Relevant bibliographies by topics / Graded modules

Contents

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

Academic literature on the topic 'Graded modules'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Graded modules"

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Bataineh, Malik, Rashid Abu-Dawwas, and Jenan Shtayat. "Almost graded multiplication and almost graded comultiplication modules." Demonstratio Mathematica 53, no. 1 (December 31, 2020): 325–31. http://dx.doi.org/10.1515/dema-2020-0023.

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AbstractLet G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=M. We investigate several properties of these classes of graded modules.
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Bataineh, Malik, Rashid Abu-Dawwas, and Jenan Shtayat. "Almost graded multiplication and almost graded comultiplication modules." Demonstratio Mathematica 53, no. 1 (December 31, 2020): 325–31. http://dx.doi.org/10.1515/dema-2020-0023.

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AbstractLet G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=M. We investigate several properties of these classes of graded modules.
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Abu-Dawwas, Rashid. "Graded semiprime multiplication modules." Boletim da Sociedade Paranaense de Matemática 39, no. 3 (January 1, 2021): 27–35. http://dx.doi.org/10.5269/bspm.40197.

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Let $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded semiprime multiplication modules. A graded $R$-module $M$ is said to be graded semiprime multiplication if $M$ has no graded semiprime $R$-submodules or for every graded semiprime $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. We introduce several results concerning graded semiprime submodules and we investigate them to present several results on graded semiprime multiplication modules.
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ZAMANI, NASER. "FINITELY GENERATED GRADED MULTIPLICATION MODULES." Glasgow Mathematical Journal 53, no. 3 (August 1, 2011): 693–705. http://dx.doi.org/10.1017/s0017089511000279.

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AbstractLet R = ⊕i ∈ ℤRi be a ℤ-graded ring and M = ⊕i ∈ ℤMi be a graded R-module. Providing some results on graded multiplication modules, some equivalent conditions for which a finitely generated graded R-module to be graded multiplication will be given. We define generalised graded multiplication module and determine some of its certain graded prime submodules. It will be shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition. Using this, we give a characterisation of graded primary submodules of M. These lead to a kind of characterisation of finitely generated generalised graded multiplication modules.
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Al-Zoubi, Khaldoun falah, and Rweili Alkhalaf. "On graded quasi-primary submodules of graded modules over graded commutative rings." Boletim da Sociedade Paranaense de Matemática 39, no. 4 (January 1, 2021): 57–64. http://dx.doi.org/10.5269/bspm.41917.

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Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded quasi-primary submodules of graded modules over graded commutative rings. Various properties of graded quasi-primary submodules are considered.
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Khashyarmaneshs, Kazem, and Ahmad Abbasi. "On the asymptotic behaviour of associated primes of generalized local cohomology modules." Journal of the Australian Mathematical Society 83, no. 2 (October 2007): 217–26. http://dx.doi.org/10.1017/s1446788700036879.

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AbstractLetMandNbe finitely generated and graded modules over a standard positive graded commutative Noetherian ringR, with irrelevant idealR+. Letbe thenth component of the graded generalized local cohomology module. In this paper we study the asymptotic behavior of AssfR+() as n → –∞ wheneverkis the least integerjfor which the ordinary local cohomology moduleis not finitely generated.
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Khaksari, A., and F. Rasti Jahromi. "Multiplication graded modules." International Journal of Algebra 7 (2013): 17–24. http://dx.doi.org/10.12988/ija.2013.13003.

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Balaba, I. N. "Prime graded modules." Journal of Mathematical Sciences 163, no. 5 (November 14, 2009): 487–92. http://dx.doi.org/10.1007/s10958-009-9686-6.

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Ghiasvand, Peyman, and Farkhonde Farzalipour. "On graded weak multiplication modules." Tamkang Journal of Mathematics 43, no. 2 (June 30, 2012): 171–77. http://dx.doi.org/10.5556/j.tkjm.43.2012.712.

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Abrams, Gene, and Claudia Menini*. "EMBEDDING MODULES IN GRADED MODULES OVER A SEMIGROUP-GRADED RING." Communications in Algebra 29, no. 6 (April 30, 2001): 2611–25. http://dx.doi.org/10.1081/agb-100002411.

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Dissertations / Theses on the topic "Graded modules"

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Söderberg, Jonas. "Graded Betti Numbers and Hilbert Functions of Graded Cohen-Macaulay Modules." Doctoral thesis, KTH, Matematik (Inst.), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4266.

