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Journal articles on the topic 'Binary Quadratic'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Peters, Meinhard. "Indecomposable binary quadratic forms." Archiv der Mathematik 57, no. 5 (1991): 467–68. http://dx.doi.org/10.1007/bf01246744.

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2

Uludağ, A. Muhammed, Ayberk Zeytin, and Merve Durmuş. "Binary quadratic forms as dessins." Journal de Théorie des Nombres de Bordeaux 29, no. 2 (2017): 445–69. http://dx.doi.org/10.5802/jtnb.987.

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3

Abdesselam, Abdelmalek, and Jaydeep Chipalkatti. "Quadratic involutions on binary forms." Michigan Mathematical Journal 61, no. 2 (2012): 279–96. http://dx.doi.org/10.1307/mmj/1339011528.

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4

Coleman, Graham. "Review of binary quadratic forms." ACM SIGACT News 41, no. 4 (2010): 34–35. http://dx.doi.org/10.1145/1907450.1907518.

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5

Séguin, François. "Composition of Binary Quadratic Forms." Resonance 24, no. 6 (2019): 633–51. http://dx.doi.org/10.1007/s12045-019-0822-4.

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6

Ji, Yun-Seong, Myeong Jae Kim, and Byeong-Kweon Oh. "Diagonal quadratic forms representing all binary diagonal quadratic forms." Ramanujan Journal 45, no. 1 (2017): 21–32. http://dx.doi.org/10.1007/s11139-016-9857-2.

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7

P.S., Banu, and Suganthi T. "Five errors correcting (73, 61, 12) quadratic residue code over ternary field." Journal of Algebra and Applied Mathematics 21, no. 1 (2023): 17–34. https://doi.org/10.5281/zenodo.7960667.

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This paper investigates the error-correcting performance of (73,61,12) quadratic residue code over a ternary eld. A technique used to determine unknown syndromes of binary quadratic residue code is applied to the non-binary case to decode the ternary quadratic residue code of length 73. Furthermore, known and unknown syn- dromes are produced using the error-locator polynomial.

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8

Luo, Jian, Shu-Cherng Fang, Zhibin Deng, and Xiaoling Guo. "Soft Quadratic Surface Support Vector Machine for Binary Classification." Asia-Pacific Journal of Operational Research 33, no. 06 (2016): 1650046. http://dx.doi.org/10.1142/s0217595916500469.

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In this paper, a kernel-free soft quadratic surface support vector machine model is proposed for binary classification directly using a quadratic function for separation. Properties (including the solvability, uniqueness and support vector representation of the optimal solution) of the proposed model are derived. Results of computational experiments on some artificial and real-world classifying data sets indicate that the proposed soft quadratic surface support vector machine model may outperform Dagher’s quadratic model and other soft support vector machine models with a Quadratic or Gaussian

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9

Spearman, Blair K., and Kenneth S. Williams. "Representing Primes by Binary Quadratic Forms." American Mathematical Monthly 99, no. 5 (1992): 423. http://dx.doi.org/10.2307/2325086.

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10

Galovich, Steven, and Jeremy Resnick. "Representing Primes by Binary Quadratic Forms." Mathematics Magazine 64, no. 1 (1991): 34. http://dx.doi.org/10.2307/2690453.

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11

Verma, Amit, and Mark Lewis. "Goal seeking Quadratic Unconstrained Binary Optimization." Results in Control and Optimization 7 (June 2022): 100125. http://dx.doi.org/10.1016/j.rico.2022.100125.

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12

Sumathi, G. "Observation on the Binary Quadratic Equation." International Journal for Research in Applied Science and Engineering Technology 7, no. 3 (2019): 951–59. http://dx.doi.org/10.22214/ijraset.2019.3168.

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13

Natarajan, Karthik, Dongjian Shi, and Kim-Chuan Toh. "Bounds for Random Binary Quadratic Programs." SIAM Journal on Optimization 28, no. 1 (2018): 671–92. http://dx.doi.org/10.1137/16m109778x.

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14

Alsina, Montserrat. "Binary quadratic forms and Eichler orders." Journal de Théorie des Nombres de Bordeaux 17, no. 1 (2005): 13–23. http://dx.doi.org/10.5802/jtnb.473.

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15

Fishback, Paul E. "Quadratic dynamics in binary number systems." Journal of Difference Equations and Applications 11, no. 7 (2005): 597–603. http://dx.doi.org/10.1080/10236190412331334482.

