Relevant bibliographies by topics / Lie group

Contents

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

Academic literature on the topic 'Lie group'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2025

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Journal articles on the topic "Lie group"

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Merati, S., and M. R. Farhangdoost. "Hom-Lie group and hom-Lie algebra from Lie group and Lie algebra perspective." International Journal of Geometric Methods in Modern Physics 18, no. 05 (January 29, 2021): 2150068. http://dx.doi.org/10.1142/s0219887821500687.

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A hom-Lie group structure is a smooth group-like multiplication on a manifold, where the structure is twisted by a isomorphism. The notion of hom-Lie group was introduced by Jiang et al. as integration of hom-Lie algebra. In this paper we want to study hom-Lie group and hom-Lie algebra from the Lie group’s point of view. We show that some of important hom-Lie group issues are equal to similar types in Lie groups and then many of these issues can be studied by Lie group theory.
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Iserles, Arieh, Hans Z. Munthe-Kaas, Syvert P. Nørsett, and Antonella Zanna. "Lie-group methods." Acta Numerica 9 (January 2000): 215–365. http://dx.doi.org/10.1017/s0962492900002154.

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Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Lie-group structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Lie-group structure, highlighting theory, algorithmic issues and a number of applications.
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Pham, David N. "On the tangent Lie group of a symplectic Lie group." Ricerche di Matematica 68, no. 2 (January 29, 2019): 699–704. http://dx.doi.org/10.1007/s11587-019-00434-2.

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Rybicki, Tomasz. "A Lie group structure on strict groups." Publicationes Mathematicae Debrecen 61, no. 3-4 (October 1, 2002): 533–48. http://dx.doi.org/10.5486/pmd.2002.2670.

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Shtern, A. I. "Connected Lie Groups Admitting an Embedding in a Connected Amenable Lie Group." Russian Journal of Mathematical Physics 26, no. 4 (October 2019): 499–500. http://dx.doi.org/10.1134/s1061920819040083.

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Lichnerowicz, Andr�. "Characterization of Lie groups on the cotangent bundle of a Lie group." Letters in Mathematical Physics 12, no. 2 (August 1986): 111–21. http://dx.doi.org/10.1007/bf00416461.

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Khalili, Valiollah. "On the structure of graded 3-Lie-Rinehart algebras." Filomat 38, no. 2 (2024): 369–92. http://dx.doi.org/10.2298/fil2402369k.

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We study the structure of a graded 3-Lie-Rinehart algebraLover an associative and commutative graded algebra A. For G an abelian group, we show that if (L,A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as L = ? i?I Li and A = ? j?J Aj, where any Li is a non-zero graded ideal of L satisfying [Li1 ,Li2 ,Li3] = 0 for any i1, i2, i3 ? I different from each other, and any Aj is a non-zero graded ideal of A satisfying AjAl = 0 for any l, j ? J such that j ?l, and both decompositions satisfy that for any i ? I there exists a unique j ? J such that AjLi ? 0. Furthermore, any (Li,Aj) is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is shown that the above decompositions of L and A are by means of the family of their, respectively, graded simple ideals.
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Glöckner, Helge. "Lie Group Structures on Quotient Groups and Universal Complexifications for Infinite-Dimensional Lie Groups." Journal of Functional Analysis 194, no. 2 (October 2002): 347–409. http://dx.doi.org/10.1006/jfan.2002.3942.

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Cárdenas, Cristian Camilo, and Ivan Struchiner. "Stability of Lie group homomorphisms and Lie subgroups." Journal of Pure and Applied Algebra 224, no. 3 (March 2020): 1280–96. http://dx.doi.org/10.1016/j.jpaa.2019.07.017.

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Kamber, Franz W., and Peter W. Michor. "Completing Lie algebra actions to Lie group actions." Electronic Research Announcements of the American Mathematical Society 10, no. 1 (February 18, 2004): 1–10. http://dx.doi.org/10.1090/s1079-6762-04-00124-6.

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Dissertations / Theses on the topic "Lie group"

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pl, tomasz@uci agh edu. "A Lie Group Structure on Strict Groups." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1076.ps.

