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Journal articles on the topic 'Algebraic chains'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

De Sterck, H., T. A. Manteuffel, S. F. McCormick, K. Miller, J. Ruge, and G. Sanders. "Algebraic Multigrid for Markov Chains." SIAM Journal on Scientific Computing 32, no. 2 (2010): 544–62. http://dx.doi.org/10.1137/090753589.

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2

Fortunato, L., and W. A. de Graaf. ""Lost chains" in algebraic models." Journal of Physics: Conference Series 284 (March 1, 2011): 012025. http://dx.doi.org/10.1088/1742-6596/284/1/012025.

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3

Wang, Ying-Zhe, and Mu-Fa Chen. "Algebraic convergence of Markov chains." Annals of Applied Probability 13, no. 2 (2003): 604–27. http://dx.doi.org/10.1214/aoap/1050689596.

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4

Albeverio, Sergio, and Shao-Ming Fei. "Symmetry, Integrable Chain Models and Stochastic Processes." Reviews in Mathematical Physics 10, no. 06 (1998): 723–50. http://dx.doi.org/10.1142/s0129055x98000239.

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A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with An symmetry and the related Temperley–Lieb algebraic structures and representations are discussed. It is shown that corresponding to these An symmetric integrable chain models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the correspondin

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5

Bagchi, Susmit. "Homotopy of Linearly Ordered Split–Join Chains in Covering Spaces of Foliated n-Manifold Charts." Symmetry 15, no. 3 (2023): 574. http://dx.doi.org/10.3390/sym15030574.

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Topological spaces can be induced by various algebraic ordering relations such as, linear, partial and the inclusion-ordering of open sets forming chains and chain complexes. In general, the classifications of covering spaces are made by using fundamental groups and lifting. However, the Riesz ordered n-spaces and Urysohn interpretations of real-valued continuous functions as ordered chains provide new perspectives. This paper proposes the formulation of covering spaces of n-space charts of a foliated n-manifold containing linearly ordered chains, where the chains do not form topologically sep

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6

Iachello, Francesco, and Piero Truini. "Algebraic Model of Anharmonic Polymer Chains." Annals of Physics 276, no. 1 (1999): 120–43. http://dx.doi.org/10.1006/aphy.1999.5940.

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7

Zhao, Pan. "Strong Stationary Duality and Algebraic Duality for Continuous Time Möbius Monotone Markov Chains." International Journal of Applied Mathematics and Machine Learning 15, no. 2 (2021): 69–86. http://dx.doi.org/10.18642/ijamml_710012241.

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Under the assumption of Möbius monotonicity, we develop the theory of strong stationary duality for continuous time Markov chains on the finite partially ordered state space, we also construct a nonexplosive algebraic duality for continuous time Markov chains on Finally, we present an application to the two-dimensional birth and death chain.

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8

Lee, C.-C., and J. M. Hervé. "Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, no. 6 (2005): 577–87. http://dx.doi.org/10.1243/095440605x31436.

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Combining planar and spherical 4R chains generates three kinds of new discontinuously movable (DM) seven-link mechanisms. The mobility analysis is based on algebraic concepts of set theory. These mechanisms are called hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6RIP DM mechanisms. Their discontinuous mobility is explained employing the Lie group algebraic properties of the displacement set. Moreover, the same given spatial arrangement of joints can be linked in two ways constituting two distinct chains, which have a quite different mobility. One chain ha

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9

Brown, Ronald, and Philip J. Higgins. "Crossed complexes and chain complexes with operators." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 1 (1990): 33–57. http://dx.doi.org/10.1017/s0305004100068353.

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Chain complexes with a group of operators are a well known tool in algebraic topology, where they arise naturally as the chain complex of cellular chains of the universal cover of a reduced CW-complex X. The group of operators here is the fundamental group of X.

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10

Hlavaty, L. "Generalized algebraic framework for open spin chains." Journal of Physics A: Mathematical and General 27, no. 16 (1994): 5645–53. http://dx.doi.org/10.1088/0305-4470/27/16/028.

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11

Hanson, James D., John R. Cary, and James D. Meiss. "Algebraic decay in self-similar Markov chains." Journal of Statistical Physics 39, no. 3-4 (1985): 327–45. http://dx.doi.org/10.1007/bf01018666.

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12

Friedland, Omer, and Yosef Yomdin. "Doubling chains on complements of algebraic hypersurfaces." Journal d'Analyse Mathématique 140, no. 2 (2020): 617–36. http://dx.doi.org/10.1007/s11854-020-0101-z.

