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1

Uygun, Hilmiye Deniz Ertugrul, Nihat Tinkilic, Azade Attar, and Ibrahim Isildak. "Development of Potentiometric Lactate Biosensor Based on Composite pH Sensor." Journal of New Materials for Electrochemical Systems 19, no. 3 (2016): 151–56. http://dx.doi.org/10.14447/jnmes.v19i3.313.

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In this study, a micro-sized lactate sensitive biosensor based on polyvinylchloride, quinhydrone and graphite composite pH sensing platform was developed. Lactate oxidase was immobilized on the composite layer as the biorecognition element. Transformation reaction of lactate to pyruvate and hydrogen peroxide was the basis of this biosensor system. In the reaction, hydrogen peroxide undergoes to give hydronium ions into solution, and the pH sensitive membrane detects the adjunct hydronium ions potentiometrically. The surface of lactate biosensor based composite pH sensing matrice was first exam
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2

admin, admin, and Mohammad Abobala. "On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm." International Journal of Advances in Applied Computational Intelligence 6, no. 2 (2024): 37–45. http://dx.doi.org/10.54216/ijaaci.060204.

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This paper is concerned with studying the matrix computations of 3-cyclic refined neutrosophic matrices and 4-cyclic refined neutrosophic matrices with 3cyclic4-cyclic real entries, where we introduce a novel method to compute eigenvalues and vectors of these matrix classes. Also, we provide a novel algorithm for diagonalization these matrices and to determine whether an n-cyclic refined matrix is diagonalizable or not for n=3, 4.
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3

Tarasov, Vitaly. "Cyclic monodromy matrices forsl(n) trigonometricR-matrices." Communications in Mathematical Physics 158, no. 3 (1993): 459–83. http://dx.doi.org/10.1007/bf02096799.

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4

Shinjo, Masato, Tan Wang, Masashi Iwasaki, and Yoshimasa Nakamura. "Roots of Characteristic Polynomial Sequences in Iterative Block Cyclic Reductions." Mathematics 9, no. 24 (2021): 3213. http://dx.doi.org/10.3390/math9243213.

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The block cyclic reduction method is a finite-step direct method used for solving linear systems with block tridiagonal coefficient matrices. It iteratively uses transformations to reduce the number of non-zero blocks in coefficient matrices. With repeated block cyclic reductions, non-zero off-diagonal blocks in coefficient matrices incrementally leave the diagonal blocks and eventually vanish after a finite number of block cyclic reductions. In this paper, we focus on the roots of characteristic polynomials of coefficient matrices that are repeatedly transformed by block cyclic reductions. We
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5

Zheng, Yanpeng, and Xiaoyu Jiang. "Quasi-cyclic displacement and inversion decomposition of a quasi-Toeplitz matrix." AIMS Mathematics 7, no. 7 (2022): 11647–62. http://dx.doi.org/10.3934/math.2022649.

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<abstract><p>We study a class of column upper-minus-lower (CUML) Toeplitz matrices, which are "close" to the Toeplitz matrices in the sense that their ($ 1, -1 $)-cyclic displacements coincide with $ \varphi $-cyclic displacement of some Toeplitz matrices. Among others, we derive the inverse formula for CUML Toeplitz matrices in the form of sums of products of factor circulants by constructing the corresponding displacement of the matrices. In addition, by the relationship between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula for CUML Hankel matrices is also
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6

Nadweh, Rama Asad, Rozina Ali, and Maretta Sarkis. "On The Algebraic Properties of 2-Cyclic Refined Neutrosophic Matrices and The Diagonalization Problem." Neutrosophic Sets and Systems 54 (April 11, 2023): 77–88. https://doi.org/10.5281/zenodo.7817646.

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The n-cyclic refined neutrosophic algebraic structures are very diverse and rich materials. In this paper, we study the elementary algebraic properties of 2-cyclic refined neutrosophic square matrices, where we find formulas for computing determinants, eigen values, and inverses. On the other hand, we solve the diagonalization problem of these matrices, where a complete algorithm to diagonlaize every diagonalizable 2-cyclic refined neutrosophic square matrix is obtained and illustrated by many related examples.
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Sergeev, A. "Interrelation of Symmetry and Antisymmetry of Quasi-Orthogonal Cyclic Matrices with Prime Numbers." Proceedings of Telecommunication Universities 8, no. 4 (2023): 14–19. http://dx.doi.org/10.31854/1813-324x-2022-8-4-14-19.

