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Academic literature on the topic 'Gradings'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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Journal articles on the topic "Gradings"

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Khazal, R., Crina Boboc, and S. Dăscălescu. "Group gradings of M2(K)." Bulletin of the Australian Mathematical Society 68, no. 2 (October 2003): 285–93. http://dx.doi.org/10.1017/s0004972700037667.

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We describe all group gradings of the matrix algebra M2(k), where k is an arbitrary field. We prove that any such grading reduces to a grading of type C2, a grading of type C2 × C2, or to a good grading. We give new simple proofs for the description of C2-gradings and C2 × C2-gradings on M2(K).

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Gordienko, Alexey, and Ofir Schnabel. "Categories and Weak Equivalences of Graded Algebras." Algebra Colloquium 26, no. 04 (November 18, 2019): 643–64. http://dx.doi.org/10.1142/s1005386719000476.

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In the study of the structure of graded algebras (such as graded ideals, graded subspaces, and radicals) or graded polynomial identities, the grading group can be replaced by any other group that realizes the same grading. Here we come to the notion of weak equivalence of gradings: two gradings are weakly equivalent if there exists an isomorphism between the graded algebras that maps each graded component onto a graded component. Each group grading on an algebra can be weakly equivalent to G-gradings for many different groups G; however, it turns out that there is one distinguished group among them, called the universal group of the grading. In this paper we study categories and functors related to the notion of weak equivalence of gradings. In particular, we introduce an oplax 2-functor that assigns to each grading its support, and show that the universal grading group functor has neither left nor right adjoint.

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Havlíček, Miloslav, Jiří Patera, and Edita Pelantová. "On the Fine Gradings of Simple Classical Lie Algebras." International Journal of Modern Physics A 12, no. 01 (January 10, 1997): 189–94. http://dx.doi.org/10.1142/s0217751x97000268.

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Using the classification of maximal commutative subgroups in group of automorphisms of gl(n,C), we describe procedure for obtaining fine gradings in simple classical Lie algebras. This algorithm is applied to the algebras sl(4,C), o(4,C) and sp(4,C). Every grading is associated with label graphs. In this way, the problem whether two gradings are equivalent is reduced to the problem whether corresponding graphs are isomorphic. It is shown that there exist exactly 9 nonequivalent fine gradings in gl(4,C), 6 fine gradings in o(4,C) and 3 fine gradings in sp(4,C).

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Hupe, Marie Christine, Anne Offermann, Verena Sailer, Axel S. Merseburger, and Sven Perner. "Das neue ISUP 2014/WHO 2016 Prostatakarzinom-Grading – Status quo 5 Jahre nach seiner Einführung." Aktuelle Urologie 50, no. 06 (August 7, 2019): 619–24. http://dx.doi.org/10.1055/a-0918-9473.

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Zusammenfassung Hintergrund Im Jahr 2014 wurde durch die ISUP (International Society of Urological Pathology) eine Modifikation des Gradings für das Prostatakarzinom (PCa) eingeführt, welches 2016 von der Weltgesundheitsorganisation (WHO) anerkannt und übernommen wurde. Neben der Definition von 5 „Grade Groups“ wurden auch einige histomorphologische Kriterien angepasst. Unsere Übersichtsarbeit stellt die Ergebnisse aller aktuellen Studien und deren Bewertungen des neuen Gradings zusammen. Material und Methoden Es erfolgte eine Literaturrecherche in der PubMed-Datenbank. Insgesamt sind aus dem Zeitraum 2016 – 2018 15 Studien identifiziert und in die Übersicht eingeschlossen worden. Ergebnisse Die Hauptziele des neuen ISUP 2014/WHO 2016 PCa-Gradings sind ein (I) präziseres und vereinfachtes Grading, (II) eine verringerte Übertherapie indolenter PCa und (III) eine verbesserte Kommunikation mit den Patienten. Die Mehrzahl der Studien wählte das biochemische Rezidiv als Endpunkt und bescheinigte dem neuen Grading eine höhere prognostische Wertigkeit im Vergleich zum früheren Gleason Grading. Interessanterweise war es jedoch nur in wenigen Studien klar ersichtlich, dass die archivierten Proben tatsächlich auch nach den modifizierten histomorphologischen Kriterien reevaluiert („Re-Grading“) und nicht nur in die neuen „Grade Groups“ übersetzt wurden („Re-Grouping“). Schlussfolgerung Die Mehrheit der analysierten Studien bestätigt die prognostische Wertigkeit des neuen ISUP 2014/WHO 2016 Gradings und empfiehlt dessen weltweite Anwendung. Jedoch muss bei der Interpretation bisheriger Studien berücksichtigt werden, dass das notwendige „Re-Grading“ als korrekte Anwendung des neuen Gradings nicht immer klar ersichtlich war.

