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Relevant bibliographies by topics / Exact polynomial

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Journal articles

Academic literature on the topic 'Exact polynomial'

Author: Grafiati

Published: 26 October 2022

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Journal articles on the topic "Exact polynomial"

1

Guilloux, Antonin, and Julien Marché. "Volume function and Mahler measure of exact polynomials." Compositio Mathematica 157, no. 4 (2021): 809–34. http://dx.doi.org/10.1112/s0010437x21007016.

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We study a class of two-variable polynomials called exact polynomials which contains $A$ -polynomials of knot complements. The Mahler measure of these polynomials can be computed in terms of a volume function defined on the vanishing set of the polynomial. We prove that the local extrema of the volume function are on the two-dimensional torus and give a closed formula for the Mahler measure in terms of these extremal values. This formula shows that the Mahler measure of an irreducible and exact polynomial divided by $\pi$ is greater than the amplitude of the volume function. We also prove a K-theoretic criterion for a polynomial to be a factor of an $A$ -polynomial and give a topological interpretation of its Mahler measure.

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2

Achter, Jeffrey, and Cassandra Williams. "Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields." Canadian Mathematical Bulletin 58, no. 4 (2015): 673–91. http://dx.doi.org/10.4153/cmb-2015-050-8.

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AbstractConsider a quartic q-Weil polynomial ƒ. Motivated by equidistribution considerations, we define, for each prime ℓ, a local factor that measures the relative frequency with which ƒ mod ℓ occurs as the characteristic polynomial of a symplectic similitude over 𝔽ℓ. For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over 𝔽q with Weil polynomial ƒ.

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3

Borwein, Peter B. "Exact Inequalities for the Norms of Factors of Polynomials." Canadian Journal of Mathematics 46, no. 4 (1994): 687–98. http://dx.doi.org/10.4153/cjm-1994-038-8.

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AbstractThis paper addresses a number of questions concerning the size of factors of polynomials. Let p be a monic algebraic polynomial of degree n and suppose q1q2 … qi is a monic factor of p of degree m. Then we can, in many cases, exactly determine Here ‖ . ‖ is the supremum norm either on [—1, 1] or on {|z| ≤ 1}. We do this by showing that, in the interval case, for each m and n, the n-th Chebyshev polynomial is extremal. This extends work of Gel'fond, Mahler, Granville, Boyd and others. A number of variants of this problem are also considered.

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4

RÜHL, WERNER, and ALEXANDER TURBINER. "EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS." Modern Physics Letters A 10, no. 29 (1995): 2213–21. http://dx.doi.org/10.1142/s0217732395002374.

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Translationally invariant symmetric polynomials as coordinates for N-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland N-body Hamiltonians, after appropriate gauge transformations, can be presented as a quadratic polynomial in the generators of the algebra sl N in finitedimensional degenerate representation. The exact solvability of these models follows from the existence of the infinite flag of such representation spaces, preserved by the above Hamiltonians. A connection with Jack polynomials is discussed.

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5

Chen, Yi-Chou. "Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results." Journal of Applied Mathematics 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/516159.

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LetFx, y=asxys+as-1xys-1+⋯+a0xbe a real-valued polynomial function in which the degreesofyinFx, yis greater than or equal to 1. For any polynomialyx, we assume thatT:Rx→Rxis a nonlinear operator withTyx=Fx, yx. In this paper, we will find an eigenfunctionyx∈Rxto satisfy the following equation:Fx, yx=ayxfor some eigenvaluea∈Rand we call the problemFx, yx=ayxa fixed point like problem. If the number of all eigenfunctions inFx, yx=ayxis infinitely many, we prove that (i) any coefficients ofFx, y, asx, as-1x,…, a0x, are all constants inRand (ii)yxis an eigenfunction inFx, yx=ayxif and only ifyx∈R.

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6

Paschos, Vangelis Th. "When polynomial approximation meets exact computation." Annals of Operations Research 271, no. 1 (2018): 87–103. http://dx.doi.org/10.1007/s10479-018-2986-9.

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7

Bhattacharyya, Rajsekhar, Robert de Mello Koch, and Michael Stephanou. "Exact multi-restricted Schur polynomial correlators." Journal of High Energy Physics 2008, no. 06 (2008): 101. http://dx.doi.org/10.1088/1126-6708/2008/06/101.

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8

Paschos, Vangelis Th. "When polynomial approximation meets exact computation." 4OR 13, no. 3 (2015): 227–45. http://dx.doi.org/10.1007/s10288-015-0294-7.

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9

Zerz, Eva, Viktor Levandovskyy, and Kristina Schindelar. "Exact linear modeling with polynomial coefficients." Multidimensional Systems and Signal Processing 22, no. 1-3 (2010): 55–65. http://dx.doi.org/10.1007/s11045-010-0125-0.

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10

Mueller, Matthias. "Polynomial Exact-3-SAT-Solving Algorithm." International Journal of Engineering & Technology 9, no. 3 (2020): 670. http://dx.doi.org/10.14419/ijet.v9i3.30749.

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This article describes an algorithm which is supposed by the author to be capable of solving any instance of a 3-SAT CNF in maximal O(n^15), whereby n is the variable index range within the 3-SAT CNF to solve. The presented algorithm imitates the proceeding of an exponential, fail-safe solver. This exponential solver stores internal data in m-SAT clauses, with 3 <= m <= n. The polynomial solver works similarly, but uses 3-SAT clauses only to save the same data. The paper explains how, and proves why this can be achieved. On the supposition the algorithm is correct, the P-NP-Problem would be solved with the result that the complexity classes NP and P are equal.

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