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THE TAYLOR SERIES OF THE GAUSSIAN KERNEL
, 2006
"... ”From some people one can learn more than mathematics” Abstract. We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of R n × R. 1. ..."
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”From some people one can learn more than mathematics” Abstract. We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of R n × R. 1.
Perturbation approaches and Taylor series
, 910
"... We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choo ..."
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We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we
Modern Taylor Series Method
, 1994
"... this paper we also define, as an important criterion, the tallying of the valid figures of a numerical computation with the analytical solution  for clarity in table Tab.2 only those digits of the numerical solution of (3) tallying with the analytical solution are shown. t(s) NUM4 NUM6 NUM8 MTSM 1. ..."
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". Similarly, the 6th order method ( ORD=6) and 1.2. POSITIVE PROPERTIES OF THE TAYLOR SERIES METHOD 7 8th order method ( ORD=8) were used for the computation of "NUM6" and "NUM8". Results in the column "MTSM" were obtained by the Modern Taylor Series Method
From Taylor Series to Taylor Models
 in AIP Conference Proceedings 405
, 1997
"... An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in ..."
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An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion
Calculus III: Taylor Series
, 2003
"... We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, ..."
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Cited by 23 (0 self)
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We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic Ktheory.
Digital Differentiators based on Taylor series
, 1999
"... It is proved that the tap coefficients of maximally linear digital differentiators are the same as those of the central difference formulas based on Taylor series. These differentiators are very easy to design and are highly accurate at low frequencies. A modification is proposed in the formula of t ..."
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Cited by 5 (3 self)
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It is proved that the tap coefficients of maximally linear digital differentiators are the same as those of the central difference formulas based on Taylor series. These differentiators are very easy to design and are highly accurate at low frequencies. A modification is proposed in the formula
Calculus III: Taylor Series
, 2003
"... We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, ..."
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We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, can be classified: they correspond to symmetric functors of n variables that are reduced and 1excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic Ktheory.
Calculus III: Taylor Series
, 2003
"... We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, ..."
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We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal nexcisive approximation, which may be thought of as its nexcisive part. Homogeneous functors, meaning nexcisive functors with trivial (n − 1)excisive part, can be classied: they correspond to symmetric functors of n variables that are reduced and 1excisive in each variable. We discuss some important examples, including the identity functor and Waldhausen’s algebraic Ktheory.
Binomial Matrices and Discrete Taylor Series
"... Every ss matrix A yields a composition map acting on polynomials on IR , mapping p(x) to p(Ax). For each n, the polynomials of degree n form an invariant subspace for this map. Its matrix representation on this subspace relative to the monomial basis gives a matrix that we denote by A and call ..."
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a binomial matrix. This paper deals with the asymptotic behavior of A as n ! 1. The special case of 2 2 matrices A with the property that A = I corresponds to discrete Taylor series and motivated our original interest in binomial matrices.
Results 1  10
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1,847