Relevant bibliographies by topics / Jacobson radical

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  2. Dissertations / Theses
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Academic literature on the topic 'Jacobson radical'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Jacobson radical"

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KOSLER, KARL A. "ON SYMMETRIC RADICALS OVER FULLY SEMIPRIMARY NOETHERIAN RINGS." Journal of Algebra and Its Applications 02, no. 03 (September 2003): 351–64. http://dx.doi.org/10.1142/s021949880300057x.

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Symmetric radicals over a fully semiprimary Noetherian ring R are characterized in terms of stability on bimodules and link closure of special classes of prime ideals. The notion of subdirect irreduciblity with respect to a torsion radical is introduced and is shown to be invariant under internal bonds between prime ideals. An analog of the Jacobson radical is produced which is properly larger than the Jacobson radical, yet satisfies the conclusion of Jacobson's conjecture for right fully semiprimary Noetherian rings.
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Ilić-Georgijević, Emil. "On graded special radicals of graded rings." Journal of Algebra and Its Applications 17, no. 06 (May 23, 2018): 1850109. http://dx.doi.org/10.1142/s0219498818501098.

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In this paper, a graded ring is a ring which is the direct sum of a family of its additive subgroups indexed by a nonempty set under the assumption that the product of homogeneous elements is again homogeneous. We study graded special radicals and special radicals of graded rings, but which contain the corresponding Jacobson radicals. There are two versions of this graded radical, which we name the graded over-Jacobson and the large graded over-Jacobson radical. We establish several characterizations of the graded over-Jacobson radical of a graded ring and also prove that the largest homogeneous ideal contained in the corresponding classical radical of a graded ring coincides with the large graded over-Jacobson radical of that ring.
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SMOKTUNOWICZ, AGATA. "A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS." Journal of Algebra and Its Applications 13, no. 04 (January 9, 2014): 1350121. http://dx.doi.org/10.1142/s0219498813501211.

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It was shown by Bergman that the Jacobson radical of a Z-graded ring is homogeneous. This paper shows that the analogous result holds for nil radicals, namely, that the nil radical of a Z-graded ring is homogeneous. It is obvious that a subring of a nil ring is nil, but generally a subring of a Jacobson radical ring need not be a Jacobson radical ring. In this paper, it is shown that every subring which is generated by homogeneous elements in a graded Jacobson radical ring is always a Jacobson radical ring. It is also observed that a ring whose all subrings are Jacobson radical rings is nil. Some new results on graded-nil rings are also obtained.
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Godloza, L., N. J. Groenewald, and W. A. Olivier. "On Jacobson Near-rings and Special Radicals." Algebra Colloquium 14, no. 01 (March 2007): 1–14. http://dx.doi.org/10.1142/s1005386707000028.

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In this paper, we construct special radicals using class pairs of near-rings. We establish necessary conditions for a class pair to be a special radical class. We then define Jacobson-type near-rings and show that in most cases the class of all near-rings of this type is a special radical class. Subsequently, we investigate the relationship between each Jacobson-type near-ring and the corresponding matrix near-ring.
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KELAREV, A. V. "ON THE STRUCTURE OF INCIDENCE RINGS OF GROUP AUTOMATA." International Journal of Algebra and Computation 14, no. 04 (August 2004): 505–11. http://dx.doi.org/10.1142/s0218196704001888.

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The Jacobson radical is one of the major tools used in the investigation of the structure of rings and ring constructions. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of group automata for all finite nilpotent groups.
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Rao, Ravi Srinivasa, K. Siva Prasad, and T. Srinivas. "Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–6. http://dx.doi.org/10.1155/2008/741609.

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By a near-ring we mean a right near-ring.J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radicalJ0rare studied. It is shown thatJ0ris a Kurosh-Amitsur radical (KA-radical) in the variety of all near-ringsR, in which the constant partRcofRis an ideal ofR. So unlike the left Jacobson radicals of types 0 and 1 of near-rings,J0ris a KA-radical in the class of all zero-symmetric near-rings.J0ris nots-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.
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Munn, W. D. "The Jacobson radical of a band ring." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 2 (March 1989): 277–83. http://dx.doi.org/10.1017/s0305004100067761.

