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Relevant bibliographies by topics / Units in rings and group rings

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Academic literature on the topic 'Units in rings and group rings'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Units in rings and group rings"

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Jespers, Eric, and C. Polcino Milies. "Units of group rings." Journal of Pure and Applied Algebra 107, no. 2-3 (March 1996): 233–51. http://dx.doi.org/10.1016/0022-4049(95)00066-6.

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Kumari, P., M. Sahai, and R. K. Sharma. "Jordan regular units in rings and group rings." Ukrains’kyi Matematychnyi Zhurnal 75, no. 3 (April 11, 2023): 351–63. http://dx.doi.org/10.37863/umzh.v75i3.1130.

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UDC 512.5 The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma and Yadav in <em>Lie regular generators of general linear groups</em>, Comm. Algebra, <strong>40</strong>, № 4, 1304–1315 (2012)]. We introduce Jordan regular elements and Jordan regular units. It is proved that the order of the set of Jordan regular units in M ( 2 , Z 2 n ) is equal to a half of the order of U ( M ( 2 , Z 2 n ) ) . Further, we show that the group ring K G of a group G over a field K of characteristic 2 has no Jordan regular units.

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Bartholdi, Laurent. "On Gardam's and Murray's units in group rings." Algebra and Discrete Mathematics 35, no. 1 (2023): 22–29. http://dx.doi.org/10.12958/adm2053.

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We show that the units found in torsion-free group rings by Gardam are twisted unitary elements. This justifies some choices in Gardam's construction that might have appeared arbitrary, and yields more examples of units. We note that all units found up to date exhibit non-trivial symmetry.

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Farkas, Daniel R., and Peter A. Linnell. "Trivial Units in Group Rings." Canadian Mathematical Bulletin 43, no. 1 (March 1, 2000): 60–62. http://dx.doi.org/10.4153/cmb-2000-008-0.

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AbstractLet G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.

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Bist, V. "Torsion units in group rings." Publicacions Matemàtiques 36 (January 1, 1992): 47–50. http://dx.doi.org/10.5565/publmat_36192_04.

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Chatzidakis, Zoé, and Peter Pappas. "Units in Abelian Group Rings." Journal of the London Mathematical Society s2-44, no. 1 (August 1991): 9–23. http://dx.doi.org/10.1112/jlms/s2-44.1.9.

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Dekimpe, Karel. "Units in group rings of crystallographic groups." Fundamenta Mathematicae 179, no. 2 (2003): 169–78. http://dx.doi.org/10.4064/fm179-2-4.

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Herman, Allen, Yuanlin Li, and M. M. Parmenter. "Trivial Units for Group Rings with G-adapted Coefficient Rings." Canadian Mathematical Bulletin 48, no. 1 (March 1, 2005): 80–89. http://dx.doi.org/10.4153/cmb-2005-007-1.

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AbstractFor each finite group G for which the integral group ring ℤG has only trivial units, we give ring-theoretic conditions for a commutative ring R under which the group ring RG has nontrivial units. Several examples of rings satisfying the conditions and rings not satisfying the conditions are given. In addition, we extend a well-known result for fields by showing that if R is a ring of finite characteristic and RG has only trivial units, then G has order at most 3.

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Herman, Allen, and Yuanlin Li. "Trivial units for group rings over rings of algebraic integers." Proceedings of the American Mathematical Society 134, no. 3 (July 18, 2005): 631–35. http://dx.doi.org/10.1090/s0002-9939-05-08018-4.

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Hoechsmann, K., and S. K. Sehgal. "Integral Group Rings Without Proper Units." Canadian Mathematical Bulletin 30, no. 1 (March 1, 1987): 36–42. http://dx.doi.org/10.4153/cmb-1987-005-6.

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AbstractIf A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.

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Dissertations / Theses on the topic "Units in rings and group rings"

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Li, Yuanlin. "Units in integral group rings." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/nq23107.pdf.

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Ferguson, Ronald Aubrey. "Units in integral cyclic group rings for order L§RP§S." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq25045.pdf.

