Relevant bibliographies by topics / Algebraic

Contents

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

Academic literature on the topic 'Algebraic'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 July 2024

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Journal articles on the topic "Algebraic"

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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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Nongmanee, Anak, and Sorasak Leeratanavalee. "Algebraic connections between Menger algebras and Menger hyperalgebras via regularity." Algebra and Discrete Mathematics 36, no. 1 (2023): 61–73. http://dx.doi.org/10.12958/adm2135.

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Menger hyperalgebras of rank n, where n is a fixed integer, can be regarded as a natural generalization of arbitrary semihypergroups. Based on this knowledge, an interesting question arises: what a generalization of regular semihypergroups is. In the article, we establish the notion of v-regular Menger hyperalgebras of rank n, which can be considered as an extension of regular semihypergroups. Furthermore, we study regularity of Menger hyperalgebras of rank n which are induced by some subsets of Menger algebras of rank n. In particular, we obtain sufficient conditions so that the Menger hyperalgebras of rank n are v-regular.
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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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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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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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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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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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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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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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Sreeja S Nair, Kumari. "Exploring Normal Covering Spaces: A Bridge between Algebraic Topology and Abstract Algebra." International Journal of Science and Research (IJSR) 12, no. 8 (August 5, 2023): 2474–77. http://dx.doi.org/10.21275/sr23824225856.

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Dissertations / Theses on the topic "Algebraic"

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Alghamdi, Mohamed A. M. A. "Some problems in algebraic topology : polynomial algebras over the Steenrod algebra." Thesis, University of Aberdeen, 1991. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=166808.

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We prove two theorems concerning the action of the Steenrod algebra in cohomology and homology. (i) Let A denote a finitely generated graded Fp polynomial algebra over the Steenrod algebra whose generators have dimensions not divisible by p. The possible sets of dimensions of the generators for such A are known. It was conjectured that if we replaced the polynomial algebra A by a polynomial algebra truncated at some height greater than p over the Steenrod algebras, the sets of all possible dimensions would coincide with the former list. We show that the conjecture is false. For example F11[x6,x10]12 truncated at height 12 supports an action of the Steenrod algebra but F11[x6,x10] does not. (ii) Let V be an elementary abelian 2-group of rank 3. The problem of determining a minimal set of generators for H*(BV,F2) over the Steenrod algebra was an unresolved problem for many years. (A solution was announced by Kameko in June 1990, but is not yet published.) A dual problem is to determine the subring M of the Pontrjagin ring H*(BV,F2). We determine this ring completely and in particular give a verification that the minimum number of generators needed in each dimension in cohomology is as announced by Kameko, but by using completely different techniques. Let v ε V - (0) and denote by a_5(v) ε H*(BV,F2) the image of the non-zero class in H2s-1(RP∞,F2) imeq F2 under the homomorphism induced by the inclusion of F2 → V onto (0,v). We show that M is isomorphic to the ring generated by (a_s(v),s ≥ 1, v ε V - (0)) except in dimensions of the form 2^r+3 + 2^r+1 + 2^r - 3, r ≥ 0, where we need to adjoin our additional generator.
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Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.

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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu], wherein we consider three levels of spaces, each possessing a linear family of Poisson spaces. It is shown that there exist Poisson mappings between these levels. We consider the two cases where the underlying Riemann surface is an elliptic curve, as well as its degeneration to a Riemann sphere with two points identified (the trigonometric case). Background in necessary areas is provided.
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Bucicovschi, Orest. "Simple Lie algebras, algebraic prolongations and contact structures." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p3307120.

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Thesis (Ph. D.)--University of California, San Diego, 2008.
Title from first page of PDF file (viewed July 1, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 82-85).
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Garrote, López Marina. "Algebraic and semi-algebraic phylogenetic reconstruction." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/672316.