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A band is a semigroup in which every element is idempotent. In this note we give an explicit description of the Jacobson radical of the semigroup ring of a band over a ring with unity. It is shown, further, that this radical is nil if and only if the Jacobson radical of the coefficient ring is nil. For the particular case of a normal band (see below for the definition) the Jacobson radical of the band ring is nilpotent if and only if the Jacobson radical of the coefficient ring is nilpotent; but this result does not extend to arbitrary bands.
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Behr, Erazm J. "Jacobson radical of filtered algebras." Proceedings of the American Mathematical Society 98, no. 4 (April 1, 1986): 545. http://dx.doi.org/10.1090/s0002-9939-1986-0861746-7.

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Najaryan, N. G. "HOMOGENEOUS IDEALS AND JACOBSON RADICAL." Proceedings of the YSU A: Physical and Mathematical Sciences 51, no. 2 (243) (June 15, 2017): 193–95. http://dx.doi.org/10.46991/pysu:a/2017.51.2.193.

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In this paper the Jacobson radical of an algebra$F\langle X\rangle / H$ is studied, where FhXi is a free associative algebra of countable rank over infinite field $F$ and $H$ is a homogeneous ideal of the algebr$F\langle X\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\langle X\rangle / H$ is a nil ideal.
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Olson, D. M., and R. Lidl. "A uniformly strongly prime radical." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (August 1987): 95–102. http://dx.doi.org/10.1017/s1446788700029013.

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AbstractThe class of all uniformly strongly prime rings is shown to be a special class of rings which generates a radical class which properly contains both the right and left strongly prime radicals and which is independent of the Jacobson and Brown-McCoy radicals.
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Dissertations / Theses on the topic "Jacobson radical"

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Della, Flora Saradia Sturza. "Sobre ações parciais torcidas de grupos e o produto cruzado parcial." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/54740.

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Neste trabalho consideramos ações parciais torcidas de um grupo G sobre um anel A. Além disso, estudamos ações parciais torcidas que admitem envolvente. No caso em que A e semiprimo, estendemos a ação parcial torcida ao anel de quocientes maximal de A. Com isso, encontramos condições necessárias e suficientes para que o produto cruzado parcial A ∗α G seja um anel semiprimo de Goldie a esquerda. Também, introduzimos o conceito de ação parcial torcida X - externa estudando algumas propriedades que se transferem de A para A ∗α G quando a ação e deste tipo.
In this work we consider twisted partial actions of a group G on a ring A. Firstly we study twisted partial actions with enveloping action. Next we assume that A is semiprime. In this case we extend the twisted partial action to the maximal left rings of quotients of A. Using this we find necessary and suficient conditions for the partial crossed product A ∗α G to be a semiprime Goldie ring. Finally we introduce the concept of the twisted partial action X -outer and study some properties that transfer from A to A ∗α G when the action is of this type.
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Filho, Gilson Reis dos Santos. "O radical de Jacobson de anéis de polinômios diferenciais." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05102015-161321/.

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O objetivo desta dissertação é estudar o radical de Jacobson de anéis de polinômios diferenciais. Mostramos um resultado de M. Ferrero, K. Kishimoro, K. Motose, que mostra que no caso geral, o radical de um anel de polinômios diferenciais é um anel de polinômios diferenciais sobre algum ideal do anel dos coeficientes. Assumindo que o anel dos coeficientes satisfaça uma identidade polinomial, mostramos seguindo B. Madill que este ideal é um ideal nil. Se o anel dos coeficientes é adicionalmente localmente nilpotente, seguindo J. Bell, B. Madill, F. Shinko, mostramos que o anel de polinômios diferenciais será localmente nilpotente. Ainda seguindo J. Bell et al, se o anel dos coeficientes é uma álgebra sobre um corpo de característica zero e tal álgebra satisfaz uma identidade polinomial, mostramos que o ideal nil é o radical de Köthe. Para tais demonstrações, cobriremos os tópicos preliminares necessários para entender os enunciados: radical nil, radical de Levitzki, radical de Baer, radical de Jacobson e propriedades, anéis PI, polinômios centrais, teorema de Kaplansky.
The aim of this work is to study the Jacobson radical of differential polynomial rings. We show a result of M. Ferrero, K. Kishimoto, K. Motose, which shows that in general, the radical of a differential polynomial ring is a differential polynomial ring over some ideal of the ring of coefficients. Assuming that the ring of coefficients satisfies a polynomial identity, we show following B. Madill that this ideal is nil. If the ring of coefficients is additionally locally nilpotent, following J. Bell, B. Madill, F. Shinko, we show that the differential polynomial ring is locally nilpotent. Still following J. Bell et al, if the ring of coefficients is an algebra over a field of zero characteristic and this algebra satisfies a polynomial identity, we show that the nil ideal is the Köthe radical. For the proofs, we cover the preliminary topics necessary for understanding the statements: nil radical, Levitzki radical, Baer radical, Jacobson radical and its properties, PI-rings, central polynomials, Kaplanskys theorem.
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Williams, Jessica Lynn. "A ring theoretic approach to radicals of extensions." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1803.