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In this thesis we study graded Cohen-Macaulay modules and their possible Hilbert functions and graded Betti numbers. In most cases the Cohen-Macaulay modules we study are level modules. In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain level modules. As in the case of level algebras, a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences. We prove that a sequence of positive integers (h0, h1, . . . ,hc) is the Hilbert function of an artinian level module of codimension two if and only if hi−1 − 2hi + hi+1<= 0 for all 0 <= i <= c, where we assume that h−1 = hc+1 = 0. This generalizes a result already known for artinian level algebras. Zanello gives a lower bound for Hilbert functions of generic level quotients of artinian level algebras. We give a new and more straightforward proof of Zanello’s result. Conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by a positive rational number are given. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified for modules of codimension two, for Gorenstein algebras of codimension three and for complete intersections. The motivation for the conjectures comes from the Multiplicity conjecture of Herzog, Huneke and Srinivasan. The h-vectors and graded Betti numbers of level modules up to multiplication by a rational number are studied. Assuming the conjecture, mentioned above, on the set of possible graded Betti numbers of Cohen-Macaulay modules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We determine, again up to multiplication by a rational number, the cancellable h-vectors and the h-vectors of level modules with the weak Lefschetz property. Furthermore, we prove that level modules of codimension three satisfy the upper bound of the Multiplicity conjecture and that the lower bound holds if the module, in addition, has the weak Lefschetz property.
QC 20100819
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Papantonis, Theocharis [Verfasser]. "Z-graded supergeometry: Differential graded modules, higher algebroid representations, and linear structures / Theocharis Papantonis." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2021. http://d-nb.info/1236401727/34.

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Alcock, Edward. "On strongly group-graded algebras and stably flat modules." Thesis, Queen Mary, University of London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326248.

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Söderberg, Jonas. "Graded Betti numbers and Hilbert functions of Cohen-Macaulay modules /." Stockholm : KTH matematik, Kungliga tekniska högskolan, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4266.

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Nash, David A. 1982. "Graded representation theory of Hecke algebras." Thesis, University of Oregon, 2010. http://hdl.handle.net/1794/10871.

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xii, 76 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
We study the graded representation theory of the Iwahori-Hecke algebra, denoted by Hd , of the symmetric group over a field of characteristic zero at a root of unity. More specifically, we use graded Specht modules to calculate the graded decomposition numbers for Hd . The algorithm arrived at is the Lascoux-Leclerc-Thibon algorithm in disguise. Thus we interpret the algorithm in terms of graded representation theory. We then use the algorithm to compute several examples and to obtain a closed form for the graded decomposition numbers in the case of two-column partitions. In this case, we also precisely describe the 'reduction modulo p' process, which relates the graded irreducible representations of Hd over [Special characters omitted.] at a p th -root of unity to those of the group algebra of the symmetric group over a field of characteristic p.
Committee in charge: Alexander Kleshchev, Chairperson, Mathematics; Jonathan Brundan, Member, Mathematics; Boris Botvinnik, Member, Mathematics; Victor Ostrik, Member, Mathematics; William Harbaugh, Outside Member, Economics
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Abbasirad, Mohammad Mahdi. "Homotopy theory of differential graded modules and adjoints of restriction of scalars." Thesis, University of Sheffield, 2014. http://etheses.whiterose.ac.uk/6568/.

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This study constructs two different model structures called projective and injective model on the category of differential graded modules over a differential graded ring and also provides an explicit description of fibrant and cofibrant objects for these models. The constructions are based on the concept and properties of semi-projective and semi-injective modules and other kinds of projectivity and injectivity in the category of differential graded modules. Also an analysis of behavior of functors; restriction, extension and co-extension of scalars is given. Furthermore, some conditions under which an adjunction becomes a Quillen pair and a Quillen pair becomes a Quillen equivalence are described. Additionally, a relationship between restriction and co-extension for compact Lie groups is discovered.
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Bartl, Eduard. "Mathematical foundations of graded knowledge spaces." Diss., Online access via UMI:, 2009.

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Thesis (Ph. D.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Systems Science and Industrial Engineering, 2009.
Includes bibliographical references.
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Malec, Sara. "Noetherian Filtrations and Finite Intersection Algebras." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/55.

