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Dissertations / Theses on the topic 'Class of functions'

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Published: 7 February 2023

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1

Harper, John-Paul. "The class number one problem in function fields." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53619.

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Thesis (MComm)--Stellenbosch University, 2003.
ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields.
AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.
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2

Soler, i. Gibert Odí. "Approximation in the Zygmund Class and Distortion under Inner Functions." Doctoral thesis, Universitat Autònoma de Barcelona, 2020. http://hdl.handle.net/10803/670865.

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En aquest treball es tracten dos problemes. El primer és un problema d’aproximació en la classe de Zygmund per funcions del subespai I_1(BMO), que és l’espai de funcions contínues amb derivada a BMO en el sentit de les distribucions. Considerem la distància definida per la semi-norma de Zygmund. En el Capítol 1, donada una funció f de la classe de Zygmund en la recta real amb suport compacte, trobem una estimació de la seva distància al subespai I_1(BMO). A més, aquest resultat s’expressa en termes de les segones diferències de f, que defineixen la seva semi-norma de Zygmund. Com a corol·lari, obtenim una caracterització de la clausura de l’espai I_1(BMO) en aquesta semi-norma. Els mètodes presentats en aquesta primera part no es poden aplicar al cas de la classe de Zygmund a l’espai euclidià de dimensió n>1. Tanmateix, presentem un resultat anàleg per mesures de Zygmund en dimensió n>=1. En aquest cas, el subespai que considerem és el de mesures absolutament contínues amb derivada de Radon-Nykodim en l’espai BMO. En el Capítol 2, considerem l’espai de funcions amb continuïtat Hölder de paràmetre 0=1. Per 0En este trabajo se tratan dos problemas. El primero es un problema de aproximación en la clase de Zygmund por funciones del subespacio I_1(BMO), que es el espacio de funciones continuas con derivada en BMO en el sentido de las distribuciones. Consideramos la distancia definida por la semi-norma de Zygmund. En el Capítulo 1, dada una función f de la clase de Zygmund en la recta real con soporte compacto, encontramos una estimación de su distancia al subespacio I_1(BMO). Además, este resultado se expresa mediante las segundas diferencias de f, que definen su semi-norma de Zygmund. Como corolario, obtenemos una caracterización de la clausura del espacio I_1(BMO) en esta semi-norma. Los métodos presentados en esta primera parte no son aplicables al caso de la clase de Zygmund en el espacio euclidiano de dimensión n>1. No obstante, presentamos un resultado análogo para medidas de Zygmund en dimensión n>=1. En este caso, el subespacio que consideramos es el de medidas absolutamente continuas con derivada de Radon-Nykodim en el espacio BMO. En el Capítulo 2, consideramos el espacio de funciones continuas Hölder de parámetro 0=1. Para 0In this work we deal with two different problems. The first one is an approximation problem in the Zygmund class by functions in the subspace I_1(BMO), which is the space of continuous functions with derivative in BMO in the sense of distributions. We consider the distance defined by the Zygmund semi-norm. In Chapter 1, given a function f in the Zygmund class in the real line with compact support, we find an estimate of its distance to the subspace I_1(BMO). In addition, this result is expressed in terms of the second differences of f, which define its Zygmund semi-norm. As a corollary, we obtain a characterisation of the closure of I_1(BMO) in this semi-norm. The methods presented in this first part are not applicable to the Zygmund class in the euclidean space of dimension n>1. However, we present an analogous result for Zygmund measures in dimension n>=1. In this case, the subspace that we consider is the space of absolutely continuous measures with Radon-Nykodim derivative in BMO. In Chapter 2, we consider the space of Hölder continuous functions with parameter 0=1. For 0
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3

Carroy, Raphaël. "Functions of the first Baire class." Paris 7, 2013. http://www.theses.fr/2013PA077071.