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The Jacobson radical of a ring was first formally studied in 1945 by Nathan Jacobson and is an important object in modern abstract algebra. The analogous notion of the Jacobson radical for a module is referred to as the radical of a module. The radical of a module is the intersection of all its maximal submodules. In general, the radical of a module is simpler than the module itself and contains important information about the module. The study of the radical of a module often appears as an incidental to other investigations. This thesis represents work towards understanding the radical of a module extension. Given a ring $R$ and $R$-modules $A,B,X$ such that $X$ is an extension of $B$ by $A$ as in the short exact sequence $$0 rightarrow A rightarrow X rightarrow B rightarrow 0 ,$$ we seek to determine properties of the radical of $X$, denoted $rad{X}$. These properties are dependent on the ring $R$ and properties of the modules $A$ and $B$. In this thesis we examine several different types of extensions and discuss a phenomenon in which a non-zero radical implies a split sequence. We work in the context of rings and their ideals. Extensions of abelian groups provide motivation for the results we prove about injectivity of radicals of extensions involving divisible modules and torsion modules. We are able to prove such properties of the radical for extensions of modules over principal ideal domains and Dedekind domains. Expanding upon these cases, we explore a more general construction of an extension and use it to explain our motivating abelian group results. We use the theorems proven about this construction to remark on possible generalizations to other types of rings and modules. We conclude with plans to generalize our statements by translating into terms of infinite matrices and $h$-local rings.
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Morgado, Andrea. "Sobre os teoremas de dualidade de Cohen e Montgomery." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/29964.

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Nessa dissertação, apresentamos os Teoremas de Dualidade de Cohen e Montgomery, [4]. Discutimos também a construção de um contexto de Morita para uma álgebra graduada por um grupo finito. Como aplicação dos resultados desenvolvidos no texto, estudamos a relação entre o radical de Jacobson e o radical de Jacobson graduado de álgebras graduadas, apresentando a solução de Cohen e Montgomery para uma conjectura de Bergman.
In this work, we will present the Cohen and Montgomery's Duality Theorems, [4]. We also discuss the construction of a Morita context to an algebra graded by a nite group. As an application of the results developed in the text, we studied the relations between the Jacobson radical and the graded Jacobson radical of graded algebras, presenting to Cohen and Montgomery's solution for a Bergman's conjecture.
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Velasco, Ulyses. "SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/533.

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The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and more. Once we reach our destination, we will examine some implications of these theorems. As a fair warning, no ring will be assumed to be commutative, or to have unity. On that note, the reader should be familiar with the basic findings from Group Theory and Ring Theory.
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Ciocanea, teodorescu Iuliana. "Algorithms for finite rings." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0121/document.