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Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/368142.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.

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Faccin, Paolo. "Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras." Doctoral thesis, University of Trento, 2014. http://eprints-phd.biblio.unitn.it/1182/1/PhdThesisFaccinPaolo.pdf.

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In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.

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Silva, Renata Rodrigues Marcuz. "Unidades de ZC2p e Aplicações." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-27062012-154612/.

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Seja p um número primo e seja uma raiz p - ésima primitiva da unidade. Considere os seguintes elementos i := 1 + + 2 + ... + i-1 para todo 1 i k do anel Z[] onde k = (p-1)/2. Nesta tese nós descrevemos explicitamente um conjunto gerador para o grupo das unidades do anel de grupo integral ZC2p; representado por U(ZC2p); onde C2p representa o grupo cíclico de ordem 2p e p satisfaz as seguintes condições: S := { -1, , u2, ... uk } gera U(Z[]) e U(Zp) = ou U(Zp)2 = e -1 U(Zp); que são verificadas para p = 7; 11; 13; 19; 23; 29; 53; 59; 61 e 67. Com o intuito de estender tais ideias encontramos um conjunto gerador para U(Z(C2p x C2) e U(Z(C2p x C2 x C2) onde p satisfaz as mesmas condições anteriores acrescidas de uma nova hipótese. Finalmente com o auxílio dos resultados anteriores apresentamos um conjunto gerador das unidades centrais do anel de grupo Z(Cp x Q8); onde Q8 representa o grupo dos quatérnios, ou seja, Q8 := .
Let p be an odd prime integer, be a pth primitive root of unity, Cn be the cyclic group of order n, and U(ZG) the units of the Integral Group Ring ZG: Consider ui := 1++2 +: : :+i1 for 2 i p + 1 2 : In our study we describe explicitly the generator set of U(ZC2p); where p is such that S := f1; ; u2; : : : ; up1 2 g generates U(Z[]) and U(Zp) is such that U(Zp) = 2 or U(Zp)2 = 2 and 1 =2 U(Zp)2; which occurs for p = 7; 11; 13; 19; 23; 29; 37; 53; 59; 61, and 67: For another values of p we don\'t know if such conditions hold. In addition, under suitable hypotheses, we extend these ideas and build a generator set of U(Z(C2p C2)) and U(Z(C2p C2 C2)): Besides that, using the previous results, we exhibit a generator set for the central units of the group ring Z(Cp Q8) where Q8 represents the quaternion group.

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Kitani, Patricia Massae. "Unidades de ZCpn." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-26042012-235529/.

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Seja Cp um grupo cíclico de ordem p, onde p é um número primo tal que S = {1, , 1+\\theta, 1+\\theta+\\theta^2, · · · , 1 +\\theta + · · · + \\theta ^{p-3/2}} gera o grupo das unidades de Z[\\theta] e é uma raiz p-ésima primitiva da unidade sobre Q. No artigo \"Units of ZCp\" , Ferraz apresentou um modo simples de encontrar um conjunto de geradores independentes para o grupo das unidades do anel de grupo ZCp sobre os inteiros. Nós estendemos este resultado para ZCp^n , considerando que um conjunto similar a S gera o grupo das unidades de Z[\\theta]. Isto ocorre, por exemplo, quando \\phi(p^n)\\leq 66. Descrevemos o grupo das unidades de ZCp^n como o produto ±ker(\\pi_1) × Im(\\pi1), onde \\pi_1 é um homomorfismo de grupos. Além disso, explicitamos as bases de ker(\\pi_1) e Im(\\pi_1).
Let Cp be a cyclic group of order p, where p is a prime integer such that S = {1, , 1 + \\theta, 1 +\\theta +\\theta ^2 , · · · , 1 + \\theta + · · · +\\theta ^{p-3/2}} generates the group of units of Z[\\theta] and is a primitive pth root of 1 over Q. In the article \"Units of ZCp\" , Ferraz gave an easy way to nd a set of multiplicatively independent generators of the group of units of the integral group ring ZCp . We extended this result for ZCp^n , provided that a set similar to S generates the group of units of Z[\\theta]. This occurs, for example, when \\phi(p^n)\\leq 66. We described the group of units of ZCp^n as the product ±ker(\\pi_1) × Im(\\pi_1), where \\pi_1 is a group homomorphism. Moreover, we explicited a basis of ker(\\pi_1) and I m(\\pi_1).

