Relevant bibliographies by topics / BMW algebras

Academic literature on the topic 'BMW algebras'

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Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "BMW algebras"

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Vaz, Pedro, and Emmanuel Wagner. "A Remark on BMW Algebra, q-Schur Algebras and Categorification." Canadian Journal of Mathematics 66, no. 2 (April 1, 2014): 453–80. http://dx.doi.org/10.4153/cjm-2013-018-1.

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AbstractWe prove that the two-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the so2N-BMW algebra embeds in the q-Schur algebra of type A. We use these results to suggest a schema providing categorifications of the 2N-BMW algebra.
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GOODMAN, FREDERICK M., and HOLLY HAUSCHILD MOSLEY. "CYCLOTOMIC BIRMAN–WENZL–MURAKAMI ALGEBRAS, I: FREENESS AND REALIZATION AS TANGLE ALGEBRAS." Journal of Knot Theory and Its Ramifications 18, no. 08 (August 2009): 1089–127. http://dx.doi.org/10.1142/s0218216509007397.

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The cyclotomic Birman–Wenzl–Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We show that the cyclotomic BMW algebras are free modules over any admissible, integral ground ring, and that they are isomorphic to cyclotomic versions of the Kauffman tangle algebras.
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LARSEN, MICHAEL J., and ERIC C. ROWELL. "An algebra-level version of a link-polynomial identity of Lickorish." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (May 2008): 623–38. http://dx.doi.org/10.1017/s0305004107000424.

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AbstractWe establish isomorphisms between certain specializations of BMW algebras and the symmetric squares of Temperley–Lieb algebras. These isomorphisms imply a link-polynomial identity due to W. B. R. Lickorish. As an application, we compute the closed images of the irreducible braid group representations factoring over these specialized BMW algebras.
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Rui, Hebing, and Jie Xu. "The representations of cyclotomic BMW algebras." Journal of Pure and Applied Algebra 213, no. 12 (December 2009): 2262–88. http://dx.doi.org/10.1016/j.jpaa.2009.04.007.

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Cohen, Arjeh M., Dié A. H. Gijsbers, and David B. Wales. "BMW algebras of simply laced type." Journal of Algebra 286, no. 1 (April 2005): 107–53. http://dx.doi.org/10.1016/j.jalgebra.2004.12.011.

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Cui, Weideng. "Fusion Procedure for Cyclotomic BMW Algebras." Algebras and Representation Theory 21, no. 3 (August 23, 2017): 565–78. http://dx.doi.org/10.1007/s10468-017-9727-7.

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Si, Mei. "Morita equivalence for cyclotomic BMW algebras." Journal of Algebra 423 (February 2015): 573–91. http://dx.doi.org/10.1016/j.jalgebra.2014.10.034.

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Goodman, Frederick M. "Admissibility Conditions for Degenerate Cyclotomic BMW Algebras." Communications in Algebra 39, no. 2 (February 15, 2011): 452–61. http://dx.doi.org/10.1080/00927871003591918.

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Rui, Hebing, and Mei Si. "The Representations of Cyclotomic BMW Algebras, II." Algebras and Representation Theory 15, no. 3 (December 1, 2010): 551–79. http://dx.doi.org/10.1007/s10468-010-9249-z.

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Xu, Xu. "Decomposition numbers of cyclotomic NW and BMW algebras." Journal of Pure and Applied Algebra 217, no. 6 (June 2013): 1037–53. http://dx.doi.org/10.1016/j.jpaa.2012.09.027.

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Dissertations / Theses on the topic "BMW algebras"

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Yu, Shona Huimin. "The Cyclotomic Birman-Murakami-Wenzl Algebras." Thesis, The University of Sydney, 2007. http://hdl.handle.net/2123/3560.

