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Polynomial continued fractions
 Acta Arithmetica
"... Abstract. Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher deg ..."
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Cited by 2 (0 self)
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Abstract. Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher
Polyhedral End Games for Polynomial Continuation
 Numerical Algorithms
, 1998
"... Bernshtein's theorem provides a generically exact upper bound on the number of isolated solutions a sparse polynomial system can have in (C ) n , with C = C n f0g. When a sparse polynomial system has fewer than this number of isolated solutions some face system must have solutions in ( ..."
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Cited by 22 (8 self)
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. Applications illustrate the practical usefulness of our approach. keywords : homotopy continuation, polynomial systems, Newton polytopes, Bernshtein bound, cycle number. AMS(MOS) Classification : 14Q99, 52A39, 52B20, 65H10. 1 Introduction All isolated complex solutions to polynomial systems can
The multiplicative structure on polynomial continuous valuations
 Geom. Funct. Anal
"... We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has especially nice properties (it is the structure of the Frobe ..."
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Cited by 15 (12 self)
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We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has especially nice properties (it is the structure
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
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Cited by 580 (6 self)
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We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di
REAL NUMBERS WITH POLYNOMIAL CONTINUED FRACTION EXPANSIONS
"... Abstract. In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, an extension of Euler’s formula equating infinite series and continued fractions, an extension of the corresponding transformation that equates infinite products and continued fractions, exte ..."
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, extensions and contractions of continued fractions and the BauerMuir transformation) to derive infinite families of inequivalent polynomial continued fractions in which each continued fraction has the same limit. This allows us, for example, to construct infinite families of polynomial continued fractions
Advances in Polynomial Continuation for Solving Problems in Kinematics
, 2004
"... For many mechanical systems, including nearly all robotic manipulators, the set of possible configurations that the links may assume can be described by a system of polynomial equations. Thus, solving such systems is central to many problems in analyzing the motion of a mechanism or in designing a m ..."
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Cited by 27 (9 self)
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mechanism to achieve a desired motion. This paper describes techniques, based on polynomial continuation, for numerically solving such systems. Whereas in the past, these techniques were focused on finding isolated roots, we now address the treatment of systems having higherdimensional solution sets
Designing Folding Rings using Polynomial Continuation
"... Two types of foldable rings are designed using polynomial continuation. The first type of ring, when deployed, forms regular polygons with an even number of sides and is designed by specifying a sequence of orientations which each bar must attain at various stages throughout deployment. A design cr ..."
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Two types of foldable rings are designed using polynomial continuation. The first type of ring, when deployed, forms regular polygons with an even number of sides and is designed by specifying a sequence of orientations which each bar must attain at various stages throughout deployment. A design
Comparison of parametric representations for monosyllabic word recognition in continuously spoken sentences
 ACOUSTICS, SPEECH AND SIGNAL PROCESSING, IEEE TRANSACTIONS ON
, 1980
"... Several parametric representations of the acoustic signal were compared as to word recognition performance in a syllableoriented continuous speech recognition system. The vocabulary included many phonetically similar monosyllabic words, therefore the emphasis was on ability to retain phonetically ..."
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Cited by 1089 (2 self)
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Several parametric representations of the acoustic signal were compared as to word recognition performance in a syllableoriented continuous speech recognition system. The vocabulary included many phonetically similar monosyllabic words, therefore the emphasis was on ability to retain
Freeform deformation of solid geometric models
 IN PROC. SIGGRAPH 86
, 1986
"... A technique is presented for deforming solid geometric models in a freeform manner. The technique can be used with any solid modeling system, such as CSG or Brep. It can deform surface primitives of any type or degree: planes, quadrics, parametric surface patches, or implicitly defined surfaces, f ..."
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Cited by 713 (1 self)
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, for example. The deformation can be applied either globally or locally. Local deformations can be imposed with any desired degree of derivative continuity. It is also possible to deform a solid model in such a way that its volume is preserved. The scheme is based on trivariate Bernstein polynomials
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken
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