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Koshrawipour, Tanja, Ingo Stricker, Andrea Tannapfel, Lars Steinstraesser, Stefan Langer, and Andrej Ring. "Risk factors leading to grading changes within 300 low-grade soft tissue sarcomas." Journal of Clinical Oncology 30, no. 15_suppl (May 20, 2012): 10059. http://dx.doi.org/10.1200/jco.2012.30.15_suppl.10059.

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10059 Background: Soft tissue sarcomas (STS) are rare, mesenchymal derived tumors. Based on malignancy, three grades are distinguished with G1 equaling low grade, G2 intermediate grade and G3 high grade, respectively. Studies have shown that some G1 tumors which underwent complete surgical resection reoccurred as lesions with a grading shift from G1 to higher malignancy. This grading change is referred to as up grading. Patients with grading changes were thoroughly examined in our study. Our aim was to find possible risk factors for up gradings, such as age, localization of tumor and tumor type. Methods: This retrospective case control study evaluated 333 Patients, who, between 1996 to 2011 were treated for G1 STS at Bergmannsheil Bochum, university clinic. These patients received complete initial surgical resection. Among our 333 patients, 9.9% (n=33) developed up gradings of their STS. These were then reviewed more closely in the aim of finding possible risk factors. We did not exclude any patients from our data or deliberately pick any grading changers and regard our collective as randomly sampled. The processed data includes age, gender, tumor type, tumor localization, occurrence of recidive and grading change. Results: Patients with up gradings were found to have a higher mean age of 4, 5 years than reference collective. The tumor type has a strong, statistically significant effect on grading change as patients with fibrosarcomas have a threefold risk of developing up gradings when compared to patients with other G1 STS. Conclusions: Our results indicate that age and tumor type play the key role in the development of up gradings in low malignant STS .Patients aged 60 and above diagnosed with fibrosarcomas are at a 3 times higher risk of developing a grading change as opposed to patients younger than 60 with other low grade STS than fibrosarcoma. We discussed the significance of these risk factors and argued whether, in addition to wide tumor resection, a short term postoperative radiotherapy should be applied for these patients to improve therapeutical outcome.

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Allison, Bruce, and Oleg Smirnov. "Coordinatization Theorems For Graded Algebras." Canadian Mathematical Bulletin 45, no. 4 (December 1, 2002): 451–65. http://dx.doi.org/10.4153/cmb-2002-048-4.

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AbstractIn this paper we study simple associative algebras with finite -gradings. This is done using a simple algebra Fg that has been constructed in Morita theory from a bilinear form g : U × V → A over a simple algebra A. We show that finite -gradings on Fg are in one to one correspondence with certain decompositions of the pair (U, V). We also show that any simple algebra R with finite -grading is graded isomorphic to Fg for some bilinear from g : U × V → A, where the grading on Fg is determined by a decomposition of (U, V) and the coordinate algebra A is chosen as a simple ideal of the zero component R0 of R. In order to prove these results we first prove similar results for simple algebras with Peirce gradings.

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Glabowski, Mariusz, Slawomir Hanczewski, Maciej Stasiak, and Joanna Weissenberg. "Modeling Erlang's Ideal Grading with Multirate BPP Traffic." Mathematical Problems in Engineering 2012 (2012): 1–35. http://dx.doi.org/10.1155/2012/456910.

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This paper presents a complete methodology for modeling gradings (also called non-full-availability groups) servicing single-service and multi-service traffic streams. The methodology worked out by the authors makes it possible to determine traffic characteristics of various types of gradings with state-dependent call arrival processes, including a new proposed structure of the Erlang’s Ideal Grading with the multirate links. The elaborated models of the gradings can be used for modeling different systems of modern networks, for example, the radio interfaces of the UMTS system, switching networks carrying a mixture of different multirate traffic streams, and video-on-demand systems. The results of the analytical calculations are compared with the results of the simulation data for selected gradings, which confirm high accuracy of the proposed methodology.