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Le but de cette thèse est de trouver de nouveaux outils permettant mieux comprendre les fonctions boréliennes. L'analyse qui nous sert de modèle est celle de Wadge des ensembles boréliens, et l'horizon lointain de ce projet est d'obtenir une hiérarchie des fonctions aussi fine que celle de Wadge l'est pour les ensembles. Nous nous sommes concentrés sur l'analyse de la première classe de Baire, et particulièrement sur les fonctions continues. Au vu de l'importance des jeux dans l'analyse de Wadge, ce sont d'abord les outils que nous avons cherché à développer. Nous nous sommes donc restreints aux espaces 0-dimensionnels, dans lesquels lies jeux sont possibles. Les fonctions considérées ici sont donc de et [dans un fermé de l'espace de Baire. Le premier but est de trouver des méthodes de théorie des jeux et les utiliser pour prouver des résultats concernant les fonctions de première classe, nous donnons ainsi de nouvelles preuves du Grand héorème de Baire, ainsi que du Théorème de Jayne-Rogers. Ensuite, nous définissons un quasi-ordre pour les fonctions qui préserve la simplicité de celles-ci, par exemple leur classe de Baire. On utilise la simplicité du quasi-ordre, i. E. Le fait d'être bon ou non, comme critère principal pour choisir entre différentes notions préservant la simplicité des fonctions. Prouver qu'un quasi-ordre assez fin, comme celui que nous voulons définir, est bon, est loin d'être une tâche aisée, donc nous indiquons celui qui a le plus de chances de jl'etre, et commençons à l'étudier sur les fonctions continues
IThe aim of this thesis is to provide new tools for handling and getting |a better understanding of Borel functions. We take the Wadge analysis |on sets as a role model for our analysis of functions, and the far horizon of the project is to get a description of functions that is as precise as the Wadge hierarchy on sets is. We focus on the first Baire (class and specifically on the continuous functions. The use of games in the analysis of the Wadge hierarchy being central, games are the first tools that we try to develop. The framework that (allows to mix games and functions is given by the Polish and 0-(dimensional spaces. So from this point onwards, we only consider (functions from and into a closed subspace of the Baire space. The first idea for this thesis is to find purely game-theoretical methods (and use them to provide new proofs of the Baire Lemma on pointwise (convergence or of the Jayne-Rogers Theorem. Then, as a second approach, we look for a reduction notion for functions that preserves the simplicity of these, so for instance the Baire class. We use the simplicity of the quasi-order, i. E. It being a well-quasi-order, as a major criterion to choose between several notions that preserve the regularity of functions. It is far from being [an easy task to prove that a fine quasi-order is a wqo, so we describe the one candidate that is most likely on a very wide class of functions. Then we begin to study it on the restricted class of continuous functions
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4

Mohamed, Abdlgader. "A new class of coherent states and it's properties." Thesis, University of Bradford, 2011. http://hdl.handle.net/10454/5724.

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The study of coherent states (CS) for a quantum mechanical system has received a lot of attention. The definition, applications, generalizations of such states have been the subject of work by researchers. A common starting point of all these approaches is the observation of properties of the original CS for the harmonic oscillator. It is well-known that they are described equivalently as (a) eigenstates of the usual annihilation operator, (b) from a displacement operator acting on a fundamental state and (c) as minimum uncertainty states. What we observe in the different generalizations proposed is that the preceding definitions are no longer equivalent and only some of the properties of the harmonic oscillator CS are preserved. In this thesis we propose to study a new class of coherent states and its properties. We note that in one example our CS coincide with the ones proposed by Glauber where a set of three requirements for such states has been imposed. The set of our generalized coherent states remains invariant under the corresponding time evolution and this property is called temporal stability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we get all coherent states by acting on one of these states [¿fiducial vector¿] with operators. They are highly non-classical states, in the sense that in general, their Bargmann functions have zeros which are related to negative regions of their Wigner functions. Examples of these coherent states with Bargmann function that involve the Gamma and also the Riemann ¿ functions are represented. The zeros of these Bargmann functions and the paths of the zeros during time evolution are also studied.
Libyan Cultural Affairs
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5

Mohamed, Abdlgader. "A new class of coherent states and its properties." Thesis, University of Bradford, 2011. http://hdl.handle.net/10454/5724.

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The study of coherent states (CS) for a quantum mechanical system has received a lot of attention. The definition, applications, generalizations of such states have been the subject of work by researchers. A common starting point of all these approaches is the observation of properties of the original CS for the harmonic oscillator. It is well-known that they are described equivalently as (a) eigenstates of the usual annihilation operator, (b) from a displacement operator acting on a fundamental state and (c) as minimum uncertainty states. What we observe in the different generalizations proposed is that the preceding definitions are no longer equivalent and only some of the properties of the harmonic oscillator CS are preserved. In this thesis we propose to study a new class of coherent states and its properties. We note that in one example our CS coincide with the ones proposed by Glauber where a set of three requirements for such states has been imposed. The set of our generalized coherent states remains invariant under the corresponding time evolution and this property is called temporal stability. Secondly, there is no state which is orthogonal to all coherent states (the coherent states form a total set). The third property is that we get all coherent states by acting on one of these states ['fiducial vector'] with operators. They are highly non-classical states, in the sense that in general, their Bargmann functions have zeros which are related to negative regions of their Wigner functions. Examples of these coherent states with Bargmann function that involve the Gamma and also the Riemann ⲝ functions are represented. The zeros of these Bargmann functions and the paths of the zeros during time evolution are also studied.
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6

Caldas, Miguel, Saeid Jafari, and R. M. Latif. "Β - open sets and a new class of functions." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96443.

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The concept of (b, s)-continuous functions in topological spaces is introduced and studied. Some of their characteristic properties are considered. Also we investigate the relationships between these classes of functions and other classes of functions.
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7

Krasowska, Anna Ewa. "Wigner functions for a class of semidirect product groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63982.pdf.