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Stack, Cora. "Some results on the structure of the groups of units of finite completely primary rings and on the structure of finite dimensional nilpotent algebras." Thesis, University of Reading, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262483.

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Filho, Antonio Calixto de Souza. "A importância das unidades centrais em anéis de grupo." Universidade de São Paulo, 2000. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-11122008-214317/.

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Na presente dissertação, discutimos o Problema do Isomorfismo em anéis de grupo para grupos infinitos da forma G × C, apresentado no artigo de Mazur [14], que enuncia um teorema mostrando a equivalência para o Problema do Isomorfismo entre essa classe de grupos infinitos e grupos finitos que satisfaçam a Conjectura do Normalizador. Nossa ênfase concentra-se na relação entre a Conjectura do Isomorfismo e a Conjectura do Normalizador, primeiramente, observada nesse artigo. Em seguida, consideramos um teorema de estrutura para as unidades centrais em anéis de grupo comunicado, pela primeira vez, no artigo de Jespers-Parmenter-Sehgal [9], e generalizado por Polcino Milies-Sehgal em [17], e Jespers-Juriaans em [7]. Evidenciamos a importância desse teorema para a Teoria de Anéis de Grupo e apresentamos uma nova demonstração para o teorema de equivalência de Mazur, considerando, para tanto, uma apropriada unidade central e sua estrutura, caracterizada pelo teorema comunicado para as unidades centrais. Concluímos a dissertação, descrevendo a construção do grupo das unidades centrais para o anel de grupo ZA5 , um grupo livre finitamente gerado de posto 1, utilizando a construção dada no artigo de Aleev [1].
In this dissertation, we discuss the Problem of the Isomorphism in group rings for infinite groups as G × C. This is presented in [14]. Such article states a theorem which shows an equivalence to the isomorphism problem between that infinite class group and finite groups verifying the Normalizer Conjecture. Our main purpose is the Normalizer Conjecture and the Isomorphism Conjecture relationship remarked in the cited article to the groups above. Following, we consider a group ring theorem to the central units subgroup firstly communicated in [9] and generalized in [17] and [7]. We point up the importance of such theorem to the Group Ring Theory and we give a short and a new demonstration to Mazurs equivalence theorem from using a suitable central unit altogether with its structure lightly by the Central Unit Theorem on focus. We conclude this work sketching the ZA5 central units subgroup on showing it is a free finitely generated group of rank 1 from the presenting construction in Aleevs article [1].

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Immormino, Nicholas A. "Clean Rings & Clean Group Rings." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1374247918.

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Weber, Harald. "Group rings and twisted group rings for a series of p-groups." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10761310.

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Books on the topic "Units in rings and group rings"

1

Sehgal, Sudarshan K. Units in integral group rings. Burnt Mill, Harlow, Essex, England: Longman Scientific & Technical, 1993.

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2

Unit groups of group rings. London: Longman Scientific & Technical, 1989.

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Karpilovsky, Gregory. Unit groups of group rings. Harlow, Essex, England: Longman Scientific & Technical, 1989.

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Group identities on units and symmetric units of group rings. London: Springer, 2010.

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Lee, Gregory T. Group Identities on Units and Symmetric Units of Group Rings. London: Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-504-0.

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Unit groups of classical rings. Oxford: Clarendon Press, 1988.

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Giambruno, Antonio, César Polcino Milies, and Sudarshan K. Sehgal, eds. Groups, Rings and Group Rings. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/conm/499.

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A, Giambruno, Milies César Polcino, and Sehgal Sudarshan K. 1936-, eds. Groups, rings, and group rings. Boca Raton: Chapman & Hall/CRC, 2006.

