to O(N lnp N). In this thesis we are concerned with wavelet methods. They have proved to be very efficient and effective basis functions due to the fact that the coefficients of a wavelet expansion decay rapidly for a large class of functions. Due to the multiresolution property of wavelets they provide accurate local descriptions of functions efficiently. For example in the presence of corners and edges, the functions can still be approximated with a linear combination of just a few basis functions. Wavelets are attractive for the numerical solution of integral equations because their vanishing moments property leads to operator compression. However, to obtain wavelets with compact support and high order of vanishing moments, the length of the support increases as the order of the vanishingmoments increases. This causes difficulties with the practical use of wavelets particularly at edges and corners. However, with multiwavelets, an increase in the order of vanishing moments is obtained not by increasing the support but by increasing the number of mother wavelets. In chapter 2 we review the methods and techniques required for these reformulations, we also discuss how these boundary integral equations may be discretised by a boundary element method. In chapter 3, we discuss wavelet and multiwavelet bases. In chapter 4, we consider two boundary element methods, namely, the standard and non-standard Galerkin methods with multiwavelet basis functions. For both methods compression strategies are developed which only require the computation of the significant matrix elements. We show that they are O(N logp N) such significant elements. In chapters 5 and 6 we apply the standard and non-standard Galerkin methods to several test problems.

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26

Fry, Jedediah Micah. "On Integral Quadratic Constraint Theory and Robust Control of Unmanned Aircraft Systems". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/102615.

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This dissertation advances tools for the certification of unmanned aircraft system (UAS) flight controllers. We develop two thrusts to this goal: (1) the validation and improvement of an uncertain UAS framework based on integral quadratic constraint (IQC) theory and (2) the development of novel IQC theorems which allow the analysis of uncertain systems having time-varying characteristics. Pertaining to the first thrust, this work improves and implements an IQC-based robustness analysis framework for UAS. The approach models the UAS using a linear fractional transformation on uncertainties and conducts robustness analysis on the uncertain system via IQC theory. By expressing the set of desired UAS flight paths with an uncertainty, the framework enables analysis of the uncertain UAS flying about any level path whose radius of curvature is bounded. To demonstrate the versatility of this technique, we use IQC analysis to tune trajectory-tracking and path-following controllers designed via H2 or H-infinity synthesis methods. IQC analysis is also used to tune path-following PID controllers. By employing a non-deterministic simulation environment and conducting numerous flight tests, we demonstrate the capability of the framework in predicting loss of control, comparing the robustness of different controllers, and tuning controllers. Finally, this work demonstrates that signal IQCs have an important role in obtaining IQC analysis results which are less conservative and more consistent with observations from flight test data. With regards to the second thrust, we prove a novel theorem which enables robustness analysis of uncertain systems where the nominal plant and the IQC multiplier are linear time-varying systems and the nominal plant may have a non-zero initial condition. When the nominal plant and the IQC multiplier are eventually periodic, robustness analysis can be accomplished by solving a finite-dimensional semidefinite program. Time-varying IQC multipliers are beneficial in analysis because they provide the possibility of reducing conservatism and are capable of expressing uncertainties that have unique time-domain characteristics. A number of time-varying IQC multipliers are introduced to better describe such uncertainties. The utility of this theorem is demonstrated with various examples, including one which produces bounds on the UAS position after an aggressive Split-S maneuver.
Doctor of Philosophy

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27

Hymo, John A. "Problems involving relative integral bases for quartic number fields". Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39404.

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In this dissertation the question of whether or not a relative extension of number fields has a relative integral basis is considered. In Chapters 2 and 3 we use a criteria of Mann to determine when a cyclic quartic field or a pure quartic field has an integral basis over its quadratic subfield. In the final chapter we study the question: if the relative discriminant of an extension K / k is principal, where [K : k] = l such that l is an odd prime and k is either a quadratic or a normal quartic number field, does K / k have an integral basis?
Ph. D.

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28

O'Sullivan, Niamh Eleanor. "The genus and localization of groups". Thesis, Queen Mary, University of London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243524.

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29

Maurer, Simon. "Efficient distance-including integral screening for Moller-Plesset perturbation theory of second order and symmetry-adapted perturbation theory". Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-183280.

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30

Mongiardo, Mauro. "Variational analysis of waveguide discontinuities by integral equation including the edge condition". Thesis, University of Bath, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305044.

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31

Schlottmann, Robert Brian. "A path integral formulation of elastic wave propagation /". Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004372.

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32

Duncan, Stainsby Hayden. "Triangular bases of integral closures". Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/284995.

