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On separable polynomials and Frobenius polynomials in skew polynomial rings
On separable polynomials and Frobenius polynomials in skew polynomial ringsopenaire
SSRN Electronic Journal, 2022 We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization.
ALEXANDER S. LOLLIKE, MOGENS STEFFENSEN
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A Polynomial Shared by Certain Differential Polynomials
Bulletin of the Iranian Mathematical Society, 2023Let \(f\) and \(g\) be two nonconstant meromorphic functions in the complex plane \(\mathbb{C}\). If \(a\in\mathbb{C}\cup\infty\), then we denote by \(\overline{E}(a;f)\) the set of zeros of \(f-a\), and by \(E(a;f)\) we denote the set of pairs \(z,\nu\) such that \(z\) is a zero of \(f-a\) with multiplicity \(\nu\) (here the poles of \(f\) are ...
Indrajit Lahiri, Kalyan Sinha
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H-POLYNOMIALS AND ROOK POLYNOMIALS
International Journal of Algebra and Computation, 2008The purpose of this paper is twofold. First we describe a useful procedure for computing the H-polynomials of reductive monoids. Second we use this procedure to compute the H-polynomial of the monoid of n × n matrices in terms of the q-analogues of the rook polynomials of Garsia and Remmel.
Can, Mahir Bilen, Renner, Lex E.
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On Multiplication of Polynomials Modulo a Polynomial
SIAM Journal on Computing, 1980The multiplicative complexity of the direct product of algebras $A_p $ of polynomials modulo a polynomial P is studied. In particular, we show that if P and Q are irreducible polynomials then the multiplicative complexity of $A_{\text{P}} \times A_{\text{Q}} $ is $2\deg ({\text{P}})\deg ({\text{Q}}) - {\text{k}}$, where k is the number of factors of P ...
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Polynomials and Complex Polynomials
1997If 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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Polynomials and Trigonometric Polynomials
1976Setting 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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On Polynomials in a Polynomial
Bulletin of the London Mathematical Society, 1972Evyatar, A., Scott, D. B.
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