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13

BAKER, T. H., and P. D. JARVIS. "QUANTUM SUPERSPIN CHAINS." International Journal of Modern Physics B 08, no. 25n26 (1994): 3623–35. http://dx.doi.org/10.1142/s0217979294001536.

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Supersymmetric formulations of spin-½ quantum chains, associated with integrable models, are considered. One class of super-extensions, based on low-dimensional classical and exceptional superalgebras containing sl(2), is illustrated with the case of osp(1/2). A more radical generalization, in which the algebra of Pauli matrices is identified with the algebra of supersymmetric quantum mechanics, is also presented, and some of its algebraic properties discussed.

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14

ARNAUDON, D., A. DOIKOU, L. FRAPPAT, É. RAGOUCY, and N. CRAMPÉ. "ANALYTICAL BETHE ANSATZ FOR OPEN SPIN CHAINS WITH SOLITON NONPRESERVING BOUNDARY CONDITIONS." International Journal of Modern Physics A 21, no. 07 (2006): 1537–54. http://dx.doi.org/10.1142/s0217751x06029077.

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We present an "algebraic treatment" of the analytical Bethe ansatz for open spin chains with soliton nonpreserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe ansatz. It allows us to deal with a generic [Formula: see text] open SNP spin chain possessing on each site an arbitrary representation. As a result, we obtain the Bethe equations in their full generality. The classification of finite dimensional irreducible representations for the twisted Yangians are directly linked to t

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15

ATALAN, FERIHE. "A NOTE ON CHAINS AND BOUNDING PAIRS OF DEHN TWISTS." Glasgow Mathematical Journal 63, no. 1 (2020): 133–38. http://dx.doi.org/10.1017/s0017089520000063.

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AbstarctLet $N_g^k$ be a nonorientable surface of genus g with k punctures. In the first part of this note, after introducing preliminary materials, we will give criteria for a chain of Dehn twists to bound a disc. Then, we will show that automorphisms of the mapping class groups map disc bounding chains of Dehn twists to such chains. In the second part of the note, we will introduce bounding pairs of Dehn twists and give an algebraic characterization for such pairs.

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16

Liu, Yuanyuan, Wendi Li, and Xiuqin Li. "On geometric and algebraic transience for block-structured Markov chains." Journal of Applied Probability 57, no. 4 (2020): 1313–38. http://dx.doi.org/10.1017/jpr.2020.69.

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AbstractBlock-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.

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17

Teh, Jyh-Haur, and Chin-Jui Yang. "Real rectifiable currents, holomorphic chains and algebraic cycles." Complex Manifolds 8, no. 1 (2021): 274–85. http://dx.doi.org/10.1515/coma-2020-0119.

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Abstract We study some fundamental properties of real rectifiable currents and give a generalization of King’s theorem to characterize currents defined by positive real holomorphic chains. Our main tool is Siu’s semi-continuity theorem and our proof largely simplifies King’s proof. A consequence of this result is a sufficient condition for the Hodge conjecture.

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18

Bolten, Matthias, Achi Brandt, James Brannick, Andreas Frommer, Karsten Kahl, and Ira Livshits. "A Bootstrap Algebraic Multilevel Method for Markov Chains." SIAM Journal on Scientific Computing 33, no. 6 (2011): 3425–46. http://dx.doi.org/10.1137/100791816.

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19

Bodroža-Pantić, Olga, and Angelina Ilić-Kovačević. "Algebraic Structure Count of Angular Hexagonal-Square Chains." Fibonacci Quarterly 45, no. 1 (2007): 3–10. http://dx.doi.org/10.1080/00150517.2007.12428237.

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20

Choi, Man Duen, Jeffrey S. Rosenthal, and Peter Rosenthal. "Linear-Algebraic Results Associated with Antiferromagnetic Heisenberg Chains." SIAM Journal on Matrix Analysis and Applications 14, no. 3 (1993): 830–52. http://dx.doi.org/10.1137/0614058.

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21

MAO, Yonghua. "Algebraic convergence for discrete-time ergodic Markov chains." Science in China Series A 46, no. 5 (2003): 621. http://dx.doi.org/10.1360/02ys0202.

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22

Pang, C. Y. Amy. "Lumpings of Algebraic Markov Chains Arise from Subquotients." Journal of Theoretical Probability 32, no. 4 (2018): 1804–44. http://dx.doi.org/10.1007/s10959-018-0834-0.

