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Relevant bibliographies by topics / Lattices theory

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Dissertations / Theses

Academic literature on the topic 'Lattices theory'

Author: Grafiati

Published: 25 May 2024

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Dissertations / Theses on the topic "Lattices theory"

1

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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2

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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3

Gragg, Karen E. (Karen Elizabeth). "Dually Semimodular Consistent Lattices." Thesis, North Texas State University, 1988. https://digital.library.unt.edu/ark:/67531/metadc330641/.

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A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly

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4

Cheng, Y. "Theory of integrable lattices." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.568779.

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This thesis deals with the theory of integrable lattices in "solitons" throughout. Chapter 1 is a general introduction, which includes an historical survey and a short surrunary of the "solitons" theory and the present work. In Chapter 2, we discuss the equivalence between two kinds of lattice AKNS spectral problems - one includes two potentials, while the other includes four. The two nonlinear lattice systems associated with those two spectral problems, respectively is also proved to be equivalent to each other. In Chapter 3, we derive a class of nonlinear differential-difference equations (N

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5

Heeney, Xiang Xia Huang. "Small lattices." Thesis, University of Hawaii at Manoa, 2000. http://hdl.handle.net/10125/25936.

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This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple gluing irreducible [Special characters omitted.] lattices are introduced. The conditions which insure [Special characters omitted.] small are discovered. This dissertation also give some triple gluing irreducible small lattices by gluing [Special characters omitted.] 's. Finally, K-structured lattices are introduced. We prove that a K-structured lattice L is triple gluing irreduc

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6

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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7

Jipsen, Peter. "Varieties of lattices." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/15851.

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Bibliography: pages 140-145.<br>An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of information has been obtained in the last twenty years. We begin with some preliminary results from universal algebra and lattice theory. The next chapter presents some properties of the lattice of all lattice sub-varieties. Here we also discuss the important notion of

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8

Bystrik, Anna. "On Delocalization Effects in Multidimensional Lattices." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278868/.

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A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype latti

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9

Madison, Kirk William. "Quantum transport in optical lattices /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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10

Ocansey, Evans Doe. "Enumeration problems on lattices." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/80393.

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Thesis (MSc)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: The main objective of our study is enumerating spanning trees (G) and perfect matchings PM(G) on graphs G and lattices L. We demonstrate two methods of enumerating spanning trees of any connected graph, namely the matrix-tree theorem and as a special value of the Tutte polynomial T(G; x; y). We present a general method for counting spanning trees on lattices in d 2 dimensions. In particular we apply this method on the following regular lattices with d = 2: rectangular, triangular, honeycomb, kagomé, diced, 9 3 lattic

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