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8

Obeid, Nabil. "Absolutely continuous invariant measures for a class of meromorphic functions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0024/MQ39959.pdf.

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9

Yokura, Shoji, and yokura@sci kagoshima-u. ac jp. "Bivariant Theories of Constructible Functions and Grothendieck." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi930.ps.

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10

ICHIHARA, Yumiko, and Kohji MATSUMOTO. "On the siegel-Tatuzawa theorem for a class of L-functions." Faculty of mathematics, Kyushu University, 2008. http://hdl.handle.net/2237/13841.

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11

Albrecht, Simon [Verfasser]. "On Functions in the Speiser Class with One Tract / Simon Albrecht." Kiel : Universitätsbibliothek Kiel, 2015. http://d-nb.info/1076270468/34.

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12

Duncan, Jonathan D. "First return recovery of Baire class one functions on ultrametric spaces." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3278219.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.
Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 5995. Advisers: Slawomir Solecki; Lawrence S. Moss. Title from dissertation home page (viewed May 9, 2008).
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13

Roppert, Josef, and Gerhard Derflinger. "On Some Definite Integrals of a certain Class of Logarithmic Functions." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1992. http://epub.wu.ac.at/504/1/document.pdf.

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14

Rakocevic, Veselin. "Dynamic bandwidth allocation in multi-class IP networks using utility functions." Thesis, Queen Mary, University of London, 2002. http://qmro.qmul.ac.uk/xmlui/handle/123456789/3818.

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15

Dao, Ngon D. (Ngon Dong) 1974. "A new class of functions for describing logical structures in text." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/28594.

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Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2004.
Includes bibliographical references (p. 49-51).
Text documents generally contain two forms of structures, logical structures and physical structures. Loosely speaking, logical structures are sections of text that are both visually and semantically distinct. For example, a document may have an "introduction", a "body", and a "conclusion" as its logical structures. These structures are so named because each section has a distinct purpose in conveying the document's logical arguments or intentions. Perfect machine recognition of logical structures in large collections of documents is an unsolved problem in computational linguistics. This thesis presents evidence that a new family of functions on text segments carries information that is useful for differentiating document logical structures. For any given text segment, a function of this form is referred to as the cadence, and it is based on a new interpretation of the vector space representation that Gerard Salton introduced in 1975. Cadence also differs from the original Salton representation in that it relies on three heuristic transformations based on authorship, location, and term coherence. To test the hypothesis that the cadence of a text segment carries information helpful to differentiating logical structures, a corpus was built containing 2800 documents with manually-annotated logical structures. Structures representing abstracts, introductions, bodies, and conclusions from this corpus were clustered with a k-means algorithm using cadence data. Precision and recall performances were computed for the results, and a chi-squared cross-tabulation test was used to determine the statistical significance of the clustering results. Precision and recall were highest for abstracts (P = 0.931 [plus-minus] 0.025, R = 0.992
(cont.) [plus-minus] 0.026), followed by introductions (P = 0.747 [plus-minus] 0.025, R = 0.802 [plus-minus] 0.026) and conclusions (P = 0.737 [plus-minus] 0.025, R = 0.813 [plus-minus] 0.026), and lowest for bodies (P = 0.876 [plus-minus] 0.03, R = 0.663 [plus-minus] 0.026). These results suggest that cadence may have substantial promise for finding logical structures in un-annotated documents.
by Ngon D. Dao.
Ph.D.
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16

Trunk, Carsten. "Spectral properties of a class of analytic operator functions and their linearizations." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=966141156.

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17

Chae, Hi-joon. "A cohomological interpretation of the scalar product on the elliptic class functions." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28091.

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18

Mustafa, Ahmad M. "Performance of resonant radar target identification algorithms using intra-class weighting functions /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487260859493835.

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19

Wu, Haifan. "Gamma-AApeptides as a New Class of Peptidomimetics: Synthesis, Structures, and Functions." Scholar Commons, 2015. https://scholarcommons.usf.edu/etd/5601.

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Peptidomimetics are synthetic oligomers that resemble the activities of peptides. Their advantages over peptides include high stability towards proteolysis and enormous chemical diversity. Over the past two decades, there have been extensive efforts to develop peptide mimics, such as beta-peptides, peptoids, D-peptides, etc. The research on peptidomimetics have led to many important applications in both medicinal and material science. In order to explore new functions, the discovery of peptidomimetics with novel frameworks is essential. We reported the synthesis and evaluation of a new class of peptidomimetics, termed as gamma-AApeptides. Previous studies of gamma-AApeptides have revealed that gamma-AApeptides are highly resistant to proteolysis, and are highly amendable to chemical diversification. However, new biological activities and folding properties of gamma-AApeptides still need to be explored. In order to expand the potential of gamma-AApeptides in chemical biology and medicinal chemistry, I have been focusing on the development of new methods to synthesize linear and cyclic gamma-AApeptides, development of one-bead-one-compound (OBOC) gamma-AApeptide libraries for the discovery of inhibitors against beta-amyloid aggregation, exploring new helical foldamers for the rational design of protein-protein interaction (PPI) inhibitors, and studying cyclic gamma-AApeptides for antimicrobial development.
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20

Guerra, Huaman Moises Daniel. "Schur-class of finitely connected planar domains: the test-function approach." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/27334.