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Cette thèse s'attache à décrire des algorithmes qui répondent à des questions provenant de la théorie des anneaux et des modules. Nous restreindrons essentiellement notre étude à des algorithmes déterministes, en temps polynomial, ainsi qu'aux anneaux et modules finis. Le premier des principaux résultats de cette thèse concerne le problème de l'isomorphisme entre modules : nous décrivons deux algorithmes distincts qui, étant donnée un anneau fini R et deux R-modules M et N finis, déterminent si M et N sont isomorphes. S'ils le sont, les deux algorithmes exhibent un tel isomorphisme. De plus, nous montrons comment calculer un ensemble de générateurs de taille minimale pour un module donné, et comment construire des couvertures projectives et des enveloppes injectives. Nous décrivons ensuite des tests mettant en évidence le caractère simple, projectif ou injectif d'un module, ainsi qu'un test constructif de l'existence d'un homomorphisme demodules surjectif entre deux modules finis, l'un d'entre eux étant projectif. Par contraste, nous montrons le résultat négatif suivant : le problème consistant à tester l'existence d'un homomorphisme de modules injectif entre deux modules, l'un des deux étant projectif, est NP-complet.La dernière partie de cette thèse concerne le problème de l'approximation du radical de Jacobson d'un anneau fini. Il s'agit de déterminer un idéal bilatère nilpotent tel que l'anneau quotient correspondant soit \presque" semi-simple. La notion de \semi-simplicité approchée" que nous utilisons est la séparabilité
In this thesis we are interested in describing algorithms that answer questions arising in ring and module theory. Our focus is on deterministic polynomial-time algorithms and rings and modules that are finite. The first main result of this thesis concerns the module isomorphism problem: we describe two distinct algorithms that, given a finite ring R and two finite R-modules M and N, determine whether M and N are isomorphic. If they are, the algorithms exhibit such a isomorphism. In addition, we show how to compute a set of generators of minimal cardinality for a given module, and how to construct projective covers and injective hulls. We also describe tests for module simplicity, projectivity, and injectivity, and constructive tests for existence of surjective module homomorphisms between two finite modules, one of which is projective. As a negative result, we show that the problem of testing for existence of injective module homomorphisms between two finite modules, one of which is projective, is NP-complete. The last part of the thesis is concerned with finding a good working approximation of the Jacobson radical of a finite ring, that is, a two-sided nilpotent ideal such that the corresponding quotient ring is \almost" semisimple. The notion we use to approximate semisimplicity is that of separability
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Gardner, Kai. "Into the Fray : Norman Jacobson, the Free Speech Movement and the Clash of Commitments." Oberlin College Honors Theses / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1432128501.

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BORGES, Alex Ramos. "Identidades polinomiais graduadas de matrizes triangulares." Universidade Federal de Campina Grande, 2012. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1360.

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Neste trabalho serão estudadas as graduações e identidades polinomiais graduadas da álgebra Un(K) das matrizes triangulares superiores n×n sobre um corpo K, o qual será sempre in nito. Primeiramente, será estudado o caso n = 2, para o qual será mostrado que existe apenas uma graduação não trivial e serão descritos as identidades, as codimensões e os cocaracteres graduados. Para o caso n qualquer, serão estudadas as identidades e codimensões graduadas, considerando-se a Zn-graduação natural de Un(K). Finalmente, será apresentada uma classi cação das graduações de Un(K) por um grupo qualquer.
In this work we study the gradings and the graded polynomial identities of the upper n × n triangular matrices algebra Un(K) over a eld K, which is always in nity. The case n = 2 will be rstly studied, for which will be shown that there is only one nontrivial grading and we shall describe the graded identities, codimensions and cocharacters. For the general n case, we shall study graded identities and codimensions, considering the natural Zn-grading of Un(K). Finally, we will present a classi cation of the gradings of Un(K) by any group.
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ARAÚJO, Laise Dias Alves. "Identidades polinomiais para álgebras e matrizes triangulares superiores em blocos." Universidade Federal de Campina Grande, 2017. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1412.

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Nesta dissertação estudamos as graduações elementares (ou boas graduações) e as identidades polinomiais graduadas correspondentes em álgebras de matrizes triangulares superiores em blocos. Uma graduação elementar por um grupo G na álgebra A = UT(α1, α2, ..., αr) de matrizes triangulares superiores em blocos é determinada por uma n-upla em Gn, onde n = α1+· · ·+αr. Mostraremos que as graduações elementares em A determinadas por duas n-uplas em Gnsão isomorfas se, e somente se, as n-uplas estão na mesma órbita da bi-ação canônica em Gn com o grupo Sα1 × · · · × Sαr agindo à esquerda e G à direita. Em seguida utilizamos estes resultados para mostrar que, sob certas hipóteses (por exemplo, se o grupo G tem ordem prima), duas álgebras de matrizes triangulares superiores em blocos, graduadas pelo grupo G, satisfazem as mesmas identidades graduadas se, e somente se, são isomorfas (como álgebras graduadas).
In this dissertation we study elementary (or good) gradings in upper block triangular matrix algebras and the corresponding graded polynomial identities. An elementary grading by a group G on the algebra A = UT(α1, α2, ..., αr) of upper block triangular matrices is determined by an n-tuple in Gn, where n = α1 + · · · + αr. It will be proved that the elementary gradings on A determined by two n-tuples in Gn are isomorphic if and only if the n-tuples are in the same orbit in the canonical bi-action on Gn with the group Sα1 × · · · × Sαr acting on the left and the group G acting on the right. These results will be used to prove that under suitable hypothesis (for example if the group G has prime order) two upper block triangular matrix algebras, graded by the group G, satisfy the same graded identities if and only if they are isomorphic (as graded algebras).
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Matos, Márcia Graci de Oliveira. "A estrutura do grupo adjunto e a propriedade do normalizador." Instituto de Matemática. Departamento de Matemática, 2016. http://repositorio.ufba.br/ri/handle/ri/22836.