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Harkins, Andrew. "Combining lattices of soluble lie groups." Thesis, University of Newcastle Upon Tyne, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341777.

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Belliart, Michel. "Actions de groupes de Lie sur les variétés compactes." Valenciennes, 1995. https://ged.uphf.fr/nuxeo/site/esupversions/9806b24c-e64d-4e28-b75a-6d3de2b5eb3a.

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Cette thèse est en deux parties. Dans la première partie, on énonce, justifie et montre partiellement la conjecture suivante : L'action localement libre de codimension 1, au moins deux fois continument différentiable et préservant le volume d'un groupe de Lie non-unimodulaire sur une variété compacte est conjuguée dans sa classe de différentiabilité à une action homogène. On fournit également des exemples de groupes auxquels ce résultat s'applique. Dans la seconde partie, on répond complètement au problème suivant, posé par J. F. Plante en 1986 : A quelles conditions un groupe de Lie connexe donné peut-il agir continument et sans point fixe global sur une surface compacte donnée ? On en déduit une réponse à trois questions posées par Plante dans le même domaine. Ces deux résultats constituent la partie originale de la thèse. Ils sont précédés de deux survols, l'un de la théorie de Lie, l'autre de celle des surfaces, et la seconde partie est suivie d'une copie du dernier chapitre de la thèse de Mostow, ce qui en facilite la lecture.
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Lupi, Giulia. "Kernel approximations in Lie groups and application to group-invariant CNN." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23905/.

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In questa tesi viene studiata un'equazione di convezione-diffusione-erosione introdotta in problemi di image processing. In particolare, si cercano approssimazioni dei nuclei per l'equazione di diffusione e per l'equazione di erosione. Per fare tali approssimazioni si é utilizzato il metodo della parametrice per l'equazione di diffusione, mentre il nucleo dell'equazione di erosione viene trovato a partire dal nucleo dell'equazione di diffusione attraverso la trasformata di Cramér-Fuorier.
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Niederkrüger, Klaus. "Compact Lie group actions on contact manifolds." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975890360.

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Shingel, Tatiana. "Structured approximation in a lie group setting." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611555.

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Sandfeldt, Sven. "Local Rigidity of Some Lie Group Actions." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-272842.

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In this paper we study local rigidity of actions of simply connected Lie groups. In particular, we apply the Nash-Moser inverse function theorem to give sufficient conditions for the action of a simply connected Lie group to be locally rigid. Let $G$ be a Lie group, $H < G$ a simply connected subgroup and $\Gamma < G$ a cocompact lattice. We apply the result for general actions of simply connected groups to obtain sufficient conditions for the action of $H$ on $\Gamma\backslash G$ by right translations to be locally rigid. We also discuss some possible applications of this sufficient condition
I den här texten så studerar vi lokal rigiditet av gruppverkan av enkelt sammanhängande Liegrupper. Mer specifikt, vi applicerar Nash-Mosers inversa funktionssats för att ge tillräckliga villkor för att en gruppverkan av en enkelt sammanhängande grupp ska vara lokalt rigid. Låt $G$ vara en Lie grupp, $H < G$ en enkelt sammanhängande delgrupp och $\Gamma < G$ ett kokompakt gitter. Vi applicerar resultatet för generella gruppverkan av enkelt sammanhängande grupper för att få tillräckliga villkor för att verkan av $H$ på $\Gamma\backslash G$ med translationer ska vara lokalt rigid. Vi diskuterar också några möjliga tillämpningar av det tillräckliga villkoret.
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Karki, Manoj Babu. "Invariant Riemannain metrics on four-dimensional Lie group." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1438906778.