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Free group rings. Providence, R.I: American Mathematical Society, 1987.

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Bergen, Jeffrey, Stefan Catoiu, and William Chin, eds. Groups, Rings, Group Rings, and Hopf Algebras. Providence, Rhode Island: American Mathematical Society, 2017. http://dx.doi.org/10.1090/conm/688.

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Book chapters on the topic "Units in rings and group rings"

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Roggenkamp, Klaus W., and Martin J. Taylor. "Global units." In Group Rings and Class Groups, 60–73. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8611-6_8.

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Polcino Milies, César, and Sudarshan K. Sehgal. "Units of Group Rings." In Algebras and Applications, 233–86. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0405-3_8.

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Roggenkamp, Klaus W., and Martin J. Taylor. "The leading coefficient of units." In Group Rings and Class Groups, 15–20. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8611-6_4.

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Lee, Gregory T. "Group Identities on Units of Group Rings." In Group Identities on Units and Symmetric Units of Group Rings, 1–43. London: Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-504-0_1.

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Parmenter, M. M. "Central Units in Integral Group Rings." In Algebra, 111–16. Gurgaon: Hindustan Book Agency, 1999. http://dx.doi.org/10.1007/978-93-80250-94-6_8.

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Parmenter, M. M. "Central Units in Integral Group Rings." In Algebra, 111–16. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-9996-3_8.

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Bhandari, Ashwani K., and I. B. S. Passi. "Unit Groups of Group Rings." In Algebra, 29–39. Gurgaon: Hindustan Book Agency, 1999. http://dx.doi.org/10.1007/978-93-80250-94-6_2.

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Bhandari, Ashwani K., and I. B. S. Passi. "Unit Groups of Group Rings." In Algebra, 29–39. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-9996-3_2.

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Bächle, Andreas, Wolfgang Kimmerle, and Leo Margolis. "Algorithmic Aspects of Units in Group Rings." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 1–22. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_1.

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Lee, Gregory T. "Group Identities on Symmetric Units." In Group Identities on Units and Symmetric Units of Group Rings, 45–75. London: Springer London, 2010. http://dx.doi.org/10.1007/978-1-84996-504-0_2.

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Conference papers on the topic "Units in rings and group rings"

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Kidner, Mike, Marty Johnson, and Brad Batton. "Distributed Sensors for Active Structural Acoustic Control Using Large Hierarchical Control Systems." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42271.

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The active structural acoustic control of sound radiation in large structures, such as launch vehicle payload fairings, can require very complex control systems if the control architecture is centralized. For this reason hierarchical, decentralized, control architectures have been suggested as one method of simplifying the complexity of the system and improving the robustness of the system to failures. In a hierarchical configuration, individual actuators or groups of actuators act on local information and use this information to drive the system locally. Higher level, slower acting, master controllers can then be used to observe the global performance and adapt the behavior of the local control systems. The local control units can use feedforward, feedback or hybrid feedforward/feedback techniques. It has been previously shown that good performance can only be achieved if the non-radiating high order wavenumber components are removed from sensor signals. This paper develops both analytically and experimentally a two dimensional distributed structural sensor designed as a wavenumber filter. Filtering in the wavenumber domain is made more attractive since it does not cause the phase problems associated with filtering in the time domain. A numerical method for combining ring shaped sensors is presented. It is shown that low and band pass sensors can be created with relatively few ring elements. Experimental results using a two dimensional ring sensor (with eight rings) attached to a large plate structure is presented. Results show that by carefully combining the outputs from the sensor rings both low pass two dimensional wavenumber filters can be created.

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Fo¨llmer, Bernhard, and Armin Schnettler. "A Main Steam Safety Valve (MSSV) With “Fixed Blowdown” According to ASME Section III, Part NC-7512." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22521.