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Phylogenetics is the study of the evolutionary history and relationships among groups of biological entities (called taxa). The modeling of those evolutionary processes is done by phylogenetic trees whose nodes represent different taxa and whose branches correspond to the evolutionary processes between them. The leaves usually represent contemporary taxa and the root is their common ancestor. Nowadays, phylogenetic reconstruction aims to estimate the phylogenetic tree that best explains the evolutionary relationships of current taxa using solely information from their genome arranged in an alignment. We focus on the reconstruction of the topology of phylogenetic trees, which means reconstructing the shape of the tree considering labels at the leaves.To this end, one usually assumes that DNA sequences evolve according to a Markov process ruled by a prescribed model of nucleotide substitutions. These substitution models specify some transition matrices at the edges of the tree and a distribution of nucleotides at the root. Given a tree T and a substitution model, one can compute the distribution of nucleotide patterns at the leaves of T in terms of the model parameters. This joint distribution is represented by a vector whose entries can be expressed as polynomials on the model parameters and satisfy certain algebraic relationships. The study of these relationships and the geometry of the algebraic varieties defined by them (called phylogenetic varieties) have provided successful insight into the problem of phylogenetic reconstruction. However, from a biological perspective we are not interested in the whole variety, but only in the region of points that arise from stochastic parameters (the so-called phylogenetic stochastic region). The description of these regions leads to semi-algebraic constraints which play an important role since they characterize distributions with biological and probabilistic meaning. One of the main motivations for this thesis follows from the following question. Could the use of semi-algebraic tools improve the already existent algebraic tools for phylogenetic reconstruction?To answer this question, we compute the Euclidean distance of data points arising from an alignment of nucleotide to the phylogenetic varieties and their stochastic regions in a some scenarios of special interest in phylogenetics, such as trees with short external branches and/or subject to the long branch attraction phenomenon. In some cases, we compute these distances analytically and we can decide which tree has stochastic region closer to the data point. As a consequence, we can prove that, even if the data point was close to the phylogenetic variety of a given tree, it might be closer to the stochastic region of another tree. In particular, considering the stochastic phylogenetic region seems to be fundamental to cope with the phylogenetic reconstruction problem when dealing with the long branch attraction phenomenon.However, incorporating semi-algebraic tools into phylogenetic reconstruction methods can be extremely difficult and the procedure to do it is not evident at all. In this thesis, we present two phylogenetic reconstruction methods that combine algebraic and semi-algebraic conditions for the general Markov model. The first method we present is SAQ, which stands for Semi-Algebraic Quartet reconstruction method. Next, we introduce a more versatile method, ASAQ (for Algebraic and Semi-Algebraic Quartet reconstruction method}), which combines SAQ with the method Erik+2 (based on certain algebraic constraints). Both are phylogenetic reconstruction methods for DNA alignments on four taxa which have been proven to be statistically consistent.We test the suggested methods on simulated and real data to check their actual performance in several scenarios. Our simulation studies show that both methods SAQ and ASAQ are highly successful, even when applied to short alignments or data that violates their assumptions.
La filogenètica és l'estudi de la història evolutiva entre grups d'entitats biològiques (anomenades tàxons). Aquests processos evolutius estan modelitzats per arbres filogenètics els nodes dels quals representen diferents tàxons i les branques corresponen als processos evolutius entre ells. Les fulles normalment representen tàxons actuals i l'arrel és el seu avantpassat comú. Actualment, la reconstrucció filogenètica pretén estimar l'arbre filogenètic que millor explica les relacions evolutives de tàxons actuals utilitzant únicament informació del seu genoma organitzada en un alineament. En aquesta tesi ens centrem en la reconstrucció de la topologia dels arbres filogenètics, és a dir, reconstruir la forma de l'arbre tenint en compte els noms associats a les fulles. Amb aquesta finalitat, assumim que les seqüències d'ADN evolucionen segons un procés de Markov d'acord amb un model de substitució de nucleòtids. Aquests models de substitució assignem matrius de transició a les arestes d’un arbre i una distribució de nucleòtids a l'arrel. Donat un arbre i un model, es pot calcular la distribució de les possibles observacions de nucleòtids a les fulles en termes dels paràmetres del model. Aquesta distribució conjunta s’expressa en forma de vector, les entrades del qual es poden escriure com polinomis en funció dels paràmetres del model i satisfan certes relacions algebraiques. L'estudi d'aquestes relacions i de la geometria de les varietats algebraiques que defineixen (anomenades varietats filogenètiques) han servit per entendre millor el problema de la reconstrucció filogenètica. No obstant això, des d'una perspectiva biològica no estem interessats en tota la varietat, sinó només en la regió de punts que resulten de paràmetres estocàstics (l'anomenada regió estocàstica). La descripció d'aquestes regions condueix a restriccions semi-algebraiques que tenen un paper important ja que caracteritzen les distribucions amb significat biològic. Una de les principals motivacions d'aquesta tesi és la següent: Podria l'ús d'eines semi-algebraiques millorar les eines algebraiques ja existents per a la reconstrucció filogenètica? Per poder respondre, calculem la distància euclidiana entre punts de dades obtinguts a partir d’un alineament i varietats filogenètiques i les seves regions estocàstiques en escenaris d'especial interès en la filogenètica. En alguns casos, podem calcular aquestes distàncies de forma analítica i això ens permet demostrar que, fins i tot si un punt de dades fos proper a la varietat filogenètica d'un arbre donat, podria estar més a prop de la regió estocàstica d'un altre arbre. En particular, considerar la regió estocàstica sembla ser fonamental per fer front al problema de la reconstrucció filogenètica quan tractem amb del fenomen d'atracció de branques llargues. Tot i això, incorporar d'eines semi-algebraiques en els mètodes de reconstrucció filogenètica pot ser extremadament difícil i el procediment per fer-ho no és gens evident. En aquesta tesi, presentem dos mètodes de reconstrucció filogenètica que combinen condicions algebraiques i semi-algebraiques per al model general de Markov. El primer mètode que presentem és el SAQ, que rep el nom de Semi-Algebraic Quartet reconstruction method. A continuació, introduïm un mètode més versàtil, l'ASAQ (Algebraic and Semi-Algebraic Quartet reconstruction method), que combina el SAQ amb el mètode Erik+2 (basat en certes restriccions algebraiques). Tots dos són mètodes de reconstrucció filogenètica per a alineaments d'ADN per quatre tàxons i hem demostrat que tots dos són estadísticament consistents. Finalment, testem els mètodes proposats amb dades simulades i dades reals per comprovar el seu rendiment en diversos escenaris. Les nostres simulacions mostren que ambdós mètodes SAQ i ASAQ obtenen
Matemàtica aplicada
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Bowman, Christopher David. "Algebraic groups, diagram algebras, and their Schur-Weyl dualities." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610216.

