Relevant bibliographies by topics / Sums of binomial squares

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Sums of binomial squares'

Author: Grafiati
Published: 6 September 2021
Last updated: 1 February 2022

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Journal articles on the topic "Sums of binomial squares"

1

Granville, Andrew, and Yiliang Zhu. "Representing Binomial Coefficients as Sums of Squares." American Mathematical Monthly 97, no. 6 (1990): 486. http://dx.doi.org/10.2307/2323831.

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Granville, Andrew, and Yiliang Zhu. "Representing Binomial Coefficients as Sums of Squares." American Mathematical Monthly 97, no. 6 (1990): 486–93. http://dx.doi.org/10.1080/00029890.1990.11995632.

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Mincu, Gabriel, and Laurenţiu Panaitopol. "Writing binomial coefficients as sums of three squares." Archiv der Mathematik 95, no. 5 (2010): 401–9. http://dx.doi.org/10.1007/s00013-010-0182-5.

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Kılıç, Emrah, and Helmut Prodinger. "Identities with squares of binomial coefficients: An elementary and explicit approach." Publications de l'Institut Math?matique (Belgrade) 99, no. 113 (2016): 243–48. http://dx.doi.org/10.2298/pim1613243k.

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In 2014, Slavik presented a recursive method to find closed forms for two kinds of sums involving squares of binomial coefficients. We give an elementary and explicit approach to compute these two kinds of sums. It is based on a triangle of numbers which is akin to the Stirling subset numbers.
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Sofo, Anthony. "Alternating cubic Euler sums with binomial squared terms." International Journal of Number Theory 14, no. 05 (2018): 1357–74. http://dx.doi.org/10.1142/s1793042118500859.

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Sofo, Anthony. "HARMONIC NUMBERS AT HALF INTEGER AND BINOMIAL SQUARED SUMS." Honam Mathematical Journal 38, no. 2 (2016): 279–94. http://dx.doi.org/10.5831/hmj.2016.38.2.279.

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Sofo, Anthony. "Identities for Alternating Inverse Squared Binomial and Harmonic Number Sums." Mediterranean Journal of Mathematics 13, no. 4 (2015): 1407–18. http://dx.doi.org/10.1007/s00009-015-0574-7.

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Belbachir, Hacène, and Abdelghani Mehdaoui. "Recurrence relation associated with the sums of square binomial coefficients." Quaestiones Mathematicae 44, no. 5 (2021): 615–24. http://dx.doi.org/10.2989/16073606.2020.1729269.

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Kilic, Emrah, and Ilker Akkus. "Partial sums of the Gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications." Miskolc Mathematical Notes 20, no. 1 (2019): 299. http://dx.doi.org/10.18514/mmn.2019.2456.

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Knopfmacher, Arnold, and Florian Luca. "Digit sums of binomial sums." Journal of Number Theory 132, no. 2 (2012): 324–31. http://dx.doi.org/10.1016/j.jnt.2011.07.004.

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Dissertations / Theses on the topic "Sums of binomial squares"

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Grimm, David [Verfasser]. "Sums of Squares in Algebraic Function Fields / David Grimm." Konstanz : Bibliothek der Universität Konstanz, 2011. http://d-nb.info/1024034984/34.

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Cunningham, Geoffrey William. "Sums of squares in function fields of elliptic curves." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/289166.

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In this dissertation we examine the problem of determining restricted representation numbers. Let k be the function field of a curve over a finite field and let w be a place of k of degree 1. Then r₂ᵢ(ξ,n) denotes the number of representations of ξ as a sum of 2Ι squares where the summands are integral away from w and have a pole of order at most n at w. This problem has been studied by Merrill and Walling in the case of the rational function field, Fq(T), by relating the restricted representation numbers to the Fourier coefficients of the 2Ι-th power of a theta function. In this dissertation
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Netzer, Tim. "Positive Polynomials, Sums of Squares and the Moment Problem." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-67376.

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Yiu, Paul Yu-Hung. "Topological and combinatoric methods for studying sums of squares." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/26037.

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We study sums of squares formulae from the perspective of normed bilinear maps and their Hopf constructions. We begin with the geometric properties of quadratic forms between euclidean spheres. Let F: Sm → Sn be a quadratic form. For every point q in the image, the inverse image F⁻¹ (q) is the intersection of Sm with a linear subspace wq, whose dimension can be determined easily. In fact, for every k ≤ m+1 with nonempty Yk = {q ∈ Sn: dim Wq = k}, the restriction F⁻¹ (Yk) → Yk is a great (k-1) - sphere bundle. The quadratic form F is the Hopf construction of a normed bilinear map if an
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Somayasa, Wayan. "Model-Checks Based on Least Squares Residual Partial Sums Processes." [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000006989.