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We study the structure of the set of extreme points of the compact convex set of matrix-valued holomorphic functions with positive real part on a finitely-connected planar domain R normalized to have value equal to the identity matrix at some prescribed point t0 in R. This leads to an integral representation for such functions more general than what would be expected from the result for the scalar-valued case. After Cayley transformation, this leads to a integral Agler decomposition for the matrix Schur class over R (holomorphic contractive matrix-valued functions over R). Application of a general theory of abstract Schur-class generated by a collection of test functions leads to a transfer-function realization for the matrix Schur-class over R, extending results known up to now only for the scalar case. We also explain how these results provide a new perspective for the dilation theory for Hilbert space operators having R as a spectral set.
Ph. D.
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21

Šimėnas, Raivydas. "Riemann'o hipotezės Speiser'io ekvivalentas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2012~D_20140704_171541-67476.

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A. Speiser'is parodė, kad Riemann'o hipotezė yra ekvivalenti tam, kad Riemann'o dzeta funkcijos išvestinė neturi netrivialių nulių į kairę nuo kritinės tiesės. Kiekybinis šio fakto rezultatas buvo pasiektas N. Levinsono ir H. Montgomerio. Šie rezultatai buvo apibendrinti daugeliui dzeta funkcijų, kurioms tikimasi, kad Riemann'o hipotezė galioja. Šiame darbe mes apibendriname Speiser'io ekvivalentą dzeta-funkcijoms. Mes tiriame sąryšį tarp netrivialių nulių išplėstinės Selbergo klasės funkcijoms ir jų išvestinėms šiame regione. Šiai klasei priklauso ir funkcijos, kurioms Riemann'o hipotezė neteisinga. Kaip pavyzdį, mes skaitiniu būdu tiriame sąryšius tarp Dirichlet L-funkcijų ir jų išvestinių tiesinių kombinacijų.
A. Speiser showed that the Riemann hypothesis is equivalent to the absence of non-trivial zeros of the derivative of the Riemann zeta-function left of the critical line. The quantitative version of this result was obtained by N. Levinson and H. Montgomery. This result (or the quantitative version of this result proved by N. Levinson and H. Montgomery) were generalized for many zeta-functions for which the Riemann hypothesis is expected. Here we generalize the Speiser equivalent for zeta-functions. We also investigate the relationship between the on-trivial zeros of the extended Selberg class functions and of their derivatives in this region. This class contains zeta functions for which Riemann hypothesis is not true. As an example, we study the relationship between the trajectories of zeros of linear combinations of Dirichlet $L$-functions and of their derivatives computationally.
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Danilczyk, Ursula G. "Understanding the functions of molecular chaperones and thiol oxidoreductases in MHC class I biogenesis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63682.pdf.

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23

Чмир, Оксана Юріївна. "THE FIRST BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATION IN THE CLASS OF GENERALIZED FUNCTIONS." Thesis, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 2020. http://sci.ldubgd.edu.ua:8080/jspui/handle/123456789/7363.

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24

Imreh, Marta P. "Modulation of cellular and viral functions in Epstein-Barr virus infected cells /." Stockholm, 2002. http://diss.kib.ki.se/2002/91-7349-171-3.

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25

Sultanova, Nargiz. "A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard." University of Ballarat, 2009. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/16160.

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It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.
Master of Mathematical Sciences (Research)
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26

Cui, Weiwei [Verfasser]. "Lebesgue Measure of Escaping Sets of Entire Functions in the Eremenko-Lyubich Class / Weiwei Cui." Kiel : Universitätsbibliothek Kiel, 2017. http://d-nb.info/1136903240/34.

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27

Fuller, Joanne Elizabeth. "Analysis of affine equivalent boolean functions for cryptography." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/15828/1/Joanne_Fuller_Thesis.pdf.

