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1

Burns, Brenda D. "The Staircase Decomposition for Reductive Monoids." NCSU, 2002. http://www.lib.ncsu.edu/theses/available/etd-20020422-102254.

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<p>Burns, Brenda Darlene. The Staircase Decomposition for Reductive Monoids. (Under the direction of Mohan Putcha.) The purpose of the research has been to develop a decomposition for the J-classes of a reductive monoid. The reductive monoid M(K) isconsidered first. A J-class in M(K) consists ofelements of the same rank. Lower and upper staircase matricesare defined and used to decompose a matrix x of rank r into theproduct of a lower staircase matrix, a matrix with a rank rpermutation matrix in the upper left hand corner, and an upperstaircase matrix, each of which is of rank r. The choice of

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2

Kwizera, Petero. "Matrix Singular Value Decomposition." UNF Digital Commons, 2010. http://digitalcommons.unf.edu/etd/381.

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This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix a

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3

Ngulo, Uledi. "Decomposition Methods for Combinatorial Optimization." Licentiate thesis, Linköpings universitet, Tillämpad matematik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-175896.

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This thesis aims at research in the field of combinatorial optimization. Problems within this field often posses special structures allowing them to be decomposed into more easily solved subproblems, which can be exploited in solution methods. These structures appear frequently in applications. We contribute with both re-search on the development of decomposition principles and on applications. The thesis consists of an introduction and three papers. In Paper I, we develop a Lagrangian meta-heuristic principle, which is founded on a primal-dual global optimality condition for discrete and non

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4

Hersh, Patricia (Patricia Lynn) 1973. "Decomposition and enumeration in partially ordered sets." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85303.

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5

Samuelsson, Saga. "The Singular Value Decomposition Theorem." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-150917.

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This essay will present a self-contained exposition of the singular value decomposition theorem for linear transformations. An immediate consequence is the singular value decomposition for complex matrices.<br>Denna uppsats kommer presentera en självständig exposition av singulärvärdesuppdelningssatsen för linjära transformationer. En direkt följd är singulärvärdesuppdelning för komplexa matriser.

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6

Simeone, Daniel. "Network connectivity: a tree decomposition approach." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18797.

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We show that the gap between the least costly 3-edge-connected metric graph and the least costly 3-vertex-connected metric graph is at most $3$. The approach relies upon tree decompositions, and a degree limiting theorem of Bienstock et al. As well, we explore the tree decomposition approach for general k-edge and vertex-connected graphs, and demonstrate a large amount of the required background theory.<br>Nous démontrons que l'écart entre un graphe métrique 3-arête-connexe de coût minimum et un graphe métrique 3-sommet-connexe de coût minimum est au plus 3. Notre approche repose sur l'existen

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7

Riaz, Samia. "Domain decomposition method for variational inequalities." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4815/.

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Variational inequalities have found many applications in applied science. A partial list includes obstacles problems, fluid flow in porous media, management science, traffic network, and financial equilibrium problems. However, solving variational inequalities remain a challenging task as they are often subject to some set of complex constraints, for example the obstacle problem. Domain decomposition methods provide great flexibility to handle these types of problems. In our thesis we consider a general variational inequality, its finite element formulation and its equivalence with linear and

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8

Korey, Michael Brian. "A decomposition of functions with vanishing mean oscillation." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2592/.

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A function has vanishing mean oscillation (VMO) on R up(n) if its mean oscillation - the local average of its pointwise deviation from its mean value - both is uniformly bounded over all cubes within R up(n) and converges to zero with the volume of the cube. The more restrictive class of functions with vanishing lower oscillation (VLO) arises when the mean value is replaced by the minimum value in this definition. It is shown here that each VMO function is the difference of two functions in VLO.

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9

Wilson, Michelle Marie Lucy. "A survey of primary decomposition using Gröbner bases." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/37005.

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10

Jung, Kyomin. "Approximate inference : decomposition methods with applications to networks." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/50595.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.<br>Includes bibliographical references (p. 147-151).<br>Markov random field (MRF) model provides an elegant probabilistic framework to formulate inter-dependency between a large number of random variables. In this thesis, we present a new approximation algorithm for computing Maximum a Posteriori (MAP) and the log-partition function for arbitrary positive pair-wise MRF defined on a graph G. Our algorithm is based on decomposition of G into appropriately chosen small components; then computing estimates locally

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11

Oyinsan, Sola. "Primary decomposition of ideals in a ring." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3289.