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This thesis presents a study of the cyclotomic BMW algebras, introduced by Haring-Oldenburg as a generalization of the BMW (Birman-Murakami-Wenzl) algebras related to the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. The motivation behind the definition of the BMW algebras may be traced back to an important problem in knot theory; namely, that of classifying knots (and links) up to isotopy. The algebraic definition of the BMW algebras uses generators and relations originally inspired by the Kauffman link invariant. They are intimately connected with the Artin braid group of type A, Iwahori-Hecke algebras of type A, and with many diagram algebras, such as the Brauer and Temperley-Lieb algebras. Geometrically, the BMW algebra is isomorphic to the Kauffman Tangle algebra. The representations and the cellularity of the BMW algebra have now been extensively studied in the literature. These algebras also feature in the theory of quantum groups, statistical mechanics, and topological quantum field theory. In view of these relationships between the BMW algebras and several objects of "type A", several authors have since naturally generalized the BMW algberas for other types of Artin groups. Motivated by knot theory associated with the Artin braid group of type B, Haring-Oldenburg introduced the cyclotomic BMW algebras B_n^k as a generalization of the BMW algebras such that the Ariki-Koike algebra h_{n,k} is a quotient of B_n^k, in the same way the Iwahori-Hecke algebra of type A is a quotient of the BMW algebra. In this thesis, we investigate the structure of these algebras and show they have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. In particular, they are shown to be R-free of rank k^n (2n-1)!! and bases that may be explicitly described both algebraically and diagrammatically in terms of cylindrical tangles are obtained. Unlike the BMW and Ariki-Koike algebras, one must impose extra so-called "admissibility conditions" on the parameters of the ground ring in order for these results to hold. This is due to potential torsion caused by the polynomial relation of order k imposed on one of the generators of B_n^k. It turns out that the representation theory of B_2^k is crucial in determining these conditions precisely. The representation theory of B_2^k is analysed in detail in a joint preprint with Wilcox in [45] (http://arxiv.org/abs/math/0611518). The admissibility conditions and a universal ground ring with admissible parameters are given explicitly in Chapter 3. The admissibility conditions are also closely related to the existence of a non-degenerate Markov trace function of B_n^k which is then used together with the cyclotomic Brauer algebras in the linear independency arguments contained in Chapter 4. Furthermore, in Chapter 5, we prove the cyclotomic BMW algebras are cellular, in the sense of Graham and Lehrer. The proof uses the cellularity of the Ariki-Koike algebras (Graham-Lehrer [16] and Dipper-James-Mathas [8]) and an appropriate "lifting" of a cellular basis of the Ariki-Koike algebras into B_n^k, which is compatible with a certain anti-involution of B_n^k. When k = 1, the results in this thesis specialize to those previously established for the BMW algebras by Morton-Wasserman [30], Enyang [9], and Xi [47]. REMARKS: During the writing of this thesis, Goodman and Hauschild-Mosley also attempt similar arguments to establish the freeness and diagram algebra results mentioned above. However, they withdrew their preprints ([14] and [15]), due to issues with their generic ground ring crucial to their linear independence arguments. A similar strategy to that proposed in [14], together with different trace maps and the study of rings with admissible parameters in Chapter 3, is used in establishing linear independency of our basis in Chapter 4. Since the submission of this thesis, new versions of these preprints have been released in which Goodman and Hauschild-Mosley use alternative topological and Jones basic construction theory type arguments to establish freeness of B_n^k and an isomorphism with the cyclotomic Kauffman Tangle algebra. However, they require their ground rings to be an integral domain with parameters satisfying the (slightly stronger) admissibility conditions introduced by Wilcox and the author in [45]. Also, under these conditions, Goodman has obtained cellularity results. Rui and Xu have also obtained freeness and cellularity results when k is odd, and later Rui and Si for general k, under the assumption that \delta is invertible and using another stronger condition called "u-admissibility". The methods and arguments employed are strongly influenced by those used by Ariki, Mathas and Rui [3] for the cyclotomic Nazarov-Wenzl algebras and involve the construction of seminormal representations; their preprints have recently been released on the arXiv. It should also be noted there are slight differences between the definitions of cyclotomic BMW algebras and ground rings used, as explained partly above. Furthermore, Goodman and Rui-Si-Xu use a weaker definition of cellularity, to bypass a problem discovered in their original proofs relating to the anti-involution axiom of the original Graham-Lehrer definition. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.
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Yu, Shona Huimin. "The Cyclotomic Birman-Murakami-Wenzl Algebras." School of Mathematics and Statistics, 2007. http://hdl.handle.net/2123/3560.

