Results 231 to 240 of about 135,613 (269)

Exponential Polynomials

The Annals of Mathematics, 1934
Verf. gibt eine eingehende Diskussion von vier besonderen Polynomklassen \(A,B,C,D\), die zueinander und zu den Klassen \(H\) und \(A_0\) der Hermiteschen bzw. Appellschen Polynome in folgender Beziehung stehen: \[ H\prec A\prec B\prec C;\quad A_0\prec B,\quad A_0\prec D. \] (\(H\prec A\) bedeutet, daß\ \(A\) eine Verallgemeinerung von \(H\) ist, usw.)
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Polynomials and Complex Polynomials

1997
If F is a field and n is a nonnegative integer, then a polynomial of degree n over F is a formal sum of the form $$P(x) = {a_0} + {a_1}x + \cdots + {a_n}{x^n}$$ With a i ∈ F for i = 0, .., n, a n ≠ 0 and x an indeterminate. A polynomial P(χ) over F is either a polynomial of some degree or the expression P(χ) = 0, which is called the zero ...
Benjamin Fine, Gerhard Rosenberger
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Polynomial Algebras

Journal of Mathematical Physics, 1970
The present work is concerned with what are called polynomial algebras as an extension of the work of Ramakrishnan and his colleagues on the algebras of matrices satisfying conditions like Lm = I and Lm = Lk. Assuming Lm to be an m-dimensional linear space, we generate a class of associative algebras called polynomial algebras by requiring that every ...
Raghavacharyulu, I. V. V., Menon, Nalini B.   +1 more
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On Polynomials in a Polynomial

Bulletin of the London Mathematical Society, 1972
Evyatar, A., Scott, D. B.
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Orthogonal Polynomials

1966
Publisher Summary This chapter focuses on simple sets of orthogonal polynomials. These sets of polynomials arise in various ways, one of which is as the solutions of a class of differential equations. It has been shown that, under certain conditions, given any interval and a positive weight function on that interval, there exists a corresponding set ...
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Polynomials and Trigonometric Polynomials

1976
Setting cos ϑ = x, the expressions $$ T_n \left( x \right) = \cos n\vartheta {\text{ }}U_n \left( x \right) = \frac{1} {{n + 1}}T'_{n + 1} \left( x \right) = \frac{{\sin \left( {n + 1} \right)\vartheta }} {{\sin \vartheta }}'{\text{ }}n = 0,1,2,...
George Pólya, Gabor Szegö
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Uncertain Polynomials. Interval Polynomials

1991
Let the set U be the closed set of values s which are not located in a desired stability region Г, e.g., U is the closed right-half plane. The polynomial a( s, Q) is denoted U-stable if and only if no root of a(s, Q) is located in the undesired region, ie., $$a(s,Q) = \{ a(s,q){\rm{ : q}} \in Q\} \ne 0{\rm{ }}\forall s \in U$$ (21.1)
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A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2021
Wen-Bo Xie, Hak-Keung Lam, Jian Zhang
exaly  

Optimal sparse polynomial chaos expansion for arbitrary probability distribution and its application on global sensitivity analysis

Computer Methods in Applied Mechanics and Engineering, 2022
Jie Liu
exaly  

Simple Local Polynomial Density Estimators

Journal of the American Statistical Association, 2020
Matias D Cattaneo, Michael Jansson
exaly