Academic literature on the topic 'Representation of lattices'

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Journal articles on the topic "Representation of lattices"

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Andrews, Lawrence C., Herbert J. Bernstein, and Nicholas K. Sauter. "A space for lattice representation and clustering." Acta Crystallographica Section A Foundations and Advances 75, no. 3 (2019): 593–99. http://dx.doi.org/10.1107/s2053273319002729.

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Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances
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Mühle, Henri. "Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group." Annals of Combinatorics 25, no. 2 (2021): 307–44. http://dx.doi.org/10.1007/s00026-021-00532-9.

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AbstractOrdering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has a canonical representation as a join of other permutations. Combinatorially, these canonical join representations can be modeled in terms of arc diagrams. Moreover, these arc diagrams also serve as a model to understand quotient lattices of the weak order. A particularly well-behaved quotient lattice of the weak order is the well-known Tamari lattic
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Luo, Congwen. "S-Lattice Congruences of S-Lattices." Algebra Colloquium 19, no. 03 (2012): 465–72. http://dx.doi.org/10.1142/s1005386712000326.

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In this paper, the S-lattices are introduced as a representation of lattice-ordered monoids. The smallest S-lattice congruence induced by a relation on an S-lattice is characterized and the correspondence between the S-lattice congruences and S-ideals in an S-distributive lattice is discussed. These generalize some recent results of lattices and lattice-ordered semigroups.
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Repnitskii, V. B. "On the representation of lattices by subgroup lattices." Algebra Universalis 37, no. 1 (1997): 81–105. http://dx.doi.org/10.1007/pl00000330.

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Allwein, Gerard, and J. Michael Dunn. "Kripke models for linear logic." Journal of Symbolic Logic 58, no. 2 (1993): 514–45. http://dx.doi.org/10.2307/2275217.

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AbstractWe present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutativity and associativity are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, similar to Curry's subtraction operator, which is residuated with Linear Logic's cotenso
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Boutonnet, Rémi, and Cyril Houdayer. "Stationary characters on lattices of semisimple Lie groups." Publications mathématiques de l'IHÉS 133, no. 1 (2021): 1–46. http://dx.doi.org/10.1007/s10240-021-00122-8.

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AbstractWe show that stationary characters on irreducible lattices $\Gamma < G$ Γ < G of higher-rank connected semisimple Lie groups are conjugation invariant, that is, they are genuine characters. This result has several applications in representation theory, operator algebras, ergodic theory and topological dynamics. In particular, we show that for any such irreducible lattice $\Gamma < G$ Γ < G , the left regular representation $\lambda _{\Gamma }$ λ Γ is weakly contained in any weakly mixing representation $\pi $ π . We prove that for any such irreducible lattice $\Gamma < G
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Yallaoui, B. "Filter Representation of Normal Lattice." Sultan Qaboos University Journal for Science [SQUJS] 1, no. 1 (1996): 63. http://dx.doi.org/10.24200/squjs.vol1iss1pp63-67.

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In this paper we will investigate the properties of normality lattices and their relationships to zero-one measures. We will establish necessary and sufficient conditions for lattices to be normal. These properties are then investigated in the case of separated lattices.
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Fleischer, Isidore. "Functional representation of vector lattices." Proceedings of the American Mathematical Society 108, no. 2 (1990): 471. http://dx.doi.org/10.1090/s0002-9939-1990-0993750-3.

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Kříz̃, I., and A. Pultr. "On a representation of lattices." Journal of Pure and Applied Algebra 68, no. 1-2 (1990): 215–23. http://dx.doi.org/10.1016/0022-4049(90)90145-8.

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Hartung, Gerd. "A topological representation of lattices." Algebra Universalis 29, no. 2 (1992): 273–99. http://dx.doi.org/10.1007/bf01190610.

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Dissertations / Theses on the topic "Representation of lattices"

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Radu, Ion. "Stone's representation theorem." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3087.

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The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.
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Juan, Blanco María Aránzazu. "Vector measures on delta-rings and representation theorems of banach lattices." Doctoral thesis, Editorial Universitat Politècnica de València, 2011. http://hdl.handle.net/10251/11300.

