Dissertations / Theses on the topic 'Exterior algebra'
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Shannon, Alexander David John. "Quantum symmetric and exterior algebras." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648247.
Full textLackey, Joshua. "Properties of ideals in the exterior algebra /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9977908.
Full textTypescript. Includes vita and abstract. Includes bibliographical references (leaves 92-93). Also available for download via the World Wide Web; free to University of Oregon users.
Laios, B. A. "A unified approach to decentralised control, based on the exterior algebra and algebraic geometry methods." Thesis, City University London, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292320.
Full textWimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.
Full textVan, Grinsven Jacob. "Generalizations of Discriminants." Bowling Green State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1615805185856192.
Full textSchüler, Axel. "Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-218057.
Full textConsider one of the standard bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a transcendental complex number. It is shown that the de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. As in the classical case all three spaces of differential forms coincide: bi- invariant forms, harmonic forms and the de-Rham-cohomology. For orthog- onal and symplectic quantum groups there is no complete Hodge decompo- sition. In case of the standard calculi on the quantum groups GLq(N) and SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed
Silva, José Naéliton Marques da. "Sobre o Complexo de Koszul." Universidade Federal da Paraíba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/7435.
Full textCoordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
O complexo de Koszul é uma ferramenta de vital importância na Álgebra Comutativa. Ele nos permitirá definir alguns invariantes que nos dão informações refinadas acerca de um determinado módulo. Entre eles podemos ressaltar a profundidade e a multiplicidade de tal módulo em relação à um ideal. A primeira mede o comprimento da maior M-sequência formada por elementos do anel e a segunda nos dà informações assintóticas acerca do comprimento de módulos quocientes
Olofsson, Rikard. "Supersymmetric Quantum Mechanics and the Gauss-Bonnet Theorem." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355985.
Full textVi introducucerar formalismen f ̈or supersymmetrisk kvantmekanik, d ̈aribland super-symmetryladdningar,Z2-graderade Hilbertrum, kiralitetsoperatorn och Wittenin-dexet. Vi visar att det r ̊ader en till en-korrespondens mellan fermioner och bosonervid energiniv ̊aer skillda fr ̊an noll, vilket medf ̈or att Wittenindexet m ̈ater skillnadeni antal fermioner och bosoner vid nolltillst ̊andet. Vi argumenterar f ̈or att Wittenin-dexet ̈ar indexet p ̊a en elliptisk operator. Kvantisering av den supersymmetriskaicke-linj ̈ara sigmamodellen visar att Wittenindexet ̈ar Eulerkarakteristiken f ̈or denunderliggande Riemannska m ̊angfald ̈over vilken teorin ̈ar definierad. Slutligenapplicerar vi v ̈agintegralrepresentationen av Wittenindexet f ̈or att h ̈arleda Gauss-Bonnets sats. Ut ̈over detta introduceras ocks ̊a grundl ̈aggande matematisk bakrundi ämnena topologisk invarians, Riemmanska m ̊angfalder och indexteori.
Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
Full textPerez, Thomas. "Problèmes d'algèbre extérieure liés au calcul de fonctions d'ondes électroniques produits de géminales." Thesis, Université Côte d'Azur, 2020. http://www.theses.fr/2020COAZ4060.
Full textIn quantum chemistry, the electronic wave functions can be viewed as multivectors, therefore all problems translate into mathematical language thanks to the exterior algebra.We first recall some results related to the exterior and the interior products of the exterior algebra of a Hilbert space, which prove useful for quantum chemistry. We follow by presenting a method to find the annihilator ideal of a multivector, corresponding in physics to the excluded space by the Pauli principle, and this technique will be used in a later chapter.In a second step, we provide a summary of the key notions of the quantum formalism of fermionic systems and their counterpart from the point of view of the exterior algebra. We also recall the main approximation methods based on wave functions in quantum chemistry. We then introduce generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are built. The generalized seniority numbers afford to establish refined hierarchies of configuration interaction spaces within those of fixed ordinary seniority.In the third and main chapter, we present the way that has led us to propose a new geminal product wave function ansatz where the geminals are not strongly orthogonal but satisfy weaker geometrical constraints to lower the computational effort without sacrificing the indistinguishability of the electrons. Our geometrical constraints translate into simple equations involving the traces of products of geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is of size 2x2 and consists of a Pauli matrix or a diagonal matrix, multiplied by a complex parameter to be optimized. With this simplified ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables, like the Hamiltonian of the Schrödinger electronic equation, is considerably reduced.Finally, in the last part, we explain the implementation of our geminal product model in the computer code “Tonto”, which is a program and library for quantum crystallography and quantum chemistry written in the “Foo” language. The validity of our code has been tested on the calculation of the electronic energy of hydrogen chains. Moreover, a proof of principle that our ansatz gives significantly more accurate results than the strongly orthogonal geminal method has been established
Justino, Júlia Maria da Rocha Vilaverde. "Nonstandard linear algebra with error analysis." Doctoral thesis, Universidade de Évora, 2013. http://hdl.handle.net/10174/16316.