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16

Li, Junxian. "A binary quadratic Titchmarsh divisor problem." Acta Arithmetica 192, no. 4 (2020): 341–61. http://dx.doi.org/10.4064/aa180802-19-2.

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17

Atkin, A. O. L., and D. J. Bernstein. "Prime sieves using binary quadratic forms." Mathematics of Computation 73, no. 246 (2003): 1023–31. http://dx.doi.org/10.1090/s0025-5718-03-01501-1.

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18

Calovich, Steven, and Jeremy Resnick. "Representing Primes by Binary Quadratic Forms." Mathematics Magazine 64, no. 1 (1991): 34–38. http://dx.doi.org/10.1080/0025570x.1991.11977571.

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19

Alaca, Ayşe, Şaban Alaca, and Kenneth S. Williams. "Arithmetic Progressions and Binary Quadratic Forms." American Mathematical Monthly 115, no. 3 (2008): 252–54. http://dx.doi.org/10.1080/00029890.2008.11920523.

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20

Oh, Byeong-Kweon, and Hoseog Yu. "Completely p-primitive binary quadratic forms." Journal of Number Theory 193 (December 2018): 373–85. http://dx.doi.org/10.1016/j.jnt.2018.05.015.

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21

Sun, Zhi-Hong. "Quartic residues and binary quadratic forms." Journal of Number Theory 113, no. 1 (2005): 10–52. http://dx.doi.org/10.1016/j.jnt.2004.11.003.

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22

Sun, Zhi-Hong. "Cubic residues and binary quadratic forms." Journal of Number Theory 124, no. 1 (2007): 62–104. http://dx.doi.org/10.1016/j.jnt.2006.08.001.

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23

Spearman, Blair K., and Kenneth S. Williams. "Representing Primes by Binary Quadratic Forms." American Mathematical Monthly 99, no. 5 (1992): 423–26. http://dx.doi.org/10.1080/00029890.1992.11995870.

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24

Liu, Yang, and Yi Ouyang. "On Binary Quadratic Forms Modulo n." Communications in Mathematics and Statistics 7, no. 1 (2018): 61–67. http://dx.doi.org/10.1007/s40304-018-0141-1.

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25

Liberti, Leo. "Compact linearization for binary quadratic problems." 4OR 5, no. 3 (2006): 231–45. http://dx.doi.org/10.1007/s10288-006-0015-3.

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26

Zemková, Kristýna. "Composition of binary quadratic forms over number fields." Mathematica Slovaca 71, no. 6 (2021): 1339–60. http://dx.doi.org/10.1515/ms-2021-0057.

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Abstract In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The article contains an explicit description of the correspondence. In the case of totally negative discriminants, equivalent conditions are given for a binary quadratic form to be totally positive definite.

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27

Vishmi, Fernando, and Mahasinghe Anuradha. "Reformulating Battleship Solitaire for Quantum Annealers." Journal of Innovation Sciences and Sustainable Technologies 2, no. 1 (2022): 17–24. https://doi.org/10.0608/JISST.2022160443.

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  We investigate the possibility of reformulating the puzzle of Battleship Solitaire as a quadratic unconstrained binary optimization problem, in order for the problem to be acceptable to a quantum annealer. Starting from a linear integer programming formulation, we develop two binary quadratic programs and compare them.

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28

Evans, Ronald J., and Kenneth S. Williams. "Quartic residuacity and the quadratic character of certain quadratic irrationalities." International Journal of Number Theory 11, no. 08 (2015): 2487–503. http://dx.doi.org/10.1142/s1793042115501158.

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We prove a general theorem that evaluates the Legendre symbol [Formula: see text] under certain conditions on the integers A, B, m and the prime p. The evaluation is in terms of parameters appearing in a binary quadratic form representing p. The theorem has applications to quartic residuacity.

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29

Shanthi, J., та M. A. Gopalan. "Formulation of Special Pythagorean Triangles through Integer Solutions of the Hyperbola 𝑦𝟐 = (𝑘𝟐 + 𝟐𝑘)𝑥𝟐 + 𝟏". Indian Journal Of Science And Technology 17, № 41 (2024): 4307–12. http://dx.doi.org/10.17485/ijst/v17i41.3132.