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23

Chakir, Ilham, and Maurice Pouzet. "The Length of Chains in Modular Algebraic Lattices." Order 24, no. 4 (2007): 227–47. http://dx.doi.org/10.1007/s11083-007-9070-4.

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24

Pong, Wai Yan. "Chains of Differential Subvarieties in an Algebraic Variety." Journal of Algebra 248, no. 2 (2002): 755–64. http://dx.doi.org/10.1006/jabr.2001.9065.

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25

BOWEN, LEWIS. "Non-abelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula." Ergodic Theory and Dynamical Systems 30, no. 6 (2009): 1629–63. http://dx.doi.org/10.1017/s0143385709000844.

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AbstractThis paper introduces Markov chains and processes over non-abelian free groups and semigroups. We prove a formula for the f-invariant of a Markov chain over a free group in terms of transition matrices that parallels the classical formula for the entropy a Markov chain. Applications include free group analogues of the Abramov–Rohlin formula for skew-product actions and Yuzvinskii’s addition formula for algebraic actions.

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26

KÜMMERER, B., and H. MAASSEN. "A SCATTERING THEORY FOR MARKOV CHAINS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 01 (2000): 161–76. http://dx.doi.org/10.1142/s0219025700000091.

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In the operator algebraic formulation of probability theory Markov processes typically appear as perturbations of Bernoulli processes. We develop a scattering theory for this situation. This theory applies to the isomorphism problem between Markov processes and Bernoulli shifts as well as to the description of open quantum systems.

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27

Yap, V. B. "Similar States in Continuous-Time Markov Chains." Journal of Applied Probability 46, no. 2 (2009): 497–506. http://dx.doi.org/10.1239/jap/1245676102.

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In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models.

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28

Yap, V. B. "Similar States in Continuous-Time Markov Chains." Journal of Applied Probability 46, no. 02 (2009): 497–506. http://dx.doi.org/10.1017/s002190020000560x.

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In a homogeneous continuous-time Markov chain on a finite state space, two states that jump to every other state with the same rate are called similar. By partitioning states into similarity classes, the algebraic derivation of the transition matrix can be simplified, using hidden holding times and lumped Markov chains. When the rate matrix is reversible, the transition matrix is explicitly related in an intuitive way to that of the lumped chain. The theory provides a unified derivation for a whole range of useful DNA base substitution models, and a number of amino acid substitution models.

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29

Perez, Alba, and J. Michael McCarthy. "Clifford Algebra Exponentials and Planar Linkage Synthesis Equations." Journal of Mechanical Design 127, no. 5 (2004): 931–40. http://dx.doi.org/10.1115/1.1904047.

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This paper uses the exponential defined on a Clifford algebra of planar projective space to show that the “standard-form” design equations used for planar linkage synthesis are obtained directly from the relative kinematics equations of the chain. The relative kinematics equations of a serial chain appear in the matrix exponential formulation of the kinematics equations for a robot. We show that formulating these same equations using a Clifford algebra yields design equations that include the joint variables in a way that is convenient for algebraic manipulation. The result is a single formula

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30

Boos, H., M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama. "Algebraic Representation of Correlation Functions in Integrable Spin Chains." Annales Henri Poincaré 7, no. 7-8 (2006): 1395–428. http://dx.doi.org/10.1007/s00023-006-0285-5.

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31

Harding, John, and Andre Kornell. "Completely hereditarily atomic OMLS." Mathematica Slovaca 74, no. 5 (2024): 1107–26. http://dx.doi.org/10.1515/ms-2024-0080.

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Abstract An irreducible complete atomic oml of infinite height cannot be algebraic and have the covering property. However, modest departure from these conditions allows infinite-height examples. We use an extension of Kalmbach’s construction to the setting of infinite chains to provide an example of an infinite-height, irreducible, algebraic oml with the 2-covering property, and Keller’s construction provides an example of an infinite-height, irreducible, complete oml that has the covering property and is completely hereditarily atomic. Completely hereditarily atomic omls generalize algebraic

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32

Accardi, Luigi, Abdessatar Souissi, and El Gheteb Soueidy. "Quantum Markov chains: A unification approach." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 02 (2020): 2050016. http://dx.doi.org/10.1142/s0219025720500162.