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Han, Gang, Yucheng Liu, and Kang Lu. "Multiplicity-Free Gradings on Semisimple Lie and Jordan Algebras and Skew Root Systems." Algebra Colloquium 26, no. 01 (March 2019): 123–38. http://dx.doi.org/10.1142/s1005386719000129.

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A G-grading on an algebra, where G is an abelian group, is called multiplicity-free if each homogeneous component of the grading is 1-dimensional. We introduce skew root systems of Lie type and skew root systems of Jordan type, and use them to construct multiplicity-free gradings on semisimple Lie algebras and on semisimple Jordan algebras respectively. Under certain conditions the corresponding Lie (resp., Jordan) algebras are simple. Two families of skew root systems of Lie type (resp., of Jordan type) are constructed and the corresponding Lie (resp., Jordan) algebras are identified. This is a new approach to study abelian group gradings on Lie and Jordan algebras.

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Cibils, Claude, María Julia Redondo, and Andrea Solotar. "On universal gradings, versal gradings and Schurian generated categories." Journal of Noncommutative Geometry 8, no. 4 (2014): 1101–22. http://dx.doi.org/10.4171/jncg/180.

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Draper, Cristina, and Cándido Martín. "Gradings on g2." Linear Algebra and its Applications 418, no. 1 (October 2006): 85–111. http://dx.doi.org/10.1016/j.laa.2006.01.017.

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Dissertations / Theses on the topic "Gradings"

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McDonnell, Benjamin [Verfasser], and Wolfgang [Akademischer Betreuer] Soergel. "Gradings and soergel bimodules." Freiburg : Universität, 2019. http://d-nb.info/1203066686/34.

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Morley, Alastair. "Involutive gradings, Peirce gradings and weak*-closed Peirce inner ideals in JBW*-triples." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497056.

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Dell'Arciprete, Alice. "Good gradings of simple Lie algebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17105/.

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This thesis aims to study the good gradings of simple finite-dimensional Lie algebras. The Dynkin grading is given as an example of good Z-grading of a semisimple Lie algebra. The main properties of a good Z-grading of a semisimple Lie algebra are proved and all good Z-gradings of gl(n), the Lie algebra of all matrices of order n, are classified. Finally, we extend the definition of good gradings to Lie superalgebras and start studying the good gradings of the Cartan superalgebra W(n). The case of W(2) and W(3) are analyzed.

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Morigi, Davide. "A combinatorial description of the good Z-gradings of the symplectic Lie algebra." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17108/.

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In this thesis we investigate the concept of good Z-grading of a finite dimensional semisimple Lie algebra over an algebraically closed field of characteristic 0. Throughout the thesis we make use of the theorem of Jacobson Morozov, a fundamental result in the Lie theory. First of all we give a fundamental example of good grading, the Dynkin one. Afterwards we study more in general some properties of the good Z-gradings of a Lie algebra. Finally we give a complete description of the good Z-gradings of the symplectic Lie algebra.

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Lubbe, Andreas A. "The inid operation and applications to peirce and involutive gradings in JBW*-triples." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509985.

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Adler, Linda [Verfasser]. "Prognostische Stratifizierung metastasierter gastroenteropankreatischer neuroendokriner Neoplasien mittels 18F-FDG-PET/CT : Möglichkeit eines metabolischen Gradings / Linda Adler." Bonn : Universitäts- und Landesbibliothek Bonn, 2015. http://d-nb.info/1080592113/34.

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Epure, Raul-Paul [Verfasser], and Mathias [Akademischer Betreuer] Schulze. "Explicit and effective Mather-Yau correspondence in view of analytic gradings / Raul-Paul Epure ; Betreuer: Mathias Schulze." Kaiserslautern : Technische Universität Kaiserslautern, 2020. http://d-nb.info/122297410X/34.

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Bagnoli, Lucia. "Z-graded Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14118/.

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This thesis investigates the role of filtrations and gradings in the study of Lie superalgebras. The main connections between the Z-grading of a Lie superalgebra and its structure are explained. As an example, the simplicity of the Lie superalgebras W(m,n) and S(m,n) is proved. Finally, the strongly symmetric gradings of length three and five of the Lie superalgebras W(m,n) and S(m,n) are classified.

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Flosdorf, Kerstin Verena [Verfasser]. "Heterogenitätsanalyse in Computer-, Magnetresonanz- und Positronenemissionstomographie zur Unterscheidung verschiedener Knochensarkom-Entitäten und Gradings sowie zur Vorhersage von progressionsfreiem Überleben / Kerstin Verena Flosdorf." Ulm : Universität Ulm, 2019. http://d-nb.info/119072751X/34.