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Boolean functions are an important area of study for cryptography. These functions, consisting merely of one's and zero's, are the heart of numerous cryptographic systems and their ability to provide secure communication. Boolean functions have application in a variety of such systems, including block ciphers, stream ciphers and hash functions. The continued study of Boolean functions for cryptography is therefore fundamental to the provision of secure communication in the future. This thesis presents an investigation into the analysis of Boolean functions and in particular, analysis of affine transformations with respect to both the design and application of Boolean functions for cryptography. Past research has often been limited by the difficulties arising from the magnitude of the search space. The research presented in this thesis will be shown to provide an important step towards overcoming such restrictions and hence forms the basis for a new analysis methodology. The new perspective allows a reduced view of the Boolean space in which all Boolean functions are grouped into connected equivalence classes so that only one function from each class need be established. This approach is a significant development in Boolean function research with many applications, including class distinguishing, class structures, self mapping analysis and finite field based s-box analysis. The thesis will begin with a brief overview of Boolean function theory; including an introduction to the main theme of the research, namely the affine transformation. This will be followed by the presentation of a fundamental new theorem describing the connectivity that exists between equivalence classes. The theorem of connectivity will form the foundation for the remainder of the research presented in this thesis. A discussion of efficient algorithms for the manipulation of Boolean functions will then be presented. The ability of Boolean function research to achieve new levels of analysis and understanding is centered on the availability of computer based programs that can perform various manipulations. The development and optimisation of efficient algorithms specifically for execution on a computer will be shown to have a considerable advantage compared to those constructed using a more traditional approach to algorithm optimisation. The theorem of connectivety will be shown to be fundamental in the provision many avenues of new analysis and application. These applications include the first non-exhaustive test for determining equivalent Boolean functions, a visual representation of the connected equivalence class structure to aid in the understanding of the Boolean space and a self mapping constant that enables enumeration of the functions in each equivalence class. A detailed survey of the classes with six inputs is also presented, providing valuable insight into their range and structure. This theme is then continued in the application Boolean function construction. Two important new methodologies are presented; the first to yield bent functions and the second to yield the best currently known balanced functions of eight inputs with respect to nonlinearity. The implementation of these constructions is extremely efficient. The first construction yields bent functions of a variety of algebraic order and inputs sizes. The second construction provides better results than previously proposed heuristic techniques. Each construction is then analysed with respect to its ability to produce functions from a variety of equivalence classes. Finally, in a further application of affine equivalence analysis, the impact to both s-box design and construction will be considered. The effect of linear redundancy in finite field based s-boxes will be examined and in particular it will be shown that the AES s-box possesses complete linear redundancy. The effect of such analysis will be discussed and an alternative construction to s-box design that ensures removal of all linear redundancy will be presented in addition to the best known example of such an s-box.
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28

Fuller, Joanne Elizabeth. "Analysis of Affine Equivalent Boolean Functions for Cryptography." Queensland University of Technology, 2003. http://eprints.qut.edu.au/15828/.

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Boolean functions are an important area of study for cryptography. These functions, consisting merely of one's and zero's, are the heart of numerous cryptographic systems and their ability to provide secure communication. Boolean functions have application in a variety of such systems, including block ciphers, stream ciphers and hash functions. The continued study of Boolean functions for cryptography is therefore fundamental to the provision of secure communication in the future. This thesis presents an investigation into the analysis of Boolean functions and in particular, analysis of affine transformations with respect to both the design and application of Boolean functions for cryptography. Past research has often been limited by the difficulties arising from the magnitude of the search space. The research presented in this thesis will be shown to provide an important step towards overcoming such restrictions and hence forms the basis for a new analysis methodology. The new perspective allows a reduced view of the Boolean space in which all Boolean functions are grouped into connected equivalence classes so that only one function from each class need be established. This approach is a significant development in Boolean function research with many applications, including class distinguishing, class structures, self mapping analysis and finite field based s-box analysis. The thesis will begin with a brief overview of Boolean function theory; including an introduction to the main theme of the research, namely the affine transformation. This will be followed by the presentation of a fundamental new theorem describing the connectivity that exists between equivalence classes. The theorem of connectivity will form the foundation for the remainder of the research presented in this thesis. A discussion of efficient algorithms for the manipulation of Boolean functions will then be presented. The ability of Boolean function research to achieve new levels of analysis and understanding is centered on the availability of computer based programs that can perform various manipulations. The development and optimisation of efficient algorithms specifically for execution on a computer will be shown to have a considerable advantage compared to those constructed using a more traditional approach to algorithm optimisation. The theorem of connectivety will be shown to be fundamental in the provision many avenues of new analysis and application. These applications include the first non-exhaustive test for determining equivalent Boolean functions, a visual representation of the connected equivalence class structure to aid in the understanding of the Boolean space and a self mapping constant that enables enumeration of the functions in each equivalence class. A detailed survey of the classes with six inputs is also presented, providing valuable insight into their range and structure. This theme is then continued in the application Boolean function construction. Two important new methodologies are presented; the first to yield bent functions and the second to yield the best currently known balanced functions of eight inputs with respect to nonlinearity. The implementation of these constructions is extremely efficient. The first construction yields bent functions of a variety of algebraic order and inputs sizes. The second construction provides better results than previously proposed heuristic techniques. Each construction is then analysed with respect to its ability to produce functions from a variety of equivalence classes. Finally, in a further application of affine equivalence analysis, the impact to both s-box design and construction will be considered. The effect of linear redundancy in finite field based s-boxes will be examined and in particular it will be shown that the AES s-box possesses complete linear redundancy. The effect of such analysis will be discussed and an alternative construction to s-box design that ensures removal of all linear redundancy will be presented in addition to the best known example of such an s-box.
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29

McKeon, R. C. "Estimating cost functions and measuring wealth neutrality of 1990-91 class size reduction implementation in selected Oklahoma school districts /." Access abstract and link to full text, 1992. http://0-wwwlib.umi.com.library.utulsa.edu/dissertations/fullcit/9222152.