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El espacio de funciones integrables con respecto a una medida vectorial, amén de interesante en si mismo, sirve de herramienta para aplicaciones en problemas importantes como la representación integral y el estudio del dominio óptimo de operadores lineales o la representación de retículos de Banach abstractos como espacios de funciones. Las medidas vectoriales clásicas se definen sobre -álgebras y con valores en un espacio de Banach, y los espacios correspondientes L1( ) y L1w( ) de funciones integrables y débilmente integrables respectivamente, han sido estudiados en profundidad por numero
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Kwuida, Leonard. "Dicomplemented Lattices." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2004. http://nbn-resolving.de/urn:nbn:de:swb:14-1101148726640-29266.

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Das Ziel dieser Arbeit ist es die mathematische Theorie der Begriffsalgebren zu entwickeln. Wir betrachten dabei hauptsaechlich das Repraesentationsproblem dieser vor Kurzem eingefuehrten Strukturen. Motiviert durch die Suche nach einer geeigneten Negation sind die Begriffsalgebren entstanden. Sie sind nicht nur fuer die Philosophie oder die Wissensrepraesentation von Interesse, sondern auch fuer andere Felder, wie zum Beispiel Logik oder Linguistik. Das Problem Negationen geeignet einzufuehren, ist sicher eines der aeltesten der wissenschaftlichen oder philosophischen Gemeinschaft und erregt
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Wild, Marcel Wolfgang. "Dreieckverbande : lineare und quadratische darstellungstheorie." Thesis, University of Zurich, 1987. http://hdl.handle.net/10019.1/70322.

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Prof. Marcel Wild completed his PhD with Zurick University and this is a copy of the original works<br>The original works can be found at http://www.hbz.uzh.ch/<br>ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school (Wille, Herrmann, Poguntke, et al), to large extent triggered by the linear representations of posets (Gabriel, Gelfand-Ponomarev, Nazarova, Roiter, Brenner, et al). Even though posets are more general than lattices,
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Jenkins, Robert David. "Higher order energy transfer : quantum electrodynamical calculations and graphical representation." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327601.

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Goosen, Gerrit. "Relational representations for bounded lattices with operators." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4343.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT: Within lattice theory, an interesting question asked is whether a given abstract lattice may be represented concretely as subsets of a closure system on a topological space. This is true for boolean algebras, bounded distributive lattices and arbitrary bounded lattices. In particular, there are a multitude of ways to represent bounded lattices. We present some of these ideas, as well as an analysis of the differences between them. We further investigate the attempts that were made to extend the above repre
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Andreja, Tepavčević. "Specijalni elementi mreže i primene." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 1993. http://dx.doi.org/10.2298/NS19930629TEPAVCEVIC.

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Data je karakterizacija raznih tipova specijalnih elemenata mreže, kao &scaron;to su kodistributivni, neutralni, skrativi, standardni, izuzetni, neprekidni, beskonačno distributivni i drugi i ti rezultati su primenjeni u strukturnim ispitivanjima algebri, posebno u mrežama kongruencija, podalgebri i slabih kongruencija algebri.&nbsp; Specijalni elementi su posebno proučavani i u bipolumrežama i dobijene su nove teoreme reprezentacije za bipolumreže. Ispitana je kolekcija svih mreža sa istim skupom i-nerazloživih elemenata, pokazano je da je ta kolekcija i sama mreža u odnosu na inkluziju i daj
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Arpin, Peter Robert. "Minimal congruence representations of finite distributive lattices." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0006/MQ41676.pdf.

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Knezevic, Marica. "Graphs of lattices in representations of finite groups." Thesis, King's College London (University of London), 2017. https://kclpure.kcl.ac.uk/portal/en/theses/graphs-of-lattices-in-representations-of-finite-groups(2f435ed5-4a11-4d45-ae2b-26e3c6264ee8).html.

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This thesis work is motivated by the Langlands program, which relates objects from number theory and representation theory. In particular it is motivated by the compatibility of the local and global cases, especially in the mod p case. Given a finite group G, E a finite extension of Qp with ring of integers OE, uniformizer E, V a finite dimensional E-vector space and : G ! AutE(V ) an absolutely irreducible representation, we associate to the following directed graph: its vertices are homothety classes of lattices in V and there is an edge from (the class of) to 0 when E 0 and the quotient =0
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Dashyan, Ruben. "Représentations de groupes fondamentaux en géométrie hyperbolique." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066242/document.