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En aquest treball, considerem el problema de computar bases triangulars de clausures enteres d'anells locals unidimensionals. Es presenta "MaxMin", un algoritme eficient que empra representacions OM d'ideals primers per computar bases locals d'ideals fraccionaris de cossos de nombres i cossos de funcions. MaxMin garanteix que les bases generades són reduïdes i triangulars. D'aquesta manera, s'evita l'aplicació de rutines de triangularització, com ara el pas a la forma normal d'Hermite, que són lentes per a cossos de grau alt. Mostrem que aquest algoritme té la mateixa complexitat computacional asimptòtica que els mètodes ja existents basats en representacions OM. MaxMin ha estat desenvolupat i inclòs en el paquet +Ideals, dissenyat per treballar qüestions aritmètiques en cossos grans. La implementació quasi sempre és més ràpida que la de les altres rutines basades en representacions OM. Respecte a les rutines que es troben actualment als sistemes d'àlgebra computacional estàndard, la nostra implementació de MaxMin és també considerablement més ràpida, exceptuant casos concrets d'extensions de cossos molt petites.
En este trabajo, consideramos el problema de computar bases triangulares de clausuras enteras de anillos locales unidimensionales. Se presenta "MaxMin", un algoritmo eficiente que emplea representaciones OM de ideales primos para computar bases locales de ideales fraccionarios de cuerpos de números y cuerpos de funciones. MaxMin garantiza que las bases generadas son reducidas y triangulares. De este modo, se evita la aplicación de rutinas de triangularización, como el paso a la forma normal de Hermite, que son lentas para cuerpos de grado alto. Mostramos que este algoritmo tiene la misma complejidad computacional asintótica que los métodos ya existentes basados en representaciones OM. MaxMin ha sido desarrollado e incluido en +Ideals, un paquete diseñado para trabajar cuestiones aritméticas en cuerpos grandes. La implementación casi siempre es más rápida que las otras rutinas basadas en representaciones OM. Respecto a las rutinas que se encuentran actualmente en los sistemas de álgebra computacional estándard, nuestra implementación de MaxMin es de nuevo considerablemente más rápida, exceptuando casos concretos de extensiones de cuerpos muy pequeñas.
In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. "MaxMin" is presented, an efficient algorithm which employs OM representations of prime ideals to compute local bases of fractional ideals of number fields and function fields. The proposed algorithm generates bases which are guaranteed to be reduced and triangular. In this way, it avoids the application of triangularisation routines, such as the Hermite Normal Form, which are slow for fields of large degree. We show that this algorithm has the same asymptotic computational complexity as existing methods based on OM representations. MaxMin has been developed and included as part of the +Ideals package for arithmetic in large fields. This implementation is almost always faster than existing OM-based routines. It is also considerably faster than the routines currently found in standard computer algebra systems, excepting some cases involving very small field extensions.

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Ehrhardt, Torsten. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip". Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972573305.

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Junghanns, P., i U. Weber. "Local theory of projection methods for Cauchy singular integral equations on an interval". Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801281.

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We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented.

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35

Pereira, Pedro Jorge da Silva. "Boundary value problems and integral relations in the continuum theory of nematicliquid crystals". Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420334.

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Leffler, Klara. "The Riemann-Stieltjes integral : and some applications in complex analysis and probability theory". Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-89199.

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The purpose of this essay is to prove the existence of the Riemann-Stieltjes integral. After doing so, we present some applications in complex analysis, where we define the complex curve integral as a special case of the Riemann- Stieltjes integral, and then focus on Cauchy’s celebrated integral theorem. To show the versatility of the Riemann-Stieltjes integral, we also present some applications in probability theory, where the integral generates a general formula for the expectation, regardless of its underlying distribution.

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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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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /". free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Li, Ge Jr. "Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier Algebras of type A". Thesis, The University of Sydney, 2012. http://hdl.handle.net/2123/8844.

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The main purpose of this thesis is to prove that the cyclotomic Khovanov-Lauda-Rouquier algebras of type A over Z are free by giving a graded cellular basis of the cyclotomic KLR algebra. We then extend it to obtain a graded cellular basis of the affine KLR algebra, which indicates that the affine KLR algebra is an affine graded cellular algebra. Finally we work with the Jucys-Murphy elements of the cyclotomic Hecke algebras of type A and proved a periodic property of these elements.

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40

Junghanns, P., i U. Weber. "Local theory of a collocation method for Cauchy singular integral equations on an interval". Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801203.

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We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials , where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.

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41

Subramanian, Ramachandran. "Quantum virial coefficients via path integral Monte Carlo| Theory and development of novel algorithms". Thesis, State University of New York at Buffalo, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10127734.