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Magron, Victor. "Formal Proofs for Global Optimization -- Templates and Sums of Squares." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/91/77/79/PDF/thesis.pdf.

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Cette thèse a pour but de certifier des bornes inférieures de fonctions multivariées à valeurs réelles, définies par des expressions semi-algébriques ou transcendantes et de prouver leur validité en vérifiant les certificats dans l'assistant de preuves Coq. De nombreuses inégalités de cette nature apparaissent par exemple dans la preuve par Thomas Hales de la conjecture de Kepler. Dans le cadre de cette étude, on s'intéresse à des fonctions non-linéaires, faisant intervenir des opérations semi-algébriques ainsi que des fonctions transcendantes univariées (cos, arctan, exp, etc). L'utilisation
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Xie, Heng. "Grothendieck-Witt groups of quadrics and sums-of-squares formulas." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/76708/.

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This thesis studies Grothendieck-Witt spectra of quadric hypersurfaces. In particular, we compute Witt groups of quadrics. Besides, by calculating Grothendieck-Witt groups of a deleted quadric over an algebraically closed field of characteristic different from 2, we improve Dugger and Isaksen’s condition (some powers of 2 dividing some binomial coefficients) on an old problem Hurwitz concerning the existence of sums-of-squares formulas.
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Gunawan, Albert. "Gauss's theorem on sums of 3 squares sheaves, and Gauss composition." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0020/document.

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Le théorème de Gauss sur les sommes de 3 carrés relie le nombre de points entiers primitifs sur la sphère de rayon la racine carrée de n au nombre de classes d'un ordre quadratique imaginaire. En 2011, Edixhoven a esquissée une preuve du théorème de Gauss en utilisant une approche de la géométrie arithmétique. Il a utilisé l'action du groupe orthogonal spécial sur la sphère et a donné une bijection entre l'ensemble des SO3(Z)-orbites de tels points, si non vide, avec l'ensemble des classes d'isomorphisme de torseurs sous le stabilisateur. Ce dernier ensemble est un groupe, isomorphe au groupe
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Chinni, Gregorio <1980&gt. "Analytic and gevrey (micro-)hypoellipticity for sums of squares: an FBI approach." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/947/.

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Burgdorf, Sabine. "Trace-positive polynomials, sums of hermitian squares and the tracial moment problem." Rennes 1, 2011. http://www.theses.fr/2011REN1S009.

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A polynomial in non-commuting variables is trace-positive if all its evaluations by symmetric matrices have positive trace. The investigation of trace-positive polynomials is related to two famous conjectures: The BMV conjecture and Connes’ embedding conjecture. Results on the question of when a trace-positive polynomial can be written as a sum of hermitian squares and commutators are presented. Further, a partial answer to the BMV conjecture is given. The second part deals with the tracial moment problem: How can one describe sequences of real numbers that are given by tracial moments of a pr
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Books on the topic "Sums of binomial squares"

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S, Wagstaff Samuel, ed. Sums of squares of integers. Chapman & Hall/CRC, 2005.

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Moreno, Carlos J. Sums of squares of integers. Chapman & Hall/CRC, 2006.

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From polynomials to sums of squares. Institute of Physics Pub., 1995.

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Positive polynomials and sums of squares. American Mathematical Society, 2008.

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Representations of integers as sums of squares. Springer-Verlag, 1985.

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Grosswald, Emil. Representations of Integers as Sums of Squares. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4613-8566-0.

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Milne, Stephen C. Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-5462-9.

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. American Mathematical Society, 2014.

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Moreno, Carlos J., and Samuel S. Wagstaff Jr. Sums of Squares of Integers. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.1201/9781420057232.

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Jackson, T. H. From Polynomials to Sums of Squares. CRC Press, 2020.

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Book chapters on the topic "Sums of binomial squares"

1

Walrand, Jean. "Multiplexing: B." In Probability in Electrical Engineering and Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49995-2_4.

