Relevant bibliographies by topics / Finite algebraic structures

Contents

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

Academic literature on the topic 'Finite algebraic structures'

Author: Grafiati
Published: 18 November 2023

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Journal articles on the topic "Finite algebraic structures"

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Aichinger, Erhard, Peter Mayr, and Ralph McKenzie. "On the number of finite algebraic structures." Journal of the European Mathematical Society 16, no. 8 (2014): 1673–86. http://dx.doi.org/10.4171/jems/472.

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Milani, Vida, Seyed M. H. Mansourbeigi, and Hossein Finizadeh. "Algebraic and topological structures on rational tangles." Applied General Topology 18, no. 1 (2017): 1. http://dx.doi.org/10.4995/agt.2017.2250.

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<p>In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.</p>
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Campercholi, Miguel, Mauricio Tellechea, and Pablo Ventura. "Deciding Quantifier-free Definability in Finite Algebraic Structures." Electronic Notes in Theoretical Computer Science 348 (March 2020): 23–41. http://dx.doi.org/10.1016/j.entcs.2020.02.003.

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Levitskaya, A. A. "Systems of Random Equations over Finite Algebraic Structures." Cybernetics and Systems Analysis 41, no. 1 (2005): 67–93. http://dx.doi.org/10.1007/s10559-005-0042-7.

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Shevlyakov, Artyom N. "Direct powers of algebraic structures and equations." Prikladnaya Diskretnaya Matematika, no. 58 (2023): 31–39. http://dx.doi.org/10.17223/20710410/58/4.

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We study systems of equations over graphs, posets and matroids. We give the criteria when a direct power of such algebraic structures is equationally Noetherian. Moreover, we prove that any direct power of any finite algebraic structure is weakly equationally Noetherian.
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Laskowski, Michael C. "Mutually algebraic structures and expansions by predicates." Journal of Symbolic Logic 78, no. 1 (2013): 185–94. http://dx.doi.org/10.2178/jsl.7801120.

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AbstractWe introduce the notions of a mutually algebraic structures and theories and prove many equivalents. A theory T is mutually algebraic if and only if it is weakly minimal and trivial if and only if no model M of T has an expansion (M, A) by a unary predicate with the finite cover property. We show that every structure has a maximal mutually algebraic reduct. and give a strong structure theorem for the class of elementary extensions of a fixed mutually algebraic structure.
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Lin, Zhe, Mihir Kumar Chakraborty, and Minghui Ma. "Residuated Algebraic Structures in the Vicinity of Pre-rough Algebra and Decidability." Fundamenta Informaticae 179, no. 3 (2021): 239–74. http://dx.doi.org/10.3233/fi-2021-2023.

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Varieties of topological quasi-Boolean algebras in the vicinity of pre-rough algebras [28, 29] are expanded to residuated algebraic structures by introducing a new implication operation and its residual in these structures. Sequent calculi for some classes of residuated algebraic structures are established. These sequent calculi have the strong finite model property which yields the decidability of the word problem for corresponding classes of algebraic structures.
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García, Darío, Dugald Macpherson, and Charles Steinhorn. "Pseudofinite structures and simplicity." Journal of Mathematical Logic 15, no. 01 (2015): 1550002. http://dx.doi.org/10.1142/s0219061315500026.

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We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted.
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Rybalov, Alexander. "On generic complexity of theories of finite algebraic structures." Journal of Physics: Conference Series 1901, no. 1 (2021): 012046. http://dx.doi.org/10.1088/1742-6596/1901/1/012046.

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Hambleton, Ian, and Matthias Kreck. "Smooth structures on algebraic surfaces with finite fundamental group." Inventiones Mathematicae 102, no. 1 (1990): 109–14. http://dx.doi.org/10.1007/bf01233422.

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Dissertations / Theses on the topic "Finite algebraic structures"

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Shminke, Boris. "Applications de l'IA à l'étude des structures algébriques finies et à la démonstration automatique de théorèmes." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4058.