Full textSantana, Marciano AraÃjo. "Proposta de abordagem do teorema do Ãngulo externo na formaÃÃo continuada de professores de matemÃtica da educaÃÃo a distÃncia (ead) com o uso do geogebra." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13731.
Full textThe use of geometry in everyday life people have significant importance because it is a subject that uses designs, shapes and theorems as studies of evidence to make its activities in various fields of society such as engineering, steel, architecture, topography, etc. In this context, we can say that geometric constructions provide the discovery of valuable ideas that help the understanding of geometric properties. The large-scale assessments presented in public education indicators in the State of Ceara clearly portray the difficulties of learning by students when related to geometric concepts specifically the exterior angle theorem in theory (algebraic concept) and in practice (geometric concept). From this analysis, we propose to conduct an investigation through this research that could identify possible barriers in existing geometry teaching so he could obtain advances to improve the teaching related to the External Angle Theorem and its Consequences using the old learning environments and Paper pen (VPC) and the virtual Learning Environment (VLE) with the operation of educational software of dynamic geometry GeoGebra. The work was attended by a group of twelve (12) mathematics teachers in continuing education of a Specialization Course in Teaching of Mathematics at the University Vale do Acaraà (UVA) in the city of Cascavel-Ce. The operational and pedagogical use of dynamic geometry software GeoGebra was applied in lectures with questionnaires problems involving the exterior angle theorem that seeks to assess the performance of students participating in the survey regarding their classroom practices with the teaching of geometry. We adopted a qualitative, exploratory and action research approaches to characterize the research and seek to build on the theoretical and reflexive assumptions according to Valente conceptions, Michele Artigue, Parents and Fiorentini and Lorenzato. The survey showed progress in the learning process of participating students that were excited by the knowledge that built and that allowed establish a collaborative relationship between the groups involved (students and teacher-researcher).
Thieu, Dinh Phong. "On graded ideals over the exterior algebra with applications to hyperplane arrangements." Doctoral thesis, 2013. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2013092311626.
Full textKämpf, Gesa. "Module theory over the exterior algebra with applications to combinatorics." Doctoral thesis, 2010. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201005176260.
Full text(10703067), Michael J. Kaminski. "Resonance Varieties and Free Resolutions Over an Exterior Algebra." Thesis, 2021.
Find full text(8782541), Dongming She. "Local Langlands Correpondence for the twisted exterior and symmetric square epsilon-factors of GL(N)." Thesis, 2020.
Find full textSchüler, Axel. "Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen." Doctoral thesis, 2000. https://ul.qucosa.de/id/qucosa%3A15260.
Full textConsider one of the standard bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a transcendental complex number. It is shown that the de Rham cohomology of Woronowicz'' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. As in the classical case all three spaces of differential forms coincide: bi- invariant forms, harmonic forms and the de-Rham-cohomology. For orthog- onal and symplectic quantum groups there is no complete Hodge decompo- sition. In case of the standard calculi on the quantum groups GLq(N) and SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed.
Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.
Full textTshilombo, Mukinayi Hermenegilde. "Cohomologies on sympletic quotients of locally Euclidean Frolicher spaces." Thesis, 2015. http://hdl.handle.net/10500/19942.
Full textMathematical Sciences
D. Phil. (Mathematics)