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Journal articles on the topic 'Algebraic'

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Author: Grafiati

Published: 4 June 2021

Last updated: 4 March 2023

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1

Arutyunov, A. A. "ON DERIVATIONS ASSOCIATED WITH DIFFERENT ALGEBRAIC STRUCTURES IN GROUP ALGEBRAS." Eurasian Mathematical Journal 9, no. 3 (2018): 8–13. http://dx.doi.org/10.32523/2077-9879-2018-9-3-8-13.

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2

Ligęza, J., and M. Tvrdý. "On systems of linear algebraic equations in the Colombeau algebra." Mathematica Bohemica 124, no. 1 (1999): 1–14. http://dx.doi.org/10.21136/mb.1999.125977.

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3

Clerbout, M., and Y. Roos. "Semicommutations and algebraic algebraic." Theoretical Computer Science 103, no. 1 (August 1992): 39–49. http://dx.doi.org/10.1016/0304-3975(92)90086-u.

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4

Nesterenko, Yu V. "ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS." Mathematics of the USSR-Sbornik 51, no. 2 (February 28, 1985): 429–54. http://dx.doi.org/10.1070/sm1985v051n02abeh002868.

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5

Armitage, J. V. "ALGEBRAIC NUMBERS AND ALGEBRAIC FUNCTIONS." Bulletin of the London Mathematical Society 27, no. 3 (May 1995): 296–98. http://dx.doi.org/10.1112/blms/27.3.296.

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6

Hone, A. N. W., Orlando Ragnisco, and Federico Zullo. "Algebraic entropy for algebraic maps." Journal of Physics A: Mathematical and Theoretical 49, no. 2 (December 10, 2015): 02LT01. http://dx.doi.org/10.1088/1751-8113/49/2/02lt01.

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7

VIALLET, C. M. "ALGEBRAIC DYNAMICS AND ALGEBRAIC ENTROPY." International Journal of Geometric Methods in Modern Physics 05, no. 08 (December 2008): 1373–91. http://dx.doi.org/10.1142/s0219887808003375.

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We give the definition of algebraic entropy, which is a global index of complexity for dynamical systems with a rational evolution. We explain its geometrical meaning, and different methods, heuristic or exact to calculate this entropy. This quantity is a very good integrability detector. It also has remarkable properties, which make it an interesting object of study by itself. It is in particular conjectured to be the logarithm of algebraic integer, with a limited range of values, still to be explored.

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8

Pták, Vlastimil, and Pavla Vrbová. "Algebraic spectral subspaces." Czechoslovak Mathematical Journal 38, no. 2 (1988): 342–50. http://dx.doi.org/10.21136/cmj.1988.102229.

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9

Giusti, Neura Maria De Rossi, and Claudia Lisete Oliveira Groenwald. "Matemática na Comunidade: um contexto educativo para a aprendizagem social e desenvolvimento do pensamento algébricoMathematics in the Community: an educational context to the social learning and development of algebraic thinking." Educação Matemática Pesquisa : Revista do Programa de Estudos Pós-Graduados em Educação Matemática 23, no. 1 (April 11, 2021): 561–90. http://dx.doi.org/10.23925/1983-3156.2021v23i1p561-590.