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In this paper, we study a unified approach for quantum Markov chains (QMCs). A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic algebraic property. We stress that this kind of algebras includes both Boson and Fermi algebras. Our main results concern two reconstruction theorems for quantum Markov chains and for quantum Markov states. Namely, we illustrate the results through examples.

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33

Ceniceros, Jose, Mohamed Elhamdadi, and Alireza Mashaghi. "Coloring Invariant for Topological Circuits in Folded Linear Chains." Symmetry 13, no. 6 (2021): 919. http://dx.doi.org/10.3390/sym13060919.

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Circuit topology is a mathematical approach that categorizes the arrangement of contacts within a folded linear chain, such as a protein molecule or the genome. Theses linear biomolecular chains often fold into complex 3D architectures with critical entanglements and local or global structural symmetries stabilised by formation of intrachain contacts. Here, we adapt and apply the algebraic structure of quandles to classify and distinguish chain topologies within the framework of circuit topology. We systematically study the basic circuit topology motifs and define quandle/bondle coloring for t

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34

Yusuf, A. O., Chinenye Nworah, and M. Isyaku. "ON THE STUDY OF CHAINS SOFT SETS, SOFT ORDERED SETS AND SOFT SEMILATTICES." FUDMA JOURNAL OF SCIENCES 5, no. 4 (2022): 44–48. http://dx.doi.org/10.33003/fjs-2021-0504-779.

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In this paper, we study the concept of chains soft sets and set-valued function of chains soft sets. The definitions of chains soft sets or linear order or total order soft set are given. The notions of binary relation of comparability of the elements of set-valued functions are also discussed. Linearization’s of a partial order soft set are also defined. The definition and some algebraic structure of soft semilattice are also given.

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35

Peng, Nan Fu. "Spectral representations of the transition probability matrices for continuous time finite Markov chains." Journal of Applied Probability 33, no. 1 (1996): 28–33. http://dx.doi.org/10.2307/3215261.

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Using an easy linear-algebraic method, we obtain spectral representations, without the need for eigenvector determination, of the transition probability matrices for completely general continuous time Markov chains with finite state space. Comparing the proof presented here with that of Brown (1991), who provided a similar result for a special class of finite Markov chains, we observe that ours is more concise.

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36

Peng, Nan Fu. "Spectral representations of the transition probability matrices for continuous time finite Markov chains." Journal of Applied Probability 33, no. 01 (1996): 28–33. http://dx.doi.org/10.1017/s0021900200103699.

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Using an easy linear-algebraic method, we obtain spectral representations, without the need for eigenvector determination, of the transition probability matrices for completely general continuous time Markov chains with finite state space. Comparing the proof presented here with that of Brown (1991), who provided a similar result for a special class of finite Markov chains, we observe that ours is more concise.

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37

Wang, Zhiyong, and Fathi H. Ghorbel. "Control of Closed Kinematic Chains Using A Singularly Perturbed Dynamics Model." Journal of Dynamic Systems, Measurement, and Control 128, no. 1 (2005): 142–51. http://dx.doi.org/10.1115/1.2171440.

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In this paper, we propose a novel approach to the control of closed kinematic chains (CKCs). This method is based on a recently developed singularly perturbed model for CKCs. Conventionally, the dynamics of CKCs are described by differential-algebraic equations (DAEs). Our approach transfers the control of the original DAE system to the control of an artificially created singularly perturbed system in which the slow dynamics corresponds to the original DAE when the perturbation parameter tends to zero. Compared to control schemes that rely on solving nonlinear algebraic constraint equations, t

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38

MIKHAILOV, A. "SYMMETRIES OF THE BFKL EQUATION." International Journal of Modern Physics A 13, no. 19 (1998): 3215–33. http://dx.doi.org/10.1142/s0217751x98001608.

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We discuss the algebraic structure of the spin chains related to high energy scattering in QCD. We study the sl(2) Yangian symmetry and possible generalizations to nonzero spin and anisotropy parameter.

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39

Brunhuber, C., F. G. Mertens, and Y. Gaididei. "Long-range effects on superdiffusive algebraic solitons in anharmonic chains." European Physical Journal B 57, no. 1 (2007): 57–65. http://dx.doi.org/10.1140/epjb/e2007-00150-3.

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40

Benson, Dave. "An algebraic model for chains on $\Omega BG{}^{^\wedge }_p$." Transactions of the American Mathematical Society 361, no. 04 (2008): 2225–42. http://dx.doi.org/10.1090/s0002-9947-08-04728-4.

