Relevant bibliographies by topics / Shuffle product

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Shuffle product'

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Published: 4 June 2021
Last updated: 26 July 2025

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Journal articles on the topic "Shuffle product"

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OBRENIĆ, BOJANA. "APPROXIMATING HYPERCUBES BY INDEX-SHUFFLE GRAPHS VIA DIRECT-PRODUCT EMULATIONS." Journal of Interconnection Networks 05, no. 04 (2004): 429–73. http://dx.doi.org/10.1142/s0219265904001258.

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Index-shuffle graphs are a family of bounded-degree hypercube-like interconnection networks for parallel computers, introduced by [Baumslag and Obrenić (1997): Index-Shuffle Graphs, …], as an efficient substitute for two standard families of hypercube derivatives: butterflies and shuffle-exchange graphs. In the theoretical framework of graph embedding and network emulations, this paper shows that the index-shuffle graph efficiently approximates the direct-product structure of the hypercube, and thereby has a unique potential to approximate efficiently all of its derivatives. One of the consequ
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Rosenberg, Arnold L. "Product-shuffle networks: toward reconciling shuffles and butterflies." Discrete Applied Mathematics 37-38 (July 1992): 465–88. http://dx.doi.org/10.1016/0166-218x(92)90152-z.

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Rotella, F. "Shuffle product of generating series." Theoretical Computer Science 79, no. 1 (1991): 257–61. http://dx.doi.org/10.1016/0304-3975(91)90155-u.

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Duchamp, Gérard, and Daniel Krob. "On the partially commutative shuffle product." Theoretical Computer Science 96, no. 2 (1992): 405–10. http://dx.doi.org/10.1016/0304-3975(92)90345-g.

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Ono, Masataka, and Shuji Yamamoto. "Shuffle product of finite multiple polylogarithms." manuscripta mathematica 152, no. 1-2 (2016): 153–66. http://dx.doi.org/10.1007/s00229-016-0856-9.

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Liu, Mengyu, and Huilan Li. "A Hopf Algebra on Permutations Arising from Super-Shuffle Product." Symmetry 13, no. 6 (2021): 1010. http://dx.doi.org/10.3390/sym13061010.

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In this paper, we first prove that any atom of a permutation obtained by the super-shuffle product of two permutations can only consist of some complete atoms of the original two permutations. Then, we prove that the super-shuffle product and the cut-box coproduct on permutations are compatible, which makes it a bialgebra. As this algebra is graded and connected, it is a Hopf algebra.
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Ito, Masami. "Shuffle Decomposition of Regular Languages." JUCS - Journal of Universal Computer Science 8, no. (2) (2002): 257–59. https://doi.org/10.3217/jucs-008-02-0257.

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Let A X* be a regular language. In the paper, we will provide an algorithm to decide whether there exist a nontrivial language B (n, X) and a nontrivial regular language C X* such that A = B C 1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen.
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Li, Zhonghua, and Chen Qin. "Shuffle product formulas of multiple zeta values." Journal of Number Theory 171 (February 2017): 79–111. http://dx.doi.org/10.1016/j.jnt.2016.07.013.

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Berstel, Jean, Luc Boasson, Olivier Carton, Jean-Éric Pin, and Antonio Restivo. "The expressive power of the shuffle product." Information and Computation 208, no. 11 (2010): 1258–72. http://dx.doi.org/10.1016/j.ic.2010.06.002.

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Shyr, H. J., and S. S. Yu. "Bi-catenation and shuffle product of languages." Acta Informatica 35, no. 8 (1998): 689–707. http://dx.doi.org/10.1007/s002360050139.

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Dissertations / Theses on the topic "Shuffle product"

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Kane, Ladji. "Combinatoire et algorithmique des factorisations tangentes à l'identité." Thesis, Paris 13, 2014. http://www.theses.fr/2014PA132059/document.

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La combinatoire a permis de résoudre certains problèmes en Mathématiques, en Physique et en Informatique, en retour celles-ci inspirent des questions nouvelles à la combinatoire. Ce mémoire de thèse intitulé "Combinatoire et algorithme des factorisations tangentes à l'identité" regroupe plusieurs travaux sur la combinatoire des déformations du produit de Shuffle. L'objectif de cette thèse est d'écrire des factorisations dont le terme principal est l'identité à travers l'utilisation d'outils portant principalement sur la combinatoire des mots (ordres, graduation etc.). Dans le cas classique, so
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Deshpande, Pranav. "Distributed Supervisory Control of Workflows." [Tampa, Fla.] : University of South Florida, 2003. http://purl.fcla.edu/fcla/etd/SFE0000209.

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Mammez, Cécile. "Deux exemples d'algèbres de Hopf d'extraction-contraction : mots tassés et diagrammes de dissection." Thesis, Littoral, 2017. http://www.theses.fr/2017DUNK0459/document.