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Ronagh, Pooya. "The inertia operator and Hall algebra of algebraic stacks." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58120.

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We view the inertia construction of algebraic stacks as an operator on the Grothendieck groups of various categories of algebraic stacks. We are interested in showing that the inertia operator is (locally finite and) diagonalizable over for instance the field of rational functions of the motivic class of the affine line q = [A¹]. This is proved for the Grothendieck group of Deligne-Mumford stacks and the category of quasi-split Artin stacks. Motivated by the quasi-splitness condition we then develop a theory of linear algebraic stacks and algebroids, and define a space of stack functions over a linear algebraic stack. We prove diagonalization of the semisimple inertia for the space of stack functions. A different family of operators is then defined that are closely related to the semisimple inertia. These operators are diagonalizable on the Grothendieck ring itself (i.e. without inverting polynomials in q) and their corresponding eigenvalue decompositions are used to define a graded structure on the Grothendieck ring. We then define the structure of a Hall algebra on the space of stack functions. The commutative and non-commutative products of the Hall algebra respect the graded structure defined above. Moreover, the two multiplications coincide on the associated graded algebra. This result provides a geometric way of defining a Lie subalgebra of virtually indecomposables. Finally, for any algebroid, an ε-element is defined and shown to be contained in the space of virtually indecomposables. This is a new approach to the theory of generalized Donaldson-Thomas invariants.
Science, Faculty of
Mathematics, Department of
Graduate
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Dias, Eduardo Manuel. "Algebraic covers." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/80934/.

