Results 21 to 30 of about 13,771 (148)
Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine functions and applications [PDF]
, 2021 Abstract In the paper, by means of the Faa di Bruno formula, with the help of explicit formulas for special values of the Bell polynomials of the second kind with respect to a specific sequence, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes Maclaurin's series expansions ...
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Maclaurin's series expansions of real powers of inverse (hyperbolic) cosine and sine functions with applications [PDF]
, 2021 Abstract In the paper, by means of the Faa di Bruno formula, with the help of explicit formulas for special values of the Bell polynomials of the second kind with respect to a specific sequence, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes Maclaurin's series expansions ...
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METHOD OF OBTAINING APPROXIMATE FORMULAS [PDF]
, 2018 The two-parameter method of approximating the sum of a power series in terms of its first three terms of the expansion, which allows one to obtain analytic approximations of various functions, decomposes into a Maclaurin series.
Ludanov, Konstantin +2 more
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Fractional Rectified Linear Unit Activation Function and Its Variants
Mathematical Problems in Engineering, 2022 This paper focuses on deriving and validating the fractional-order form of rectified linear unit activation function and its linear and nonlinear variants.
Megha S. Job +4 more
semanticscholar +1 more source
, 2021 Abstract In the paper, by means of the Faa di Bruno formula, with the help of explicit formulas for special values of partial Bell polynomials with respect to two specific sequences generated by derivatives at the origin of the inverse sine or inverse cosine, and by virtue of two combinatorial identities containing the Stirling numbers of the ...
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The Natural Components of a Regular Linear System
Oxford Bulletin of Economics and Statistics, EarlyView.ABSTRACT The analysis of a finite‐dimensional regular linear system may be simplified by separating the system into its natural components. The natural components are smaller linear systems on separate subspaces whose dimensions sum to the dimension of the original linear system.
Brendan K. Beare, Phil Howlett
wiley +1 more source
Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, Volume 98, Issue 7, Page 804-839, July 2026.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
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Negativity‐preserving transforms of tuples of symmetric matrices
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments relying on well‐chosen test matrices, Sidon ...
Alexander Belton +3 more
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Equivariant toric geometry and Euler–Maclaurin formulae
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 451-557, March 2026.Abstract We first investigate torus‐equivariant motivic characteristic classes of toric varieties, and then apply them via the equivariant Riemann–Roch formalism to prove very general Euler–Maclaurin‐type formulae for full‐dimensional simple lattice polytopes.
Sylvain E. Cappell +3 more
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