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Cette thèse contribue à une recherche de modèles finis et à la démonstration automatisée de théorèmes, en se concentrant principalement, mais sans s'y limiter, sur les méthodes d'intelligence artificielle. Dans la première partie, nous résolvons une question de recherche ouverte à partir de l'algèbre abstraite en utilisant une recherche automatisée de modèles finis massivement parallèles, en utilisant l'assistant de preuve Isabelle. À savoir, nous établissons l'indépendance de certaines lois de distributivité abstraites dans les binaires résiduels dans le cas général. En tant que sous-produit de cette découverte, nous apportons un client Python au serveur Isabelle. Le client a déjà trouvé son application dans les travaux d'autres chercheurs et de l'enseignement supérieur. Dans la deuxième partie, nous proposons une architecture de réseau neuronal génératif pour produire des modèles finis de structures algébriques appartenant à une variété donnée d'une manière inspirée des modèles de génération d'images tels que les GAN (réseaux antagonistes génératifs) et les autoencodeurs. Nous contribuons également à un paquet Python pour générer des semi-groupes finis de petite taille comme implémentation de référence de la méthode proposée. Dans la troisième partie, nous concevons une architecture générale de guidage des vérificateurs de saturation avec des algorithmes d'apprentissage par renforcement. Nous contribuons à une collection d'environnements compatibles OpenAI Gym pour diriger Vampire et iProver et démontrons sa viabilité sur des problèmes sélectionnés de la bibliothèque TPTP (Thousand of Problems for Theorem Provers). Nous contribuons également à une version conteneurisée d'un modèle ast2vec existant et montrons son applicabilité à l'incorporation de formules logiques écrites sous la forme clausal-normale. Nous soutenons que l'approche modulaire proposée peut accélérer considérablement l'expérimentation de différentes représentations de formules logiques et de schémas de génération de preuves synthétiques à l'avenir, résolvant ainsi le problème de la rareté des données, limitant notoirement les progrès dans l'application des techniques d'apprentissage automatique pour la démonstration automatisée de théorèmes<br>This thesis contributes to a finite model search and automated theorem proving, focusing primarily but not limited to artificial intelligence methods. In the first part, we solve an open research question from abstract algebra using an automated massively parallel finite model search, employing the Isabelle proof assistant. Namely, we establish the independence of some abstract distributivity laws in residuated binars in the general case. As a by-product of this finding, we contribute a Python client to the Isabelle server. The client has already found its application in the work of other researchers and higher education. In the second part, we propose a generative neural network architecture for producing finite models of algebraic structures belonging to a given variety in a way inspired by image generation models such as GANs (generative adversarial networks) and autoencoders. We also contribute a Python package for generating finite semigroups of small size as a reference implementation of the proposed method. In the third part, we design a general architecture of guiding saturation provers with reinforcement learning algorithms. We contribute an OpenAI Gym-compatible collection of environments for directing Vampire and iProver and demonstrate its viability on select problems from the Thousands of Problems for Theorem Provers (TPTP) library. We also contribute a containerised version of an existing ast2vec model and show its applicability to embedding logical formulae written in the clausal-normal form. We argue that the proposed modular approach can significantly speed up experimentation with different logic formulae representations and synthetic proof generation schemes in future, thus addressing the data scarcity problem, notoriously limiting the progress in applying the machine learning techniques for automated theorem proving
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Bergvall, Olof. "Cohomology of arrangements and moduli spaces." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-132822.

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This thesis mainly concerns the cohomology of the moduli spaces ℳ3[2] and ℳ3,1[2] of genus 3 curves with level 2 structure without respectively with a marked point and some of their natural subspaces. A genus 3 curve which is not hyperelliptic can be realized as a plane quartic and the moduli spaces 𝒬[2] and 𝒬1[2] of plane quartics without respectively with a marked point are given special attention. The spaces considered come with a natural action of the symplectic group Sp(6,𝔽2) and their cohomology groups thus become Sp(6,𝔽2)-representations. All computations are therefore Sp(6,𝔽2)-equivariant. We also study the mixed Hodge structures of these cohomology groups. The computations for ℳ3[2] are mainly via point counts over finite fields while the computations for ℳ3,1[2] primarily uses a description due to Looijenga in terms of arrangements associated to root systems. This leads us to the computation of the cohomology of complements of toric arrangements associated to root systems. These varieties come with an action of the corresponding Weyl group and the computations are equivariant with respect to this action.
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D'Andrea, Alessandro 1972. "Structure theory of finite conformal algebras." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47476.

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Kim, Sang Hyun. "On the structure of finite AW*-algebras /." Search for this dissertation online, 2004. http://wwwlib.umi.com/cr/ksu/main.

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North, Evan I. "A Study on the Algebraic Structure of SL(2,p)." Ohio University Honors Tutorial College / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1461266377.

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Avery, Thomas Charles. "Structure and semantics." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/29517.