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ResumoO artigo apresenta um recorte de uma pesquisa desenvolvida no município de Vacaria, no estado do Rio Grande do Sul, onde investigou-se a integração e divulgação de conhecimentos matemáticos na comunidade, a partir de um contexto educativo para a socialização de conceitos da educação básica, tendo em vista a aprendizagem social e, especificamente neste trabalho, o desenvolvimento do pensamento algébrico. Para a pesquisa qualitativa de investigação-ação foram utilizadas entrevistas dirigidas a comunidade participante e registros fotográficos com as resoluções das tarefas. As análises se apoiam sobre a Base Nacional Comum Curricular e as demandas cognitivas. As diferentes formas de aprender a aprender matemática, a mobilização, o interesse, os compartilhamentos dos conhecimentos matemáticos foram considerados, assim como as diferentes formas de resoluções e de raciocínio matemático empregado perante as tarefas apresentadas. As evidências apontam que os conhecimentos relacionados ao desenvolvimento do pensamento algébrico ofereceram empecilhos na interpretação e na compreensão da simbologia algébrica, visto que operar com letras e outros símbolos requer conhecimentos da linguagem algébrica para que se possa estabelecer generalizações, análises e resoluções. Também destacamos a importância da escola sobre o desenvolvimento de competências básicas.Palavras-chave: Educação matemática, Aprendizagem social, Aprender a aprender, Pensamento algébrico.AbstractThe article presents a snippet of a research developed in Vacaria in the state of Rio Grande do Sul, where the integration and disclosure of mathematical knowledge in the community was investigated, from an educational context to the socialisation of basic education concepts, in view of the social learning and, specifically in this study, the development of algebraic thinking. With a qualitative approach of investigation-action we verified direct interviews to the participating community and photographic records with the resolutions of the tasks. The analyses are based on the Common National Curriculum Base and the cognitive demands. The different forms of learn to learn mathematics, the mobilisation, the interest, the mathematical knowledge sharing were considered, as the different forms of resolutions and mathematical reasoning employed in front of presented tasks. The evidences indicate that knowledge related to development of algebraic thinking offered obstacles in the interpretation and understanding of algebraic simbology, since operating with letters and others symbols requires knowledge of algebraic language to establish generalisations, analyses, and resolutions. We also emphasise the importance of school for basic skills development.Keywords: Mathematical education, Social learning, Learn to learn, Algebraic thinking.ResumenEl artículo presenta un extracto de una investigación desarrollada en la ciudad de Vacaria, en el estado de Rio Grande do Sul, donde se investigó la integración y divulgación del conocimiento matemático en la comunidad, desde un contexto educativo para la socialización de conceptos de la enseãnza básica, con miras al aprendizaje social y, específicamente en este trabajo, el desarrollo del pensamiento algebraico. Con un enfoque cualitativo de la investigación-acción, se verificaron entrevistas orientadas a la comunidad participante y registros fotográficos con las resoluciones de las tareas. Los análisis se basan en la Base Curricular Nacional Común y las demandas cognitivas. Se consideraron las diferentes maneras de aprender a aprender matemáticas, la movilización, el interés, el intercambio de conocimientos matemáticos, así como las diferentes maneras de resoluciones y razonamientos matemáticos empleados en las tareas presentadas. Las evidencias apuntan que los conocimientos relacionados con el desarrollo del pensamiento algebraico ofrecieron obstáculos en la interpretación y comprensión de la simbología algebraica, ya que operar con letras y otros símbolos requiere conocimientos del lenguaje algebraico para poder establecer generalizaciones, análisis y resoluciones. También destacamos la importancia de la escuela en el desarrollo de habilidades básicas.Palabras clave: Educación matemática, Aprendizaje social, Aprender a aprender, Pensamiento algebraico.

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10

Hsiang, Jieh, and Anita Wasilewska. "Automating Algebraic Proofs in Algebraic Logic." Fundamenta Informaticae 28, no. 1,2 (1996): 129–40. http://dx.doi.org/10.3233/fi-1996-281208.

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11

Wampler, Charles W., and Andrew J. Sommese. "Numerical algebraic geometry and algebraic kinematics." Acta Numerica 20 (April 28, 2011): 469–567. http://dx.doi.org/10.1017/s0962492911000067.

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In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

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12

Abánades, Miguel, and Wojciech Kucharz. "Algebraic equivalence of real algebraic cycles." Annales de l’institut Fourier 49, no. 6 (1999): 1797–804. http://dx.doi.org/10.5802/aif.1738.

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13

Gao, Lingyun. "Algebraic solutions of algebraic differential equations." Applied Mathematics-A Journal of Chinese Universities 20, no. 1 (March 2005): 45–50. http://dx.doi.org/10.1007/s11766-005-0035-3.

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14

Bader, Uri, Bruno Duchesne, and Jean Lécureux. "Almost algebraic actions of algebraic groups and applications to algebraic representations." Groups, Geometry, and Dynamics 11, no. 2 (2017): 705–38. http://dx.doi.org/10.4171/ggd/413.