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Objectives: The objective of this research paper is to formulate Pythagorean triangles, each of which satisfies the relation: Hypotenuse = (𝑘 + 1) times the leg with even values added with unity, through employing the integer solutions to the Hyperbola 𝑦2 = (𝑘2 + 2𝑘)𝑥2 + 1. Methods: The sides of the Pythagorean triangle satisfying the requirement are obtained by suitably choosing its generators consisting of the integer solutions to the considered hyperbola. Findings : There are plenty of Pythagorean triangles satisfying the given characterization for each value of k > 0 in the binary quadr

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30

Bondarenko, Alexandr A. "The birational composition of arbitrary quadratic form with binary quadratic form." Journal of the Belarusian State University. Mathematics and Informatics, no. 1 (April 1, 2022): 14–20. http://dx.doi.org/10.33581/2520-6508-2022-1-14-20.

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Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n respectively over a field K, charK ≠ 2. Herein, the problem of the birational composition of f(X) and g(Y) is considered, namely, the condition is established when the product f(X)g(Y) is birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The main result of this paper is the complete solution of the problem of the birational composition for quadratic forms f(X) and g(Y) over a field K when m = 2. The sufficient and necessary conditions for the existence of birational composition h(Z) for qu

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31

J, Shanthi, та A. Gopalan M. "Formulation of Special Pythagorean Triangles through Integer Solutions of the Hyperbola 𝑦𝟐 = (𝑘𝟐 + 𝟐𝑘)𝑥𝟐 + 𝟏". Indian Journal of Science and Technology 17, № 41 (2024): 4307–12. https://doi.org/10.17485/IJST/v17i41.3132.

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Abstract <strong>Objectives:</strong> The objective of this research paper is to formulate Pythagorean triangles, each of which satisfies the relation: Hypotenuse = (𝑘 + 1) times the leg with even values added with unity, through employing the integer solutions to the Hyperbola 𝑦2 = (𝑘2 + 2𝑘)𝑥2 + 1. <strong>Methods:</strong> The sides of the Pythagorean triangle satisfying the requirement are obtained by suitably choosing its generators consisting of the integer solutions to the considered hyperbola. <strong>Findings :</strong> There are plenty of Pythagorean triangles

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32

Patane, Frank. "A proof of Hecke’s formula for binary quadratic forms." International Journal of Number Theory 16, no. 02 (2019): 233–40. http://dx.doi.org/10.1142/s179304212050013x.

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In Mathematische Werke, Hecke defines the operator [Formula: see text] and describes their utility in conjunction with theta series of quadratic forms. In particular, he shows that the image of theta series associated to classes of binary quadratic forms in CL[Formula: see text] is again a theta series associated to a collection of forms in CL[Formula: see text]. We state and prove an explicit formula for the action of [Formula: see text] on a binary quadratic form of negative discriminant.

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33

Hong, Seo Woo, Pierre Miasnikof, Roy Kwon, and Yuri Lawryshyn. "Market Graph Clustering via QUBO and Digital Annealing." Journal of Risk and Financial Management 14, no. 1 (2021): 34. http://dx.doi.org/10.3390/jrfm14010034.

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We present a novel technique for cardinality-constrained index-tracking, a common task in the financial industry. Our approach is based on market graph models. We model our reference indices as market graphs and express the index-tracking problem as a quadratic K-medoids clustering problem. We take advantage of a purpose-built hardware architecture to circumvent the NP-hard nature of the problem and solve our formulation efficiently. The main contributions of this article are bridging three separate areas of the literature, market graph models, K-medoid clustering and quadratic binary optimiza

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34

Halter-Koch, Franz. "On a class of insoluble binary quadratic diophantine equations." Nagoya Mathematical Journal 123 (September 1991): 141–51. http://dx.doi.org/10.1017/s002776300000369x.

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The binary quadratic diophantine equationis of interest in the class number problem for real quadratic number fields and was studied in recent years by several authors (see [4], [5], [2] and the literature cited there).

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35

Brüdern, Jörg, and Rainer Dietmann. "On the gaps between values of binary quadratic forms." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (2010): 25–32. http://dx.doi.org/10.1017/s0013091509000285.

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AbstractAmong the values of a binary quadratic form, there are many twins of fixed distance. This is shown in quantitative form. For quadratic forms of discriminant −4 or 8 a corresponding result is obtained for triplets.

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36

Karandashev, I., and B. Kryzhanovsky. "Matrix transformation method in quadratic binary optimization." Optical Memory and Neural Networks 24, no. 2 (2015): 67–81. http://dx.doi.org/10.3103/s1060992x1502006x.