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Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either a linear or exponential upper bound; also we show that for certain polycyclic metabelian groups it is at most exponential. We also investigate how taking a wreath product effects conjugacy length, as well as other group extensions. The Magnus embedding is an important tool in the study of free solvable groups. It embeds a free solvable group into a wreath product of a free abelian group and a free solvable group of shorter derived length. Within this thesis we show that the Magnus embedding is a quasi-isometric embedding. This result is not only used for obtaining an upper bound on the conjugacy length function of free solvable groups, but also for giving a lower bound for their Lp compression exponents. Conjugacy length is also studied between certain types of elements in lattices of higher-rank semisimple real Lie groups. In particular we obtain linear upper bounds for the length of a conjugator from the ambient Lie group within certain families of real hyperbolic elements and unipotent elements. For the former we use the geometry of the associated symmetric space, while for the latter algebraic techniques are employed.
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Giroux, Yves. "Degenerate enveloping algebras of low-rank groups." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74026.

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Books on the topic "Lie group"

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Duistermaat, J. J. Lie groups. Berlin: Springer, 2000.

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Bröcker, Theodor. Representations of compact Lie groups. New York: Springer-Verlag, 1985.

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Bröcker, Theodor. Representations of compact Lie groups. 2nd ed. New York: Springer, 1995.

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Sabinin, Lev V. Mirror geometry of lie algebras, lie groups, and homogeneous spaces. New York: Kluwer Academic Publishers, 2004.

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Onishchik, Arkadij L. Lie Groups and Algebraic Groups. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990.

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Akhiezer, Dmitri N. Lie Group Actions in Complex Analysis. Wiesbaden: Vieweg+Teubner Verlag, 1995. http://dx.doi.org/10.1007/978-3-322-80267-5.

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Akhiezer, Dmitri N. Lie group actions in complex analysis. Wiesbaden: Vieweg, 1995.

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Ibragimov, Nail H. Selected works: Lie group analysis, differential equations, Riemannian geometry, Lie-Ba cklund groups, mathematical physics. Karlskrona: ALGA Publications, 2006.

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Robert, Gilmore. Lie Groups, Physics, and Geometry: An Introduction for Physicists, Engineers and Chemists. Leiden: Cambridge University Press, 2008.

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Heinrich, Hofmann Karl. Lie groups and subsemigroups with surjective exponential fuction. Providence, R.I: American Mathematical Society, 1997.

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Book chapters on the topic "Lie group"

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Soh, Gim Song. "Lie Group." In Encyclopedia of Robotics, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-642-41610-1_132-1.

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Majumdar, Manjusha, and Arindam Bhattacharyya. "Lie Group." In An Introduction to Smooth Manifolds, 175–207. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0565-2_4.

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Sato, Ryuzo. "Group (Lie Group) Theory." In The New Palgrave Dictionary of Economics, 5538–41. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-349-95189-5_959.

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Sato, Ryuzo. "Group (Lie Group) Theory." In The New Palgrave Dictionary of Economics, 1–5. London: Palgrave Macmillan UK, 1987. http://dx.doi.org/10.1057/978-1-349-95121-5_959-1.

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Sharma, Ramesh, and Sharief Deshmukh. "Lie Group and Lie Derivative." In Infosys Science Foundation Series, 17–25. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-9258-4_2.

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Gan, Woon Siong. "Lie Group and Lie Algebra." In Time Reversal Acoustics, 7–13. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-3235-8_2.

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Gao, Xiang, and Tao Zhang. "Lie Group and Lie Algebra." In Introduction to Visual SLAM, 63–86. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4939-4_3.

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San Martin, Luiz A. B. "Lie Group Actions." In Lie Groups, 267–98. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7_13.

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Michor, Peter. "Lie groups and group actions." In Graduate Studies in Mathematics, 41–97. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/093/02.

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Schwichtenberg, Jakob. "Lie Group Theory." In Undergraduate Lecture Notes in Physics, 25–89. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19201-7_3.

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Conference papers on the topic "Lie group"

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Liang, Yuxuan, Yibing Li, and Tao Jiang. "Lie Group-Based Detector for Signal Detection." In 2024 IEEE INC-USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), 240–41. IEEE, 2024. http://dx.doi.org/10.23919/inc-usnc-ursi61303.2024.10632326.

