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The Factorization of a Polynomial Defined by Partitions ∗
"... Itisbesttoworkwithunorderedpartitions.Thusif kisapositiveinteger,apartitionof length roftheinterval [0, k]isasequence, 0 = k0 < k1 < · · · < kr = k,ofpositiveintegers. Set k ′ 1 = k − ki. ..."
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Itisbesttoworkwithunorderedpartitions.Thusif kisapositiveinteger,apartitionof length roftheinterval [0, k]isasequence, 0 = k0 < k1 < · · · < kr = k,ofpositiveintegers. Set k ′ 1 = k − ki.
Polynomials associated with Partitions: Their Asymptotics and Zeros
, 711
"... Let pn be the number of partitions of an integer n. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting behavior of their zeros as sets and densities. 1 ..."
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Let pn be the number of partitions of an integer n. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting behavior of their zeros as sets and densities. 1
Partitions, Kostka polynomials and pairs of trees
"... Bennett et al. [2] presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions a ..."
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Bennett et al. [2] presented a recursive algorithm to create a family of partitions from one or several partitions. They were mainly interested in the cases when we begin with a single square partition or with several partitions with only one part. The cardinalities of those families of partitions
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 231 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.
1 SelfDual Symmetric Polynomials and Conformal Partitions
, 2008
"... A conformal partition function Pm n (s), which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with selfdual symmetric polynomials – reciprocal R {m} and skewreciprocal S{m} algebraic polynomials ..."
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A conformal partition function Pm n (s), which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with selfdual symmetric polynomials – reciprocal R {m} and skewreciprocal S{m} algebraic polynomials
POLYNOMIALS, MEANDERS, AND PATHS IN THE LATTICE OF NONCROSSING PARTITIONS
"... Abstract. For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n−1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n − 1 singular fibres. ..."
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Cited by 1 (0 self)
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Abstract. For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n−1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n − 1 singular fibres
The conditioning of linearizations of matrix polynomials
 Manchester Institute for Mathematical Sciences, The University of Manchester
, 2005
"... Abstract. The standard way of solving the polynomial eigenvalue problem of degree m in n×n matrices is to “linearize ” to a pencil in mn×mn matrices and solve the generalized eigenvalue problem. For a given polynomial, P, infinitely many linearizations exist and they can have widely varying eigenva ..."
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Cited by 54 (21 self)
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Abstract. The standard way of solving the polynomial eigenvalue problem of degree m in n×n matrices is to “linearize ” to a pencil in mn×mn matrices and solve the generalized eigenvalue problem. For a given polynomial, P, infinitely many linearizations exist and they can have widely varying
Efficient Array Partitioning
, 1997
"... We consider the problem of partitioning an array of n items into p intervals so that the maximum weight of the intervals is minimized. The currently best known bound for this problem is O(np) [MS95]. In this paper, we present two improved algorithms for this problem: one runs in time O(n + p²(log ..."
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Cited by 26 (3 self)
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We consider the problem of partitioning an array of n items into p intervals so that the maximum weight of the intervals is minimized. The currently best known bound for this problem is O(np) [MS95]. In this paper, we present two improved algorithms for this problem: one runs in time O(n + p
Results 1  10
of
51,782