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Probabilistic combinatorics in factoring, percolation and related topicsLee, Jonathan David January 2015 (has links)
No description available.
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Factorization of isometries of hyperbolic 4-space and a discreteness conditionPuri, Karan Mohan, January 2009 (has links)
Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematical Sciences." Includes bibliographical references (p. 52-53).
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Bayesian and Positive Matrix Factorization approaches to pollution source apportionment /Lingwall, Jeff W. January 2006 (has links) (PDF)
Thesis (M.S.)--Brigham Young University. Dept. of Statistics, 2006. / Includes bibliographical references (p. 96-98).
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Faktorisierungssysteme in der Kategorie der partiellen Algebren, Kennzeichnung von (Homo)Morphismenklassen /Pasztor, Ana. January 1979 (has links)
Thesis--Darmstadt. / Includes bibliographical references (p. 109-112).
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Studies on factoring polynomials over global fieldsBenzaoui, Ilhem 12 1900 (has links)
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2007. / In this thesis, we surveyed the most important methods for factorization of polynomials over a global
field, focusing on their strengths and showing their most striking disadvantages. The algorithms we
have selected are all modular algorithms. They rely on the Hensel factorization technique, which can
be applied to all global fields giving an output in a local field that can be computed to a large enough
precision. The crucial phase of the reconstruction of the irreducible global factors from the local ones,
determines the difference between these algorithms. For different fields and cases, different techniques
have been used such as residue class computations, ideal calculus, lattice techniques.
The tendency to combine ideas from different methods has been of interest as it improves the running
time. This appears for instance in the latest method due to van Hoeij, concerning the factorization over a
number field. The ideas here can be used over a global function field in the form given by Belabas et al.
using the logarithmic derivative instead of Newton sums.
Complexity analysis was not our objective, nevertheless it was important to mention certain results as
part of the properties of these algorithms.
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Primary decomposition of ideals in a ringOyinsan, Sola 01 January 2007 (has links)
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 domain.
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Drinfeld modules and their application to factor polynomialsRandrianarisoa, Tovohery Hajatiana 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between
the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While
an algorithm has been discovered to factor integers using elliptic curves, the
discovery of Drinfeld modules, which are analogous to elliptic curves, made it
possible to exhibit an algorithm for factorising polynomials in the ring Fq[T].
In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate
the analogy between Drinfeld modules and Elliptic curves. Finally, we
present an algorithm for factoring polynomials over a nite eld using Drinfeld
modules. / AFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi
is toon 'n sterk verband tussen die ring van heelgetalle, Z; en die ring van
polinome oor 'n eindige liggaam, F[T]: Terwyl daar alreeds 'n algoritme, wat
gebruik maak van elliptiese kurwes, ontwerp is om heelgetalle te faktoriseer,
het die ontdekking van Drinfeld modules, wat analoog is aan elliptiese kurwes,
dit moontlik gemaak om 'n algoritme te konstrueer om polinome in die ring
F[T] te faktoriseer.
In hierdie tesis maak ons die konsep van Drinfeld modules bekend deur sekere
aspekte daarvan te bestudeer. Ons gaan voort deur 'n voorbeeld te voorsien
wat die analoog tussen Drinfeld modules en elliptiese kurwes illustreer. Uiteindelik,
deur gebruik te maak van Drinfeld modules, bevestig ons hierdie analoog
deur die algoritme vir die faktorisering van polinome oor eindige liggame te
veskaf.
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On the analysis of refinable functions with respect to mask factorisation, regularity and corresponding subdivision convergenceDe Wet, Wouter de Vos 12 1900 (has links)
Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007. / We study refinable functions where the dilation factor is not always assumed to be 2. In
our investigation, the role of convolutions and refinable step functions is emphasized as a
framework for understanding various previously published results. Of particular importance
is a class of polynomial factors, which was first introduced for dilation factor 2 by
Berg and Plonka and which we generalise to general integer dilation factors.
We obtain results on the existence of refinable functions corresponding to certain reduced
masks which generalise similar results for dilation factor 2, where our proofs do not
rely on Fourier methods as those in the existing literature do.
We also consider subdivision for general integer dilation factors. In this regard, we extend
previous results of De Villiers on refinable function existence and subdivision convergence
in the case of positive masks from dilation factor 2 to general integer dilation factors.
We also obtain results on the preservation of subdivision convergence, as well as on the
convergence rate of the subdivision algorithm, when generalised Berg-Plonka polynomial
factors are added to the mask symbol.
We obtain sufficient conditions for the occurrence of polynomial sections in refinable
functions and construct families of related refinable functions.
We also obtain results on the regularity of a refinable function in terms of the mask
symbol factorisation. In this regard, we obtain much more general sufficient conditions
than those previously published, while for dilation factor 2, we obtain a characterisation of
refinable functions with a given number of continuous derivatives.
We also study the phenomenon of subsequence convergence in subdivision, which explains
some of the behaviour that we observed in non-convergent subdivision processes
during numerical experimentation. Here we are able to establish different sets of sufficient
conditions for this to occur, with some results similar to standard subdivision convergence,
e.g. that the limit function is refinable. These results provide generalisations of the corresponding
results for subdivision, since subsequence convergence is a generalisation of
subdivision convergence. The nature of this phenomenon is such that the standard subdivision
algorithm can be extended in a trivial manner to allow it to work in instances where
it previously failed.
Lastly, we show how, for masks of length 3, explicit formulas for refinable functions can
be used to calculate the exact values of the refinable function at rational points.
Various examples with accompanying figures are given throughout the text to illustrate
our results.
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Using hyperbolic tangents in integer factoringPinter, Ron Y January 1980 (has links)
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING / Bibliography: leaf 45. / by Ron Yair Pinter. / M.S.
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Edge-transitive homogeneous factorisations of complete graphsLim, Tian Khoon January 2004 (has links)
[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis concerns the study of homogeneous factorisations of complete graphs with edge-transitive factors. A factorisation of a complete graph Kn is a partition of its edges into disjoint classes. Each class of edges in a factorisation of Kn corresponds to a spanning subgraph called a factor. If all the factors are isomorphic to one another, then a factorisation of Kn is called an isomorphic factorisation. A homogeneous factorisation of a complete graph is an isomorphic factorisation where there exists a group G which permutes the factors transitively, and a normal subgroup M of G such that each factor is M-vertex-transitive. If M also acts edge-transitively on each factor, then a homogeneous factorisation of Kn is called an edge-transitive homogeneous factorisation. The aim of this thesis is to study edge-transitive homogeneous factorisations of Kn. We achieve a nearly complete explicit classification except for the case where G is an affine 2-homogeneous group of the form ZR p x G0, where G0 is less than or equal to ΓL(1,p to the power of R). In this case, we obtain necessary and sufficient arithmetic conditions on certain parameters for such factorisations to exist, and give a generic construction that specifies the homogeneous factorisation completely, given that the conditions on the parameters hold. Moreover, we give two constructions of infinite families of examples where we specify the parameters explicitly. In the second infinite family, the arc-transitive factors are generalisations of certain arc-transitive, self-complementary graphs constructed by Peisert in 2001.
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