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Seo, Joohwan, Nikhil Potu Surya Prakash, Jongeun Choi, and Roberto Horowitz. "A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control." In 2024 American Control Conference (ACC), 1335–42. IEEE, 2024. http://dx.doi.org/10.23919/acc60939.2024.10644201.

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Xu, Xinpeng, Yukai Du, and Chuan Qin. "Lie Group-Based Optimization of the Greater Cane Rat Algorithm." In 2024 International Symposium on Parallel Computing and Distributed Systems (PCDS), 1–10. IEEE, 2024. http://dx.doi.org/10.1109/pcds61776.2024.10743786.

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Huang, Yini, and Xiaopeng Luo. "A Method Based on Lie Group Machine Learning for Multivariate Time-Series Clustering." In 2024 6th International Conference on Data-driven Optimization of Complex Systems (DOCS), 638–43. IEEE, 2024. http://dx.doi.org/10.1109/docs63458.2024.10704262.

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Forest, Étienne, James Murphy, and Michael F. Reusch. "Explicit Lie group integrators." In Nonlinear−dynamics and particle acceleration. AIP, 1991. http://dx.doi.org/10.1063/1.40779.

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Yan, Yusong, and Hongmei Zhu. "Invertible Integer Lie Group Transforms." In 2009 Data Compression Conference (DCC). IEEE, 2009. http://dx.doi.org/10.1109/dcc.2009.38.

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Yang, Mengduo, and Fanzhang Li. "Lie group impression for deep learning." In 2017 International Smart Cities Conference (ISC2). IEEE, 2017. http://dx.doi.org/10.1109/isc2.2017.8090853.

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Christandl, Matthias, Brent Doran, and Michael Walter. "Computing Multiplicities of Lie Group Representations." In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2012. http://dx.doi.org/10.1109/focs.2012.43.

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Wang, Zhichao, and Victor Solo. "Lie Group State Estimation via Optimal Transport." In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2020. http://dx.doi.org/10.1109/icassp40776.2020.9053636.

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Tian, YiMin. "A Numerical Experiment on Lie Group Method." In 2010 Ninth International Symposium on Distributed Computing and Applications to Business, Engineering and Science (DCABES). IEEE, 2010. http://dx.doi.org/10.1109/dcabes.2010.20.

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Reports on the topic "Lie group"

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Cranfill, C. W., S. V. Coggeshall, C. E. Knapp, D. P. Smitherman, E. J. Caramana, and R. A. Axford. Lie group applications to the solution of differential equations. Office of Scientific and Technical Information (OSTI), August 1997. http://dx.doi.org/10.2172/515634.

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Boumaiza, Mohamed. Poisson-Lie Structure on the Tangent Bundle of a Poisson-Lie Group and Poisson Action Lifting. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-4-2005-1-18.

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O'Rourke, Patrick, and Scott Ramsey. Lectures on Lie Group Analysis: Solving Differential Equations Using Symmetries. Office of Scientific and Technical Information (OSTI), September 2024. http://dx.doi.org/10.2172/2447587.

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Jaegers, Peter James. Lie group invariant finite difference schemes for the neutron diffusion equation. Office of Scientific and Technical Information (OSTI), June 1994. http://dx.doi.org/10.2172/10165908.

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Slawianowski, Jan J., Vasyl Kovalchuk, Agnieszka Martens, and Barbara Golubowska. Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mehanics on Lie Groups and Meyhods of Group Algebras. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-22-2011-67-94.

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Shai, Yechiel, Arthur Aronson, Aviah Zilberstein, and Baruch Sneh. Study of the Basis for Toxicity and Specificity of Bacillus thuringiensis d-Endotoxins. United States Department of Agriculture, January 1996. http://dx.doi.org/10.32747/1996.7573995.bard.