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Doctor of Philosophy
This thesis presents a study of the cyclotomic BMW algebras, introduced by Haring-Oldenburg as a generalization of the BMW (Birman-Murakami-Wenzl) algebras related to the cyclotomic Hecke algebras of type G(k,1,n) (also known as Ariki-Koike algebras) and type B knot theory involving affine/cylindrical tangles. The motivation behind the definition of the BMW algebras may be traced back to an important problem in knot theory; namely, that of classifying knots (and links) up to isotopy. The algebraic definition of the BMW algebras uses generators and relations originally inspired by the Kauffman link invariant. They are intimately connected with the Artin braid group of type A, Iwahori-Hecke algebras of type A, and with many diagram algebras, such as the Brauer and Temperley-Lieb algebras. Geometrically, the BMW algebra is isomorphic to the Kauffman Tangle algebra. The representations and the cellularity of the BMW algebra have now been extensively studied in the literature. These algebras also feature in the theory of quantum groups, statistical mechanics, and topological quantum field theory. In view of these relationships between the BMW algebras and several objects of "type A", several authors have since naturally generalized the BMW algberas for other types of Artin groups. Motivated by knot theory associated with the Artin braid group of type B, Haring-Oldenburg introduced the cyclotomic BMW algebras B_n^k as a generalization of the BMW algebras such that the Ariki-Koike algebra h_{n,k} is a quotient of B_n^k, in the same way the Iwahori-Hecke algebra of type A is a quotient of the BMW algebra. In this thesis, we investigate the structure of these algebras and show they have a topological realization as a certain cylindrical analogue of the Kauffman Tangle algebra. In particular, they are shown to be R-free of rank k^n (2n-1)!! and bases that may be explicitly described both algebraically and diagrammatically in terms of cylindrical tangles are obtained. Unlike the BMW and Ariki-Koike algebras, one must impose extra so-called "admissibility conditions" on the parameters of the ground ring in order for these results to hold. This is due to potential torsion caused by the polynomial relation of order k imposed on one of the generators of B_n^k. It turns out that the representation theory of B_2^k is crucial in determining these conditions precisely. The representation theory of B_2^k is analysed in detail in a joint preprint with Wilcox in [45] (http://arxiv.org/abs/math/0611518). The admissibility conditions and a universal ground ring with admissible parameters are given explicitly in Chapter 3. The admissibility conditions are also closely related to the existence of a non-degenerate Markov trace function of B_n^k which is then used together with the cyclotomic Brauer algebras in the linear independency arguments contained in Chapter 4. Furthermore, in Chapter 5, we prove the cyclotomic BMW algebras are cellular, in the sense of Graham and Lehrer. The proof uses the cellularity of the Ariki-Koike algebras (Graham-Lehrer [16] and Dipper-James-Mathas [8]) and an appropriate "lifting" of a cellular basis of the Ariki-Koike algebras into B_n^k, which is compatible with a certain anti-involution of B_n^k. When k = 1, the results in this thesis specialize to those previously established for the BMW algebras by Morton-Wasserman [30], Enyang [9], and Xi [47]. REMARKS: During the writing of this thesis, Goodman and Hauschild-Mosley also attempt similar arguments to establish the freeness and diagram algebra results mentioned above. However, they withdrew their preprints ([14] and [15]), due to issues with their generic ground ring crucial to their linear independence arguments. A similar strategy to that proposed in [14], together with different trace maps and the study of rings with admissible parameters in Chapter 3, is used in establishing linear independency of our basis in Chapter 4. Since the submission of this thesis, new versions of these preprints have been released in which Goodman and Hauschild-Mosley use alternative topological and Jones basic construction theory type arguments to establish freeness of B_n^k and an isomorphism with the cyclotomic Kauffman Tangle algebra. However, they require their ground rings to be an integral domain with parameters satisfying the (slightly stronger) admissibility conditions introduced by Wilcox and the author in [45]. Also, under these conditions, Goodman has obtained cellularity results. Rui and Xu have also obtained freeness and cellularity results when k is odd, and later Rui and Si for general k, under the assumption that \delta is invertible and using another stronger condition called "u-admissibility". The methods and arguments employed are strongly influenced by those used by Ariki, Mathas and Rui [3] for the cyclotomic Nazarov-Wenzl algebras and involve the construction of seminormal representations; their preprints have recently been released on the arXiv. It should also be noted there are slight differences between the definitions of cyclotomic BMW algebras and ground rings used, as explained partly above. Furthermore, Goodman and Rui-Si-Xu use a weaker definition of cellularity, to bypass a problem discovered in their original proofs relating to the anti-involution axiom of the original Graham-Lehrer definition. This Ph.D. thesis, completed at the University of Sydney, was submitted September 2007 and passed December 2007.
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Rowell, Eric C. "On tensor categories arising from quantum groups and BMW-algebras at odd roots of unity /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3091329.