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Em um anel R, o conjunto de todos os elementos quaserregulares determina o, assim chamado, grupo adjunto G, cuja operação, conhecida como círculo, foi definida por S. Perlis como x_y = x+y+xy: Este trabalho, tem como objetivo determinar a estrutura do grupo adjunto G de um anel finito R e verificar a validade da propriedade do normalizador em anéis de grupo integrais (Nor) com respeito ao grupo geral linear. Explorando a decomposição do anel R em suas pi-componentes, concluímos que G é produto direto dos grupos adjuntos, Gpi , em cada pi-componente Rpi do anel; demonstraremos então, que para cada fator Gpi , o quociente Gpi=pRpi , admite uma decomposição como o produto semidireto (munido da operação círculo) de Jpi=pRpi , em que Jpi é o radical de Jacobson do anel Rpi , por um produto direto de grupos gerais lineares. Uma vez estabelecida esta estrutura, aplicamos técnicas próprias da teoria de anéis de grupo integrais e mostramos a validade de (Nor) para o grupo geral linear, GL(n; Fqi), onde Fqi é um corpo finito e qi = PI n. Provamos que vale (Nor) para cada fator GL(n; Fqi) e portanto concluímos que o produto direto desses fatores, é solução para (Nor).
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Books on the topic "Jacobson radical"

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The Jacobson radical of group algebras. Amsterdam: North-Holland, 1987.

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Karpilovsky, Gregory. The Jacobson radical of classical rings. Harlow, Essex, England: Longman Scientific & Technical, 1991.

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The Jacobson Radical of Group Algebras. Elsevier, 1987. http://dx.doi.org/10.1016/s0304-0208(08)x7052-5.

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Book chapters on the topic "Jacobson radical"

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Farb, Benson, and R. Keith Dennis. "The Jacobson Radical." In Graduate Texts in Mathematics, 57–79. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0889-1_3.

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Lam, T. Y. "Jacobson Radical Theory." In Graduate Texts in Mathematics, 51–105. New York, NY: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-0406-7_2.

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Lam, T. Y. "Jacobson Radical Theory." In Exercises in Classical Ring Theory, 35–68. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4757-3987-9_2.

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Lam, T. Y. "Jacobson Radical Theory." In Graduate Texts in Mathematics, 48–100. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4419-8616-0_2.

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Krylov, Piotr A., Alexander V. Mikhalev, and Askar A. Tuganbaev. "The Jacobson Radical of the Endomorphism Ring." In Algebras and Applications, 135–80. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0345-1_4.

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Gateva-Ivanova, Tatiana. "Algorithmic determination of the jacobson radical of monomial algebras." In Lecture Notes in Computer Science, 355–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51517-8_139.

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Smoktunowicz, Agata. "R[x, y] is Brown-McCoy Radical if R[x] is Jacobson Radical." In Proceedings of the Third International Algebra Conference, 235–40. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0337-6_11.

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Williamson, Arthur. "Radical Britain: David Hume of Godscroft and the Challenge to the Jacobean British Vision." In The Accession of James I, 48–68. London: Palgrave Macmillan UK, 2006. http://dx.doi.org/10.1057/9780230501584_4.

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Flagg, Mary. "The Jacobson Radical’s Role in Isomorphism Theorems for p-Adic Modules Extends to Topological Isomorphism." In Groups, Modules, and Model Theory - Surveys and Recent Developments, 285–300. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51718-6_14.

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Faith, Carl. "Introduction to ring theory: Schur’s Lemma and semisimple rings, prime and primitive rings, Noetherian and Artinian modules, nil, prime and Jacobson radicals." In Rings and Things and a Fine Array of Twentieth Century Associative Algebra, 17–52. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/065/02.

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Conference papers on the topic "Jacobson radical"

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K. Pushpalatha, S. Venu Madhava Sarma, P. S. Prema Kumar, M. Babu Prasad, and M. Nagarjuna. "A note on Jacobsan radicals in special Boolean like rings." In ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0066297.