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Deux méthodes de construction de représentations de groupes sont présentées. La première propose une stratégie essayant de déterminer les représentations de groupes libres de type fini à valeurs dans tout réseau de groupes de Lie réel. La seconde, après avoir revu une construction d'une surface hyperbolique complexe, c'est-à-dire le quotient du plan hyperbolique complexe par un réseau, et examiné soigneusement ses propriétés, produit une infinité de représentations non-conjuguées, à valeurs dans un réseau du groupe des isométries du plan hyperbolique complexe, de groupes fondamentaux de variét
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Books on the topic "Representation of lattices"

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Ihringer, T. Congruence lattices of finite algebras: The characterization problem and the role of binary operations. R. Fischer, 1986.

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Kaburlasos, Vassilis G. Towards a Unified Modeling and Knowledge-Representation based on Lattice Theory. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-34170-3.

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Wiedemann, A. Die Auslander-Reiten Köcher der gitterendlichen Gorensteinordnungen. [Universitätsbibliothek], 1987.

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Virtual topology and functor geometry. Taylor & Francis, 2007.

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Matthias, Beck, ed. Integer points in polyhedra: AMS-IMS-SIAM Joint Summer Research Conference Integer Points in Polyhedra-Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics, June 11-15, 2007, Snow Bird, Utah. American Mathematical Society, 2008.

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Hrushovski, Ehud, and François Loeser. A closer look at the stable completion. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0005.

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This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is ex
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Educational Resources Information Center (U.S.), ed. Quantifying the characteristics of knowledge structure representations: A lattice-theoretic framework. Center for the Study of Evaluation, National Center for Research on Evaluation, Standards, and Student Testing, Graduate School of Education & Information Studies, University of California, Los Angeles, 1998.

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Speicher, Roland. Random banded and sparse matrices. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.23.

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This article discusses some mathematical results and conjectures about random band matrix ensembles (RBM) and sparse matrix ensembles. Spectral problems of RBM and sparse matrices can be expressed in terms of supersymmetric (SUSY) statistical mechanics that provides a dual representation for disordered quantum systems. This representation offers important insights into nonperturbative aspects of the spectrum and eigenfunctions of RBM. The article first presents the definition of RBM ensembles before considering the density of states, the behaviour of eigenvectors, and eigenvalue statistics for
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Kaburlasos, Vassilis G. Towards a Unified Modeling and Knowledge-Representation based on Lattice Theory: Computational Intelligence and Soft Computing Applications (Studies in Computational Intelligence). Springer, 2006.

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Kaburlasos, Vassilis G. G. Towards a Unified Modeling and Knowledge-Representation based on Lattice Theory: Computational Intelligence and Soft Computing Applications. Springer, 2010.

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Book chapters on the topic "Representation of lattices"

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Priss, Uta. "Visualising Lattices with Tabular Diagrams." In Diagrammatic Representation and Inference. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86062-2_38.

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Wille, Rudolf. "Geometric Representation of Concept Lattices." In Conceptual and Numerical Analysis of Data. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-75040-3_17.

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Düntsch, Ivo, Wendy MacCaull, Dimiter Vakarelov, and Michael Winter. "Topological Representation of Contact Lattices." In Relations and Kleene Algebra in Computer Science. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11828563_9.

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Perfilieva, Irina. "Linear Representation of Residuated Lattices." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31715-6_23.

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Torim, Ants, Marko Mets, and Kristo Raun. "Covering Concept Lattices with Concept Chains." In Graph-Based Representation and Reasoning. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23182-8_14.

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Gutman, A. E., and G. A. Losenkov. "Functional Representation of a Boolean Valued Universe." In Nonstandard Analysis and Vector Lattices. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4305-9_2.

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Buchi, J. Richard. "Representation of Complete Lattices by Sets." In The Collected Works of J. Richard Büchi. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-8928-6_7.

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Anderson, D. D. "Representation and Embedding Theorems for Noether Lattices and r-Lattices." In The Dilworth Theorems. Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4899-3558-8_38.