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This paper presents the theory of Noetherian filtrations, an important concept in commutative algebra. The paper describes many aspects of the theory of these objects, presenting basic results, examples and applications. In the study of Noetherian filtrations, a few other important concepts are introduced such as Rees algebras, essential powers filtrations, and filtrations on modules. Basic results on these are presented as well. This thesis discusses at length how Noetherian filtrations relate to important constructions in commutative algebra, such as graded rings and modules, dimension theory and associated primes. In addition, the paper presents an original proof of the finiteness of the intersection algebra of principal ideals in a UFD. It concludes by discussing possible applications of this result to other areas of commutative algebra.
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Sánchez, Jesús. "About E-infinity-structures in L-algebras." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC204/document.

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Dans cette thèse nous rappelons la notion de L-algèbre, qui a pour objet d'être un modèle algébrique des types d'homotopie. L'objectif principal de cette thèse est la description d'une structure de E-infini-coalgèbre sur l'élément principal d'une L-algèbre. Ceci peut être vu comme une généralisation de la structure de E-infini-coalgèbre sur le complexe des chaînes d'un ensemble simplicial, telle que décrite par Smith dans Iterating the cobar construction, 1994. Nous construisons une E-infini-opérade, notée K, utilisée pour construire la E-infini-coalgèbre sur l'élément principal d'une L-algèbre. Cette structure de E-infini-coalgèbre montre que la L-algèbre canoniquement associée à un ensemble simplicial contient au moins autant d'information homotopique que la E-infini-coalgèbre couramment associée à un ensemble simplicial
In this thesis we recall the notion of L-algebra. L-algebras are intended as algebraic models for homotopy types. L-algebras were introduced by Alain Prouté in several talks since the eighties. The principal objective of this thesis is the description of an E-infinity-coalgebra structure on the main element of an L-algebra. This can be seen as a generalization of the E-infinity-coalgebra structure on the chain complex associated to a simplicial set given by Smith in Iterating the cobar construction, 1994. We construct an E-inifity-operad, denoted K, used to construct the E-inifity-coalgebra on the main element of a L-algebra. This E-inifity-coalgebra structure shows that the canonical L-algebra associated to a simplicial set contains at least as much homotopy information as the E-inifity-coalgebras usually associated to simplicial sets
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Alshaniafi, Y. S. "The homological grade of a module over a commutative ring." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280830.

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Books on the topic "Graded modules"

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Krasner, Marc. Structures paragraduées (groupes, anneaux, modules). Kingston, Ont: Queen's University, 1987.

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Introduction to liaison theory and deficiency modules. Boston: Birkhäuser, 1998.

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Learning, Alberta Alberta. Handwriting: Special interest module, grades 4-6. [Edmonton]: Alberta Learning, 2002.

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Juirnarongrit, Teerawut. Effect of pile diameter on the modulus of sub-grade reaction. La Jolla, Calif: Department of Structural Engineering, University of California, San Diego, 2005.

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Bland, Sue. The living soil: A renewable resource : a science module. Edmonton: Weigl Educational Publishers, 1991.

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Discover the Wonder/Modules A-F (Grade 4). Scott Foresman & Co, 1993.

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Common Core Mathematics Grade K Module 2. John Wiley & Sons Inc, 2013.

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ScienceFusion : Lab Manual Module C Grades 6-8 Module C: The Human Body. Houghton Mifflin Harcourt Publishing Company, 2011.

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Education, PCG. English Language Arts B Module, Grade 6 Module 3B: Understanding Perspectives, Teacher Guide. Wiley & Sons, Incorporated, John, 2020.

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Scott Foresman Earth Science Grade 4 (Module B). Pearson/Scott Foresman, 2006.

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Book chapters on the topic "Graded modules"

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Stückrad, Jürgen, and Wolfgang Vogel. "Rees modules and associated graded modules of a Buchsbaum module." In Buchsbaum Rings and Applications, 199–228. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-02500-0_6.

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Herrmann, Manfred, Ulrich Orbanz, and Shin Ikeda. "Z-Graded Rings and Modules." In Equimultiplicity and Blowing Up, 44–116. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61349-4_2.

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Félix, Yves, Stephen Halperin, and Jean-Claude Thomas. "Projective resolutions of graded modules." In Graduate Texts in Mathematics, 273–82. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0105-9_21.

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Martı́nez, Consuelo, and Efim Zelmanov. "Graded Modules over Superconformal Algebras." In Non-Associative and Non-Commutative Algebra and Operator Theory, 41–53. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32902-4_3.

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Vasconcelos, Wolmer V. "Cohomological Degrees of Graded Modules." In Six Lectures on Commutative Algebra, 345–92. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0346-0329-4_6.

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Nastasescu, Constantin, and Freddy Van Oystaeyen. "2. The Category of Graded Modules." In Methods of Graded Rings, 19–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40998-4_2.

