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The Algebraic Group Model and its Applications [chapter]

Georg Fuchsbauer, Eike Kiltz, Julian Loss
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
To overcome this limitation, we propose the Algebraic Group Model (AGM), a model that lies in between the Standard Model and the GGM.  ...  It is the first restricted model of computation covering group-specific algorithms yet allowing to derive simple and meaningful security statements.  ...  The first author is supported by the French ANR EfTrEC project (ANR-16-CE39-0002). The second author was supported in part by ERC Project ERCC (FP7/615074) and by DFG SPP 1736 Big Data.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-96881-0_2">doi:10.1007/978-3-319-96881-0_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6cfqqtscgvd5dakps7qwh5adqi">fatcat:6cfqqtscgvd5dakps7qwh5adqi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190219221357/http://pdfs.semanticscholar.org/1b90/204d6127f326680cb2cf65fa314c3715aea7.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1b/90/1b90204d6127f326680cb2cf65fa314c3715aea7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-96881-0_2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Editorial Messages

Journal Of Algebraic Statistics
<span title="2010-04-30">2010</span> <i title="Paul V. Galvin Library/Illinois Institute of Technology"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pceem56g7zg55pexqhqrmek2om" style="color: black;">Journal of Algebraic Statistics</a> </i> &nbsp;
focused on the applications of algebraic geometry and its computational tools in the study of statistical models.  ...  Just as it has been continually happening in the world of mathematical sciences, the group of mathematical scientists led by (for example) Professor Eyup Cetin and his colleagues (who are responsible for  ...  Algebraic Statistics is the emerging new field focused on the applications of algebraic geometry and its computational tools in the study of statistical models.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18409/jas.v1i1.3">doi:10.18409/jas.v1i1.3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yqtet6ucbja2pmf3vsgp4jhzke">fatcat:yqtet6ucbja2pmf3vsgp4jhzke</a> </span>
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Model-Theoretic Algebra With particular emphasis on fields, rings, modules

M. Prest
<span title="">1993</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/djmawcsftbaaxk2nkcppkone3i" style="color: black;">Bulletin of the London Mathematical Society</a> </i> &nbsp;
As a whole, this book is highly recommended for the serious student of models of arithmetic.  ...  On the other hand, I feel that the author missed an opportunity by not including any account of the development in the last ten years of connections between weak arithmetic and computational complexity  ...  The use of the term 'algebra' in 'model-theoretic algebra' is at once too restrictive and too general: too general since, for example, the model theory of fields takes its character from its objects of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1112/blms/25.2.195">doi:10.1112/blms/25.2.195</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnriywskevbfxmguff6z3dewky">fatcat:pnriywskevbfxmguff6z3dewky</a> </span>
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Wigner and the groups in classifying elementary particles and nuclear states

J. Cseh, S. Varró, P. Ádám, T.S. Biró, G.G. Barnaföldi, P. Lévai
<span title="">2014</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oduy4e4fvfhovftixyndrlkomi" style="color: black;">EPJ Web of Conferences</a> </i> &nbsp;
The application of group-representations in nuclear and particle physics, as initiated by Wigner [1], is considered.  ...  The role of the U(4) group is discussed, first in relation with the spin-isospin supermultiplets [3] both in nuclear and in particle physics, then as a dynamical group of the two-body systems in both disciplines  ...  In conclusion we can say that the "Gruppenpest", how the application of the group theoretical methods was called (after its invention by Wigner and others) turned out to be a funny disease.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/epjconf/20147803002">doi:10.1051/epjconf/20147803002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ybmhjyk6fnbp7jtmj6l2e7eayq">fatcat:ybmhjyk6fnbp7jtmj6l2e7eayq</a> </span>
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Connecting Factors for the Application of a Digital Algebra Learning System: A Study with Textbook AuthorsFacteurs de connexion pour l'application d'un système d'apprentissage d'algèbre numérique: une étude avec un auteur de manuels

Maike Braukmüller
<span title="2020-09-15">2020</span> <i title="Pontifical Catholic University of Sao Paulo (PUC-SP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qutk6jrizfaxxpkawcrgl57gle" style="color: black;">Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática</a> </i> &nbsp;
A key issue is its applicability in schools and textbooks.  ...  In the paper, the study and preliminary results are presented.Keywords: ATD; Digital Learning, Textbooks, Algebra Learning.  ...  Acknowledgement The MAL-project (Multimodal Algebra Learning) is funded by the German Federal Ministry of Education and Research in the grant programme "Erfahrbares Lernen" (experiencable learning).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23925/1983-3156.2020v22i4p232-239">doi:10.23925/1983-3156.2020v22i4p232-239</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zlce4belwzcazihvfu35rpu5ua">fatcat:zlce4belwzcazihvfu35rpu5ua</a> </span>
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Page 4628 of Mathematical Reviews Vol. , Issue 98G [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Hamermesh’s classic Group theory and its application to physical problems [Addison- Wesley Publishing Co., Inc., Reading, Mass.  ...  98¢:8 1052 of explaining nature by means of a model. The value of this book is mathematical: it offers the readers a consolidated description of the symmetric and unitary groups. M.  ... 
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Linear algebra and statistics: Second special issue