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Lampe, Dorothea [Verfasser], and Heinz [Akademischer Betreuer] Handels. "Computerunterstütze Vermessung der Nasennebenhöhlen auf der Grundlage von 3D-CT-Daten und Differentialdiagnose in fünf unterschiedliche Gradings / Dorothea Lampe. Betreuer: Heinz Handels." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1030366365/34.

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Books on the topic "Gradings"

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1977-, Kochetov Mikhail, ed. Gradings on simple Lie algebras. Providence, Rhode Island: American Mathematical Society, 2013.

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Brookhart, Susan M. Grading. 2nd ed. New York: Merrill, 2009.

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Grading. Upper Saddle River, N.J: Pearson, 2004.

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Grading. 2nd ed. Upper Saddle River,N.J: Pearson Education, 2008.

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Walvoord, Barbara E. Fassler. Effective Grading. New York: John Wiley & Sons, Ltd., 2009.

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Staab, Steffen. Grading Knowledge. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46618-5.

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Pagel-Theisen, Verena. Diamond grading abc: Handbook for diamond grading. Antwerp: Rubin & Son, 1993.

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United States. Agricultural Marketing Service. Poultry-grading manual. [Washington, D.C.?]: U.S. Dept. of Agriculture, Agricultural Marketing Service, 1989.

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United States. Agricultural Marketing Service. Poultry-grading manual. [Washington, D.C.?]: U.S. Dept. of Agriculture, Agricultural Marketing Service, 1989.

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Excavation & grading handbook. 2nd ed. Carlsbad, CA: Craftsman Book Co., 1987.

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Book chapters on the topic "Gradings"

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Elduque, Alberto, and Mikhail Kochetov. "Gradings on algebras." In Gradings on Simple Lie Algebras, 9–26. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/02.

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Soergel, Wolfgang. "Gradings on Representation Categories." In Proceedings of the International Congress of Mathematicians, 800–806. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_73.

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Russell, Peter. "Gradings of Polynomial Rings." In Algebraic Geometry and its Applications, 365–73. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2628-4_22.

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Giambruno, Antonio, and Mikhail Zaicev. "Group gradings and group actions." In Mathematical Surveys and Monographs, 61–85. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/surv/122/03.

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Iyengar, Srikanth, Graham Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, Anurag Singh, and Uli Walther. "Gradings, filtrations, and Gröbner bases." In Graduate Studies in Mathematics, 55–65. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/gsm/087/05.

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Elduque, Alberto, and Mikhail Kochetov. "Introduction." In Gradings on Simple Lie Algebras, 1–8. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/01.

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Elduque, Alberto, and Mikhail Kochetov. "Associative algebras." In Gradings on Simple Lie Algebras, 27–61. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/03.

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Elduque, Alberto, and Mikhail Kochetov. "Classical Lie algebras." In Gradings on Simple Lie Algebras, 63–122. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/04.

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Elduque, Alberto, and Mikhail Kochetov. "Composition algebras and type 𝐺₂." In Gradings on Simple Lie Algebras, 123–61. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/05.

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Elduque, Alberto, and Mikhail Kochetov. "Jordan algebras and type 𝐹₄." In Gradings on Simple Lie Algebras, 163–206. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/189/06.

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Conference papers on the topic "Gradings"

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Manturov, Vassily Olegovich. "Additional Gradings in Khovanov Homology." In Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812819116_0013.

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Shen, Yang, Hua-yang Ge, and Hui Liang. "Compaction Characteristics of Calcareous Sand with Different Gradings." In International Conference on Geotechnical and Earthquake Engineering 2018. Reston, VA: American Society of Civil Engineers, 2019. http://dx.doi.org/10.1061/9780784482049.033.

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Horn, LC, AK Höhn, B. Hentschel, and CE Brambs. "Prognoserelevanz des Gradings beim Plattenepithelkarzinom der Cervix uteri Stadium pT1b1 bei radikal hysterektomierten Patientinnen." In Kongressabstracts zur 13. Jahrestagung der Mitteldeutschen Gesellschaft für Frauenheilkunde und Geburtshilfe e.V. (MGFG). Georg Thieme Verlag KG, 2019. http://dx.doi.org/10.1055/s-0039-1692085.