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Neaime, Georges. "Interval structures, Hecke algebras, and Krammer’s representations for the complex braid groups B(e,e,n)." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC214/document.

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Nous définissons des formes normales géodésiques pour les séries générales des groupes de réflexions complexes G(de,e,n). Ceci nécessite l'élaboration d'une technique combinatoire afin de déterminer des décompositions réduites et de calculer la longueur des éléments de G(de,e,n) sur un ensemble générateur donné. En utilisant ces formes normales géodésiques, nous construisons des intervalles dans G(e,e,n) qui permettent d'obtenir des groupes de Garside. Certains de ces groupes correspondent au groupe de tresses complexe B(e,e,n). Pour les autres groupes de Garside, nous étudions certaines de leurs propriétés et nous calculons leurs groupes d'homologie sur Z d'ordre 2. Inspirés par les formes normales géodésiques, nous définissons aussi de nouvelles présentations et de nouvelles bases pour les algèbres de Hecke associées aux groupes de réflexions complexes G(e,e,n) et G(d,1,n) ce qui permet d'obtenir une nouvelle preuve de la conjecture de liberté de BMR (Broué-Malle-Rouquier) pour ces deux cas. Ensuite, nous définissons des algèbres de BMW (Birman-Murakami-Wenzl) et de Brauer pour le type (e,e,n). Ceci nous permet de construire des représentations de Krammer explicites pour des cas particuliers des groupes de tresses complexes B(e,e,n). Nous conjecturons que ces représentations sont fidèles. Enfin, en se basant sur nos calculs heuristiques, nous proposons une conjecture sur la structure de l'algèbre de BMW
We define geodesic normal forms for the general series of complex reflection groups G(de,e,n). This requires the elaboration of a combinatorial technique in order to determine minimal word representatives and to compute the length of the elements of G(de,e,n) over some generating set. Using these geodesic normal forms, we construct intervals in G(e,e,n) that give rise to Garside groups. Some of these groups correspond to the complex braid group B(e,e,n). For the other Garside groups that appear, we study some of their properties and compute their second integral homology groups. Inspired by the geodesic normal forms, we also define new presentations and new bases for the Hecke algebras associated to the complex reflection groups G(e,e,n) and G(d,1,n) which lead to a new proof of the BMR (Broué-Malle-Rouquier) freeness conjecture for these two cases. Next, we define a BMW (Birman-Murakami-Wenzl) and Brauer algebras for type (e,e,n). This enables us to construct explicit Krammer's representations for some cases of the complex braid groups B(e,e,n). We conjecture that these representations are faithful. Finally, based on our heuristic computations, we propose a conjecture about the structure of the BMW algebra
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Levaillant, Claire Isabelle Wales David B. Wales David B. "Irreducibility of the Lawrence-Krammer representation of the BMW algebra of type An-1 /." Diss., Pasadena, Calif. : Caltech, 2008. http://resolver.caltech.edu/CaltechETD:etd-05292008-110016.