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Ce manuscrit est consacré à l'étude de la combinatoire de deux algèbres de Hopf d'extraction-contraction. La première est l'algèbre de Hopf de mots tassés WMat introduite par Duchamp, Hoang-Nghia et Tanasa dont l'objectif était la construction d'un modèle de coproduit d'extraction-contraction pour les mots tassés. Nous expliquons certains sous-objets ou objets quotients ainsi que des applications vers d'autres algèbres de Hopf. Ainsi, nous considérons une algèbre de permutations dont le dual gradué possède un coproduit de déconcaténation par blocs et un produit de double battage décalé. Le dou
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LIN, CHIA-HSUN, and 林佳勳. "Shuffle Product Formulae of Some Multiple Zeta Values." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/32736832781484351899.

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碩士<br>國立中正大學<br>數學所<br>97<br>In section 1, we introduce the classic Euler sums and some results concerning the evaluations of S_{p,q}. In section 2, we introduce the integral representations for multiple zeta values and use them to prove some interesting relations. In section 3, we express some products of multiple zeta values as sums of multiple zeta values by shuffle product.
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Lee, Tung-Yang, and 李東洋. "Algebraic Relations for Multiple Zeta Values Through Shuffle Product Formulas." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/23314838914548492550.

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博士<br>國立中正大學<br>數學研究所<br>100<br>For a multi-index $\mfa = (\seq{a}{1}{2}{p})$ of positive integers with $a_{p} \geq 2$, a multiple zeta value of depth $p$ and weight $\av{\mfa} = \fsum{a}{1}{2}{p}$ or $p$-fold Euler sum is defined to be \[ \zeta(\seq{a}{1}{2}{p}) = \sum_{1 \leq n_{1} < n_{2} < \cdots < n_{p}} n_{1}^{-a_{1}} n_{2}^{-a_{2}} \cdots n_{p}^{-a_{p}}, \] which is a natural generalization of the classical Euler sum \[ S_{a, b} = \sum_{k=1}^{\infty} \frac{1}{k^{b}} \sum_{j=1}^{k} \frac{1}{j^{a}}, \quad a, b \in \bn, \quad b \geq 2. \] Multiple zeta values can b
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Hong, Yi-Hui, and 洪宜慧. "Some Combinatorial Identities Produced from Shuffle Products of Two Sums of Multiple Zeta Values." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/38125669081032208248.

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碩士<br>國立中正大學<br>數學研究所<br>101<br>Abstract A multiple zeta value of depth r and weight j with a multi-index = (1; 2; : : : ; r) of positive integers with r 2. After the shuffle process product of a particular multiple zeta value of weight w1 and the sum of the multiple zeta value of weight w2. It will produce some combinatorial identities of convolution type.
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Yen, Miau-Hua, and 顏妙樺. "Combinatorial Identities of Convolution Type through Shuffle Products." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/26112638583487325303.

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碩士<br>國立中正大學<br>應用數學研究所<br>102<br>For an $r$-tuple of positive integers $\alpha_1, \alpha_2, \ldots , \alpha_r$ with $\alpha_r \geq 2$ ,the multiple zeta value or $r$-fold Euler sum $\zeta(\boldsymbol{\alpha})$ is defined as \[ \zeta(\boldsymbol{\alpha}) = \sum_{1 \leq n_1 < n_2 < \cdots <n_r} n_1^{- \alpha_1} n_2^{- \alpha_2} \cdots n_r^{- \alpha_r}, \] the numbers $\vert \boldsymbol{\alpha} \vert = \alpha_1 + \alpha_2 + \cdots + \alpha_r$ is called the weight of $\zeta(\alpha_1, \alpha_2, \ldots , \alpha_r)$ and $r$ is its depth. In this thesis, we shall use shuffle products of multiple
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LIU, YI-RU, and 劉羿汝. "Weighted Sum Formulas from Shuffle Products of Riemann Zeta Values." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/80024797345262779733.

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碩士<br>國立中正大學<br>應用數學研究所<br>103<br>The classical Euler decomposition expresses a product of two Riemann zeta values as double Euler sums and it leads to a weighted sum formula among double Euler sums. Through a particular integral representation of Riemann's zeta values, we are able to carry out the shuffle product of $n$ Riemann zeta values. As results, we produce some weighted sum formulas among multiple zeta values of depth 2, 3 and 4. In particular when the depth $n=4$, the weighted sum formula is given by \begin{align*} &\sum_{|\balpha|=k+7}\zeta(\alpha _{1},\alpha_2
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Wu, Chieni, and 吳建儀. "Shuffle Relations of Multiple Zeta Values Produced from Integrations." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/96546892605955841541.