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37

Ceselli, Alberto, Lucas Létocart, and Emiliano Traversi. "Dantzig–Wolfe reformulations for binary quadratic problems." Mathematical Programming Computation 14, no. 1 (2022): 85–120. http://dx.doi.org/10.1007/s12532-021-00206-w.

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38

Liu, Zhi, Zhensheng Yu, and Yunlong Wang. "A Continuous Approach to Binary Quadratic Problems." Journal of Applied Mathematics and Physics 06, no. 08 (2018): 1720–32. http://dx.doi.org/10.4236/jamp.2018.68147.

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39

ZEYTIN, AYBERK. "On the reduction of binary quadratic forms." Publicationes Mathematicae Debrecen 89, no. 1-2 (2016): 203–21. http://dx.doi.org/10.5486/pmd.2016.7470.

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40

Rizomiliotis, P., N. Kolokotronis, and N. Kalouptsidis. "On the Quadratic Span of Binary Sequences." IEEE Transactions on Information Theory 51, no. 5 (2005): 1840–48. http://dx.doi.org/10.1109/tit.2005.846428.

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41

Hanson, Brandon, and Robert Vaughan. "Density of positive diagonal binary quadratic forms." Acta Arithmetica 193, no. 1 (2020): 1–48. http://dx.doi.org/10.4064/aa180519-8-4.

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42

Saouter, Y. "Fast decoding of binary quadratic residue codes." Electronics Letters 55, no. 24 (2019): 1292–94. http://dx.doi.org/10.1049/el.2019.2143.

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43

Lewis, Mark, John Metcalfe, and Gary Kochenberger. "Robust optimisation of unconstrained binary quadratic problems." International Journal of Operational Research 36, no. 4 (2019): 441. http://dx.doi.org/10.1504/ijor.2019.10025701.

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44

Lewis, Mark, John Metcalfe, and Gary Kochenberger. "Robust optimisation of unconstrained binary quadratic problems." International Journal of Operational Research 36, no. 4 (2019): 441. http://dx.doi.org/10.1504/ijor.2019.104050.

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45

Berend, Daniel, and William Moran. "The inhomogeneous minimum of binary quadratic forms." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (1992): 7–19. http://dx.doi.org/10.1017/s0305004100070717.

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AbstractAn indefinite binary quadratic form ƒ gives rise to a certain function M on the torus. The properties of M, especially those related to its maximum – the so-called inhomogeneous minimum of ƒ – are the subject of numerous papers. Here we continue this study, putting more emphasis on the general behaviour of M.

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46

Eum, Ick Sun, Ja Kyung Koo, and Dong Hwa Shin. "Binary quadratic forms and ray class groups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (2019): 695–720. http://dx.doi.org/10.1017/prm.2018.163.

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AbstractLet K be an imaginary quadratic field different from $\open{Q}(\sqrt {-1})$ and $\open{Q}(\sqrt {-3})$. For a positive integer N, let KN be the ray class field of K modulo $N {\cal O}_K$. By using the congruence subgroup ± Γ1(N) of SL2(ℤ), we construct an extended form class group whose operation is basically the Dirichlet composition, and explicitly show that this group is isomorphic to the Galois group Gal(KN/K). We also present an algorithm to find all distinct form classes and show how to multiply two form classes. As an application, we describe Gal(KNab/K) in terms of these extend

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47

Boettcher, S. "Extremal Optimization for Quadratic Unconstrained Binary Problems." Physics Procedia 68 (2015): 16–19. http://dx.doi.org/10.1016/j.phpro.2015.07.102.

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48

DUNAJSKI, MACIEJ, and ROGER PENROSE. "On the quadratic invariant of binary sextics." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 3 (2016): 435–45. http://dx.doi.org/10.1017/s0305004116000542.

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49

Chang, Mei-Chu. "On character sums of binary quadratic forms." Journal of Number Theory 129, no. 9 (2009): 2064–71. http://dx.doi.org/10.1016/j.jnt.2009.02.017.

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50

Anthony, Martin, Endre Boros, Yves Crama, and Aritanan Gruber. "Quadratic reformulations of nonlinear binary optimization problems." Mathematical Programming 162, no. 1-2 (2016): 115–44. http://dx.doi.org/10.1007/s10107-016-1032-4.

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