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Graber, John Eric. "Cellularity and Jones basic construction." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/292.

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This thesis establishes a framework for cellularity of algebras related to the Jones basic construction. The framework allows a uniform proof of cellularity of Brauer algebras, BMW algebras, walled Brauer algebras, partition algebras, and others. In this setting, the cellular bases are labeled by paths on certain branching diagrams rather than by tangles. Moreover, for this class of algebras, the cellular structures are compatible with restriction and induction of modules.
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Mei, Tao. "Operator valued Hardy spaces and related subjects." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4427.

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We give a systematic study of the Hardy spaces of functions with values in the non-commutative Lp-spaces associated with a semifinite von Neumann algebra M. This is motivated by matrix valued harmonic analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by non-commutative Lusin integral functions. It is proved in this dissertation that they are equivalent to those defined by the non-commutative Littlewood-Paley G-functions. We also study the Lp boundedness of operator valued dyadic paraproducts and prove that their Lq boundedness implies their Lp boundedness for all 1 < q < p < ∞.
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Hong, Guixiang. "Quelques problèmes en analyse harmonique non commutative." Phd thesis, Université de Franche-Comté, 2012. http://tel.archives-ouvertes.fr/tel-00979472.

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Cette thèse présente quelques résultats de la théorie des probabilités quantiques et de l'analyse harmonique non commutative. Elle est constituée de trois parties. La première partie démontre l'analogue non commutatif de l'inégalité de John-Nirenberg et la décomposition atomique pour les martingales non commutatives. Ces résultats étendent et améliorent ceux qui existent déjà, et correspondent exactement à ceux que l'on connaît dans le cas classique. La deuxième partie est consacrée à l'étude des espaces de Hardy à valeurs opérateurs via la méthode d'ondelettes. Il est montré que les espaces de Hardy définis par ondelettes coïncident avec ceux définis par les fonctions carrées de Littlewood-Paley et Lusin. Cette approche est similaire à celle du cas des martingales non commutatives, mais l'utilisation des outils de martingales en analyse harmonique permet une démonstration plus rapide. Dans la troisième partie, nous nous tournons vers des applications de la théorie bien établie des espaces de Hardy, c'est-à-dire des opérateurs de Calderón-Zygmund (OCZ pour abréviation) associés à des noyaux à valeurs matricielles. On obtient des estimations de type faible (1, 1) pour des OCZ dyadiques parfaites et des shifts de Haar annulateurs associés à des noyaux non commutatifs, ainsi que des estimations de type H1 → L1 pour des OCZ arbitaires d'après une décomposition d'une fonction en ligne/colonne. En conjonction avec L∞ → BMO, nous établissons certaines estimations de type Lp. Cette approche s'applique aussi à des paraproduits et des transformées de martingales avec des symboles et coefficients non commutatifs respectivement.
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Levaillant, Claire Isabelle. "Irreducibility of the Lawrence-Krammer Representation of the BMW Algebra of Type An-1." Thesis, 2008. https://thesis.library.caltech.edu/2255/1/thesis.pdf.

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We show that the Lawrence-Krammer representation of the BMW algebra of type An-1 over the field Q(l,r) is generically irreducible, but that for some values of the parameters l and r, when these are specialized in the field of complex numbers, it becomes reducible. When the representation is reducible, we describe the invariant subspaces by giving their dimension and some spanning vectors.
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Heglasová, Veronika. "Algebraicko-geometrické kódy a Gröbnerovy báze." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-324636.

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In this master thesis we introduce algebraic geometry codes (AG codes). Be- sides basic definitions, properties and attributes of AG codes and algebraic ge- ometry we show how to encode AG codes that has nontrivial Abelian group of permutation automorphisms and how to decode one-point AG codes. We also present Hermitian codes, which are example of one-point AG codes with nontriv- ial Abelian group of permutation automorphisms. We demonstrate the method for encoding and the method for decoding on specific Hermitian code. 1
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Books on the topic "BMW algebras"

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Simon, Barry. Harmonic analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "BMW algebras"

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Lehrer, G. I., and R. B. Zhang. "A Temperley–Lieb Analogue for the BMW Algebra." In Representation Theory of Algebraic Groups and Quantum Groups, 155–90. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4697-4_7.