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Nastasescu, Constantin, and Freddy Van Oystaeyen. "3. Modules over Strongly Graded Rings." In Methods of Graded Rings, 81–113. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40998-4_3.

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Caenepeel, S. "Cancellation theorems for projective graded modules." In Ring Theory, 50–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0100914.

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Polishchuk, Alexander, and Leonid Positselski. "Operations on graded algebras and modules." In University Lecture Series, 55–80. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/ulect/037/03.

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Krause, Günter, and Thomas Lenagan. "Graded and filtered algebras and modules." In Graduate Studies in Mathematics, 61–72. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/gsm/022/07.

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Conference papers on the topic "Graded modules"

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He, J. W., and Q. S. Wu. "Koszul differential graded algebras and modules." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0007.

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Clegg, Benjamin, Maria-Cruz Villa-Uriol, Phil McMinn, and Gordon Fraser. "Gradeer: An Open-Source Modular Hybrid Grader." In 2021 IEEE/ACM 43rd International Conference on Software Engineering: Software Engineering Education and Training (ICSE-SEET). IEEE, 2021. http://dx.doi.org/10.1109/icse-seet52601.2021.00015.

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Ghatak, Kamakhya P. "Photoemission from periodic structure of graded superlattices under magnetic field." In Process Module Metrology, Control and Clustering, edited by Cecil J. Davis, Irving P. Herman, and Terry R. Turner. SPIE, 1992. http://dx.doi.org/10.1117/12.56626.

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Tyagi, Pawan. "Student Presentation Based Effective Teaching (SPET) Approach for Advanced Courses." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66029.

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A student activity based effective teaching approach can significantly improve student learning. However, implementing student activity based teaching for the advanced level courses can be very challenging. Incomplete course coverage and the amount of time required by an instructor for designing active teaching strategies are cited as the common inhibiting factors in the adoption of active student teaching. This paper discusses a student presentation based effective teaching (SPET) approach that covers more course material than that covered in the conventional or other student-active teaching methods. Moreover, SPET approach requires less preparation time on instructor behalf. This paper is based on the effective teaching experiments conducted on senior level science and technology courses at University of the District of Columbia. Under the SPET approach, students are given reading assignment to prepare ∼ 10–20 minutes long power point presentation on well-defined conceptual topics, questions, or chapter modules. In every class typically three presentations take place on the same questions or topics. However, non-presenter students are required to generate conceptual questions. These questions were asked during or after the presentation by the designated students. Students’ presentations were graded according to the rubric focusing on coverage of suggested topics, quality of presentation, and questions and answers. Hence, the whole class is engaged in understanding the topic either for making the presentation or for creating conceptual questions. These grades were posted right after the class in the Blackboard’s online grade center to provide quick feedback. The following are key advantages of this approach. (1) Students understand 50–100% about the intended topic during self-reading and while making a presentation or participating in class discussion. (2) Repeating same concepts thrice during a class period and occasionally with instructor’s insights enable deep learning. (3) Students get quick quantitative feedback after each class and qualitative feedback during the class from instructor and peers. (4) This approach allowed coverage of very complex topics. (5) Students improved their communication skills by making coherent presentations and doing class discussion. In the survey, students reflected a higher degree of satisfaction with their learning as compared to instructor’s lecture-based classroom education system. This approach is highly suitable for advanced-level elective courses with small enrollment.
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Xiao, Guoxian, Xiaoning Jin, Qing Chang, Stephan Biller, Jun Ni, and S. Jack Hu. "Performance Analysis and Optimization of Remanufacturing Systems With Stochastic Returns." In ASME 2012 International Manufacturing Science and Engineering Conference collocated with the 40th North American Manufacturing Research Conference and in participation with the International Conference on Tribology Materials and Processing. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/msec2012-7383.

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This paper considers a modular product assembly and inventory planning and control problem in a remanufacturing environment. The return process of end-of-life product is a stochastic process in terms of arriving time, quality and quantity. We investigate the returned module reassembly policies in an assemble-to-order strategy. A threshold policy is considered to control the admission of the product returns and its effect on the trade-off between excessive inventory and stock out. We study how the control parameters in these strategies relate to the average inventory level and stock out level of the remanufacturable modules. Starting with a single quality grade problem, we extend the analysis to a multiple quality grade problem and derive exact expression of the system performance measures as function of the control parameters. Main objective of this paper is to provide managerial insights into decision-making for stochastic remanufacturing systems.
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Theotokoglou, Efstathios E., Ioannis H. Stampouloglou, Glaucio H. Paulino, Marek-Jerzy Pindera, Robert H. Dodds, Fernando A. Rochinha, Eshan Dave, and Linfeng Chen. "Analysis of Bonded Elastic Wedges with Angular Moduli Variation." In MULTISCALE AND FUNCTIONALLY GRADED MATERIALS 2006. AIP, 2008. http://dx.doi.org/10.1063/1.2896888.