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The main goal of this thesis is the description of the section ring of a surface R(S,L) = O∞n=0 H0(S,nL) where L is an ample base point free divisor defining a covering map φL: S -> P2 such that φ*OS = OP2 O Ω1P2 O Ω1P2 O Op2(-3). This is an abelian surface with a polarization of type (1,3) which was studied before in [BL94, Cas99, Cas12]. Given a covering map φ: X -> Y, following the methods introduced by Miranda for general d covers, in chapter 3 we will define a cover homomorphism that will induce a commutative and associative multiplication in φ*OX. Chapter 4 focuses in the OP2-modules Hom (S2Ω1P2,Ω1P2) that will be used to define a commutative multiplication for our surface. Chapter 5 is about the associative condition. It is a computational method based on the paper [Rei90]. In the last chapter we use the ring R(S,L) to prove that the moduli space of abelian surfaces with a polarization of type (1,3) and canonical level structure is rational. We will also show how to use the same method to find models for covering maps such that φ*OS = OP2 O Ω1P2(-m1) O Ω1P2(-m2) O OP2(-m1-m2-3). The last section contains new problems whose goal is to construct and study algebraic varieties given by the vanishing of a high codimensional Gorenstein ideal.
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Milione, Piermarco. "Shimura curves and their p-adic uniformization = Corbes de Shimura i les seves uniformitzacions p-àdiques." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/402209.

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The main purpose of this dissertation is to introduce Shimura curves from the non-Archimedean point of view, paying special attention to those aspects that can make this theory amenable for computations. Despite the fact that the theory of p-adic uniformization of Shimura curves goes back to the 1960s with the results of Cerednik and Drinfeld, only in the last years explicit examples related to these uniformizations have been computed. The structure of this dissertation is as follows. In Chapter 1 we introduce Shimura curves starting from an indefinite quaternion algebra H over a totally real field F. This is done mostly following the fundamental paper of Shimura [Shi67]. We also give the definitions using the adelic approach of [Shi70b] and [Shi70c]. The point of view we adopt is the arithmetical one, since we try to make clear the link connecting Shimura curves to the arithmetic of quaternion algebras. In this sense, we give evidence of why Shimura curves have to be considered a geometric interpretation of most arithmetical phenomena in quaternion orders. Chapter 2 has the aim of introducing those non-Archimedean objects which appear later in the statements of the theorems of Cerednik and Drinfeld. In Chapter 3 we start the study of fundamental domains in Hp for the action of discrete and cocompact subgroups of PGL2(Qp) arising in the p-adic uniformization of Shimura curves. In Chapter 4 we associate to the p-adic uniformization of the Shimura curve X(DH;N) certain parameters in Hp(Cp) analogous to the complex multiplication parameters in H: we refer to them by p-imaginary multiplication paramters, since they are defined over the unramified quadratic extension of Qp. In the study of these parameters, we follow the p-adic analog of the line adopted in [AB04]. Specifically, we are able to recover these parameters as zeros of certain binary quadratic forms with p-adic coefficients.
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Sinn, Rainer [Verfasser]. "Algebraic Boundaries of Convex Semi-Algebraic Sets / Rainer Sinn." Konstanz : Bibliothek der Universität Konstanz, 2014. http://d-nb.info/1052418252/34.

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Sharif, H. "Algebraic functions, differentially algebraic power series and Hadamard operations." Thesis, University of Kent, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235336.

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Books on the topic "Algebraic"

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Cohn, P. M. Algebraic Numbers and Algebraic Functions. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-3444-4.

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Bosch, Siegfried. Algebraic Geometry and Commutative Algebra. London: Springer London, 2013.

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Bliss, Gilbert Ames. Algebraic functions. Mineola, N.Y: Dover Publications, 2004.

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Vostokov, Sergei, and Yuri Zarhin, eds. Algebraic Number Theory and Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/300.

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Popov, Vladimir L., ed. Algebraic Transformation Groups and Algebraic Varieties. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05652-3.