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15

Żołądek, Henryk. "On algebraic solutions of algebraic Pfaff equations." Studia Mathematica 114, no. 2 (1995): 117–26. http://dx.doi.org/10.4064/sm-114-2-117-126.

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16

Buchner, M., and W. Kucharz. "Algebraic vector bundles over real algebraic varieties." Bulletin of the American Mathematical Society 17, no. 2 (October 1, 1987): 279–83. http://dx.doi.org/10.1090/s0273-0979-1987-15558-3.

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17

Jamshidpey, Armin, Nicole Lemire, and Éric Schost. "Algebraic construction of quasi-split algebraic tori." Journal of Algebra and Its Applications 19, no. 11 (November 7, 2019): 2050206. http://dx.doi.org/10.1142/s0219498820502060.

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The main purpose of this work is to give a constructive proof for a particular case of the no-name lemma. Let [Formula: see text] be a finite group, [Formula: see text] a field that is equipped with a faithful [Formula: see text]-action, and [Formula: see text] a sign permutation [Formula: see text]-lattice (see the Introduction for the definition). Then [Formula: see text] acts naturally on the group algebra [Formula: see text] of [Formula: see text] over [Formula: see text], and hence also on the quotient field [Formula: see text]. A well-known variant of the no-name lemma asserts that the invariant sub-field [Formula: see text] is a purely transcendental extension of [Formula: see text]. In other words, there exist [Formula: see text] which are algebraically independent over [Formula: see text] such that [Formula: see text]. In this paper, we give an explicit construction of suitable elements [Formula: see text].

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18

Yuan, Pingzhi. "On algebraic approximations of certain algebraic numbers." Journal of Number Theory 102, no. 1 (September 2003): 1–10. http://dx.doi.org/10.1016/s0022-314x(03)00068-4.

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19

Janssen, Theo M. V. "Algebraic translations, correctness and algebraic compiler construction." Theoretical Computer Science 199, no. 1-2 (June 1998): 25–56. http://dx.doi.org/10.1016/s0304-3975(97)00267-3.

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20

Krishna, Amalendu, and Jinhyun Park. "Algebraic cobordism theory attached to algebraic equivalence." Journal of K-Theory 11, no. 1 (February 2013): 73–112. http://dx.doi.org/10.1017/is013001028jkt210.

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AbstractBased on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.

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21

Morgan, John W. "The algebraic topology of smooth algebraic varieties." Publications mathématiques de l'IHÉS 64, no. 1 (January 1986): 185. http://dx.doi.org/10.1007/bf02699195.

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22

Daniyarova, E. Yu, A. G. Myasnikov, and V. N. Remeslennikov. "Algebraic geometry over algebraic structures. II. Foundations." Journal of Mathematical Sciences 185, no. 3 (August 1, 2012): 389–416. http://dx.doi.org/10.1007/s10958-012-0923-z.

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23

Lindström, B. "Matroids algebraic overF(t) are algebraic overF." Combinatorica 9, no. 1 (March 1989): 107–9. http://dx.doi.org/10.1007/bf02122691.

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24

Tanimoto, Ryuji. "Algebraic torus actions on affine algebraic surfaces." Journal of Algebra 285, no. 1 (March 2005): 73–97. http://dx.doi.org/10.1016/j.jalgebra.2004.10.021.

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25

Voutsadakis, George. "Categorical Abstract Algebraic Logic: Referential Algebraic Semantics." Studia Logica 101, no. 4 (June 28, 2013): 849–99. http://dx.doi.org/10.1007/s11225-013-9500-9.

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26

Ehrmann, Silvia, Sebastian Gries, and Marc Alexander Schweitzer. "Generalization of algebraic multiscale to algebraic multigrid." Computational Geosciences 24, no. 2 (June 21, 2019): 683–96. http://dx.doi.org/10.1007/s10596-019-9826-0.

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27

Tao, Changli, Shijie Lu, and Peixin Chen. "Weakly algebraic reflexivity and strongly algebraic reflexivity." Applied Mathematics-A Journal of Chinese Universities 17, no. 2 (June 2002): 193–98. http://dx.doi.org/10.1007/s11766-002-0045-3.