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In 1986, the NRC issued the Information Notice (IN) 86-05 “Main Steam Safety Valve test failures and ring setting adjustments”. Shortly after this IN was issued, the Code was revised to require that a full flow test has to be performed on each CL.2 MSSV by the manufacturer to verify that the valve was adjusted so that it would reach full lift and thus full relieving capacity and would reclose at a pressure as specified in the valve Design Specification. In response to the concern discussed in the IN, the Westinghouse Owners Group (WOG) performed extensive full flow testing on PWR MSSVs and found that each valve required a unique setting of a combination of two rings in order to achieve full lift at accumulation of 3% and reclosing at a blowdown of 5%. The Bopp & Reuther MSSV type SiZ 2507 has a “fixed blowdown” i.e. without any adjusting rings to adjust the “blowdown” so that the blowdown is “fixed”. More than 1000 pieces of this type are successfully in nuclear power plants in operation. Many of them since about 25 years. Therefore it can be considered as a proven design. It is new that an optimization of this MSSV type SiZ 2507 fulfill the requirements of part NC-7512 of the ASME Section III although there are still no adjusting rings in the flow part. In 2000, for the Qinshan Candu unit 1&2 full flow tests were performed with 32 MSSV type SiZ 2507 size 8” × 12” at 51 bar saturated steam in only 6 days. In all tests the functional performance was very stable. It was demonstrated by recording the signals lift and system pressure that all valves had acceptable results to achieve full lift at accumulation of 3% and to reclose at blowdown of 5% . This is an advantage which gives a reduction in cost for flow tests and which gives more reliability after maintenance work during outage compared to the common MSSV design with an individual required setting of the combination of the two rings. The design of the type SiZ 2507 without any adjusting rings in the flow path is presented. The stable performance depends on the interaction of flow force and spring force. The optimization of the flow path to create a suitable flow-force-curve was managed by Computational Fluid Dynamics (CFD) and flow-force-characteristic-measurements at a model 1: 2.5 ! The method of the flow-force-characteristic-measurement permits systematic dimensioning of valve spring forces by means of measurement of the fluid mechanical forces occurring on the valve spindle during flow [1], [2]. A special procedure was established to verify a spring force versus lift curve with an accuracy of 1% for each production valve. This gives high reliability at required stable performance and this can not be influenced by wrong setting of any adjusting ring during maintenance work.

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Kessler, Travis, Amina SubLaban, and J. Hunter Mack. "Predicting the Cetane Number, Sooting Tendency, and Energy Density of Terpene Fuel Additives." In ASME 2022 ICE Forward Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icef2022-91163.

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Abstract Discovering renewable fuels and fuel additives is paramount in reducing carbon emissions from internal combustion engines. Terpenes, a group of compounds that can be synthesized from plant matter and microorganisms, have gained significant interest in recent years as promising candidates for fuels/additives. Terpenes are a diverse class of compounds that contain rings and methyl branches, resulting in high energy densities and optimal cold weather behavior. Their variation in bond order, carbon chains, and functional groups lead to varying degrees of soot formation and performance in existing engines. The present work leverages predictive models, namely artificial neural networks, to predict the cetane number (CN), sooting tendency (quantified with yield sooting index, YSI), and energy density (quantified with lower heating value, LHV) of terpenes and hydrogenated terpenes whose sooting propensities were previously determined through experimental means. Predicted sooting propensities of these terpenes are compared with experimental values, and predicted cetane numbers and energy densities are used to comment on the compounds’ ability to act as fuels/additives. Expected prediction errors for CN, YSI, and LHV, defined by blind test set median absolute error, are within 5.56 cetane units, 3.63 yield sooting index units, and 0.77 MJ/kg respectively. Additionally, the present work investigates a variety of correlation/dependence metrics for property-property relationships, furthering our understanding of how combustion-relevant properties are related.

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Epitropov, Yordan. "Semilinear isomorphisms of group rings." In The 5th Virtual International Conference on Advanced Research in Scientific Areas. Publishing Society, 2016. http://dx.doi.org/10.18638/arsa.2016.5.1.816.

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Hurley, Paul, and Ted Hurley. "Module Codes in Group Rings." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557511.

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Lück, Wolfgang. "K- and L-theory of Group Rings." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0087.