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41

Mao, Yong-Hua, and Yan-Hong Song. "On geometric and algebraic transience for discrete-time Markov chains." Stochastic Processes and their Applications 124, no. 4 (2014): 1648–78. http://dx.doi.org/10.1016/j.spa.2013.12.012.

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42

Chen, Changbo, and Marc Moreno Maza. "Quantifier elimination by cylindrical algebraic decomposition based on regular chains." Journal of Symbolic Computation 75 (July 2016): 74–93. http://dx.doi.org/10.1016/j.jsc.2015.11.008.

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43

Marek, Ivo, and Daniel B. Szyld. "Algebraic Schwarz methods for the numerical solution of Markov chains." Linear Algebra and its Applications 386 (July 2004): 67–81. http://dx.doi.org/10.1016/j.laa.2003.12.046.

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44

Doikou, A., and P. P. Martin. "Hecke algebraic approach to the reflection equation for spin chains." Journal of Physics A: Mathematical and General 36, no. 9 (2003): 2203–25. http://dx.doi.org/10.1088/0305-4470/36/9/301.

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45

Berikashvili, N. "An Algebraic Model of Fibration with the Fiber K(π, n)-Space". gmj 3, № 1 (1996): 27–48. http://dx.doi.org/10.1515/gmj.1996.27.

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Abstract For a fibration with the fiber K(π, n)-space, the algebraic model as a twisted tensor product of chains of the base with standard chains of K(π, n)-complex is given which preserves multiplicative structure as well. In terms of this model the action of the n-cohomology of the base with coefficients in π on the homology of fibration is described.

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46

COBELI, CRISTIAN, and ALEXANDRU ZAHARESCU. "On the geometry behind a recurrent relation." Carpathian Journal of Mathematics 31, no. 2 (2015): 165–72. http://dx.doi.org/10.37193/cjm.2015.02.03.

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We consider a certain linear recursive relation with integer parameters and study some of its algebraic and geometric properties, with the purpose of estimating the number of chains of valences in the Farey series.

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47

Richter, Birgit, and Stephanie Ziegenhagen. "A spectral sequence for the homology of a finite algebraic delooping." Journal of K-theory 13, no. 3 (2014): 563–99. http://dx.doi.org/10.1017/is014004016jkt264.

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AbstractIn the world of chain complexes En-algebras are the analogues of based n-fold loop spaces in the category of topological spaces. Fresse showed that operadic En-homology of an En-algebra computes the homology of an n-fold algebraic delooping. The aim of this paper is to construct two spectral sequences for calculating these homology groups and to treat some concrete classes of examples such as Hochschild cochains, graded polynomial algebras and chains on iterated loop spaces. In characteristic zero we gain an identification of the summands in Pirashvili's Hodge decomposition of higher o

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48

FOERSTER, ANGELA, ITZHAK RODITI, and LIGIA M. C. S. RODRIGUES. "INTEGRABLE MULTIPARAMETRIC SU(N) CHAIN." Modern Physics Letters A 11, no. 12 (1996): 987–93. http://dx.doi.org/10.1142/s0217732396001016.

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We analyze integrable models associated to a multiparametric SU (N)R-matrix. We show that the Hamiltonians describe SU (N) chains with twisted boundary conditions and that the underlying algebraic structure is the multiparametric deformation of SU (N) enlarged by the introduction of a central element.

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49

DUPARC, JACQUES, та MARIANE RISS. "THE MISSING LINK FOR ω-RATIONAL SETS, AUTOMATA, AND SEMIGROUPS". International Journal of Algebra and Computation 16, № 01 (2006): 161–85. http://dx.doi.org/10.1142/s0218196706002871.

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In 1997, following the works of Klaus W. Wagner on ω-regular sets, Olivier Carton and Dominique Perrin introduced the notions of chains and superchains for ω-semigroups. There is a clear correspondence between the algebraic representation of each of these operations and the automata-theoretical one. Unfortunately, chains and superchains do not suffice to describe the whole Wagner hierarchy. We introduce a third notion that completes the task undertaken by these two authors.

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50

Allouche, Benyamine, Antoine Dequidt, Laurent Vermeiren, and Michel Dambrine. "Modeling and PDC fuzzy control of planar parallel robot." International Journal of Advanced Robotic Systems 14, no. 1 (2017): 172988141668711. http://dx.doi.org/10.1177/1729881416687112.

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Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characte

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