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Algebraic theories describe mathematical structures that are defined in terms of operations and equations, and are extremely important throughout mathematics. Many generalisations of the classical notion of an algebraic theory have sprung up for use in different mathematical contexts; some examples include Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. The purpose of an algebraic theory is to describe its models, which are structures in which each of the abstract operations of the theory is given a concrete interpretation such that the equations of the theory hold. The process of going from a theory to its models is called semantics, and is encapsulated in a semantics functor. In order to define a model of a theory in a given category, it is necessary to have some structure that relates the arities of the operations in the theory with the objects of the category. This leads to the second central notion of this thesis, that of an interpretation of arities, or aritation for short. We show that any aritation gives rise to a semantics functor from the appropriate category of proto-theories, and that this functor has a left adjoint called the structure functor, giving rise to a structure{semantics adjunction. Furthermore, we show that the usual semantics for many existing notions of algebraic theory arises in this way by choosing an appropriate aritation. Another aim of this thesis is to find a convenient category of monads in the following sense. Every right adjoint into a category gives rise to a monad on that category, and in fact some functors that are not right adjoints do too, namely their codensity monads. This is the structure part of the structure{semantics adjunction for monads. However, the fact that not every functor has a codensity monad means that the structure functor is not defined on the category of all functors into the base category, but only on a full subcategory of it. This deficiency is solved when passing to general proto-theories with a canonical choice of aritation whose structure{semantics adjunction restricts to the usual one for monads. However, this comes at a cost: the semantics functor for general proto-theories is not full and faithful, unlike the one for monads. The condition that a semantics functor be full and faithful can be thought of as a kind of completeness theorem | it says that no information is lost when passing from a theory to its models. It is therefore desirable to retain this property of the semantics of monads if possible. The goal then, is to find a notion of algebraic theory that generalises monads for which the semantics functor is full and faithful with a left adjoint; equivalently the semantics functor should exhibit the category of theories as a re ective subcategory of the category of all functors into the base category. We achieve this (for well-behaved base categories) with a special kind of proto-theory enriched in topological spaces, which we call a complete topological proto-theory. We also pursue an analogy between the theory of proto-theories and that of groups. Under this analogy, monads correspond to finite groups, and complete topological proto-theories correspond to profinite groups. We give several characterisations of complete topological proto-theories in terms of monads, mirroring characterisations of profinite groups in terms of finite groups.
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Stack, Cora. "Some results on the structure of the groups of units of finite completely primary rings and on the structure of finite dimensional nilpotent algebras." Thesis, University of Reading, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262483.

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Psioda, Matthew. "An examination of the structure of extension families of irreducible polynomials over finite fields /." Electronic version (PDF), 2006. http://dl.uncw.edu/etd/2006/psiodam/matthewpsioda.pdf.

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Tappe, Stefan. "Finite dimensional realizations for term structure models driven by semimartingales." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2005. http://dx.doi.org/10.18452/15369.

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Es sei ein Heath-Jarrow-Morton Zinsstrukturmodell df(t,T) = alpha(t,T)dt + sigma(t,T)dX_t gegeben, angetrieben von einem mehrdimensionalen Semimartingal X. Das Ziel dieser Arbeit besteht darin, die Existenz endlich dimensionaler Realisierungen für solche Modelle zu untersuchen, wobei wir als treibende Prozesse die Klasse der Grigelionis Prozesse wählen, die insbesondere Levy Prozesse enthält. Zur Bearbeitung der Fragestellung werden zwei veschiedene Ansätze verfolgt. Wir dehnen die Ideen aus der Differenzialgeometrie von Björk und Svensson (2001) auf die vorliegende Situation aus und zeigen, dass das in der zitierten Arbeit bewiesene Kriterium für die Existenz endlich dimensionaler Realisierungen in unserem Fall als notwendiges Kriterium dienlich ist. Dieses Resultat wird auf konkrete Volatilitätsstrukturen angewandt. Im Kontext von sogenannten Benchmark Realisierungen, die eine natürliche Verallgemeinerung von Short Rate Realisierungen darstellen, leiten wir Integro-Differenzialgleichungen her, die für die Untersuchung der Existenz endlich dimensionaler Realisierungen hilfreich sind. Als Verallgemeinerung eines Resultats von Jeffrey (1995) beweisen wir außerdem, dass Zinsstrukturmodelle, die eine generische Benchmark Realisierung besitzen, notwendigerweise eine singuläre Hessesche Matrix haben. Beide Ansätze zeigen, dass neue Phänomene auftreten, sobald der treibende Prozess X Sprünge macht. Es gibt dann auf einmal nur noch sehr wenige Zinsstrukturmodelle, die endlich dimensionale Realisierungen zulassen, was ein beträchtlicher Unterschied zu solchen Modellen ist, die von einer Brownschen Bewegung angetrieben werden. Aus diesem Grund zeigen wir, dass für die in der Literatur oft behandelten Modelle mit deterministischer Richtungsvolatilität eine Folge von endlich dimensionalen Systemen existiert, die gegen das Zinsmodell konvergieren.<br>Let f(t,T) be a term structure model of Heath-Jarrow-Morton type df(t,T) = alpha(t,T)dt + sigma(t,T)dX_t, driven by a multidimensional semimartingale X. Our objective is to study the existence of finite dimensional realizations for equations of this kind. Choosing the class of Grigelionis processes (including in particular Levy processes) as driving processes, we approach this problem from two different directions. Extending the ideas from differential geometry in Björk and Svensson (2001), we show that the criterion for the existence of finite dimensional realizations, proven in the aforementioned paper, still serves as a necessary condition in our setup. This result is applied to concrete volatility structures. In the context of benchmark realizations, which are a natural generalization of short rate realizations, we derive integro-differential equations, suitable for the analysis of the realization problem. Generalizing Jeffrey (1995), we also prove a result stating that forward rate models, which generically possess a benchmark realization, must have a singular Hessian matrix. Both approaches reveal that, with regard to the results known for driving Wiener processes, new phenomena emerge, as soon as the driving process X has jumps. In particular, the occurrence of jumps severely limits the range of models that admit finite dimensional realizations. For this reason we prove, for the often considered case of deterministic direction volatility structures, the existence of finite dimensional systems converging to the forward rate model.
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Filho, Antonio Calixto de Souza. "Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-30012009-163028/.