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Sakata, Shojiro. "A vector version of the BMS algorithm for implementing fast erasure-and-error decoding of one-point AG codes." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 291–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63163-1_23.

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Minty, Michiko G., and Frank Zimmermann. "Polarization Issues." In Particle Acceleration and Detection, 239–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-08581-3_10.

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AbstractThe study of spin dynamics in synchrotrons has evolved over the years as has the desire for achieving polarized particle beams of the highest possible beam energies. A selection of reviews of the dynamics of polarized beams may be found in [1]–[9]. In this chapter, we focus on experimental data and describe spin transport in circular accelerators and transport lines. Except where explicitly mentioned, radiative effects in electron accelerators or very high energy proton accelerators are not treated here. We begin with a review of the Thomas-BMT equation for spin motion. This will be given in terms of the SU(2) spinor representation. Spinor algebra will be introduced and applied in the description of techniques used for preserving the beam polarization during acceleration through depolarizing resonances at moderate beam energies.
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"Backmatter." In Algebra, 318. De Gruyter, 2013. http://dx.doi.org/10.1515/9783110290714.bm.

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"Backmatter." In Lineare Algebra, 367–416. De Gruyter, 2003. http://dx.doi.org/10.1515/9783110200041.bm.

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Algebra leichtergemacht, 293–99. München: Oldenbourg Verlag, 2011. http://dx.doi.org/10.1524/9783486710847.bm.

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"Backmatter." In Algebraic Geometry, 347–55. De Gruyter, 2002. http://dx.doi.org/10.1515/9783110198072.bm.

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"Backmatter." In Approximations and Endomorphism Algebras of Modules. Berlin, New York: Walter de Gruyter, 2006. http://dx.doi.org/10.1515/9783110199727.bm.

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"Backmatter." In Applied Algebraic Dynamics. Berlin, New York: Walter de Gruyter, 2009. http://dx.doi.org/10.1515/9783110203011.bm.

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"Backmatter." In An Introduction to Abstract Algebra. Berlin, New York: Walter de Gruyter, 2003. http://dx.doi.org/10.1515/9783110198164.bm.

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Conference papers on the topic "BMW algebras"

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Miettinen, Pauli, and Stefan Neumann. "Recent Developments in Boolean Matrix Factorization." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/685.

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The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem is computationally hard, it is also attractive because the binary nature of the factor matrices makes them highly interpretable. In the last decade, BMF has received a considerable amount of attention in the data mining and formal concept analysis communities and, more recently, the machine learning and the theory communities also started studying BMF. In this survey, we give a concise summary of the efforts of all of these communities and raise some open questions which in our opinion require further investigation.
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Maltsev, Alexander, Amsini Sadiki, and Johannes Janicka. "Numerical Prediction of Partially Premixed Flames Based on Extended BML Model Coupled With Mixing Transport and ILDM Chemical Model." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38265.

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To improve the numerical prediction of partially premixed flames occurring in gas turbine combustors the extension of the well-known Bray-Moss-Libby model for premixed combustion is presented. The model modification based on the algebraic closure for a mean chemical source term is coupled to the mixing transport model providing variable equivalence ratio distinguishing partially premixed flames. Finite rate chemistry is incorporated by means of ILDM model solving transport equations for two reaction progress variables conditioned on the flame front. Multivariate presumed PDF model is used for the turbulence chemistry interaction treatment. Turbulence models of two levels of complexity are applied in order to investigate the influence of non-gradient turbulent transport phenomenon. Redistribution terms in second moment transport equations are extended to take into account strongly variable density effects. Model combinations considered are assessed simulating piloted partially premixed flame. The obtained results agree well with experimental data.
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Lara, Pedro Carlos da S., Felipe da R. Henriques, and Fábio B. de Oliveira. "Converting Symmetric Cryptography to SAT Problems Using Model Checking Tools." In Simpósio Brasileiro de Segurança da Informação e de Sistemas Computacionais. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/sbseg.2020.19226.

