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1 
The computation of kdefect polynomials, suspended Y trees and its applicationsWerner, Simon 06 February 2015 (has links)
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in partial fulfilment of requirements for the degree of Master of Science. June 2014. / We start by defining a class of graphs called the suspended Y trees and give some
of its properties. We then classify all the closed sets of a general suspended Y tree.
This will lead us to counting the graph compositions of the suspended Y tree. We
then contract these closed sets one by one to obtain a set of minors for the suspended
Y trees. We will use this information to compute some of the general expression of
the kdefect polynomial of a suspended Y tree. Finally we compute the explicit Tutte
polynomial of the suspended Y trees.

2 
Estimates for the number of polynomials with bounded degree and bounded Mahler measure /Chern, Sheyjey, January 2000 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 7173). Available also in a digital version from Dissertation Abstracts.

3 
Polynomial addition sets /Ma, Siulun. January 1985 (has links)
ThesisPh. D., University of Hong Kong, 1985.

4 
Zero distribution of polynomials and polynomial systemsCheung, Pakleong, 張伯亮 January 2014 (has links)
The new framework of random polynomials developed by R. Pemantle, I. Rivin and the late O. Schramm has been studied in this thesis. The strong PemantleRivin conjecture asks whether for random polynomials with independent and identically distributed zeros with a common probability distribution μon the complex plane, the empirical measures of their critical points would converge weakly to μ almost surely. This convergence question has connection with geometry of polynomials. S. D. Subramanian confirmed the conjecture whenμis a nonuniform distribution supported in the unit circle ∂D.
In this thesis, the conjecture has been extended to considering not only the critical points of the random polynomials, but also the zeros of their higher order, polar and Sz.Nagy's generalized derivatives. The case thatμ(uniform or not) is supported in ∂D has been studied, where the derivative of each order has been proved to satisfy the conjecture. Subramanian's work has thereby been completed plus generalization. The same almost sure weak convergence has also been shown for polar and Sz.Nagy's generalized derivatives, under some mild conditions. In particular, the result on polar derivative is the crux of filling up Subramanian's missing case of uniform μ.
Meanwhile, the original Pemantle{Rivin conjecture asks about convergence in probability instead of the aforesaid stronger almost sure convergence. Z. Kabluchko fully solved this conjecture. In this thesis, his methodologies have been adapted to prove the analogous conjecture for random finite Blaschke products.
More precisely, for random finite Blaschke products with independent and identically distributed zeros with a common probability distributionμon the unit disc, the empirical measures of their critical points have been shown to converge weakly toμin probability. Consequently, this work contributes the very first probabilistic result to T. W. Ng and C. Y. Tsang's polynomialfiniteBlaschkeproduct dictionary.
While the above works address probabilistic problems about zero distribution of polynomials and finite Blaschke products (regarded as noneuclidean polynomials by J. L. Walsh), the other part of this thesis is an application of the BKK theory in deterministic polynomial systems.
The numbers of various configurations for vortex dynamics in an ideal plane fluid without background flow had been investigated by many researchers for decades. In this thesis, fixed equilibria have been studied in the presence of a steady, incompressible and irrotational background flow. A more physically significant definition of a fixed equilibrium configuration has been suggested. Under this new definition, an attainable generic upper bound for their number has been found (in terms of the degree of the nonconstant polynomial that determines the background flow and of the sizes of vortex species).
Our result is established by transforming the rational function system arisen from fixed equilibria into a polynomial system, whose form is good enough to apply the aforesaid BKK theory (named after D. N. Bernshtein, A. G. Khovanskii and A. G. Kushnirenko) to show the finiteness of its number of solutions. Having this finiteness, the required bound follows from Bézout's theorem. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

5 
Iterated construction of irreducible polynomials over a finite field朱偉文, Chu, Waiman. January 1994 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

6 
Polynomial addition sets馬少麟, Ma, Siulun. January 1985 (has links)
published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

7 
Criteria for the irreducibility of a polynomial into linear factors with an application to Fermat's last theoremWebb, Donald Loomis, 1907 January 1933 (has links)
No description available.

8 
Nonclassical orthogonal polynomials with even weight functions on symmetric intervalsReese, Howard Watson 12 1900 (has links)
No description available.

9 
Recursively generated SturmLiouville polynomial systemsJayne, John William 12 1900 (has links)
No description available.

10 
General expressions for certain coefficients in the cyclotomic polynomial [psi][alpha](x)Johnston, Mary Andrea, January 1954 (has links)
ThesisCatholic University of America, 1954. / Includes bibliographical references.

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