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28

Grone, Robert, and Russell Merris. "Algebraic connectivity of trees." Czechoslovak Mathematical Journal 37, no. 4 (1987): 660–70. http://dx.doi.org/10.21136/cmj.1987.102192.

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29

Chajda, Ivan, and Petr Emanovský. "$\Sigma$-isomorphic algebraic structures." Mathematica Bohemica 120, no. 1 (1995): 71–81. http://dx.doi.org/10.21136/mb.1995.125890.

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30

KONG, XIAOLI, HONGJIA CHEN, and CHENGMING BAI. "CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS." International Journal of Mathematics 22, no. 02 (February 2011): 201–22. http://dx.doi.org/10.1142/s0129167x11006751.

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We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

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31

Praeger, Cheryl E. "Kronecker classes of fields and covering subgroups of finite groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 1 (August 1994): 17–34. http://dx.doi.org/10.1017/s1446788700036028.

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AbstractKronecker classes of algebraci number fields were introduced by W. Jehne in an attempt to understand the extent to which the structure of an extension K: k of algebraic number fields was influenced by the decomposition of primes of k over K. He found an important link between Kronecker equivalent field extensions and a certain covering property of their Galois groups. This surveys recent contributions of Group Theory to the understanding of Kronecker equivalence of algebraic number fields. In particular some group theoretic conjectures related to the Kronecker class of an extension of bounded degree are explored.

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32

Davis, James F., Qayum Khan, and Andrew Ranicki. "AlgebraicK–theory over the infinite dihedral group: an algebraic approach." Algebraic & Geometric Topology 11, no. 4 (September 5, 2011): 2391–436. http://dx.doi.org/10.2140/agt.2011.11.2391.

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33

Fletcher, Colin R., and C. F. Gardiner. "Algebraic Structures." Mathematical Gazette 71, no. 456 (June 1987): 172. http://dx.doi.org/10.2307/3616534.

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34

De Concini, Corrado, Philippe Gille, and Peter Littelmann. "Algebraic Groups." Oberwolfach Reports 18, no. 2 (August 24, 2022): 1087–148. http://dx.doi.org/10.4171/owr/2021/20.

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35

Bryant, Victor, and C. D. Godsil. "Algebraic Combinatorics." Mathematical Gazette 79, no. 484 (March 1995): 238. http://dx.doi.org/10.2307/3620119.

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36

Brion, Michel, Jens Carsten Jantzen, and Zinovy Reichstein. "Algebraic Groups." Oberwolfach Reports 10, no. 2 (2013): 1025–85. http://dx.doi.org/10.4171/owr/2013/17.

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37

Hacon, Christopher, Daniel Huybrechts, Yujiro Kawamata, and Bernd Siebert. "Algebraic Geometry." Oberwolfach Reports 12, no. 1 (2015): 783–836. http://dx.doi.org/10.4171/owr/2015/15.

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38

Drton, Mathias, Thomas Kahle, Bernd Sturmfels, and Caroline Uhler. "Algebraic Statistics." Oberwolfach Reports 14, no. 2 (April 27, 2018): 1207–79. http://dx.doi.org/10.4171/owr/2017/20.

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39

De Concini, Corrado, Peter Littelmann, and Zinovy Reichstein. "Algebraic Groups." Oberwolfach Reports 14, no. 2 (April 27, 2018): 1281–347. http://dx.doi.org/10.4171/owr/2017/21.

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40

Schwarzweller, Christoph, and Agnieszka Rowińska-Schwarzweller. "Algebraic Extensions." Formalized Mathematics 29, no. 1 (April 1, 2021): 39–47. http://dx.doi.org/10.2478/forma-2021-0004.

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Summary In this article we further develop field theory in Mizar [1], [2], [3] towards splitting fields. We deal with algebraic extensions [4], [5]: a field extension E of a field F is algebraic, if every element of E is algebraic over F. We prove amongst others that finite extensions are algebraic and that field extensions generated by a finite set of algebraic elements are finite. From this immediately follows that field extensions generated by roots of a polynomial over F are both finite and algebraic. We also define the field of algebraic elements of E over F and show that this field is an intermediate field of E|F.