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Ésik, Zoltán. "A Representation Theorem for Stratified Complete Lattices." In Logic, Language, and Computation. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-54332-0_15.

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König, Heinz. "The Daniell-Stone-Riesz Representation Theorem." In Operator Theory in Function Spaces and Banach Lattices. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9076-2_12.

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Conference papers on the topic "Representation of lattices"

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AL-msie'deen, R., M. Huchard, A. D. Seriai, C. Urtado, S. Vauttier, and A. Al-Khlifat. "Concept lattices: A representation space to structure software variability." In 2014 5th International Conference on Information and Communication Systems (ICICS). IEEE, 2014. http://dx.doi.org/10.1109/iacs.2014.6841949.

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Cuciurean-Zapan, Clara, and Edward R. Dougherty. "Computational morphology and representation of operators between complete lattices." In Visual Communications '93, edited by Barry G. Haskell and Hsueh-Ming Hang. SPIE, 1993. http://dx.doi.org/10.1117/12.157913.

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Holdon, Liviu-Constantin. "A Representation Theorem, Based on Ideals, for Stonean Residuated Lattices." In 2020 IEEE 10th International Conference on Intelligent Systems (IS). IEEE, 2020. http://dx.doi.org/10.1109/is48319.2020.9199961.

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Kazemi, Hesaneh, Ashkan Vaziri, and Julián Norato. "Topology Optimization of Multi-Material Lattices for Maximal Bulk Modulus." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97370.

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Abstract In this paper, we present a method for multi-material topology optimization of lattice structures for maximum bulk modulus. Unlike ground structure approaches that employ 1-d finite elements such as bars and beams to design periodic lattices, we employ a 3-d representation where each lattice bar is described as a cylinder. To accommodate the 3-d bars, we employ the geometry projection method, whereby a high-level parametric description of the bars is smoothly mapped onto a density field over a fixed analysis grid. In addition to the geometric parameters, we assign a size variable per
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Tschernig, Konrad, Armando-Pérez Leija, and Kurt Busch. "Pseudo energy representation of multi-photon states in photonic tight-binding lattices." In Quantum Information and Measurement. OSA, 2019. http://dx.doi.org/10.1364/qim.2019.t5a.5.

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Nguyen, Dan T., Daniel A. Nolan, and Nicholas F. Borrelli. "A Novel Approach for All Optical Representation of Binaries using Linear Photonics Lattices." In Photonics in Switching and Computing. OSA, 2020. http://dx.doi.org/10.1364/psc.2020.psth3f.3.

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Callanan, Jesse, Oladapo Ogunbodede, Maulikkumar Dhameliya, Jun Wang, and Rahul Rai. "Hierarchical Combinatorial Design and Optimization of Quasi-Periodic Metamaterial Structures." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85914.

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As advanced manufacturing techniques such as additive manufacturing become widely available, it is of interest to investigate the potential advantages that arise when designing periodic metamaterials to achieve a specific desired behavior or physical property. Designing the fine scale detailed geometry of periodic metamaterials to achieve a specified behavior falls under the category of notoriously intractable inverse problems. To simplify solving the inverse problem, most relevant works represent metamaterials as periodic single unit cell structures repeated in regular lattices. Such represen
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Korzec, Tomasz, and Ulli Wolff. "Simulating the Random Surface representation of Abelian Gauge Theories." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0038.

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Sinha, Divyendu, and Edward R. Dougherty. "Computational representation of lattice operators." In IS&T/SPIE's Symposium on Electronic Imaging: Science & Technology, edited by Edward R. Dougherty, Jaakko T. Astola, Harold G. Longbotham, Nasser M. Nasrabadi, and Aggelos K. Katsaggelos. SPIE, 1995. http://dx.doi.org/10.1117/12.205217.

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Ji, Gang, Jeff Bilmes, Jeff Michels, Katrin Kirchhoff, and Chris Manning. "GRAPHICAL MODEL REPRESENTATIONS OF WORD LATTICES." In 2006 IEEE Spoken Language Technology Workshop. IEEE, 2006. http://dx.doi.org/10.1109/slt.2006.326842.

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Reports on the topic "Representation of lattices"

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Fairley, Gerard T. Quantum Lattice-Gas Representation of the Dirac Equation. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada415538.

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