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Virial coefficients are unique thermodynamic properties of a system owing to their link be- tween interactions at the molecular level to macroscopic quantities such as the pressure. In this work, we take advantage of this feature and compute virial coefficients of a variety of systems by performing simulation studies. The nature and quality of the interaction potential used in such studies highly affects the quality of the resulting virial coefficients. Therefore, we have employed ab initio based interaction potentials that are state-of-the-art and have been developed using high quality quantum chemistry calculations. Naturally, the complexity of such simulations is a strong motivator for the development of algorithms that are highly efficient and yield precise results. In this regard, we have developed two efficient and novel algorithms for use in Path Integral Monte Carlo (PIMC), a method used to incorporate nuclear quantum effects in virial coefficient calculations for diatomic molecules. We have successfully applied these algorithms to compute virial coefficients including quantum effects or, in short, quantum virial coefficients, for H₂, N₂ and O₂ sys- tems. In addition to applying these algorithms to study diatomic molecules, we have also investigated other algorithms like PIMC using semi-classical beads and compared them to conventional PIMC, for He as well as N₂ systems. Finally, we have also evaluated virial coefficients including quantum corrections, or, in short, semi-classical virial coefficients for a latest ab initio potential of water.

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42

Cvijanovic, Zoran. "A computer laboratory for generalized information theory (COLGIT)". Diss., Online access via UMI:, 2007.

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Thesis (Ph. D.)--State University of New York at Binghamton, Department or Systems Science and Industrial Engineeering, Thomas J. Watson School of Engineering and Applied Science, 2007.
Includes bibliographical references.

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Hidle, Frederick B. "Application of the integral equation asymptotic phase method to penetrable scatterers". Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/15797.

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Fernandez-Borsot, Gabriel. "A Theoretical Analysis of Integral Theory and the Participatory Paradigm through the Lens of Otherness". Thesis, California Institute of Integral Studies, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10618494.

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This dissertation aims to fulfill two objectives. First, to establish a critical perspective of analysis based on the construct of otherness. I term this perspective the “Lens of Otherness” (LoO) and it consists in analyzing the ways otherness is integrated in a theory. A significant part of this work is devoted to substantiate it and provide a theoretical and methodological foundation for it. The second goal is to apply the LoO to two major transpersonal theories, integral theory and the participatory paradigm. The application of the LoO to these two transpersonal theories brings their problematic aspects to the fore.

The overall argument is broken down into several steps. The first step consists of compiling a significant number of critiques of transpersonalism that point to a common problem: an inadequate treatment of otherness. Next, the study shows that otherness is a fundamental aspect for both the human being and the universe at large. In order to demonstrate this, a model for otherness in transpersonal studies is created. This model contains five modalities of otherness with increasing significance. Once having shown the relevance of otherness, a critical perspective of analysis based on otherness, the LoO, is formed. A method to guide the application of this critical perspective to transpersonal theories is provided as well.

Then the LoO is applied to exemplars of the two major orientations in transpersonal theories, integral theory and the participatory paradigm. The main conclusion of this analysis is that while integral theory presents many flaws from the perspective of otherness, otherness is a foundational constituent of the participatory paradigm. Many other critiques are developed that are of paramount relevance for transpersonal studies.

This work will be of interest to all scholars interested in transpersonal studies, and more generally to spiritual seekers who are attracted to the ideas and principles of transpersonal theories.

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Diomedi, II Kevin Paul. "A Curvature-Corrected Rough Surface Scattering Theory Through The Single-Scatter Subtraction Method". Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/88512.

