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Relevant bibliographies by topics / Sum of two squares

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Journal articles

Academic literature on the topic 'Sum of two squares'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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Journal articles on the topic "Sum of two squares"

1

Roy, S. C. Dutta. "Approximating the Square Root of the Sum of Two Squares." IETE Journal of Education 32, no. 2 (1991): 11–13. http://dx.doi.org/10.1080/09747338.1991.11436322.

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2

Gutierrez, Jaime, Álvar Ibeas, and Antoine Joux. "Recovering a sum of two squares decomposition." Journal of Symbolic Computation 64 (August 2014): 16–21. http://dx.doi.org/10.1016/j.jsc.2013.12.003.

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3

Hourong, Qin. "The sum of two squares in a quadratic field." Communications in Algebra 25, no. 1 (1997): 177–84. http://dx.doi.org/10.1080/00927879708825844.

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4

Dresden, Greg, Kylie Hess, Saimon Islam, et al. "When is an+ 1 the sum of two squares ?" Involve, a Journal of Mathematics 12, no. 4 (2019): 585–605. http://dx.doi.org/10.2140/involve.2019.12.585.

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5

Troupe, Lee. "Divisor sums representable as the sum of two squares." Proceedings of the American Mathematical Society 148, no. 10 (2020): 4189–202. http://dx.doi.org/10.1090/proc/15104.

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6

Crocker, Roger Clement. "On the sum of two squares and two powers of k." Colloquium Mathematicum 112, no. 2 (2008): 235–67. http://dx.doi.org/10.4064/cm112-2-3.

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7

van Ginkel, Joost R., and Pieter M. Kroonenberg. "Much ado about nothing: Multiple imputation to balance unbalanced designs for two-way analysis of variance." Methodology 16, no. 4 (2020): 335–53. http://dx.doi.org/10.5964/meth.4327.

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In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type III sum of squares in two-way ANOVA. In the current simulation study we studied four pooled statistics for multiple imputation, namely D₀, D₁, D₂, and D₃ in unbalanced data, and compared these statistics with Type III sum of squares. Statistics D₀ and D₂ generally performed best regarding Type-I error rates, and had power rates closest to that of Type III sum of squares. However, none of the statistics produced power rates higher than Type III sum of squares. The results l

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8

van Ginkel, Joost R., and Pieter M. Kroonenberg. "Multiple imputation to balance unbalanced designs for two-way analysis of variance." Methodology 17, no. 1 (2021): 39–57. http://dx.doi.org/10.5964/meth.6085.

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A balanced ANOVA design provides an unambiguous interpretation of the F-tests, and has more power than an unbalanced design. In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type-III sum of squares. In the current simulation study we studied four pooled statistics for multiple imputation, namely D₀, D₁, D₂, and D₃ in unbalanced data, and compared them with Type-III sum of squares. Statistics D₁ and D₂ generally performed best regarding Type-I error rates, and had power rates closest to that of Type-III sum of squares. Additio

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9

David J. Platt and Timothy S. Trudgian. "On the Sum of Two Squares and At Most Two Powers of 2." American Mathematical Monthly 124, no. 8 (2017): 737. http://dx.doi.org/10.4169/amer.math.monthly.124.8.737.

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10

Gandhi, K. Raja Rama. "Primes of the form x²+ ny²." Bulletin of Society for Mathematical Services and Standards 3 (September 2012): 67–72. http://dx.doi.org/10.18052/www.scipress.com/bsmass.3.67.

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We know that, Fermat Showed a prime can be expressed as a sum of two squares if and only if it is a multiple of four plus one and its decomposition is unique. This paper will discuss the similar writings of primes as a sum of squares and multiple of another square.

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