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30

Martínez, Cruz Armando Moisés. "Knowledge and development of functions in a technology-enhanced high school precalculus class : a case study." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1240410195.

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31

Xayphakatsa, Kosonh. "Analysis of biological functions of a class 2 chitinase gene Cht11 in rice (Oryza sativa L.)." Kyoto University, 2008. http://hdl.handle.net/2433/136617.

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Kyoto University (京都大学)
0048
新制・課程博士
博士(農学)
甲第13890号
農博第1705号
新制||農||955(附属図書館)
学位論文||H20||N4357(農学部図書室)
UT51-2008-C806
京都大学大学院農学研究科農学専攻
(主査)教授 谷坂 隆俊, 教授 井上 國世, 教授 山末 祐二
学位規則第4条第1項該当
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32

Langley, Thomas. "The plethysm of two schur functions at hook, near-hook, and two-row shapes and a class of (q, t)-symmetric functions arising from plethysm /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2001. http://wwwlib.umi.com/cr/ucsd/fullcit?p3022197.

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33

Ringdahl, Benjamin. "Gaussian Process Multiclass Classification : Evaluation of Binarization Techniques and Likelihood Functions." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-87952.

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In binary Gaussian process classification the prior class membership probabilities are obtained by transforming a Gaussian process to the unit interval, typically either with the logistic likelihood function or the cumulative Gaussian likelihood function. Multiclass classification problems can be handled by any binary classifier by means of so-called binarization techniques, which reduces the multiclass problem into a number of binary problems. Other than introducing the mathematics behind the theory and methods behind Gaussian process classification, we compare the binarization techniques one-against-all and one-against-one in the context of Gaussian process classification, and we also compare the performance of the logistic likelihood and the cumulative Gaussian likelihood. This is done by means of two experiments: one general experiment where the methods are tested on several publicly available datasets, and one more specific experiment where the methods are compared with respect to class imbalance and class overlap on several artificially generated datasets. The results indicate that there is no significant difference in the choices of binarization technique and likelihood function for typical datasets, although the one-against-one technique showed slightly more consistent performance. However the second experiment revealed some differences in how the methods react to varying degrees of class imbalance and class overlap. Most notably the logistic likelihood was a dominant factor and the one-against-one technique performed better than one-against-all.
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34

Jin, Meilan. "Signal Structure for a Class of Nonlinear Dynamic Systems." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6829.

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The signal structure is a partial structure representation for dynamic systems. It characterizes the causal relationship between manifest variables and is depicted in a weighted graph, where the weights are dynamic operators. Earlier work has defined signal structure for linear time-invariant systems through dynamical structure function. This thesis focuses on the search for the signal structure of nonlinear systems and proves that the signal structure reduces to the linear definition when the systems are linear. Specifically, this work: (1) Defines the complete computational structure for nonlinear systems. (2) Provides a process to find the complete computational structure given a state space model. (3) Defines the signal structure for dynamic systems in general. (4) Provides a process to find the signal structure for a class of dynamic systems from their complete computational structure.
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35

Norrgård, Malena A. "Modulating Enzyme Functions by Semi-Rational Redesign and Chemical Modifications : A Study on Mu-class Glutathione Transferases." Doctoral thesis, Uppsala universitet, Institutionen för biokemi och organisk kemi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-149326.

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Today, enzymes are extensively used for many industrial applications, this includes bulk and fine-chemical synthesis, pharmaceuticals and consumer products. Though Nature has perfected enzymes for many millions of years, they seldom reach industrial performance targets. Natural enzymes could benefit from protein redesign experiments to gain novel functions or optimize existing functions. Glutathione transferases (GSTs) are detoxification enzymes, they also display disparate functions. Two Mu-class GSTs, M1-1 and M2-2, are closely related but display dissimilar substrate selectivity profiles. Saturation mutagenesis of a previously recognized hypervariable amino acid in GST M2-2, generated twenty enzyme variants with altered substrate selectivity profiles, as well as modified thermostabilities and expressivities. This indicates an evolutionary significance; GST Mu-class enzymes could easily alter functions in a duplicate gene by a single-point mutation. To further identify residues responsible for substrate selectivity in the GST M2-2 active site, three residues were chosen for iterative saturation mutagenesis. Mutations in position10, identified as highly conserved, rendered enzyme variants with substrate selectivity profiles resembling that of specialist enzymes. Ile10 could be conserved to sustain the broad substrate acceptance displayed by GST Mu-class enzymes. Enzymes are constructed from primarily twenty amino acids, it is a reasonable assumption that expansion of the amino acid repertoire could result in functional properties that cannot be accomplished with the natural set of building blocks. A combination approach of site-directed mutagenesis and chemical modifications in GST M2-2 and GST M1-1 resulted in novel enzyme variants that displayed altered substrate selectivity patterns as well as improved enantioselectivities. The results presented in this thesis demonstrate the use of different protein redesign techniques to modulate various functions in Mu-class GSTs. These techniques could be useful in search of optimized enzyme variants for industrial targets.
biokemi och organisk kemi
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36

Saito, Shingo. "Knot points of typical continuous functions and Baire category in families of sets of the first class." Thesis, University College London (University of London), 2008. http://discovery.ucl.ac.uk/1446078/.