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Quasi-orthogonal Hadamard matrices and Mersenne matrices with two and three values of the elements, used in digital data processing, are considered, as well as the basis of error-correcting codes and algorithms for transforming orthogonal images. Attention is paid to the structures of cyclic matrices with symmetries and antisymmetries. The connection between symmetry and antisymmetry of structures of cyclic Hadamard and Mersenne matrices on a orders equal to prime numbers, products of close primes, composite numbers, powers of a prime number is shown. Separately, orders equal to the degrees of
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8

Neumann, Peter M., and Cheryl E. Praeger. "Cyclic Matrices Over Finite Fields." Journal of the London Mathematical Society 52, no. 2 (1995): 263–84. http://dx.doi.org/10.1112/jlms/52.2.263.

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9

Dazheng, Lin. "Fibonacci-Lucas Quasi-Cyclic Matrices." Fibonacci Quarterly 40, no. 3 (2002): 280–86. http://dx.doi.org/10.1080/00150517.2002.12428658.

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Tam, Bit-Shun. "On matrices with cyclic structure." Linear Algebra and its Applications 302-303 (December 1999): 377–410. http://dx.doi.org/10.1016/s0024-3795(99)00097-x.

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11

Riaza, Ricardo. "Cyclic matrices of weighted digraphs." Discrete Applied Mathematics 160, no. 3 (2012): 280–90. http://dx.doi.org/10.1016/j.dam.2011.09.005.

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12

Grigoriev, E. "Spectral Characteristics Analysis of Images Matrix Masking Results." Proceedings of Telecommunication Universities 10, no. 2 (2024): 76–82. http://dx.doi.org/10.31854/1813-324x-2024-10-2-76-82.

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The article describes the results of a computational experiment to assess the capabilities of extracting useful information if an image masked by quasi-orthogonal matrices sent over an open channel became available to a third party. Hadamard and Mersenne matrices of symmetric and cyclic structure are considered. The results confirm the data that images masked by small-sized matrix leaves edges of the original image on the masked image. However, with an increase in the size of the masking matrix, all considered in the article matrices reliably hides the original image during visual analysis. Ma
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13

Malath., F. Aswad. "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices." Neutrosophic Knowledge 3, no. 2 (2021): 6–13. https://doi.org/10.5281/zenodo.5507528.

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This paper is dedicated to study for the first time the concept of n-cyclic refined neutrosophic vector space as a direct application of n-cyclic refined neutrosophic sets. Also, It presents some elementary properties of these spaces such as homomorphisms and subspaces. On the other hand, this work defines n-cyclic refined neutrosophic real matrices, and illustrates some examples to clarify these structures.
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14

Corr, Brian P., and Cheryl E. Praeger. "Primary cyclic matrices in irreducible matrix subalgebras." Journal of Group Theory 21, no. 4 (2018): 667–94. http://dx.doi.org/10.1515/jgth-2018-0012.

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AbstractPrimary cyclic matrices were used (but not named) by Holt and Rees in their version of Parker’s MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices X with at least one cyclic component in the primary decomposition of the underlying vector space as an X-module. Let {\operatorname{M}(c,q^{b})} be an irreducible subalgebra of {\operatorname{M}(n,q)}, where {n=bc>c}. We prove a generalisation of the Kung–Stong cycle index theorem, and use it to obtain a lower bound for the proportion of primary cyclic matrices in {\operatorname{M}(c,q^{b})}.
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15

MONTGOMERY, AARON M. "Asymptotic Enumeration of Difference Matrices over Cyclic Groups." Combinatorics, Probability and Computing 27, no. 1 (2017): 84–109. http://dx.doi.org/10.1017/s0963548317000281.

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We identify a relationship between a certain family of random walks on Euclidean lattices and difference matrices over cyclic groups. We then use the techniques of Fourier analysis to estimate the return probabilities of these random walks, which in turn yields the asymptotic number of difference matrices over cyclic groups as the number of columns increases.
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16

Deveci, Omur, Yesim Akuzum, Erdal Karaduman, and Ozgur Erdag. "The Cyclic Groups via Bezout Matrices." Journal of Mathematics Research 7, no. 2 (2015): 34. http://dx.doi.org/10.5539/jmr.v7n2p34.

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<p>In this paper, we define the Bezout matrices by the aid of the characteristic polynomials of the <em>k</em>-step Fibonacci, the generalized order-<em>k</em> Pell and the generalized order-<em>k</em> Jacobsthal sequences then we consider the multiplicative orders of the Bezout matrices when read modulo <em>m</em>. Consequently, we obtain the rules for the order of the cyclic groups by reducing the Bezout matrices modulo <em>m</em>.</p>
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17

Mahmoodi Rishakani, Akbar, Seyed Mojtaba Dehnavi, Mohmmadreza Mirzaee Shamsabad, and Nasour Bagheri. "Cryptographic properties of cyclic binary matrices." Advances in Mathematics of Communications 15, no. 2 (2021): 311–27. http://dx.doi.org/10.3934/amc.2020068.

