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Добірка наукової літератури з теми "Lattice theory"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 25 липня 2025

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Статті в журналах з теми "Lattice theory"

Day, Alan. "Doubling Constructions in Lattice Theory." Canadian Journal of Mathematics 44, no. 2 (1992): 252–69. http://dx.doi.org/10.4153/cjm-1992-017-7.

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AbstractThis paper examines the simultaneous doubling of multiple intervals of a lattice in great detail. In the case of a finite set of W-failure intervals, it is shown that there in a unique smallest lattice mapping homomorphically onto the original lattice, in which the set of W-failures is removed. A nice description of this new lattice is given. This technique is used to show that every lattice that is a bounded homomorphic image of a free lattice has a projective cover. It is also used to give a sufficient condition for a fintely presented lattice to be weakly atomic and shows that the p

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Harremoës, Peter. "Entropy Inequalities for Lattices." Entropy 20, no. 10 (2018): 784. http://dx.doi.org/10.3390/e20100784.

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We study entropy inequalities for variables that are related by functional dependencies. Although the powerset on four variables is the smallest Boolean lattice with non-Shannon inequalities, there exist lattices with many more variables where the Shannon inequalities are sufficient. We search for conditions that exclude the existence of non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group. In order to formulate and prove the results, one has to bridge lattice theory, group theory,

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Flaut, Cristina, Dana Piciu, and Bianca Liana Bercea. "Some Applications of Fuzzy Sets in Residuated Lattices." Axioms 13, no. 4 (2024): 267. http://dx.doi.org/10.3390/axioms13040267.

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Many papers have been devoted to applying fuzzy sets to algebraic structures. In this paper, based on ideals, we investigate residuated lattices from fuzzy set theory, lattice theory, and coding theory points of view, and some applications of fuzzy sets in residuated lattices are presented. Since ideals are important concepts in the theory of algebraic structures used for formal fuzzy logic, first, we investigate the lattice of fuzzy ideals in residuated lattices and study some connections between fuzzy sets associated to ideals and Hadamard codes. Finally, we present applications of fuzzy set

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Ježek, J., P. PudláK, and J. Tůma. "On equational theories of semilattices with operators." Bulletin of the Australian Mathematical Society 42, no. 1 (1990): 57–70. http://dx.doi.org/10.1017/s0004972700028148.

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In 1986, Lampe presented a counterexample to the conjecture that every algebraic lattice with a compact greatest element is isomorphic to the lattice of extensions of an equational theory. In this paper we investigate equational theories of semi-lattices with operators. We construct a class of lattices containing all infinitely distributive algebraic lattices with a compact greatest element and closed under the operation of taking the parallel join, such that every element of the class is isomorphic to the lattice of equational theories, extending the theory of a semilattice with operators.

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Ježek, Jaroslav, and George F. McNulty. "The existence of finitely based lower covers for finitely based equational theories." Journal of Symbolic Logic 60, no. 4 (1995): 1242–50. http://dx.doi.org/10.2307/2275885.

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By an equational theory we mean a set of equations from some fixed language which is closed with respect to logical consequences. We regard equations as universal sentences whose quantifier-free parts are equations between terms. In our notation, we suppress the universal quantifiers. Once a language has been fixed, the collection of all equational theories for that language is a lattice ordered by set inclusion The meet in this lattice is simply intersection; the join of a collection of equational theories is the equational theory axiomatized by the union of the collection. In this paper we p

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McCulloch, Ryan. "Finite groups with a trivial Chermak–Delgado subgroup." Journal of Group Theory 21, no. 3 (2018): 449–61. http://dx.doi.org/10.1515/jgth-2017-0042.

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Abstract The Chermak–Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups of G. The least element of the Chermak–Delgado lattice of G is known as the Chermak–Delgado subgroup of G. This paper concerns groups with a trivial Chermak–Delgado subgroup. We prove that if the Chermak–Delgado lattice of such a group is lattice isomorphic to a Cartesian product of lattices, then the group splits as a direct product, with the Chermak–Delgado lattice of each direct factor being lattice isomorphic to one of the lattices in the Cartesian product. We establish man

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Ballal, Sachin, and Vilas Kharat. "Zariski topology on lattice modules." Asian-European Journal of Mathematics 08, no. 04 (2015): 1550066. http://dx.doi.org/10.1142/s1793557115500667.

