Results 41 to 50 of about 1,163,681 (226)
Proceedings of the American Mathematical Society, 1957 We make use of an elegant method of Professor H. Davenport [l] in the Geometry of Numbers. Without loss of generality we will prove Theorem 1 only when m is square free. (In the following m will be assumed to be square free.) In §1 we shall prove Theorem 1 when m = 3 (mod 8).
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Univariate rational sums of squares
Revista de la Unión Matemática Argentina, 2022 Dados los polinomios racionales univariados f y g tales que gcd(f, g) y f / gcd(f, g) son relativamente primos, mostramos que g es no negativo en todas las raíces reales de f si y solo si g es una suma de cuadrados de polinomios racionales módulo f. Completamos nuestro estudio exhibiendo un algoritmo que produce un certificado de que un polinomio g es ...
Teresa Krick +2 more
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Approximate Dynamic Programming via Sum of Squares Programming [PDF]
, 2012 We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables.
Kamgarpour, Maryam +5 more
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Sum of Squares Approach for Nonlinear H∞ Control
Complexity, 2018 A proper Hamilton-Jacobi-Isaacs (HJI) inequality must be solved in a nonlinear H∞ control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem.
Ai-ping Pang +5 more
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Mathematics, 2022 In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if and
Muhammad Faisal Iqbal, Faizan Ahmed
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Sums of Squares and Sums of Triangular Numbers [PDF]
gmj, 2006 Abstract Motivated by two results of Ramanujan, we give a family of 15 results and 4 related ones. Several have interesting interpretations in terms of the number of representations of an integer by a quadratic form , where λ1 + . . . + λ𝑚 = 2, 4 or 8.
Cooper, Shaun, Hirschhorn, Michael
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Certifiably Optimal and Robust Camera Pose Estimation From Points and Lines
IEEE Access, 2020 The Perspective-n-Point-and-Line (PnPL) problem, as a cornerstone in geometric computer vision, seeks to estimate the absolute pose of a calibrated camera from 3D-to-2D point and line correspondences.
Lei Sun, Zhongliang Deng
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DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization [PDF]
SIAM Journal on applied algebra and geometry, 2017 In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied ...
Amir Ali Ahmadi, Anirudha Majumdar
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Journal of Algebra, 1988 The level of a commutative ring R is the least integer n for which \(-1\) is a sum of n squares in R. In this paper the author defines the hermitian level of a ring with involution \(x\to \bar x\) in the same way except that he considers hermitian squares \(x\bar x\) instead of squares. Among others the following results are proved.
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On Sums of Consecutive Squares [PDF]
Journal of Number Theory, 1997 The authors consider the problem of deciding when a sum of consecutive squares is itself a square. More precisely, they aim at determining all pairs of integers \((n,t)\) for which the relation \[ k^2+(k+1)^2+ \cdots +\bigl(k+(n-1)\bigr)^2 =t^2 \tag{*} \] holds for a fixed parameter \(k\in\mathbb{Z}\).
Bremner, A. +2 more
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