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18

Łosiak, Janina, E. Neuman, and Jolanta Nowak. "The inversion of cyclic tridiagonal matrices." Applicationes Mathematicae 20, no. 1 (1988): 93–102. http://dx.doi.org/10.4064/am-20-1-93-102.

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19

Dubeau, F., and J. Savoie. "A remark on cyclic tridiagonal matrices." Applicationes Mathematicae 21, no. 2 (1991): 253–56. http://dx.doi.org/10.4064/am-21-2-253-256.

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20

Li, Zhongshan, Carolyn A. Eschenbach, and Frank J. Hall. "The structure of nonnegative cyclic matrices." Linear and Multilinear Algebra 41, no. 1 (1996): 23–33. http://dx.doi.org/10.1080/03081089608818458.

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21

Evans, D. J., and C. Li. "Sor method andp-cyclic matrices (I)." International Journal of Computer Mathematics 36, no. 1-2 (1990): 57–76. http://dx.doi.org/10.1080/00207169008803911.

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22

Evans, D. J., and Changjun Li. "Sor method andP-cyclic matrices (II)." International Journal of Computer Mathematics 37, no. 3-4 (1990): 239–50. http://dx.doi.org/10.1080/00207169008803952.

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23

McDonald, Judith J., and Pietro Paparella. "Jordan chains of h-cyclic matrices." Linear Algebra and its Applications 498 (June 2016): 145–59. http://dx.doi.org/10.1016/j.laa.2015.02.029.

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24

Karawia, A. A. "Inversion of General Cyclic Heptadiagonal Matrices." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/321032.

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25

Sturmfels, Bernd. "Totally positive matrices and cyclic polytopes." Linear Algebra and its Applications 107 (August 1988): 275–81. http://dx.doi.org/10.1016/0024-3795(88)90250-9.

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26

Audit, Philippe. "Functions of infinite generalized cyclic matrices." Journal of Mathematical Physics 26, no. 3 (1985): 361–64. http://dx.doi.org/10.1063/1.526668.

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27

Baldi, Marco, Giovanni Cancellieri, and Franco Chiaraluce. "Iterative Soft-Decision Decoding of Binary Cyclic Codes." Journal of Communications Software and Systems 4, no. 2 (2008): 142. http://dx.doi.org/10.24138/jcomss.v4i2.227.

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Binary cyclic codes achieve good error correction performance and allow the implementation of very simpleencoder and decoder circuits. Among them, BCH codesrepresent a very important class of t-error correcting codes, with known structural properties and error correction capability. Decoding of binary cyclic codes is often accomplished through hard-decision decoders, although it is recognized that softdecision decoding algorithms can produce significant coding gain with respect to hard-decision techniques. Several approaches have been proposed to implement iterative soft-decision decoding of b
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28

Arizmendi, Octavio, and James A. Mingo. "The cyclic group and the transpose of an R-cyclic matrix." Journal of Operator Theory 85, no. 1 (2020): 135–51. http://dx.doi.org/10.7900/jot.2019oct09.2281.

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We show that using the cyclic group the transpose of an R-cyclic matrix can be decomposed along diagonal parts into a sum of parts which are freely independent over diagonal scalar matrices. Moreover, if the R-cyclic matrix is self-adjoint then the off-diagonal parts are R-diagonal.
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29

BARBÉ, ANDRÉ M. "FRACTALS BY NUMBERS." Fractals 03, no. 04 (1995): 651–61. http://dx.doi.org/10.1142/s0218348x95000588.

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We introduce an extension of an earlier defined simple, number-based matrix substitution system for obtaining fractal matrices, by considering cyclic substitutions. The elements of the resulting matrices are related to representations of their addresses in a mixed number base. The Hutchinson operator for the limit form of a geometrical representation of the fractal matrix is derived. It is shown that the class of fractal limit sets obtainable from cyclic substitutions does not extend the class obtainable from the simple substitutions.
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30

Zheng, Yanpeng, Sugoog Shon, and Jangyoung Kim. "Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices." Journal of Mathematical Analysis and Applications 455, no. 1 (2017): 727–41. http://dx.doi.org/10.1016/j.jmaa.2017.06.016.