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Singh, Mukesh. "Corelation of MRC gradings within a large single practice primary care COPD cohort in the UK." In Annual Congress 2015. European Respiratory Society, 2015. http://dx.doi.org/10.1183/13993003.congress-2015.pa1043.

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Chodyla, M., J. Grueneisen, O. Martin, J. Haubold, F. Nensa, and L. Umutlu. "Maschinelles Lernen und radiomische Analyse von Datensätzen aus der MR-Mammografie zur Vorhersage des Gradings, Hormonrezeptorstatus und Lymphknotenmetastasen bei Patientinnen mit Brustkrebs." In 101. Deutscher Röntgenkongress und 9. Gemeinsamer Kongress der DRG und ÖRG. © Georg Thieme Verlag KG, 2020. http://dx.doi.org/10.1055/s-0040-1703327.

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Tsiklakov, Alexander, Peter John Weinheber, Wicher Roelf Wichers, J. Zuo, Sergey Zimin, Anna Driller, and Roman Andreevich Oshmarin. "Determining Reservoir Connectivity and Compositional Grading by Mapping Asphaltene Gradients (Russian)." In SPE Russian Oil and Gas Exploration and Production Technical Conference and Exhibition. Society of Petroleum Engineers, 2012. http://dx.doi.org/10.2118/160590-ru.

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Patel, Shaswat, Maithili Lohakare, Samyak Prajapati, Shaanya Singh, and Nancy Patel. "DiaRet: A Browser-Based Application for the Grading of Diabetic Retinopathy with Integrated Gradients." In 2021 IEEE International Conference on Robotics, Automation and Artificial Intelligence (RAAI). IEEE, 2021. http://dx.doi.org/10.1109/raai52226.2021.9507938.

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Ellis, Heidi J. C. "Self-grading." In the 11th annual SIGCSE conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1140124.1140258.

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Bode, Martina, Jenny Ross, and Irene Tsapara. "ONLINE GRADING PLATFORMS, IMPROVE QUALITY AND EFFICIENCY OF GRADING!" In 10th International Conference on Education and New Learning Technologies. IATED, 2018. http://dx.doi.org/10.21125/edulearn.2018.2693.

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Shashidhar, Vinay, Nishant Pandey, and Varun Aggarwal. "Spoken English Grading." In KDD '15: The 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2783258.2788595.

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Reports on the topic "Gradings"

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Whitney, D., and V. Pope. Risk Grading Spreadsheet Tool. Office of Scientific and Technical Information (OSTI), July 2012. http://dx.doi.org/10.2172/1406455.

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Chong, Alberto, Rafael La Porta, Florencio Lopez-de-Silanes, and Andrei Shleifer. Letter Grading Government Efficiency. Cambridge, MA: National Bureau of Economic Research, August 2012. http://dx.doi.org/10.3386/w18268.

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Judge, A., and W. Bawden. Geothermal Gradients. Natural Resources Canada/ESS/Scientific and Technical Publishing Services, 1987. http://dx.doi.org/10.4095/126947.

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Crane, P. W., and E. V. Lewis. Use grading of classified slugs. Office of Scientific and Technical Information (OSTI), August 1994. http://dx.doi.org/10.2172/86772.

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Xia, Xiaofeng. Spectroscopic Biomarkers For Breast Tumor Grading. Fort Belvoir, VA: Defense Technical Information Center, December 2010. http://dx.doi.org/10.21236/ada542537.

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Figlio, David, and Maurice Lucas. Do High Grading Standards Affect Student Performance? Cambridge, MA: National Bureau of Economic Research, October 2000. http://dx.doi.org/10.3386/w7985.

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Ulrich, Andri, and Denver Lee Smith. Apollo-19 Ventilator Project Comparisons, Grading and Alternatives. Office of Scientific and Technical Information (OSTI), April 2020. http://dx.doi.org/10.2172/1617334.

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Cort, G., S. Donahue, J. Frank, B. Perkins, and J. Wrye. Grading standards, prepared by the Configuration Management Office. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10117311.

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Castelluccio, Gustavo, Hojun Lim, John Emery, and Corbett Battaile. Fracture Toughness of Microstructural Gradients. Office of Scientific and Technical Information (OSTI), October 2016. http://dx.doi.org/10.2172/1761823.

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Lavy, Victor. Performance Pay and Teachers' Effort, Productivity and Grading Ethics. Cambridge, MA: National Bureau of Economic Research, July 2004. http://dx.doi.org/10.3386/w10622.

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