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A new technique is presented to study radio propagation and rough surface scattering problems based on a reformulation of the Magnetic Field Integration Equation (MFIE) called the Single-Scatter Subtraction (S^3) method. This technique amounts to a physical preconditioning by separating the single- and multiple-scatter currents and removing the single-scattering contribution from the integral term that is present in the MFIE. This requires the calculation of a new quantity that is the kernel of the MFIE integral call the kernel integral or Gbar. In this work, 1-dimensional deterministically rough surfaces are simulated by surfaces consisting of single and multiple cosines. In order to truncate the problem domain, a beam illumination is used as the source term and it is shown that this also causes the kernel integral to have a finite support. Using the Single Scatter Subtraction method on these surfaces, closed-form expressions are found for the kernel integral and thus the single-scatter current for a well defined region of validity of surface parameters which may then be efficiently radiated into the far field numerically. Both the closed-form expressions, and the computed radiated fields are studied for their physical significance. This provides a clear physical intuition for the technique as an augmentation to existing ones as a bent-plane approximation as shown analytically and also validated by numeric results. Further analysis resolves a controversy on the nature of Bragg scatter which is found to be a multiple-scatter phenomenon. Error terms present in the kernel integral also raise new questions on the effect of truncation for any MFIE-based solution. Additionally, a dramatic enhancement of backscatter predicted by this new approach versus the Kirchhoff method is observed as the angle of incidence increases due to the error terms.
Doctor of Philosophy
A new technique is presented to study the interaction of electromagnetic waves with rough surfaces. Building on the technique called the Magnetic Field Integral Equation (MFIE) which allows the solution for the electromagnetic fields scattered from the surface by considering only the induced electric and magnetic currents on the surface, the Single-Scatter Substraction (S 3 ) method separates the surface currents into those that interact with the surface only once or single-scatter, and those that interact multiple times called multiple-scatter. Since this is the introduction of this technique, only the former is investigated. In this study, a new quantity which is an integral of one of the components of the standard MFIE is studied and closed-form approximations are presented along with bounds of validity. This provides closed form solutions for the single-scattering currents, from which the radiated fields may be efficiently found numerically. Since they are closed form, the expressions provide insight into the nature of the physical scattering process. Numerical results of these expressions are compared to the standard approximate technique as well as the ”exact” solution found by numerically solving the MFIE. Compared to the standard approximate technique which approximates the surface by a tangent plane at each point on the surface, the single-scatter currents approximate the surface with a bent-plane at each point. This shifts the scattered fields from certain directions to others, and highlights where single- and multiple-scattering have an effect.

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46

Hocaoğlu, Ali Köksal. "Choquet integral based-morphological operators with applications to object detection and information fusion /". free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9988671.

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Cohen, Paul Anthony. "Design for sustainable communities : an integral perspective". Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4302.

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Thesis (MPhil (Sustainable Development Planning and Management))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Given the complexities facing humanity in the light of impending social and environmental collapse, it is the design of sustainable communities at all levels of our society that must be achieved to limit this potential outcome. Attaining such a goal, it is known, requires that humanity ‘consciously evolve’. Furthermore I suggest that Integral Theory, because it is grounded in the evolution of consciousness, provides an important map to help navigate this tremendous journey. In this thesis I use Integral Theory as a lens through which to understand and reflect on my experiences over the past eighteen years of the design and development of the Tlholego Village, one of the early experimental Permaculture and Ecovillage communities developed in South Africa.
AFRIKAANSE OPSOMMING: Gegewe die kompleksiteite wat die samelewing in die gesig staar as gevolg van die dreigende sosiale en omgewings verval, is die ontwikkeling van volhoubare gemeenskappe op alle vlakke van ons samelewing noodsaaklik om so ‘n uitkoms te verhoed. Om hierdie doel te bereik word dit voorgestel dat die samelewing bewustelik moet ontwikkel (‘consciously evolve’). Verder stel ek voor dat Integraal Teorie (‘Integral Theory’), gegrond in die evolusie van bewustheid, ‘n belangrike roetekaart verskaf om die geweldige reis te navigeer. In hierdie tesis gebruik ek Integraal Teorie as ‘n lens waardeur my ervarings tydens die ontwerp en ontwikkeling van die Tlholego Village (een van die vroee eksperimentele Permakultuur en Eko-dorp gemeenskappe wat ontwikkel is in Suid Afrika oor die afgelope agtien jaar) verstaan en nabetrag kan word.

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Cakmakci, Ufuk M. "The political economy of governance : an integral economic analysis of textile and apparel sectors in Turkey". Thesis, Lancaster University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364318.

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Domingo, Salazar Carlos. "Endpoint estimates via extrapolation theory". Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/396143.

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In this thesis, we study different variants of Rubio de Francia’s extrapolation that allow us to obtain estimates near L1. This theory is subsequently applied to deduce enpoint boundedness for the Bochner-Riesz operator and other classes of multipliers. We also present results related to Yano’s extrapolation on Lorentz spaces and how it can be related to the theory of weights.
En aquesta tesi, estudiem variants de l’extrapolació de Rubio de Francia que permetin obtenir estimacions a prop de l’espai L1. Aquesta teoria l’apliquem després per deduïr acotacions a l’extrem per l’operador de Bochner-Riesz i altres classes de multiplicadors. També presentem altres resultats sobre teoria d’extrapolació de tipus Yano en espais de Lorentz i sobre com es pot relacionar amb la teoria de pesos.

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Kasahara, Kento. "Integral Equation Theories of Diffusion and Solvation for Molecular Liquids". Kyoto University, 2018. http://hdl.handle.net/2433/232056.

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