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碩士<br>國立中正大學<br>應用數學研究所<br>99<br>In this thesis, we shall use an elementary shuffle relation to produce many double weighted sum formulae. Furthermore, we use the shuffle relations of multiple zeta values with two parameters to produce some interesting formulae as shown in Main Theorems 1, 2 and 3.
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Book chapters on the topic "Shuffle product"

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Duchamp, Gérard, and Jean-Gabriel Luque. "Congruences Compatible with the Shuffle Product." In Formal Power Series and Algebraic Combinatorics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04166-6_38.

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Restivo, Antonio. "The Shuffle Product: New Research Directions." In Language and Automata Theory and Applications. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15579-1_5.

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Pin, Jean-Éric. "Shuffle Product of Regular Languages: Results and Open Problems." In Algebraic Informatics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19685-0_3.

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Harju, Tero, Alexandra Mateescu, and Arto Salomaa. "Shuffle on trajectories: The schützenberger product and related operations." In Mathematical Foundations of Computer Science 1998. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0055800.

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Rizzi, Romeo, and Stéphane Vialette. "On Recognizing Words That Are Squares for the Shuffle Product." In Computer Science – Theory and Applications. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-38536-0_21.

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Heuts, Gijs, and Ieke Moerdijk. "Simplicial Sets." In Simplicial and Dendroidal Homotopy Theory. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10447-3_2.

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AbstractSimplicial sets form a very convenient tool to study the homotopy theory of topological spaces. In this chapter we will present an introduction to the theory of simplicial sets. We assume some basic acquaintance with the language of category theory, but no prior knowledge of simplicial sets on the side of the reader. We present the basic definitions and constructions, including the geometric realization of a simplicial set, the nerve of a category, and the description of the product of two simplicial sets in terms of shuffles.
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Lange, Otto. "Kronecker products of matrices and their implementation on shuffle/exchange-type processor networks." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-16811-7_190.

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Maier, Robert S., and René Schott. "Regular approximations to shuffle products of context-free languages, and convergence of their generating functions." In Fundamentals of Computation Theory. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/3-540-57163-9_30.

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Reutenauer, Christophe. "Shuffle Algebra and Subwords." In Free Lie Algebras. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536796.003.0007.

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Abstract The shuffle algebra is a free commutative algebra over the set of Lyndon words; this result is presented in Section 6.1, together with a precise identity on the shuffie product of Lyndon words, which implies that actually there is a canonical structure of algebra of divided powers. In Section 6.2 a remarkable presentation of the shuffle algebra is given; the generators are the nonempty words, and the relations the nontrivial shuffle products. In Section 6.3 we introduce subword functions on the free group, the Magnus transformation of the free group, the algebra structure on the modul
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Reutenauer, Christophe. "Lie polynomials." In Free Lie Algebras. Oxford University PressOxford, 1993. http://dx.doi.org/10.1093/oso/9780198536796.003.0002.

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Abstract After introducing words, noncommutative polynomials and series, we define Lie polynomials. One of the main results presents the various characterizations of Lie polynomials. This naturally leads us to define the shuffle product, and to study the duality between concatenation and shuffle product; in other words: the Hopf-algebra-like properties of the free associative algebra. Related questions are treated in the appendix, including the support of the free Lie algebra (the set of words which may appear in Lie polynomials), the free Lie p-algcbra and the Jacobson identities, the kernel
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Conference papers on the topic "Shuffle product"

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Miller, A. S., and A. A. Sawchuk. "Pipelining issues in a free-space shuffle-exchange system." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.tuuu3.

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An optoelectronic shuffle-exchange interconnection system consists of many duplicate stages of shuffle optics and electronic bypass-exchange switches. Haney1 has suggested that for "reasonable" size arrays, an optical shuffle has a great deal of unutilized space-bandwidth product (SBWP). Thus, instead of replicating the optics, we could use a single lens array to perform the shuffle for all stages of the system. We have developed a simple procedure to optimize the packing capability of a free-space perfect shuffle2 to define reasonable array sizes, and where unutilized SBWP actually exists.
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Haney, Michael W. "The Application of Self-Similar Patterns to Opto-electronic Shuffle/Exchange Network Design." In Optical Computing. Optica Publishing Group, 1993. http://dx.doi.org/10.1364/optcomp.1993.othb.2.

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Multistage Interconnection Networks (MINs), based on free-space optical interconnects, were proposed to overcome the communications bottlenecks, skew, and crosstalk associated with long electronic interconnects.1 Versions based on 2-D arrays of processing elements (PEs) were suggested that more fully utilize the third dimension for higher density and efficient use of optical space bandwidth product (SBWP).2,3,4 Several of these concepts are based on off-axis imaging techniques which perform shuffle5 based permutations by optically interleaving equal sized sectors (such as quadrants) of the sou
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Marsden, Gary C., Philippe J. Marchand, Phil Harvey, and Sadik C. Esener. "Optical transpose interconnection system." In OSA Annual Meeting. Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.tud6.