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AbstractChapter 10.1007/978-3-030-49995-2_3 used the Central Limit Theorem to determine the number of users that can safely share a common cable or link. We saw that this result is also fundamental to calculate confidence intervals. In this section, we prove this theorem. A key tool is the characteristic function that provides a simple way to study sums of independent random variables.Section 4.1 introduces the characteristic function and calculates it for a Gaussian random variable. Section 4.2 uses that function to prove the Central Limit Theorem. Section 4.3 uses the characteristic function to calculate the moments of a Gaussian random variable. The sum of squares of Gaussian random variables is a common model of noise in communication links. Section 4.4 proves a remarkable property of such a sum. Section 4.5 shows how to use characteristic functions to approximate binomial and geometric random variables. The error function arises in the calculation of the probability of errors in transmission systems and also in decisions based on random observations. Section 4.6 derives useful approximations of that function. Section 4.7 concludes the chapter with a discussion of an adaptive multiple access protocol similar to one used in WiFi networks.
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Moll, Victor. "Binomial sums." In The Student Mathematical Library. American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/065/05.

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Sofo, Anthony. "Binomial Type Sums." In Computational Techniques for the Summation of Series. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0057-5_4.

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Aka, Menny, Manfred Einsiedler, and Thomas Ward. "Sums of Squares." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55233-6_3.

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Jones, Gareth A., and J. Mary Jones. "Sums of Squares." In Springer Undergraduate Mathematics Series. Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-0613-5_10.

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Sofo, Anthony. "Sums of Binomial Variation." In Computational Techniques for the Summation of Series. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0057-5_8.

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Klotz, W. "On Certain Binomial Sums." In Topics in Combinatorics and Graph Theory. Physica-Verlag HD, 1990. http://dx.doi.org/10.1007/978-3-642-46908-4_49.

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Jakob, Rebecca Ulrike. "Sums of Two Squares of Sums of Two Squares." In From Arithmetic to Zeta-Functions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28203-9_14.

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Aka, Menny, Manfred Einsiedler, and Thomas Ward. "Sums of Two Squares." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55233-6_4.

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Bumby, Richard T. "Sums of Four Squares." In Number Theory: New York Seminar 1991–1995. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4612-2418-1_1.

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Conference papers on the topic "Sums of binomial squares"

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Ablinger, Jakob. "Binomial Sums in the package HarmonicSums." In Loops and Legs in Quantum Field Theory. Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.260.0067.

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Mikić, Jovan. "New class of binomial sums and their applications." In 3rd Croatian Combinatorial Days. Faculty of Civil Engineering, University of Zagreb, 2021. http://dx.doi.org/10.5592/co/ccd.2020.05.

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Simsek, Yilmaz. "Identities and relations containing finite sums of powers of binomial coefficients." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026604.

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Yilmaz, N., N. Taskara, K. Uslu, et al. "On the Binomial Sums of k-Fibonacci and k -Lucas sequences." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636734.

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Parrilo, Pablo A. "Sums of squares of polynomials and their applications." In the 2004 international symposium. ACM Press, 2004. http://dx.doi.org/10.1145/1005285.1005286.

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Raab, Clemens Gunter, Jakob Ablinger, Johannes Bluemlein, and Carsten Schneider. "Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams." In Loops and Legs in Quantum Field Theory. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.211.0020.

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Sadati, Nasser, and Mansoor Isvand Yousefi. "Rank Minimization Using Sums of Squares of Nonnegative Matrices." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377719.

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Majumdar, Anirudha, Amir Ali Ahmadi, and Russ Tedrake. "Control design along trajectories with sums of squares programming." In 2013 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2013. http://dx.doi.org/10.1109/icra.2013.6631149.

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Posa, Michael, Twan Koolen, and Russ Tedrake. "Balancing and Step Recovery Capturability via Sums-of-Squares Optimization." In Robotics: Science and Systems 2017. Robotics: Science and Systems Foundation, 2017. http://dx.doi.org/10.15607/rss.2017.xiii.032.

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Moore, Joseph, and Russ Tedrake. "Adaptive control design for underactuated systems using sums-of-squares optimization." In 2014 American Control Conference - ACC 2014. IEEE, 2014. http://dx.doi.org/10.1109/acc.2014.6859508.

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Reports on the topic "Sums of binomial squares"

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Pengelley, David. Sums of Powers in Discrete Mathematics: Archimedes Sums Squares in the Sand. The MAA Mathematical Sciences Digital Library, 2013. http://dx.doi.org/10.4169/loci003986.

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