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The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization d

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12

Gu, Fangqing. "Many objective optimization: objective reduction and weight design." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/315.

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Many-objective optimization problems (MaOPs), in which the number of objectives is greater than three, are common in various applications, and have drawn many scholars' attention. Evolutionary multiobjective optimization (EMO) algorithms have been successfully applied to solve bi- and tri-objective optimization problems. However, MaOPs are more challenging compared with the bi- and tri-objective optimization problems. The performances of most existing classical EMO algorithms generally deteriorate over the number of objectives. Thus, this thesis presents a weight design method to modify classi

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13

Kammogne, Kamgaing Rodrigue. "Domain decomposition methods for reaction-diffusion systems." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4599/.

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Domain Decomposition (DD) methods have been successfully used to solve elliptic problems, as they deal with them in a more elegant and efficient way than other existing numerical methods. This is achieved through the division of the domain into subdomains, followed by the solving of smaller problems within these subdomains which leads to the solution. Furthermore DD-techniques can incorporate in their implementation not only the physics of the different phenomena associated with the modeling, but also the enhancement of parallel computing. They can be divided into two major categories: with an

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14

Li, Weigang. "Atomic decomposition of H1 spaces and exponential square classes." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41682.

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Let $u sb0$ be the harmonic extension of the function f (defined on $R sp{n})$ to $R sbsp{+}{n+1}$. It is well known that $f in H sp{p}(R sp{n}), 00, C sp{ prime prime}< infty,$ which depend only on $ alpha$ and the dimension n. We also get a new proof for an L-harmonic version.

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15

Loisel, Sébastien. "Optimal and optimized domain decomposition methods on the sphere." Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85572.

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The numerical solution of partial differential equations and boundary value problems is one of the most important tools of modern science. For various reasons (parellelizing, improving condition numbers, finding good preconditioners, etc...) it is desirable to turn a boundary value problem over a large domain O into a set of boundary value problems over domains O1,...,O n such that ∪kO k; this is the domain decomposition method. The solutions u1,...,un of the local problems rarely glue together into a solution u of the global problem, hence we must use an iteration whereby we repeatedly

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16

Li, Zhi Xiong. "A revision of adaptive Fourier decomposition." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2590642.

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17

Kardamis, Joseph R. "Audio watermarking techniques using singular value decomposition /." Online version of thesis, 2007. http://hdl.handle.net/1850/4493.

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18

Chapovalova, Valentina. "Decomposition of Certain C[Sn]-modules into Specht Modules." Thesis, Uppsala universitet, Matematiska institutionen, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120505.

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19

Ortiz, Marcos A. "Convex decomposition techniques applied to handlebodies." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1713.

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Contact structures on 3-manifolds are 2-plane fields satisfying a set of conditions. The study of contact structures can be traced back for over two-hundred years, and has been of interest to mathematicians such as Hamilton, Jacobi, Cartan, and Darboux. In the late 1900's, the study of these structures gained momentum as the work of Eliashberg and Bennequin described subtleties in these structures that could be used to find new invariants. In particular, it was discovered that contact structures fell into two classes: tight and overtwisted. While overtwisted contact structures are relatively w

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20

Shankar, Jayashree. "Analysis of a nonhierarchical decomposition algorithm." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-09192009-040336/.

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21

Cho, Young Jin. "Effects of decomposition level on the intrarater reliability of multiattribute alternative evaluation." Diss., This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-06062008-171537/.

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22

Niyobuhungiro, Japhet. "Optimal Decomposition in Real Interpolation and Duality in Convex Analysis." Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94506.

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This thesis is devoted to the study of mathematical properties of exact minimizers for the K–,L–, and E– functionals of the theory of real interpolation. Recently exact minimizers for these functionals have appeared in important results in image processing. In the thesis, we present a geometry of optimal decomposition for L– functional for the couple (ℓ2, X), where space ℓ2 is defined by the standard Euclidean norm ǁ · ǁ2 and where X is a Banach space on Rn. The well known ROF denoising model is a special case of an L– functional for the couple (L2, BV) where L2 and BV stand for the space of s

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23

Azzato, Jeffrey Donald. "Linked tree-decompositions of infinite represented matroids : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Mathematics /." ResearchArchive@Victoria e-Thesis, 2008. http://hdl.handle.net/10063/322.