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Koeser, Philipp S., Frank Berbig, Florian Pohlmann-Tasche, Friedrich Dinkelacker, Yuesen Wang, and Tian Tian. "Predictive Piston Cylinder Unit Simulation - Part II: Novel Methodology of Friction Simulation Validation Utilizing Floating-Liner Measurements." In WCX SAE World Congress Experience. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2023. http://dx.doi.org/10.4271/2023-01-0415.

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<div class="section abstract"><div class="htmlview paragraph">The increasing demand for environmentally friendly and fuel-efficient transportation and power generation requires further optimization and minimization of friction power losses. With up to 50% of the overall friction, the piston cylinder unit (PCU) shows most potential within the internal combustion engine (ICE) to increase mechanical efficiency. Calculating friction of internal combustion engines, especially the friction contribution from piston rings and skirt, requires detailed knowledge of the dynamics and lubrication regime of the components being in contact. Part I of this research presents a successful match of simulated and measured piston inter-ring pressures at numerous operation points [<span class="xref">1</span>] and constitutes the starting point for the comparison of simulated and measured piston group friction forces as presented in this research.</div><div class="htmlview paragraph">The authors utilized a single-cylinder floating-liner engine (FLE), based on a heavy-duty diesel truck engine, to determine crank angle resolved friction of the piston cylinder unit. The temperatures of the PCU were measured, and surface temperature distribution and thermal deformation were calculated to ensure realistic oil viscosity and piston and liner deformation under operating condition within the friction simulation.</div><div class="htmlview paragraph">Friction measurements were conducted under motored and fired engine condition. To derive the friction contribution of each ring and the piston skirt separately, motored strip-down tests were conducted as well. Piston ring friction was simulated with a validated ring dynamic simulation tool in combination with flow simulations of the surfaces using a deterministic correlation approach. To consider friction properly within the simulation, high-quality surface representation is needed. Precise optical three-dimensional measurements of the cylinder liner surface and the artificially surface generation for accurate numerical surface representation without measurement errors, revealed to be key. With the simulation model the friction contribution of each ring was compared separately with the strip-down measurement. Moreover, the piston secondary motion and the friction behavior of the piston skirt was calculated and compared to the measurements as well. As a result, the overall friction of the PCU was compared for motored and fired condition. The friction mean effective pressure (FMEP) as well as the crank-angle resolved friction forces from measurement and simulation were analyzed in detail. The comparison between simulation and FLE measurement was done for engine speeds from 10 to 1500 rpm, at oil temperatures from 40° to 100° C and engine loads up to 15.5 bar IMEP (indicated mean effective pressure).</div><div class="htmlview paragraph">The friction contribution (FMEP) of the simulation and measurement matches very well. The detailed examination of the crank angle resolved friction forces shows very good correlation for the hydrodynamic, and boundary lubrication regions.</div><div class="htmlview paragraph">This research successfully proves the ability to predict the friction forces and power losses of the different components of the PCU in combination with honed cylinder liners. It also reveals the importance of the quality of the input parameters such as surface topographies, surface temperatures respectively thermal deformations, oil parameters and contact geometries. Reliable input in combination with experimental data for the validation of the simulation models, enables the utilization of the simulation tools for reliable predictive design approaches.</div></div>

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8

Ruggiero, Alessandro G. "Comments on working group C: Methods." In Stability of particle motion in storage rings. AIP, 1992. http://dx.doi.org/10.1063/1.45101.

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9

Madlener, Klaus, and Birgit Reinert. "Computing Gröbner bases in monoid and group rings." In the 1993 international symposium. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/164081.164139.

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10

Iselin, Christoph F. "Summary for working group A on short-term stability." In Stability of particle motion in storage rings. AIP, 1992. http://dx.doi.org/10.1063/1.45099.

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Reports on the topic "Units in rings and group rings"

1

Holmes, S. D., G. Dugan, and J. Marriner. Report of the New Rings Study Group. Office of Scientific and Technical Information (OSTI), October 1987. http://dx.doi.org/10.2172/5937717.

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