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Let [Formula: see text] be a lattice module over a [Formula: see text]-lattice [Formula: see text] and [Formula: see text] be the set of all prime elements in lattice modules [Formula: see text]. In this paper, we study the generalization of the Zariski topology of multiplicative lattices [N. K. Thakare, C. S. Manjarekar and S. Maeda, Abstract spectral theory II: Minimal characters and minimal spectrums of multiplicative lattices, Acta Sci. Math. 52 (1988) 53–67; N. K. Thakare and C. S. Manjarekar, Abstract spectral theory: Multiplicative lattices in which every character is contained in a uni

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Futa, Yuichi, та Yasunari Shidama. "Lattice of ℤ-module". Formalized Mathematics 24, № 1 (2016): 49–68. http://dx.doi.org/10.1515/forma-2016-0005.

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Summary In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].

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Horváth, Eszter K., Sándor Radeleczki, Branimir Šešelja, and Andreja Tepavčević. "A Note on Cuts of Lattice-Valued Functions and Concept Lattices." Mathematica Slovaca 73, no. 3 (2023): 583–94. http://dx.doi.org/10.1515/ms-2023-0043.

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ABSTRACT Motivated by applications of lattice-valued functions (lattice-valued fuzzy sets) in the theory of ordered structures, we investigate a special kind of posets and lattices induced by these mappings. As a framework, we use the Formal Concept Analysis in which these ordered structures can be naturally observed. We characterize the lattice of cut sets and the Dedekind-MacNeille completion of the set of images of a lattice valued function by suitable concept lattices and we give necessary and sufficient conditions under which these lattices coincide. In addition, we give conditions under

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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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Дисертації з теми "Lattice theory"

Race, David M. (David Michael). "Consistency in Lattices." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc331688/.

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Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular 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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Endres, Michael G. "Topics in lattice field theory /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/9713.

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Bowman, K. "A lattice theory for algebras." Thesis, Lancaster University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234611.

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Michels, Amanda Therese. "Aspects of lattice gauge theory." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297217.

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Buckle, John Francis. "Computational aspects of lattice theory." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/106446/.

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The use of computers to produce a user-friendly safe environment is an important area of research in computer science. This dissertation investigates how computers can be used to create an interactive environment for lattice theory. The dissertation is divided into three parts. Chapters two and three discuss mathematical aspects of lattice theory, chapter four describes methods of representing and displaying distributive lattices and chapters five, six and seven describe a definitive based environment for lattice theory. Chapter two investigates lattice congruences and pre-orders and demonstra

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Craig, Andrew Philip Knott. "Lattice-valued uniform convergence spaces the case of enriched lattices." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1005225.

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Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the

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Pugh, David John Rhydwyn. "Topological structures in lattice gauge theory." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279896.

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Schaich, David. "Strong dynamics and lattice gauge theory." Thesis, Boston University, 2012. https://hdl.handle.net/2144/32057.

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Thesis (Ph.D.)--Boston University<br>In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new,

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Schenk, Stefan. "Density functional theory on a lattice." kostenfrei, 2009. http://d-nb.info/998385956/34.

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Книги з теми "Lattice theory"

Bunk, B., K. H. Mütter, and K. Schilling, eds. Lattice Gauge Theory. Springer US, 1986. http://dx.doi.org/10.1007/978-1-4613-2231-3.

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Grätzer, George. General Lattice Theory. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9326-8.

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Grätzer, George. Lattice Theory: Foundation. Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0018-1.

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service), SpringerLink (Online, ed. Lattice Theory: Foundation. Springer Basel AG, 2011.

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Stern, Manfred. Semimodular lattices: Theory and applications. Cambridge University Press, 1999.

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Krätzel, Ekkehard. Lattice points. Kluwer Academic Publishers, 1988.

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Satz, Helmut, Isabel Harrity, and Jean Potvin, eds. Lattice Gauge Theory ’86. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-1909-2.

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Satz, H. Lattice Gauge Theory '86. Springer US, 1987.

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H, Satz, Harrity Isabel, Potvin Jean, North Atlantic Treaty Organization. Scientific Affairs Division., and International Workshop "Lattice Gauge Theory 1986" (1986 : Brookhaven National Laboratory), eds. Lattice gauge theory '86. Plenum Press, 1987.

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os, Paul Erd. Lattice points. Longman Scientific & Technical, 1989.

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Частини книг з теми "Lattice theory"

Zheng, Zhiyong, Kun Tian, and Fengxia Liu. "Random Lattice Theory." In Financial Mathematics and Fintech. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-7644-5_1.