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Apresentamos duas construções para unidades de uma ordem em uma classe de álgebras de quatérnios que é anel de divisão: as unidades de Pell e as unidades de Gauss. Classificamos os anéis de inteiros de extensões quadráticas racionais, $R$, cujo grupo de unidades $\\U (R G)$ é hiperbólico para um certo grupo $G$ fixado. Também classificamos os semigrupos finitos $S$, tal que, para a álgebra unitária $\\Q S$ e para toda $\\Z$-ordem $\\Gamma$ de $\\Q S$, o grupo de unidades $\\U (\\Gamma)$ é hiperbólico. Nesse mesmo contexto, classificamos os {\\it RA}-loops $L$ cujo loop de unidades $\\U (\\Z L)$ não contém um subgrupo abeliano livre de posto dois.<br>For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\\Gamma$ of $\\Q S$ have hyperbolic unit group $\\U(\\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two.
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Books on the topic "Finite algebraic structures"

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Kandasamy, W. B. Vasantha. Finite neutrosophic complex numbers. Zip Publishing, 2011.

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Flannery, D. L. (Dane Laurence), 1965-, ed. Algebraic design theory. American Mathematical Society, 2011.

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WAIFI 2010 (2010 Istanbul, Turkey). Arithmetic of finite fields: Third international workshop, WAIFI 2010, Istanbul, Turkey, June 27-30, 2010 ; proceedings. Springer, 2010.

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Germany) International Conference on Finite Fields and Applications (11th 2013 Magdeburg. Topics in finite fields: 11th International Conference on Finite Fields and Their Applications, July 22--26, 2013, Magdeburg, Germany. Edited by Kyureghyan Gohar 1974 editor, Mullen Gary L. editor, and Pott Alexander 1961 editor. American Mathematical Society, 2015.

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Francisco, Rodríguez-Henríquez, and SpringerLink (Online service), eds. Arithmetic of Finite Fields: 4th International Workshop, WAIFI 2012, Bochum, Germany, July 16-19, 2012. Proceedings. Springer Berlin Heidelberg, 2012.

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Ralph, McKenzie, ed. The structure of finite algebras. American Mathematical Society, 1988.

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Jungnickel, D. Finite fields: Structure and arithmetics. B.I. Wissenschaftsverlag, 1993.

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Finite mathematics, models, and structure. Kendall/Hunt Pub. Co., 1995.

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Adams, William J. Finite mathematics, models, and structure. Xlibris Corporation, 2009.

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Matthew, Valeriote, ed. The structure of decidable locally finite varieties. Birkhäuser, 1989.

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Book chapters on the topic "Finite algebraic structures"

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Cherlin, Gregory. "Large Finite Structures with Few Types." In Algebraic Model Theory. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8923-9_3.

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Miller, Matthew. "Multiplicative Structures on Finite Free Resolutions." In Free Resolutions in Commutative Algebra and Algebraic Geometry. A K Peters/CRC Press, 2023. http://dx.doi.org/10.1201/9781003420187-4.