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The optical transpose interconnection system (OTIS) is an optical interconnection scheme that provides transpose transformations on 2-D indexed 2-D arrays of transmitters and detectors. These transformations are required in shuffle-tree graph1 (STG) architectures. The STG supports various matrix computations, such as matrix transpose, vector outer-product, and matrix-vector multiplications. These computations are useful for signal processing, artificial intelligence, relational databases, artificial neural systems, and crossbar interconnections. The OTIS optical system can also be used to impl
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Hudson, Robin L. "The Z2-graded sticky shuffle product Hopf algebra." In Quantum Probability. Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-17.

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Haney, M. W., and J. J. Levy. "Optically cascadable folded perfect shuffle." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mq2.

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The folded perfect shuffle1 (FPS) was proposed to overcome the space-bandwidth product limitations of 1-D optics. The approach is based on 2-D raster formatting of the input data and an off-axis magnifying imaging system which overlays and shifts the data to the proper format. Pixel interlacing is achieved via subpixel masking, shifted input elements, or shifted imaging lenses. The interconnection patterns comprising a multistage network generally must be cascadable to preclude the need for active interstage regeneration. In a cascadable network both output and input have the same intensity, f
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Haney, Michael W. "Optoelectronic shuffle-exchange network for multiprocessing architectures." In OSA Annual Meeting. Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.tux5.

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A shuffle-exchange network based on free-space optical interconnects is proposed for multiprocessor architectures. The processing elements (PEs) are arrayed on a planar rectilinear grid. For packet switching applications, an optical source/detector pair is located at each PE. A folded perfect shuffle (FPS) optical system,1 located above the plane, uses reflective or folded optics to shuffle the array of sources onto the array of detectors. The exchange/bypass function is performed electronically on each pair of PEs. If M source/detector pairs are located at each PE site, then a single FPS opti
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Hendrick, W. Lee, Philippe J. Marchand, Frederick B. McCormick, Ilkan Çokgör, and Sadik C. Esener. "Optical Transpose Interconnection System: System Design and Component Development." In Optical Computing. Optica Publishing Group, 1995. http://dx.doi.org/10.1364/optcomp.1995.othb4.

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The optical transpose interconnection system1 (OTIS) is a simple means of providing a transpose interconnection using only a pair of lenslet arrays. This system has been shown useful for shuffle based multi-stage interconnection networks, mesh-of-trees matrix processors, and hypercube interconnections. The transpose interconnection is a one-to-one interconnection between L transmitters and L receivers, where L is the product of two integers, M and N. To implement the interconnection a N×N array of lenslets is placed in front of the input plane, and a M×M array of lenslets is located before the
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Li, Wanzhen, Tao Sun, Xinming Huo, and Yimin Song. "CGA Approach to Kinematic Analysis of a 2-DoF Parallel Positioning Mechanism." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60529.

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This paper proposes CGA based approach to determine motions and constraints, analyze mobility, identify singularity of parallel mechanisms, which is perfectly demonstrated by taking 3-RSR&amp;SS parallel positioning mechanism as an example. By introducing CGA, which combining elements of geometry and algebra, the motions and constraints are expressed as simple formulas and their relations are calculated by means of outer product with clear physical meaning, these lead to the motions and constraints are determined in a visual, concise and efficient way, and the number and type of DoF and access
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Fan, ChenYang, JiaCun Wang, XiWang Guo, ShuJin Qin, MengChu Zhou, and Liang Qi. "Discrete Shuffled Frog Leading Algorithm for Multiple-product Human-robot Collaborative Disassembly Line Balancing Problem." In 2022 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2022. http://dx.doi.org/10.1109/smc53654.2022.9945365.

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Walker, A. C., F. A. P. Tooley, M. R. Taghizadeh, et al. "Development of an Optoelectronic Parallel Data Sorter based on CMOS/InGaAs Smart Pixel Arrays." In Optics in Computing. Optica Publishing Group, 1997. http://dx.doi.org/10.1364/oc.1997.otha.4.

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As part of the Scottish Collaborative Initiative in Optoelectronic Sciences (SCIOS) we have been developing an optoelectronic parallel data sorter as a technology demonstrator [1]. This system is based on 32 x 32 arrays of smart pixels produced by flip-chip solder bump assembly of InGaAs/GaAs MQW modulator/detectors with Si CMOS electronics. These devices are linked by an optical system which implements a perfect shuffle interconnection. The functionality of each of the processing nodes is selected by a combination of global electronic control signals and local optical control information whic
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