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AbstractIn this chapter, we introduce the basic random theory of lattice, including Fourier transform, discrete Gauss measure, smoothing parameter and some properties of discrete Gauss distribution. Random lattice is a new research topic in lattice theory. However, only a special class of random lattices named Gauss lattice has been defined and studied. We will introduce Gauss lattice, define the smoothing parameter on Gauss lattice, and calculate the statistical distance based on the smoothing parameter

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Al-Haj Baddar, Sherenaz W., and Kenneth E. Batcher. "Lattice Theory." In Designing Sorting Networks. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1851-1_10.

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Yadav, Santosh Kumar. "Lattice Theory." In Discrete Mathematics with Graph Theory. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-21321-2_6.

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Ritter, Gerhard X., and Gonzalo Urcid. "Lattice Theory." In Introduction to Lattice Algebra. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003154242-3.

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Grätzer, George. "Lattice Constructions." In Lattice Theory: Foundation. Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0018-1_4.

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Stone, Michael. "Lattice Field Theory." In Graduate Texts in Contemporary Physics. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-0507-4_15.

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Yanagihara, Ryosuke. "Lattice Field Theory." In Springer Theses. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-6234-8_3.

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Grätzer, George. "First Concepts." In General Lattice Theory. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-9326-8_1.

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Grätzer, George. "Distributive Lattices." In General Lattice Theory. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-9326-8_2.

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Grätzer, George. "Congruences and Ideals." In General Lattice Theory. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-9326-8_3.

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Тези доповідей конференцій з теми "Lattice theory"

Riess, Hans, Gregory Henselman-Petrusek, Michael C. Munger, Robert Ghrist, Zachary I. Bell, and Michael M. Zavlanos. "Network Preference Dynamics Using Lattice Theory." In 2024 American Control Conference (ACC). IEEE, 2024. http://dx.doi.org/10.23919/acc60939.2024.10645007.

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Monahan, Christopher. "Automated Lattice Perturbation Theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0021.

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Lambrou, Eliana, Luigi Del Debbio, R. D. Kenway, and Enrico Rinaldi. "Searching for a continuum 4D field theory arising from a 5D non-abelian gauge theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0107.

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Bursa, F., and Michael Kroyter. "Lattice String Field Theory." In The XXVIII International Symposium on Lattice Field Theory. Sissa Medialab, 2011. http://dx.doi.org/10.22323/1.105.0047.

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Kieburg, Mario, Jacobus Verbaarschot, and Savvas Zafeiropoulos. "A classification of 2-dim Lattice Theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0337.

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Shao, Yingchao, Li Fu, Fei Hao, and Keyun Qin. "Rough Lattice: A Combination with the Lattice Theory and the Rough Set Theory." In 2016 International Conference on Mechatronics, Control and Automation Engineering. Atlantis Press, 2016. http://dx.doi.org/10.2991/mcae-16.2016.23.

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Bietenholz, Wolfgang, Ivan Hip, and David Landa-Marban. "Spectral Properties of a 2d IR Conformal Theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0486.

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Zubkov, Mikhail. "Gauge theory of Lorentz group on the lattice." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0095.

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Veernala, Aarti, and Simon Catterall. "Four Fermion Interactions in Non Abelian Gauge Theory." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0108.

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Bergner, Georg, Jens Langelage, and Owe Philipsen. "Effective lattice theory for finite temperature Yang Mills." In 31st International Symposium on Lattice Field Theory LATTICE 2013. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.187.0133.

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Звіти організацій з теми "Lattice theory"

McCune, W., and R. Padmanabhan. Single identities for lattice theory and for weakly associative lattices. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/510566.

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Yee, Ken. Lattice gaugefixing and other optics in lattice gauge theory. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/10156563.

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Yee, Ken. Lattice gaugefixing and other optics in lattice gauge theory. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/5082303.

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Becher, Thomas G. Continuum methods in lattice perturbation theory. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/808671.

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Hasslacher, B. Lattice gas hydrodynamics: Theory and simulations. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/6441616.

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Hasslacher, B. Lattice gas hydrodynamics: Theory and simulations. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/6590163.

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Brower, Richard C. National Computational Infrastructure for Lattice Gauge Theory. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1127446.

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Negele, John W. National Computational Infrastructure for Lattice Gauge Theory. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1165874.

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Reed, Daniel, A. National Computational Infrastructure for Lattice Gauge Theory. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/951263.

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Creutz, M. Lattice gauge theory and Monte Carlo methods. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/6530895.

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