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41

Bloom, Stephen L., and Zoltan Ésik. "Algebraic Ordinals." Fundamenta Informaticae 99, no. 4 (2010): 383–407. http://dx.doi.org/10.3233/fi-2010-255.

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42

Wild, P. "ALGEBRAIC COMBINATORICS." Bulletin of the London Mathematical Society 27, no. 2 (March 1995): 191–92. http://dx.doi.org/10.1112/blms/27.2.191.

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43

Kollár, János. "Algebraic hypersurfaces." Bulletin of the American Mathematical Society 56, no. 4 (January 28, 2019): 543–68. http://dx.doi.org/10.1090/bull/1663.

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44

Huneke, Craig, and Bernd Ulrich. "Algebraic linkage." Duke Mathematical Journal 56, no. 3 (June 1988): 415–29. http://dx.doi.org/10.1215/s0012-7094-88-05618-9.

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45

Galaktionova, E. "algebraic groups." Duke Mathematical Journal 77, no. 1 (January 1995): 63–69. http://dx.doi.org/10.1215/s0012-7094-95-07703-5.

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46

Vaninsky, Alexander. "Algebraic trigonometry." International Journal of Mathematical Education in Science and Technology 42, no. 3 (April 15, 2011): 406–11. http://dx.doi.org/10.1080/0020739x.2010.526307.

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47

Watase, Yasushige. "Algebraic Numbers." Formalized Mathematics 24, no. 4 (December 1, 2016): 291–99. http://dx.doi.org/10.1515/forma-2016-0025.

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Summary This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to the polynomial ring of ℚ[x] turns to be a field.

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48

Watt, Stephen M. "Algebraic generalization." ACM SIGSAM Bulletin 39, no. 3 (September 2005): 93–94. http://dx.doi.org/10.1145/1113439.1113452.

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49

HERLIHY, MAURICE, and SERGIO RAJSBAUM. "Algebraic spans." Mathematical Structures in Computer Science 10, no. 4 (August 2000): 549–73. http://dx.doi.org/10.1017/s0960129500003170.

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50

NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (December 1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

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Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homologies are functorial on the class of type-[Formula: see text] algebras and are characterized by a natural topological interpretation. All these notions extend to subsets of algebras. One obtains for this algebraic connectivity, the long exact sequences, relative [co]homologies, and the analogues of the usual [co]homological notions of the algebraic topologists. In fact, we show that the [co]homologies are actually the same as the simplicial [co]homology of simplicial complexes that depend functorially on the algebras. Thus the connectivities in question have a natural geometric meaning. This allows the wholesale import into algebra of the concepts, results, and techniques of algebraic topology. In particular, functoriality implies that the [co]homology of a pair of algebras A ⊆ B is an invariant of the position of A in B. When one V contains another, we obtain relationships between the [co] homology theories in the form of long exact sequences. Furthermore for finite algebras, V-[co]homology is effectively computable if membership in V is. We obtain an analogue of the Poincaré lemma (stating that subsets of an algebra in V are V-homologically trivial), extremely general guarantees of the existence of subsets with non-trivial V-homology for algebras not in V, long exact V-homotopy sequences, as well as analogues of the powerful Eilenberg-Zilber theorems and Kunneth theorems in the setting of V-connectivity for V a variety or pseudo-variety. Also in the more general case of any divisionally closed V, we construct the long exact Mayer-Vietoris sequences for V-homology. Results for homomorphisms include an algebraic version of contiguity for homomorphisms (which implies they are V-homotopic) and a proof that V-surmorphisms are V-homotopy equivalences. If we allow the divisional classes to vary, then algebraic connectivity may be viewed as a functor from the category of pairs W ⊆ V of divisional classes of [Formula: see text]-algebras with inclusions as morphisms' to the category of functors from pairs of [Formula: see text]-algebras to pairs of simplicial complexes. Examples show the non-triviality of this theory (e.g. "associativity tori"), and two preliminary applications to semigroups are given: 1) a proof that the group connectivity of a torsion semigroup S is homotopy equivalent to a space whose points are the maximal subgroups of S, and 2) an aperiodic connectivity analogue of the fundamental lemma of complexity.

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