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Goerss, P. G., and J. F. Jardine, eds. Algebraic K-Theory and Algebraic Topology. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0695-7.

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1950-, Shokurov Vyacheslav V., ed. Algebraic curves, algebraic manifolds, and schemes. Berlin: Springer, 1998.

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Benedetti, R. Real algebraic and semi-algebraic sets. Paris: Hermann, 1990.

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Gregory, Goerss Paul, Jardine J. F. 1951-, and NATO Advanced Study Institute, eds. Algebraic K-theory and algebraic topology. Dordrecht: Kluwer Academic, 1994.

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A, Martsinkovsky, Todorov G, Auslander Maurice, and Maurice Auslander Memorial Conference (1995 : Brandeis University), eds. Representation theory and algebraic geometry. Cambridge, UK: Cambridge University Press, 1997.

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Book chapters on the topic "Algebraic"

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Villoria, Alejandro, Henning Basold, and Alfons Laarman. "Enriching Diagrams with Algebraic Operations." In Lecture Notes in Computer Science, 121–43. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57228-9_7.

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AbstractIn this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad. Under the condition that this monad is monoidal and there is an adjunction between the free algebra functor and the underlying category functor, we construct an adjunction between symmetric monoidal categories and symmetric monoidal categories enriched over algebras for the monad. This allows us to devise an extension, and its semantics, of the ZX-calculus with probabilistic choices by freely enriching over convex algebras, which are the algebras of the finite distribution monad. We show how this construction can be used for diagrammatic reasoning of noise in quantum systems.
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Birkmann, Fabian, Henning Urbat, and Stefan Milius. "Monoidal Extended Stone Duality." In Lecture Notes in Computer Science, 144–65. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-57228-9_8.

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AbstractExtensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental for proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions, subsuming various incarnations of classical extended Stone and Priestley duality as a special case. Guided by these categorical foundations, we investigate residuation algebras, which are algebraic models of language derivatives, and show the subcategory of derivation algebras to be dually equivalent to the category of profinite ordered monoids, restricting to a duality between boolean residuation algebras and profinite monoids. We further extend this duality to capture relational morphisms of profinite ordered monoids, which dualize to natural morphisms of residuation algebras.
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Schmid, Todd, Tobias Kappé, and Alexandra Silva. "A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests." In Programming Languages and Systems, 309–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30044-8_12.

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AbstractGuarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with Tests (KAT) that was recently introduced to reason efficiently about imperative programs. In contrast to KAT, GKAT does not have an algebraic axiomatization, but relies on an analogue of Salomaa’s axiomatization of Kleene Algebra. In this paper, we present an algebraic axiomatization and prove two completeness results for a large fragment of GKAT consisting of skip-free programs.
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Finkelberg, Michael, and Victor Ginzburg. "Cherednik Algebras for Algebraic Curves." In Representation Theory of Algebraic Groups and Quantum Groups, 121–53. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4697-4_6.

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Crespo, Teresa, and Zbigniew Hajto. "Lie algebras and algebraic groups." In Graduate Studies in Mathematics, 75–117. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/gsm/122/04.

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Fokkink, Wan. "Process Algebra: An Algebraic Theory of Concurrency." In Algebraic Informatics, 47–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03564-7_3.

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Kolmogorov, A. N., and A. P. Yushkevich. "Algebra and Algebraic Number Theory." In Mathematics of the 19th Century, 35–135. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8293-4_2.

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Bashmakova, I. G., and A. N. Rudakov. "Algebra and Algebraic Number Theory." In Mathematics of the 19th Century, 35–135. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-5112-1_2.

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Bourbaki, Nicolas. "Commutative Algebra. Algebraic Number Theory." In Elements of the History of Mathematics, 93–115. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-61693-8_7.

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Plotkin, B. "Category Algebra and Algebraic Theories." In Universal Algebra, Algebraic Logic, and Databases, 129–52. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0820-1_7.