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The report contains three parts which summarizes the three years achievements of the three participating research groups; The Weizmann group, Tel-Aviv group and Purdue group. The firs part describes the achievements obtained by Shai's group toward the elucidation of the mechanism of membrane insertion and the structural organization of the pores formed by the Cry3A and Cry1Ac B. thuringiensis d-endotoxins. For that purpose Shai's group synthesized, fluorescently labeled and structurally and functionally characterized peptides corresponding to the seven helices that compose the pore-forming domain of Cry3A toxin, including mutants peptides and the hairpin a4G-a5 of both Cry3A and Cry 1Ac toxins composed of a4, a5 and the loop connecting a4-a5. Among the synthesized peptides were three mutated a4 helices based on site directed mutagenesis done at Aronson's group that decreased or increased Cry 1Ac toxicity. The results of these studies are consistent with a situation in which only helices a4 anda5 insert into the membrane as a helical hairpin in an antiparallel manner, while the other helices lie on the membrane surface like ribs of an umbrella (the "umbrella model"). In order to test this model Shai's group synthesized the helical hairpin a4<-->a5 of both Cry3A and Cry 1 Ac toxins, as well. Initial functional and structural studies showed direct correlation between the properties of the mutated helices and the mutated Cry1Ac. Based on Shai's findings that a4 is the second helix besides a5 that insert into the membrane, Aronson and colleagues performed extensive mutation on this helix in the CrylAc toxin, as well as in the loop connecting helices 4 and 5, and helix 3 (part two of the report). In addition, Aronson performed studies on the effect of mutations or type of insect which influence the oligomerization either the Cry 1Ab or Cry 1Ac toxins with vesicles prepared from BBMV. In the third part of the report Zilberstein's and Sneh's groups describe their studies on the three domains of Cry 1C, Cry 1E and crylAc and their interaction with the epithelial membrane of the larval midgut. In these studies they cloned all three domains and combinations of two domains, as well as cloning of the pore forming domain alone and studying its interaction with BBMV. In addition they investigated binding of Cry1E toxin and Cry1E domains to BBMV prepared from resistant (R) or sensitive larvae. Finally they initiated expression of the loop a4G<-->a5 Cry3A in E. coli to be compared with the synthetic one done by Shai's group as a basis to develop a system to express all possible pairs for structural and functional studies by Shai's group (together with Y. Shai).
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Howard, Jo. Practical Guides for Participatory Methods: Rivers of Life. Institute of Development Studies, January 2023. http://dx.doi.org/10.19088/ids.2023.001.

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Through drawing of a river, this method helps to access and communicate personal experiences, and facilitate group dialogue around the issues that the groups themselves identify. The expectation is that, through staged group activities moving from individual activity to group discussion, trust and rapport can be built with the researcher, and between the participants.
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Arvanitoyeorgos, Andreas. Lie Transformation Groups and Geometry. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-11-35.

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Mascagni, Giulia, Roel Dom, and Fabrizio Santoro. The VAT in Practice: Equity, Enforcement and Complexity. Institute of Development Studies (IDS), January 2021. http://dx.doi.org/10.19088/ictd.2021.002.

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The value added tax (VAT) is supposed to be a tax on consumption that achieves greater economic efficiency than alternative indirect taxes. It is also meant to facilitate enforcement through the ‘self-enforcing mechanism’ – based on opposed incentives for buyers and sellers, and because of the paper trail it creates. Being a rather sophisticated tax, however, the VAT is complex to administer and costly to comply with, especially in lower-income countries. This paper takes a closer look at how the VAT system functions in practice in Rwanda. Using a mixed-methods approach, which combines qualitative information from focus group discussions with the analysis of administrative and survey data, we document and explain a number of surprising inconsistencies in the filing behaviour of VAT-remitting firms, which lead to suboptimal usage of electronic billing machines, as well as failure to claim legitimate VAT credits. The consequence of these inconsistencies is twofold. It makes it difficult for the Rwanda Revenue Authority to exploit its VAT data to the fullest, and leads to firms, particularly smaller ones, bearing a higher VAT burden than larger ones. There are several explanations for these inconsistencies. They appear to lie in a combination of taxpayer confusion, fear of audit, and constraints in administrative capacity.
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Axford, R. A. Construction of Difference Equations Using Lie Groups. Office of Scientific and Technical Information (OSTI), August 1998. http://dx.doi.org/10.2172/1172.

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