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Wang, Xiushan, and Gang Li. "Prediction Model of Graded Gravel Resilient Modulus." In Third International Conference on Transportation Engineering (ICTE). Reston, VA: American Society of Civil Engineers, 2011. http://dx.doi.org/10.1061/41184(419)257.

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Culp, William G., and Brendaly Cintron-De Leon. "Graded Approach to Small Modular Reactor Implementation." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78602.

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The regulatory process covers health and safety issues in the context of large power reactors; this paper addresses how requirements on designers and owners might be scaled for small modular reactors (SMR) in proportion to the risks for the type of technology. Light water SMRs are designed to incorporate many of the fuel and passive safety features already described in the Design Control Documents and Final Safety Analysis Report (FSARs) for large power reactors. Regulations are written to principally address large and advanced power reactors. This paper proposes a several step process to simplify the process of getting design certification, a license to manufacture LWR type SMR, construct a SMR at multiple sites, and accelerate an applicant’s Early Site Review and Combined Operating License process. This paper looks at issues identified by the NRC Commissioners in SECY 10, 0034, 3/28/10, Potential Policy, Licensing, and Key Technical Issues for Small Modular Reactor Designs, from the industry perspective. Since the SMR issues are less complex and involve less risk than the corresponding issues for large reactors, this paper describes theoretical means of reducing the scope, schedule, and cost of a SMR.
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Modro, S. Michael, James Fisher, Kevan Weaver, Pierre Babka, Jose Reyes, John Groome, and Gary Wilson. "Generation-IV Multi-Application Small Light Water Reactor (MASLWR)." In 10th International Conference on Nuclear Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/icone10-22435.

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The Idaho National Engineering and Environmental Laboratory (INEEL), Nexant Inc. and the Oregon State University (OSU) have developed a Multi-Application Small Light Water Reactor (MASLWR) concept. The MASLWR is a small, safe and economic natural circulation pressurized light water reactor. MASLWR reactor module consists of an integral reactor/steam generator located in a steel cylindrical containment. The entire module is to be entirely shop fabricated and transported to site on most railways or roads. Two or more modules are located in a reactor building, each being submersed in a common, below grade cavity filled with water. For the most severe postulated accident, the volume of water in the cavity provides a passive ultimate heat sink for 3 or more days allowing the restoration of lost normal active heat removal systems. MASLWR thermal power of a single module is 150 MWt, primary system pressure 10.5 MPa, steam pressure 1.52 MPa and the net electrical output is 35–50 MWe.
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Liu, Rui, Hamid Nayeb-Hashemi, Masoud Olia, and Ashkan Vaziri. "On Transverse Vibrations of Functionally Graded Rotating Hollow Disk." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39383.

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We studied the stress field and vibration characteristics of functionally graded rotating disks by solving the governing equation of motion using the finite difference scheme. The material was assumed to have a constant Poisson’s ratio with the elastic modulus varying as a power law function of the disk radius. Such a material could be developed by using particle reinforced composites with various reinforcements or reinforcement volume fraction. The results show that the first critical speed of the rotating disk could be increased by using FGMs. The first critical speed is greater for disks having higher elastic modulus at the outer radius. However, the disk may be unstable for certain distribution functions.
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Reports on the topic "Graded modules"

1

King, Bruce Hardison, and Charles David Robinson. Comparative Angle of Incidence Characterization of Utility Grade Photovoltaic Modules. Office of Scientific and Technical Information (OSTI), October 2018. http://dx.doi.org/10.2172/1481528.

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2

Windes, Willaim, G. Strydom, J. Kane, and R. Smith. Role of nuclear grade graphite in controlling oxidation in modular HTGRs. Office of Scientific and Technical Information (OSTI), November 2014. http://dx.doi.org/10.2172/1167529.

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3

Gee, J. M. High-efficiency one-sun photovoltaic module demonstration using solar-grade CZ silicon. Final report. Office of Scientific and Technical Information (OSTI), October 1996. http://dx.doi.org/10.2172/399682.

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