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Generalized Polynomials
, 2005
"... ABSTRACT: In this paper we introduce two generalized knot polynomials, the Kauffman and HOMFLY polynomials, show that they are distinct invariants and show that the Jones polynomial is a special case of each. We then use properties of the Kauffman polynomial to prove invariance of the writhe of diff ..."
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ABSTRACT: In this paper we introduce two generalized knot polynomials, the Kauffman and HOMFLY polynomials, show that they are distinct invariants and show that the Jones polynomial is a special case of each. We then use properties of the Kauffman polynomial to prove invariance of the writhe
ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
"... A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal w ..."
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Cited by 97 (3 self)
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A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal
On Generalized Polynomials I
"... Abstract:Voronowskajain 1932 proved his result forBernstein polynomial. We have extended the corresponding result of Voronowskaja for Lebesgueintegrable function in L1norm by our newly defined Generalized Polynomial. ..."
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Abstract:Voronowskajain 1932 proved his result forBernstein polynomial. We have extended the corresponding result of Voronowskaja for Lebesgueintegrable function in L1norm by our newly defined Generalized Polynomial.
Generalized polynomials and mild mixing
"... An unsettled conjecture of V. Bergelson and I. Håland proposes that if (X,A, µ,T) is an invertible weak mixing measure preserving system, where µ(X) <∞, and if p1, p2,..., pk are generalized polynomials (functions built out of regular polynomials via iterated use of the greatest integer or flo ..."
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An unsettled conjecture of V. Bergelson and I. Håland proposes that if (X,A, µ,T) is an invertible weak mixing measure preserving system, where µ(X) <∞, and if p1, p2,..., pk are generalized polynomials (functions built out of regular polynomials via iterated use of the greatest integer
Distribution of values of bounded generalized polynomials
"... A generalized polynomial is a realvalued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized polynomial mapping is a vectorvalued mapping whose coordinates are generalized polynomials. We show ..."
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Cited by 27 (9 self)
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A generalized polynomial is a realvalued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized polynomial mapping is a vectorvalued mapping whose coordinates are generalized polynomials. We show
Generalized Polynomial Bases and the Bezoutian
"... A foundation polynomial is used to induce polynomial bases for F n\Gamma1 [x], the vector space of polynomials of degree less than n over an arbitrary field F. The associated bases are then used to block diagonalize the Bezout matrix of two polynomials under congruence. ..."
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Cited by 1 (0 self)
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A foundation polynomial is used to induce polynomial bases for F n\Gamma1 [x], the vector space of polynomials of degree less than n over an arbitrary field F. The associated bases are then used to block diagonalize the Bezout matrix of two polynomials under congruence.
A General Polynomial Sieve
 Designs, Codes and Crpyotgraphy
, 1999
"... An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach and so ..."
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Cited by 1 (0 self)
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An important component of the index calculus methods for finding discrete logarithms is the acquisition of smooth polynomial relations. Gordon and McCurley (1992) developed a sieve to aid in finding smooth Coppersmith polynomials for use in the index calculus method. We discuss their approach
On The Degree of Approximation of Functions by the Generalized Polynomials
"... Abstract: Popoviciu ( 1935) proved his result for Bernstein Polynomials. We have tested the degree of approximation of function by a newly defined Generalized Polynomials, and so the corresponding results of Popoviciuhave been extended for Lebesgue integrable function in ..."
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Abstract: Popoviciu ( 1935) proved his result for Bernstein Polynomials. We have tested the degree of approximation of function by a newly defined Generalized Polynomials, and so the corresponding results of Popoviciuhave been extended for Lebesgue integrable function in
Sets of recurrence and generalized polynomials
 Convergence in Ergodic Theory and Probability, Walter de Gruyter
, 1996
"... A set S ⊂ Z is called a set of recurrence if for any invertible measure preserving system (X,B, µ, T) and any A ∈ B with µ(A)> 0 there exists n ∈ S, n 6 = 0, such that µ(A ∩ T−nA)> 0. For example, for any infinite E ⊂ N, the set of differences E − E = {x − y  x, y ∈ E, x> y} is a set of re ..."
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Cited by 3 (1 self)
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A set S ⊂ Z is called a set of recurrence if for any invertible measure preserving system (X,B, µ, T) and any A ∈ B with µ(A)> 0 there exists n ∈ S, n 6 = 0, such that µ(A ∩ T−nA)> 0. For example, for any infinite E ⊂ N, the set of differences E − E = {x − y  x, y ∈ E, x> y} is a set of recurrence. Another simple example
CANONICAL FORMS FOR GENERAL POLYNOMIALS
"... It has been known for a long time that every ternary cubic form over the field C of complex numbers, which defines a nonsingular curve in P2(C), can be reduced to the following canonical form, ..."
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Cited by 1 (0 self)
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It has been known for a long time that every ternary cubic form over the field C of complex numbers, which defines a nonsingular curve in P2(C), can be reduced to the following canonical form,
Results 1  10
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