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24

Williams, Adrian Leonard. "Some more decomposition numbers for modular representations of symmetric groups." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313541.

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25

Turner, James Anthony. "Application of domain decomposition methods to problems in topology optimisation." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5842/.

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Determination of the optimal layout of structures can be seen in everyday life, from nature to industry, with research dating back to the eighteenth century. The focus of this thesis involves investigation into the relatively modern field of topology optimisation, where the aim is to determine both the optimal shape and topology of structures. However, the inherent large-scale nature means that even problems defined using a relatively coarse finite element discretisation can be computationally demanding. This thesis aims to describe alternative approaches allowing for the practical use of topo

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26

Ahiati, Veroncia Sitsofe. "Cardinal spline wavelet decomposition based on quasi-interpolation and local projection." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2580.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2009.<br>Wavelet decomposition techniques have grown over the last two decades into a powerful tool in signal analysis. Similarly, spline functions have enjoyed a sustained high popularity in the approximation of data. In this thesis, we study the cardinal B-spline wavelet construction procedure based on quasiinterpolation and local linear projection, before specialising to the cubic B-spline on a bounded interval. First, we present some fundamental results on cardinal B-splines, which are piecewise polynomials with uniformly space

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27

Palansuriya, Charaka Jeewana. "Domain decomposition based algorithms for some inverse problems." Thesis, University of Greenwich, 2000. http://gala.gre.ac.uk/8226/.

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The work presented in this thesis develop algorithms to solve inverse problems where source terms are unknown. The algorithms are developed 011frameworks provided by domain decomposition methods and the numerical schemes use finite volume and finite difference discretisations. Three algorithms are developed in the context of a metal cutting problem. The algorithms require measurement data within the physical body in order to retrieve the temperature field and the unknown source terms. It is shown that the algorithms can retrieve both the temperature field and the unknown source accurately. App

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28

Ozkan, Sibel. "Hamilton decompositions of graphs with primitive complements." Auburn, Ala., 2007. http://repo.lib.auburn.edu/2007%20Spring%20Dissertations/OZKAN_SIBEL_27.pdf.

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29

Chapovalova, Valentina. "Decomposition of Certain C[Sn]-modules into Specht Modules." Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120505.

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30

Stalvey, Harrison. "Weak Primary Decomposition of Modules Over a Commutative Ring." Digital Archive @ GSU, 2010. http://digitalarchive.gsu.edu/math_theses/84.

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This paper presents the theory of weak primary decomposition of modules over a commutative ring. A generalization of the classic well-known theory of primary decomposition, weak primary decomposition is a consequence of the notions of weakly associated prime ideals and nearly nilpotent elements, which were introduced by N. Bourbaki. We begin by discussing basic facts about classic primary decomposition. Then we prove the results on weak primary decomposition, which are parallel to the classic case. Lastly, we define and generalize the Compatibility property of primary decomposition.

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31

Muiny, Somaya. "Primary Decomposition in Non Finitely Generated Modules." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/70.

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In this paper, we study primary decomposition of any proper submodule N of a module M over a noetherian ring R. We start by briefly discussing basic facts about the very well known case where M is a finitely generated module over a Noetherian ring R, then we proceed to discuss the general case where M is any module over a Noetherian ring R. We put a lot of focus on the associated primes that occur with the primary decomposition, essentially studying their uniqueness and their relation to the associated primes of M/N.

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32

Tomczuk, Randal Wade. "Autocorrelation and decomposition methods in combinational logic design." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1996. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21952.pdf.

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33

Culver, Chance. "Decompositions of the Complete Mixed Graph by Mixed Stars." Digital Commons @ East Tennessee State University, 2020. https://dc.etsu.edu/etd/3782.

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In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions of the c

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34

Culver, Chance. "Decompositions of the Complete Mixed Graph by Mixed Stars." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/3782.

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In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions of the c

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35

Jagadeesh, Vasudevamurthy. "On the testability-preserving decomposition and factorization of Boolean expressions." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74653.