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31

Schell, S. V. "Asymptotic moments of estimated cyclic correlation matrices." IEEE Transactions on Signal Processing 43, no. 1 (1995): 173–80. http://dx.doi.org/10.1109/78.365296.

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32

Chien, Mao-Ting, and Hiroshi Nakazato. "Singular points of cyclic weighted shift matrices." Linear Algebra and its Applications 439, no. 12 (2013): 4090–100. http://dx.doi.org/10.1016/j.laa.2013.10.012.

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33

Baker, Charles E., and Boris S. Mityagin. "Localization of eigenvalues of doubly cyclic matrices." Linear Algebra and its Applications 540 (March 2018): 160–202. http://dx.doi.org/10.1016/j.laa.2017.11.016.

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34

Jang, Ji-Woong, Jong-Seon No, and Habong Chung. "Butson Hadamard matrices with partially cyclic core." Designs, Codes and Cryptography 43, no. 2-3 (2007): 93–101. http://dx.doi.org/10.1007/s10623-007-9065-6.

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35

Lampio, Pekka H. J., and Patric R. J. Östergård. "Classification of difference matrices over cyclic groups." Journal of Statistical Planning and Inference 141, no. 3 (2011): 1194–207. http://dx.doi.org/10.1016/j.jspi.2010.09.023.

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36

Glasby, S. P. "The Meat-axe and f-cyclic matrices." Journal of Algebra 300, no. 1 (2006): 77–90. http://dx.doi.org/10.1016/j.jalgebra.2006.01.026.

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37

Prayitno, M. I. A., Y. Susanti, S. Wahyuni, and A. Suparwanto. "On Eigenvalues of Complement Digraphs." Malaysian Journal of Mathematical Sciences 19, no. 2 (2025): 749–66. https://doi.org/10.47836/mjms.19.2.20.

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Adigraph’s antiadjacency matrix is defined as its complement’s adjacency matrix. Therefore,we can distinguish the complement of digraphs by analysing the properties of their antiadjacency matrices. In this paper, our interest lies in exploring the properties of eigenvalues of the antiadjacency matrix of digraphs and establishing their relation to the characterisation of digraphs. Recent results regarding the eigenvalues of the antiadjacency matrices of certain classes of cyclic digraphs allow us to generalise the bounds of the spectral radius of a complement digraph. Additionally, we establish
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38

Bianco, Mariachiara, Giovanni Ventura, Cosima Damiana Calvano, Ilario Losito, Tommaso R. I. Cataldi, and Antonio Monopoli. "Matrix Selection Strategies for MALDI-TOF MS/MS Characterization of Cyclic Tetrapyrroles in Blood and Food Samples." Molecules 29, no. 4 (2024): 868. http://dx.doi.org/10.3390/molecules29040868.

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Cyclic tetrapyrrole derivatives such as porphyrins, chlorins, corrins (compounds with a corrin core), and phthalocyanines are a family of molecules containing four pyrrole rings usually coordinating a metal ion (Mg, Cu, Fe, Zn, etc.). Here, we report the characterization of some representative cyclic tetrapyrrole derivatives by MALDI-ToF/ToF MS analyses, including heme b and c, phthalocyanines, and protoporphyrins after proper matrix selection. Both neutral and acidic matrices were evaluated to assess potential demetallation, adduct formation, and fragmentation. While chlorophylls exhibited ma
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Lv, Xiao-Guang, and Ting-Zhu Huang. "The Inverses of Block Toeplitz Matrices." Journal of Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/207176.

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We study the inverses of block Toeplitz matrices based on the analysis of the block cyclic displacement. New formulas for the inverses of block Toeplitz matrices are proposed. We show that the inverses of block Toeplitz matrices can be decomposed as a sum of products of block circulant matrices. In the scalar case, the inverse formulas are proved to be numerically forward stable, if the Toeplitz matrix is nonsingular and well conditioned.
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40

Brahmi, Amine, Hicham Ghennioui, Christophe Corbier, François Guillet, and M’hammed Lahbabi. "Blind Separation of Cyclostationary Sources Sharing Common Cyclic Frequencies Using Joint Diagonalization Algorithm." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/2546838.

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We propose a new method for blind source separation of cyclostationary sources, whose cyclic frequencies are unknown and may share one or more common cyclic frequencies. The suggested method exploits the cyclic correlation function of observation signals to compose a set of matrices which has a particular algebraic structure. The aforesaid matrices are automatically selected by proposing two new criteria. Then, they are jointly diagonalized so as to estimate the mixing matrix and retrieve the source signals as a consequence. The nonunitary joint diagonalization (NU-JD) is ensured by Broyden-Fl
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41

Gavelia, S. P. "To construction of Green matrices of edge problems of theory of flat hulls with cyclic periodicity." Researches in Mathematics, no. 2 (July 10, 2021): 10. http://dx.doi.org/10.15421/246903.