Michael D. Perlman, Friedrich Pukelsheim, George P.H. Styan
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
The 36 research papers in this second Special Issue of Linear Algebra and Its Applications on Statistics include applications to statistics and probability of circulants, determinantal equations, generalized  ...  As was noted in its Preface the application of linear algebraic methods in statistics can be traced back to the work of Gauss on the optimality of the least squares estimator under a very general set-up  ...  The 36 research papers in this second Special Issue of Linear Algebra and Its Applications on Statistics include applications to statistics and probability of circulants, determinantal equations, generalized  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(90)90331-6">doi:10.1016/0024-3795(90)90331-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ljwby4yvqzge3isjjhkwzzllyq">fatcat:ljwby4yvqzge3isjjhkwzzllyq</a> </span>
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Infinite Dimensional Algebras and their Applications to Quantum Integrable Systems

Andreas Fring, Petr P Kulish, Nenad Manojlović, Zoltán Nagy, Joana Nunes da Costa, Henning Samtleben
<span title="2008-04-29">2008</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nzcpmvl7nzgojf4q47bpg2qrdu" style="color: black;">Journal of Physics A: Mathematical and Theoretical</a> </i> &nbsp;
This issue provides some further progress in the investigations of the algebraic structures, such as Lie groups and Lie algebras, quantum groups, algebroids, etc, which have always played an important  ...  It is now well understood that the reality of the spectrum of these models can be attributed either to the unbroken PT-symmetry of the entire system or to its pseudo(quasi)-Hermiticity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1751-8121/41/19/190301">doi:10.1088/1751-8121/41/19/190301</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dquws45gandtrhcjbbfrlzi6ji">fatcat:dquws45gandtrhcjbbfrlzi6ji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180727042748/http://iopscience.iop.org/article/10.1088/1751-8121/41/19/190301/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/af/25/af25ff2525f6c2c7328ebe1c3b1359ea0aebbbd1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1751-8121/41/19/190301"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> iop.org </button> </a>

Page 1231 of Mathematical Reviews Vol. , Issue 98B [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
quasitriangularity, and application to the g-rotator model.  ...  After a self-contained introduction to the necessary mathematical tools (g-numbers, g-analysis, g-oscillators, g-algebras), the su,(2) rota- tor model and its extensions, the construction of deformed exactly  ... 
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Page 2542 of Mathematical Reviews Vol. , Issue 84g [page]

<span title="">1984</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
California Los Angeles, Los Angeles, Calif., 1971] and R. D. Kopperman [ Model theory and its applications, Allyn & Bacon, Boston, Mass., 1972; MR 51 #128]).  ...  Voiculescu (Bucharest) L 84g:03105 On fundamental transformation groups in the algebra of logic. Finite algebra and multiple-valued logic (Szeged, 1979), pp. 669-691, Collog. Math. Soc.  ... 
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Page 6581 of Mathematical Reviews Vol. , Issue 92m [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
cohomol- ogy of arithmetic groups and its applications to number theory (779-790).  ...  transform and its applications] (437-445); Yuri Nesterenko [Yu.  ... 
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Perspectives and reflections on teaching linear algebra

Ragnhild Johanne Rensaa, Ninni Marie Hogstad, John Monaghan
<span title="2020-06-03">2020</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xxsf25dzjngtdbynbtq7qbpcgi" style="color: black;">Teaching Mathematics and its Applications</a> </i> &nbsp;
The results of the investigation, these experts' opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications) and what students should be able to do.  ...  This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course  ...  Acknowledgement We thank MatRIC (www.matric.no) and UiT The Arctic University of Norway for financial support for this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/teamat/hraa002">doi:10.1093/teamat/hraa002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hu6qdqtjczg6vl3bjy35bucb5a">fatcat:hu6qdqtjczg6vl3bjy35bucb5a</a> </span>
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Page 3269 of Mathematical Reviews Vol. , Issue 2000e [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Teimuraz Pirashvili (D-BLF; Bielefeld) See also 17001, 55009. 19 K-THEORY 2000e:19001 19-06 * Algebraic K-theory and its applications.  ...  They then show that if the pushout of two quasi-model maps exists, it is the model of the pullback of the fiber square. Donald M.  ... 
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Page 3378 of Mathematical Reviews Vol. , Issue 86h [page]

<span title="">1986</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The second group of applications is to set theory and concerns the existence of the real 0# and Silver indiscernibles.  ...  A model of a theory is said to be algebraically prime if it is embeddable in any model of the theory. J. T. Baldwin and D. W. Kueker [Ann. Math.  ... 
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Page 4819 of Mathematical Reviews Vol. , Issue 911 [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author studies applications of Yang-Baxter algebras (YBA) to lattice models of statistical mechanics and QFT. The definitions and main facts concerning YBAs and their representations are given.  ...  These objects are closely connected with the YBA symmetry (quantum groups related to the y-deformation of the YBA underlying Lie group) and with the corresponding conformal model (braid group representations  ... 
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