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This thesis presents a new concurrent method for the decomposition and factorization of Boolean expressions based on two simple objects: two-literal single-cube divisors, and double-cube divisors along with their complements. It is proved that the presence of common multiple-cube algebraic divisors, from a set of Boolean expressions, can be found by analyzing the set of double-cube divisors. It is also shown that in order to find the duality relations that may exist between various objects, only a subset of two-literal single-cube and double-cube divisors needs to be analyzed. Since the number

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36

Siahaan, Antony. "Defect correction based domain decomposition methods for some nonlinear problems." Thesis, University of Greenwich, 2011. http://gala.gre.ac.uk/7144/.

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Defect correction schemes as a class of nonoverlapping domain decomposition methods offer several advantages in the ways they split a complex problem into several subdomain problems with less complexity. The schemes need a nonlinear solver to take care of the residual at the interface. The adaptive-∝ solver can converge locally in the ∞-norm, where the sufficient condition requires a relatively small local neighbourhood and the problem must have a strongly diagonal dominant Jacobian matrix with a very small condition number. Yet its advantage can be of high signicance in the computational cost

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37

Toal, David J. J. "Proper orthogonal decomposition & kriging strategies for design." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/72023/.

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The proliferation of surrogate modelling techniques have facilitated the application of expensive, high fidelity simulations within design optimisation. Taking considerably fewer function evaluations than direct global optimisation techniques, such as genetic algorithms, surrogate models attempt to construct a surrogate of an objective function from an initial sampling of the design space. These surrogates can then be explored and updated in regions of interest. Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately represent complicated res

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38

Pfister, Noah. "Using Empirical Mode Decomposition to Study Periodicity and Trends in Extreme Precipitation." ScholarWorks @ UVM, 2015. http://scholarworks.uvm.edu/graddis/366.

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Classically, we look at annual maximum precipitation series from the perspective of extreme value statistics, which provides a useful statistical distribution, but does not allow much flexibility in the context of climate change. Such distributions are usually assumed to be static, or else require some assumed information about possible trends within the data. For this study, we treat the maximum rainfall series as sums of underlying signals, upon which we perform a decomposition technique, Empirical Mode Decomposition. This not only allows the study of non-linear trends in the data, but could

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39

Ho, Io Tong. "Experiments in relation to adaptive decomposition of signals into mono-components." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1943004.

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40

Lawlor, Matthew. "Tensor Decomposition by Modified BCM Neurons Finds Mixture Means Through Input Triplets." Thesis, Yale University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3580742.

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41

Garay, Jose. "Asynchronous Optimized Schwarz Methods for Partial Differential Equations in Rectangular Domains." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/510451.

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Mathematics<br>Ph.D.<br>Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve

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42

Volzer, Joseph R. "An Invariant Embedding Approach to Domain Decomposition." Case Western Reserve University School of Graduate Studies / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396522159.

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43

Wang, Yan Bo. "Adaptive decomposition of signals into mono-components." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2489954.

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44

Hogan, Ian. "The Brauer Complex and Decomposition Numbers of Symplectic Groups." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1489766963453771.

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45

Seater, Robert. "Minkowski sum decompositions of convex polygons." Diss., Connect to the thesis, 2002. http://hdl.handle.net/10066/1479.

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46

Wen, Mi. "An investigation on H∞ control in relation to adaptive decomposition of signal." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1780627.

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47

Bilinski, Mark. "Approximating the circumference of 3-connected claw-free graphs." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26516.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.<br>Committee Chair: Yu, Xingxing; Committee Member: Duke, Richard; Committee Member: Tetali, Prasad; Committee Member: Thomas, Robin; Committee Member: Vigoda, Eric. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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48

Eren, Levent. "Bearing damage detection via wavelet packet decomposition of stator current /." free to MU campus, to others for purchase, 2002. http://wwwlib.umi.com/cr/mo/fullcit?p3074397.

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49

Lewenczuk, Janice Gail. "Decomposition, Packings and Coverings of Complete Digraphs with a Transitive-Triple and a Pendant Arc." Digital Commons @ East Tennessee State University, 2007. https://dc.etsu.edu/etd/2053.

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In the study of design theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K3∪{e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings and coverings of the complete digraph with each of the six transitive triples with a pendant arc.

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50

Mathews, Chad Ullery William D. "Mixed groups with decomposition bases and global k-groups." Auburn, Ala., 2006. http://repo.lib.auburn.edu/2006%20Summer/Theses/MATHEWS_CHAD_59.pdf.

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