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Showing 1 to 20 of 570 for “"polynomials"”.
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Waring's Problem for Linear Polynomials and Laurent Polynomials
… K. Hayman obtained lower bounds of p1 and p2 for polynomials, entire functions, rational functions and meromorphic functions. First, we consider Waring's problem for linear polynomials and get p 1 = k and p2 ≥ k + 1. Next, we study Waring's problem for Laurent polynomials and obtain lower …
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Nice Polynomials
… of finding, constructing, and classifying nice polynomials. After a short history of previous results, we present a general property of nice polynomials which leads to an important modification of the concept of equivalence classes of nice polynomials. We give several important results on nice …
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Knot polynomials
… of the Knot type, is the one called Knot polynomials. The Knot polynomials are somehow easy to calculate, or at least they are easier to handle than other invariants of the Knot type, such as the presentation of the group of the Knot, or the elementary ideals. The Knot polynomials have …
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Multivariate orthogonal polynomials
… of this thesis is to define special orthogonal polynomials and develop efficient methods for employing them which have the same advantages with respect to functions of the type (1.2) as do univariate orthogonal polynomials in the simple case k=1. These new polynomials may be usefully termed …
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Partially-Symmetric Macdonald Polynomials
Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald …
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Polynomials in algebraic combinatorics
… functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous functions, however, the introduction of K-theoretic combinatorics has led to increased interest in finding inhomogeneous deformations of classical bases. Joint with A. Yong and N. Tokcan, we …
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Classifying Polynomials With Reducible Nonreciprocal Parts and the Factorization of Values of Polynomials
… classification results for additional sparse polynomials.</p> <p>Let Sbe a finite set of rational primes. For a non-zero integer n, we define [n]<sub>S</sub> = &pi<sub>p in S</sub> |n|<sub>p</sub>-1, where |n|<sub>p</sub> is the usual p-adic norm of n. In 1984, Stewart applied Baker's theorem …
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Wavelet Factorization and Related Polynomials
… implementing the Euclidean algorithm for Laurent polynomials, which introduces multiple choices of factorizations of a polyphase matrix associated with a filter, and are the main focus of this work.
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Independence Polynomials of Molecular Graphs
… This thesis is an investigation of independence polynomials of several classes of graphs, some directly related to molecules of hydrocarbons. In particular, for the graphs of alkanes, alkenes, and cycloalkanes, we have determined the Merrifield-Simmons index, the independence polynomial, and, in …
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Some Metric Theorems on Polynomials
… in this thesis all concern questions on integer polynomials. Simultaneous rational approximation to integer polynomials is studied in the p-adic metric. Next, the nature of the closest root to an argument of a leading polynomial is studied in the Euclidian and p-adic metrics. Finally the nature …
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Periodic Bernoulli Numbers and Polynomials
Made available in DSpace on 2014-12-14T13:09:45Z (GMT). No. of bitstreams: 1 8009200.pdf: 1901905 bytes, checksum: fd94244d4e5dd00fb27c129d8a14e348 (MD5) Previous issue date: 1979
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Wreath Macdonald polynomials as eigenstates
We show that the wreath Macdonald polynomials for $\ZZ/\ell\ZZ\wr\Sigma_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\qqq,\ddd}(\ddot{\mathfrak{sl}}_\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of …
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Invariant polynomials and machine learning
… start by focusing on the algebras of invariant polynomials in these vectors and design systematic methods to obtain sets of generating variables. To do so, we build on two theorems of Weyl which tell us that the algebra of orthogonal group-invariant polynomials in $n$ $d$-dimensional vectors is …
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Graph polynomials and statistical physics
We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial and establish its correlations to the other graph polynomials. Finally, …
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Multiparameter BCn-Kostka-Foulkes Polynomials
The Kostka-Foulkes polynomials describe the change of basis between Schur polynomials and Hall-Littlewood polynomials. In this paper, we extend this idea to the family of BCn Macdonald spherical functions, with multiparameter Kostka-Foulkes polynomials acting as the change of basis from the BC_n …
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Time-series analysis using orthogonal polynomials
Advances in the study of non-linear dynamics have encouraged the construction of models and simulators of non-linear time-series. Researchers in the field of both science and statistics have come up with innovative methods that are useful in extracting information from systems that exhibit …
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Roots of polynomials and their connections
… in secondary mathematics remains the zeros of polynomials. This paper will present various ways to explore this topic while preserving the fundamental concept as a whole. In addition, this paper will reveal some distinct relationships between roots and their behavior within the different …
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Prime Rational Functions and Integral Polynomials
… derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) …
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On the coefficients of cyclotomic polynomials
Let $\Phi\sb{n}(z)$ denote the $n$th cyclotomic polynomial, given by$$\Phi\sb{n}(z) = {\prod\limits\sbsp{a=1\atop(a,n)=1}{n}}\ (z - \exp(2\pi ia/n)) = {\sum\limits\sbsp{m=0}{\phi(n)}} a(m,n)z\sp{m}.$$It is easily verified that for $n > 1$ $$\Phi\sb{n}(z)={\prod\limits\sb{d\vert …
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