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37

Macedo, Lins de Araujo Paula [Verfasser]. "Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes / Paula Macedo Lins de Araujo." Bielefeld : Universitätsbibliothek Bielefeld, 2019. http://d-nb.info/1177989360/34.

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38

Matsumoto, Kohji. "On the speed of convergence to limit distributions for Hecke L-functions associated with ideal class characters." Walter de Gruyter GmbH, 2009. http://hdl.handle.net/2237/20430.

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39

Cottrell, Seth S. "Some Applications of Quantum Walks to a General Class of Searches and the Computation of Boolean Functions." Thesis, New York University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3665129.

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In previous papers about searches on star graphs several patterns have been made apparent; the speed up only occurs when graphs are ''tuned'' so that their time step operators have degenerate eigenvalues, and only certain initial states are effective. More than that, the searches are never faster than order square root of N time. In this thesis the problem is defined rigorously, the causes for all of these patterns are identified, sufficient and necessary conditions for quadratic-speed searches for any connected subgraph are demonstrated, the tolerance of these conditions is investigated, and it is shown that (unfortunately) we can do no better than order square root of N time. Along the way, a useful formalism is established that may be useful in future work involving highly symmetric graphs.

The tools and techniques so derived are then used to demonstrate that tree graphs can be used for the computation of Boolean functions. The philosophy of Farhi's work on the continuous-time NAND tree is applied to a discrete-time walk with any (AND, OR, NAND, or NOR) gate at each vertex. Tentative results show that the vast majority of possible Boolean functions on N bits can be calculated in order square root of N time.

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40

Siddig, Yousif Ashraf. "Differential regulation of S-region hypermutation and class switch recombination by noncanonical functions of uracil DNA glycosylase." Kyoto University, 2014. http://hdl.handle.net/2433/189357.

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The final publication is available at http://dx.doi.org/10.1073/pnas.1402391111. Ashraf S. Yousif, Andre Stanlie, Samiran Mondal, Tasuku Honjo, and Nasim A. Begum. Differential regulation of S-region hypermutation and class-switch recombination by noncanonical functions of uracil DNA glycosylase. PNAS 2014 111 (11) E1016-E1024; published ahead of print March 3, 2014.
Kyoto University (京都大学)
0048
新制・課程博士
博士(医科学)
甲第18464号
医科博第55号
新制||医科||4(附属図書館)
31342
京都大学大学院医学研究科医科学専攻
(主査)教授 清水 章, 教授 萩原 正敏, 教授 武田 俊一
学位規則第4条第1項該当
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41

Teixeira, de Matos Cristina. "Modulation of natural killer cell and T-cell functions by CD94/NKG2A receptors /." Stockholm, 2006. http://diss.kib.ki.se/2006/91-7140-846-0/.

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42

Williams, Matthew Richard. "Likelihood-based testing and model selection for hazard functions with unknown change-points." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/26835.

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The focus of this work is the development of testing procedures for the existence of change-points in parametric hazard models of various types. Hazard functions and the related survival functions are common units of analysis for survival and reliability modeling. We develop a methodology to test for the alternative of a two-piece hazard against a simpler one-piece hazard. The location of the change is unknown and the tests are irregular due to the presence of the change-point only under the alternative hypothesis. Our approach is to consider the profile log-likelihood ratio test statistic as a process with respect to the unknown change-point. We then derive its limiting process and find the supremum distribution of the limiting process to obtain critical values for the test statistic. We first reexamine existing work based on Taylor Series expansions for abrupt changes in exponential data. We generalize these results to include Weibull data with known shape parameter. We then develop new tests for two-piece continuous hazard functions using local asymptotic normality (LAN). Finally we generalize our earlier results for abrupt changes to include covariate information using the LAN techniques. While we focus on the cases of no censoring, simple right censoring, and censoring generated by staggered-entry; our derivations reveal that our framework should apply to much broader censoring scenarios.
Ph. D.
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43

Anil, Gautham. "A Fitness Function Elimination Theory for Blackbox Optimization and Problem Class Learning." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5106.