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K. Pushpalatha, S. Venu Madhava Sarma, P. S. Prema Kumar, M. Babu Prasad, and M. Nagarjuna. "A note on Jacobsan radicals in special Boolean like rings." In ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0066297.

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Sui, Wenbo, and Carrie M. Hall. "SCR Control System Design Based on On-Line Radial Basis Function and Backpropagation Neural Networks." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5095.

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Because of its high NOx reduction efficiency, selective catalyst reduction (SCR) has become an indispensable part of diesel vehicle aftertreatment. This paper presents a control strategy for SCR systems that is based on an on-line radial basis function neural network (RBFNN) and an on-line backpropagation neural network (BPNN). In this control structure, the radial basis function neural network is employed as an estimator to provide Jacobian information for the controller; and the backpropagation neural network is utilized as a controller, which dictates the appropriate urea-solution to be injected into the SCR system. This design is tested by simulations based in Gamma Technologies software (GT-ISE) as well as MATLAB Simulink. The results show that the RBF-BPNN control technique achieves a 1–5 % higher NOx reduction efficiency than a PID controller.
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Strömberg, Niclas. "Reliability Based Design Optimization by Using a SLP Approach and Radial Basis Function Networks." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59522.

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In this paper reliability based design optimization by using radial basis function networks (RBFN) as surrogate models is presented. The RBFN are treated as regression models. By taking the center points equal to the sampling points an interpolation is obtained. The bias of the network is taken to be known a priori or posteriori. In the latter case, the well-known orthogonality constraint between the weights of the RBFN and the polynomial basis functions of the bias is adopted. The optimization is performed by using a first order reliability method (FORM)-based sequential linear programming (SLP) approach, where the Taylor expansions are generated in intermediate variables defined by the iso-probabilistic transformation. In addition, the reliability constraints are expanded at the most probable points which are found by using Newton’s method. The Newton algorithm is derived by proposing an in-exact Jacobian. In such manner, a FORM-based LP-formulation in the standard normal space of problems with non-Gaussian variables is suggested. The solution from the LP-problem is mapped back to the physical space and the suggested procedure continues in a sequence until convergence is reached. This is implemented for five different distributions: normal, lognormal, Gumbel, gamma and Weibull. It is also presented how the FORM-based SLP approach can be corrected by using second order reliability methods (SORM) and Monte Carlo simulations. In particular, the SORM approach of Hohenbichler is studied. The outlined methodology is both efficient and robust. This is demonstrated by solving established benchmarks as well as finite element problems.
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Gan, Dongming, Jian S. Dai, Jorge Dias, and Lakmal D. Seneviratne. "Controllable Rotation Workspace of a Metamorphic Parallel Mechanism With Reconfigurable Universal Joints." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12462.

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This paper introduces a metamorphic parallel mechanism which has three topologies with pure translational, pure rotational and 3T1R degrees of freedom. Mobility change stemming from the reconfigurability of a reconfigurable Hooke (rT) joint is illustrated by change of the limb twist screw systems and the platform constraint screw system. Then the paper focuses on the pure rotational topology of the mechanism of which the rotational center can be altered along the central line perpendicular to the base plane by altering the radial rotational axes in the limbs. Singularity analysis is conducted based on the dependency of constraint forces and actuation forces in a screw based Jacobian matrix. Following these, rotation workspace variation is demonstrated in a 2D projection format using the Tilt-and-Torsion Euler angles based on the actuation limits and joint rotation ranges.
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Jeon, Soo. "Singularity Tolerant Robotic Manipulation for Autonomous Field Tracking in an Unknown Environment." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28793.

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This paper presents a comprehensive motion control strategy for the autonomous operation of robotic manipulators combined with the sensor-driven recursive estimation of an unknown field of interest. The spatial distribution of the environmental phenomenon is modeled by a radial basis function (RBF) network and their weight parameters are estimated by a recursive least square (RLS) method using the collective measurements from the on-board sensors mounted to the manipulator. The asymptotic tracking has been simultaneously achieved by the control law based on the gradient of the estimated field. Since the target location cannot be known a priori, the motion controller has to be designed in explicit consideration of tolerating the singular configuration of the manipulator kinematics. By using the null space decomposition of the task space for the Jacobian near the singularities, a systematic method is suggested to command the task space control law in spite of the singular configurations. Simulation results using the three link planar robot are presented to support the main ideas.
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