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Conference papers on the topic "Algebraic"

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Hubert, Evelyne. "Algebraic invariants and their differential algebras." In the 2010 International Symposium. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1837934.1837936.

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Gautier, Thierry, Jean-Louis Roch, Ziad Sultan, and Bastien Vialla. "Parallel algebraic linear algebra dedicated interface." In PASCO '15: International Workshop on Parallel Symbolic Computation. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2790282.2790286.

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Kumar, Harshat, Alejandro Parada-Mayorga, and Alejandro Ribeiro. "Algebraic Convolutional Filters on Lie Group Algebras." In ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2023. http://dx.doi.org/10.1109/icassp49357.2023.10095164.

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Smith, Larry. "An algebraic introduction to the Steenrod algebra." In School and Conference in Algebraic Topology. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.11.327.

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Bijev, G. "Semigroups and computer algebra in algebraic structures." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766808.

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Kitahara, Daichi, and Isao Yamada. "Algebraic phase unwrapping with self-reciprocal polynomial algebra." In 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2017. http://dx.doi.org/10.1109/sampta.2017.8024443.

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Ehrmann, S., S. Gries, and M. A. Schweitzer. "Transition Of Algebraic Multiscale To Algebraic Multigrid." In ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201802124.

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Kozhukhov, Igor Borisovich, and Ksenia Anatolievna Kolesnikova. "Some conditions of finiteness on polygons over semigroups." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-68.

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A polygon over a semigroup is an algebraic model machine. A finiteness condition in algebra is any condition which is satisfied by all finite algebras. The following finiteness conditions in acts over semigroups: Artinianity, Noetherian, Hopfian, Kohopfian, Cantorian, Cocantorian, the relationship between them is discussed. In addition, issues are discussed preserving or not preserving these properties with respect to the take operation direct product and coproduct.
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Sullivant, Seth. "Algebraic statistics." In the 37th International Symposium. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2442829.2442835.

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L. Nehaniv, Chrystopher, and Masami Ito. "Algebraic Engineering." In Proceedings of the International Workshop on Formal Languages and Computer Systems. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814527958.

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Reports on the topic "Algebraic"

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Feikes, David, William Walker, Natalie McGathey, and Bir Kafle. Algebra Readiness and Algebraic Structure as Foundational Ideas for Algebraic Learning. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317454.

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Hoffmann, Christoph M. Algebraic Curves. Fort Belvoir, VA: Defense Technical Information Center, May 1987. http://dx.doi.org/10.21236/ada231940.

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Gear, C. W. Differential algebraic equations, indices, and integral algebraic equations. Office of Scientific and Technical Information (OSTI), April 1989. http://dx.doi.org/10.2172/6307619.

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McGuire, Dennis W. Lattice-Algebraic Morphology. Fort Belvoir, VA: Defense Technical Information Center, September 1998. http://dx.doi.org/10.21236/ada353568.

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IOWA STATE UNIV AMES DEPT OF MATHEMATICS. Applications of Algebraic Logic and Universal Algebra to Computer Science. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada210556.

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Moses, Joel. Research on Algebraic Manipulation. Fort Belvoir, VA: Defense Technical Information Center, April 1987. http://dx.doi.org/10.21236/ada190149.

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Shashua, Amnon. Algebraic Functions for Recognition. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada276803.

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Bashelor, Andrew Clark. Enumerative Algebraic Geometry: Counting Conics. Fort Belvoir, VA: Defense Technical Information Center, May 2005. http://dx.doi.org/10.21236/ada437184.

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Bank, R., S. Lu, C. Tong, and P. Vassilevski. Scalable Parallel Algebraic Multigrid Solvers. Office of Scientific and Technical Information (OSTI), March 2005. http://dx.doi.org/10.2172/15015127.

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Baker, A., R. Falgout, H. Gahvari, T. Gamblin, W. Gropp, T. Kolev, K. Jordan, M. Schulz, and U. Yang. Preparing Algebraic Multigrid for Exascale. Office of Scientific and Technical Information (OSTI), February 2012. http://dx.doi.org/10.2172/1090013.

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