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Algebraic attack is a recent technique used to break symmetric cryptography including Crypto-1, which is used in smart NFC cards around the world. The main method is to convert a cryptography algorithm to a system of equations over a finite field, to translate it into a SAT problem and to use a good solver. The main advantage of converting cryptography problems into SAT is that we can use a lot of well know tools for SAT solving and test it in an instance. However, the high degree labor intensiveness on converting cryptography to SAT instances is a difficult task for advancement of research. To pursue this problem, this work presents a technique to quickly translate symmetric cryptography into SAT problems using Bounded Model Checking (BMC) tools. Computational experiments are performed, converting the RC4 and AES algorithms into a SAT problem.
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4

Knobbe, Henry, and Eberhard Nicke. "Shock Induced Vortices in Transonic Compressors: Aerodynamic Effects and Design Correlations." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-69004.

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Gas turbine total pressure ratio, efficiency and accurate stage matching prediction are of increasing importance in multi-stage compressor design. These highly challenging objectives can only be met if all components are highly loaded and optimally designed. Stage matching and efficiency improvements still depend on the designer’s experience and on empirical correlations. The upper blade part in highly loaded transonic compressors is especially difficult to design because of complex flow phenomena like compression shocks. On the one hand this region is of major interest, because of the high pressure ratios. On the other hand it is the most difficult area for the designer because of blade row interaction effects, tip leakage flows and high gradients in general. Recent publications investigated shock induced vortices (SIV), caused by the rotor bow shock. The shock interacts with the trailing edge of the upstream stator/IGV blade row. These vortices convect downstream through the rotor passage. But the unsteady flow phenomena inside transonic compressors are still worthwhile endeavor because of insufficient understanding regarding the unsteady effects onto the overall compressor performance. The vortex trajectory is predictable inside the rotor-passage. However, correlations for vorticity magnitude, vortex-frequency (number of vortices) and vortex-trajectory on the overall compressor performance were never described by equations. Furthermore it has not yet been clarified whether a small or a wide axial spacing is beneficial in highly loaded axial compressors. Therefore a transonic front stage (DLR Test Rig 250, 4 front stages of a state of the art gas turbine compressor) was chosen. The Q3D (quasi 3D) planes were extracted from 3D-Simulations for IGV/Rotor1 and Stator1/Rotor2. The approach is to separate the blade to blade effects from 3D effects, like tip leakage flow. This was achieved by different Q3D streamtubes in the upper blade part. These streamtubes allow a variation of the axial spacing without changing the steady flow solution. A wide range of the axial spacings have been simulated to get an overview about the resulting performance change. Furthermore a change of blade count ratio, inlet condition, outlet conditions and computational domain should lead to a better understanding. Physical relations between the shedded vortices and compressor overall performance should be derived. The results show a wide spreading of the compressor performance speedlines. This spreading indicates the unsteady effects caused by interaction effects. The spreading becomes wider towards the surge margin. The reduced number of IGVs result into a smaller spreading. The higher inlet temperature result into a neglectable change in data spreading. The changed computational domain (stator/rotor) result into a very small data spreading, compared to the front stage data distribution. The change of performance data is periodic to the established B3-factor [1]. This factor predicts the vortex trajectory inside the rotor passage. The analysis of rotor pre shock Mach number and blade count ratio leads to a systematic correlation factor (HK). This correlation takes the pre shock Mach number, the blade count ratio, the B3-factor and some algebraic elements into account to make a prediction of the unsteady effects regarding the total pressure ratio: HK = pt, unsteady−pt, steady. The developed correlations may be useful in 3D to calculate optimal axial spacings at a specific blade to blade plane or to make compressor performance prediction during the design process based on RANS-Simulations (reduced gap between simulation and measurement). Furthermore it was identified that neither a wide nor a short axial spacing is beneficial for a transonic compressor inside a blade to blade plane.
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