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42

Dessalew, Gashaye, Tesfaye Kebede, Gurju Awgichew, and Assaye Walelign. "Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices." Abstract and Applied Analysis 2021 (May 31, 2021): 1–7. http://dx.doi.org/10.1155/2021/8343207.

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This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration
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Balonin, Nikolay, and Dragomir Dokovic. "Three new lengths for cyclic Legendre pairs." Information and Control Systems, no. 1 (February 25, 2021): 2–7. http://dx.doi.org/10.31799/1684-8853-2021-1-2-7.

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Introduction: It is conjectured that the cyclic Legendre pairs of odd lengths >1 always exist. Such a pair consists of two functions a, b: G→Z, whose values are +1 or −1, and whose periodic autocorrelation function adds up to the constant value −2 (except at the origin). Here G is a finite cyclic group and Z is the ring of integers. These conditions are fundamental and the closely related structure of Hadamard matrices having a two circulant core and double border is incompletely described in literature, which makes its study especially relevant. Purpose: To describe the two-border two-circ
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44

Devecı˙, Ömür, and Erdal Karaduman. "The cyclic groups via the Pascal matrices and the generalized Pascal matrices." Linear Algebra and its Applications 437, no. 10 (2012): 2538–45. http://dx.doi.org/10.1016/j.laa.2012.06.024.

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Wang, Yue, Yali Qin, and Hongliang Ren. "Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets." Electronics 12, no. 9 (2023): 2063. http://dx.doi.org/10.3390/electronics12092063.

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It is of great significance to construct deterministic measurement matrices with good practical characteristics in Compressed Sensing (CS), including good reconstruction performance, low memory cost and low computing resources. Low-density-parity check (LDPC) codes and CS codes can be closely related. This paper presents a method of constructing compressed sensing measurement matrices based on quasi-cyclic (QC) LDPC codes and arithmetic sequence sets. The cyclic shift factor in each submatrix of QC-LDPC is determined by arithmetic sequence sets. Compared with random matrices, the proposed meth
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46

KOPELIOVICH, YAACOV. "THETA CONSTANT IDENTITIES AT PERIODS OF COVERINGS OF DEGREE 3." International Journal of Number Theory 04, no. 05 (2008): 725–33. http://dx.doi.org/10.1142/s1793042108001663.

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47

Sabri, K., M. El Badaoui, F. Guillet, A. Adib, and D. Aboutajdine. "On Blind MIMO System Identification Based on Second-Order Cyclic Statistics." Research Letters in Signal Processing 2008 (2008): 1–5. http://dx.doi.org/10.1155/2008/539139.

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This letter introduces a new frequency domain approach for either MIMO System Identification or Source Separation of convolutive mixtures in cyclostationary context. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each in
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48

Kocik, Jerzy. "A Porism Concerning Cyclic Quadrilaterals." Geometry 2013 (August 13, 2013): 1–5. http://dx.doi.org/10.1155/2013/483727.

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We present a geometric theorem on a porism about cyclic quadrilaterals, namely, the existence of an infinite number of cyclic quadrilaterals through four fixed collinear points once one exists. Also, a technique of proving such properties with the use of pseudounitary traceless matrices is presented. A similar property holds for general quadrics as well as for the circle.
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49

Oliynyk, A. "Free products of cyclic groups in groups of infinite unitriangular matrices." Matematychni Studii 60, no. 1 (2023): 28–33. http://dx.doi.org/10.30970/ms.60.1.28-33.

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Groups of infinite unitriangular matrices over associative unitary rings are considered. These groups naturally act on infinite dimensional free modules over underlying rings. They are profinite in case underlying rings are finite. Inspired by their connection with groups defined by finite automata the problem to construct faithful representations of free products of groups by banded infinite unitriangular matrices is considered.For arbitrary prime p a sufficient conditions on a finite set of banded infinite unitriangular matrices over unitary associative rings of characteristic p under which
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50

TARASOV, VITALY O. "CYCLIC MONODROMY MATRICES FOR THE R-MATRIX OF THE SIX-VERTEX MODEL AND THE CHIRAL POTTS MODEL WITH FIXED SPIN BOUNDARY CONDITIONS." International Journal of Modern Physics A 07, supp01b (1992): 963–75. http://dx.doi.org/10.1142/s0217751x92004129.

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Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.
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