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The modern view of optimization is that optimization algorithms are not designed in a vacuum, but can make use of information regarding the broad class of objective functions from which a problem instance is drawn. Using this knowledge, we want to design optimization algorithms that execute quickly (efficiency), solve the objective function with minimal samples (performance), and are applicable over a wide range of problems (abstraction). However, we present a new theory for blackbox optimization from which, we conclude that of these three desired characteristics, only two can be maximized by any algorithm. We put forward an alternate view of optimization where we use knowledge about the problem class and samples from the problem instance to identify which problem instances from the class are being solved. From this Elimination of Fitness Functions approach, an idealized optimization algorithm that minimizes sample counts over any problem class, given complete knowledge about the class, is designed. This theory allows us to learn more about the difficulty of various problems, and we are able to use it to develop problem complexity bounds. We present general methods to model this algorithm over a particular problem class and gain efficiency at the cost of specifically targeting that class. This is demonstrated over the Generalized Leading-Ones problem and a generalization called LO'', and efficient algorithms with optimal performance are derived and analyzed. We also tighten existing bounds for LO'''. Additionally, we present a probabilistic framework based on our Elimination of Fitness Functions approach that clarifies how one can ideally learn about the problem class we face from the objective functions. This problem learning increases the performance of an optimization algorithm at the cost of abstraction. In the context of this theory, we re-examine the blackbox framework as an algorithm design framework and suggest several improvements to existing methods, including incorporating problem learning, not being restricted to blackbox framework and building parametrized algorithms. We feel that this theory and our recommendations will help a practitioner make substantially better use of all that is available in typical practical optimization algorithm design scenarios.
Ph.D.
Doctorate
Computer Science
Engineering and Computer Science
Computer Science
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44

Rodgerson, Joanne Kelly. "Contributions to the study of a class of optimal control problems on the matrix lie group SO(3)." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1007199.

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The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states.
KMBT_363
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45

Vahlne, Gustaf. "Natural killer cell inhibitory and activating receptors : regulatory role in effector functions against normal and tumor cells /." Stockholm : Karolinska institutet, 2007. http://diss.kib.ki.se/2007/978-91-7357-430-3/.

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46

Castillo, René Erlin. "Generalized Non-Autonomous Kato Classes and Nonlinear Bessel Potentials." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1121964346.

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47

Singh, Rupesh Kumar. "Distance Learning and Attribute Importance Analysis by Linear Regression on Idealized Distance Functions." Wright State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1495909607902884.

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48

Dunster, T. M. "Uniform asymptotic solutions of a class of second-order linear differential equations, with an application to legendre and prolate spheroidal functions." Thesis, University of Bristol, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355098.

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49

Khan, Mumtaz Ahmad, and Khvurshed Ahmad. "On a general class of Polynomials Ln (x, y) of two variables suggested by the Polynomials Ln (x, y) of Ragab and Ln (x) of Prabhakar and Rekha." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95290.

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50

Chagnon, Mélanie J. 1977. "Physiological and molecular functions of the murine receptor protein tyrosine phosphatase sigma (RPTP[sigma])." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115661.

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The control of cellular tyrosine phosphorylation levels is of great importance in many biological systems. Among the kinases and phosphatases that modulate these levels, the LAR-RPTPs have been suggested to act in several key aspects of neural development, and in a dysfunctional manner in various pathologies from diabetes to cancer. The aim of this thesis is to describe the physiological functions of one of the members of this subfamily of RPTPs, namely RPTPsigma. First, we showed that glucose homeostasis is altered in RPTPsigma null mice. They are hypoglycemic and more sensitive to exogenous insulin and we proposed that the insulin hypersensitivity observed in RPTPsigma-null mice is likely secondary to their neuroendocrine dysplasia and GH/IGF-1 deficiency. In addition to regulating nervous system development, RPTPsigma was previously shown to regulate axonal regeneration after injury. In the absence of RPTPsigma, axonal regeneration in the sciatic, facial and optical nerves was enhanced following nerve crush. However, myelin-associated growth inhibitory proteins and components of the glial scar such as CSPGs (chondroitin sulfate proteoglycans) have long been known to inhibit axonal regeneration in the CNS, making spinal cord injury irreversible. In collaboration with Dr Samuel David, we unveiled that RPTPsigma null mice are able to regenerate their corticospinal tract following spinal cord hemisections as opposed to their WT littermates. We then isolated primary neurons from both sets of animals and found that the absence of RPTPsigma promotes the ability of the neurons to adhere to certain inhibitory substrates. Finally, in order to better understand the physiological role of RPTPsigma, we used a yeast substrate-trapping approach, to screen a murine embryonic library for new substrates. This screen identified the RhoGAP p250GAP as a new substrate, suggesting a downstream role for RPTPsigma in RhoGTPase signaling. We also identified p130Cas and Fyn as new binding partners. All these proteins have clear functional links to neurite extension. The characterization of RPTPsigma and its signaling partners is essential for understanding its role in neurological development and may one day translate into treatments of neural diseases and injuries.
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