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Schenberg, Mario. "Algebraic Structures of Finite Point Sets I." In Clifford Algebras and their Applications in Mathematical Physics. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8090-8_47.

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Balakrishnan, R., and Sriraman Sridharan. "Algebraic Structures II (Vector Spaces and Finite Fields)." In Discrete Mathematics. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429486326-4.

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Khoussainov, Bakhadyr, and Jiamou Liu. "Decision Problems for Finite Automata over Infinite Algebraic Structures." In Implementation and Application of Automata. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40946-7_1.

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Avanzi, Roberto Maria, and Preda Mihăilescu. "Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures." In Selected Areas in Cryptography. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24654-1_23.

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Yang, Zhixuan, Marco Paviotti, Nicolas Wu, Birthe van den Berg, and Tom Schrijvers. "Structured Handling of Scoped Effects." In Programming Languages and Systems. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99336-8_17.

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AbstractAlgebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely in conjunction with algebraic operations. Although proposals for scoped operations exist, they are either ad-hoc and unprincipled, or too inconvenient for practical programming. This paper provides the best of both worlds: a theoretically-founded model of scoped effects that is convenient for implementation and reasoning. Our new model is based on an adjunction between a locally finitely presentable category and a category of functorial algebras. Using comparison functors between adjunctions, we show that our new model, an existing indexed model, and a third approach that simulates scoped operations in terms of algebraic ones have equal expressivity for handling scoped operations. We consider our new model to be the sweet spot between ease of implementation and structuredness. Additionally, our approach automatically induces fusion laws of handlers of scoped effects, which are useful for reasoning and optimisation.
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Myers, Robert S. R., Stefan Milius, and Henning Urbat. "Nondeterministic Syntactic Complexity." In Lecture Notes in Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_23.

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AbstractWe introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the ‘canonical boolean representation’ of the syntactic monoid. Equivalently, it is the least number of states of any subatomic nondeterministic acceptor. It turns out that essentially all previous structural work on nondeterministic state-minimality computes this measure. Our approach rests on an algebraic interpretation of nondeterministic finite automata as deterministic finite automata endowed with semilattice structure. Crucially, the latter form a self-dual category.
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McKenzie, Ralph, and Matthew Valeriote. "Centerless algebras." In Structure of Decidable Locally Finite Varieties. Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4612-4552-0_4.

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Alexandru, Andrei, and Gabriel Ciobanu. "Algebraic Structures in Finitely Supported Mathematics." In Finitely Supported Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42282-4_3.

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Conference papers on the topic "Finite algebraic structures"

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Li, Xianhua. "On Some Results of Finite Solvable Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0029.

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Mazurov, V. D. "On Recognizability of Finite Groups by Spectrum." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0031.

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Denecke, K., and Y. Susanti. "Semigroups of n-ary Operations on Finite Sets." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0011.

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Guo, Xiuyun. "Power Automorphisms and Induced Automorphisms in Finite Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0021.

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Moghaddamfar, A. R. "Recognizability of Finite Groups by Order and Degree Pattern." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0032.

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Muchtadi-Alamsyah, I., F. Yuliawan, and A. Muchlis. "Finite Field Basis Conversion and Normal Basis in Characteristic Three." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0034.

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Ballester-Bolinches, A., R. Esteban-Romero, and Yangming Li. "Cover and Avoidance Properties and the Structure of Finite Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0003.

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Guo, Wenbin, Vasilii G. Safonov, and Alexander N. Skiba. "On Some Constructions and Results of the Theory of Partially Soluble Finite Groups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0019.

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Krot, Alexander M., Mikhail N. Dolgikh, and Natalya A. Romanovskaya. "Coding of images based on finite algebraic structures and fast convolution algorithms." In AeroSense '97, edited by Abinash C. Dubey and Robert L. Barnard. SPIE, 1997. http://dx.doi.org/10.1117/12.280907.

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Salisbury, Chris. "Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-4974.

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Abstract:
A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.
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Reports on the topic "Finite algebraic structures"

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Borgwardt, Stefan, and Rafael Peñaloza. Complementation and Inclusion of Weighted Automata on Infinite Trees: Revised Version. Technische Universität Dresden, 2011. http://dx.doi.org/10.25368/2022.180.

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Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.
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Borgwardt, Stefan, and Rafael Peñaloza. Complementation and Inclusion of Weighted Automata on Infinite Trees. Technische Universität Dresden, 2010. http://dx.doi.org/10.25368/2022.178.

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Abstract:
Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.
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