Results 41 to 50 of about 185,457 (163)
SUMS OF SQUARES FROM ELLIPTIC PFAFFIANS [PDF]
International Journal of Number Theory, 2008 We give a new proof of Milne's formulas for the number of representations of an integer as a sum of 4m2and 4m(m + 1) squares. The proof is based on explicit evaluation of pfaffians with elliptic function entries, and relates Milne's formulas to Schur Q-polynomials and to correlation functions for continuous dual Hahn polynomials.
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Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
MathematicsWe study positive semi-definite (PSD) biquadratic forms and their sum-of-squares (SOS) representations. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definiteness and prove that
Liqun Qi, Chunfeng Cui, Yi Xu
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Optimization of Pearson Ⅲ Frequency Curve Based on R Software
Renmin Zhujiang, 2021 The Pearson Ⅲ frequency curve is a common frequency curve in hydrological analysis process. Based on the 47-year annual runoff data of a hydrological station, this paper defines the optimal fitting parameters and frequency distribution curve according to
HE Mei, ZHAO Huarong, YAO Yue, JIN Xin
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Cyclotomic equations and square properties in rings
International Journal of Mathematics and Mathematical Sciences, 1986 If R is a ring, the structure of the projective special linear group PSL2(R) is used to investigate the existence of sum of square properties holding in R.
Benjamin Fine
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NeuroImage, 2020 In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator.
Tom Dela Haije +2 more
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Application of Sum of Squares Method in Nonlinear H∞ Control for Satellite Attitude Maneuvers
Complexity, 2019 The Hamilton–Jacobi–Issacs (HJI) inequality is the most basic relation in nonlinear H∞ design, to which no effective analytical solution is currently available. The sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to
Fanwei Meng +3 more
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Pacific Journal of Mathematics, 1985 This paper asks some easily understood matrix questions and gives answers which are equally simple. Indeed, the proofs are also at a level which are within reach of any competent undergraduate. Yet this does not detract from the interest of the paper and also does not mean that some ingenuity was required in finding the proofs.
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Stability Analysis of Nonlinear Time–Delayed Systems with Application to Biological Models
International Journal of Applied Mathematics and Computer Science, 2017 In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used ...
Kruthika H.A. +2 more
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On the rational function field of real curves without real points
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2019 Let F be the field of rational functions of a real algebraic curve without real points. It is well-known that in F we can express -1 as a sum of two squares. We show that -1 is also a sum of four fourth powers, six sixth powers, and so on.
Manuel Ojanguren
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Sums of Squares on Hypersurfaces
Results in MathematicsWe show that the Pythagoras number of rings of type $\mathbb{R}[x,y, \sqrt{f(x,y)}]$ is infinite, provided that the polynomial $f(x,y)$ satisfies some mild conditions.
Kacper Błachut, Tomasz Kowalczyk
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