Relevant bibliographies by topics / Isomorphisme de type

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

Academic literature on the topic 'Isomorphisme de type'

Author: Grafiati
Published: 14 December 2024

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Journal articles on the topic "Isomorphisme de type"

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Eriksson, Dennis. "Un isomorphisme de type Deligne–Riemann–Roch." Comptes Rendus Mathematique 347, no. 19-20 (October 2009): 1115–18. http://dx.doi.org/10.1016/j.crma.2009.09.003.

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Gonzalez-Lorca, Jorge. "Structure des algèbres de Hecke de type A: Un isomorphisme explicite." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 2 (January 1998): 147–52. http://dx.doi.org/10.1016/s0764-4442(97)89460-8.

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Hampiholi, Prabhakar R., and Meenal M. Kaliwal. "Operations on Semigraphs." Bulletin of Mathematical Sciences and Applications 18 (May 2017): 11–22. http://dx.doi.org/10.18052/www.scipress.com/bmsa.18.11.

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Abstract. In this paper the structural equivalence of union, intersection ring sum and decomposition of semigraphs are explored by using the various types of isomorphisms such as isomorphism, ev-isomorphism, a-isomorphism and e-isomorphism for Ge, Ga and Gca. We establish various types of binary operations in semigraphs.
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Poulain d'Andecy, L., and R. Walker. "Affine Hecke algebras and generalizations of quiver Hecke algebras of type B." Proceedings of the Edinburgh Mathematical Society 63, no. 2 (March 9, 2020): 531–78. http://dx.doi.org/10.1017/s0013091519000294.

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AbstractWe define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalization, for type B, of cyclotomic quiver Hecke algebras, which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev, we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result.
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Stroppel, Markus J. "An isomorphism between unitals and between related classical groups." Advances in Geometry 24, no. 4 (October 1, 2024): 463–71. http://dx.doi.org/10.1515/advgeom-2024-0022.

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Abstract An isomorphism between two hermitian unitals is provided, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
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Ye, Junming. "A study of sign-changing Poisson-type equations in two configurations." Theoretical and Natural Science 55, no. 1 (November 1, 2024): 67–84. http://dx.doi.org/10.54254/2753-8818/55/20240206.

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Abstract. In this paper, We are interested in specific non-coercive issues concerning electromagnetic wave propagation in the presence of metals or particular metamaterials. We focus on some non-coercive problems which cannot be studied by a classical Lax-Milgram approach. We consider the sign-changing Poisson-type equations with the homogeneous Dirichlet boundary conditions in the circular configuration and in the three square configuration. We utilize a method called T-isomorphism, which allows the conversion of non-coercive problems into coercive ones, to examine specific Poisson-type equations with sign-changing parameters. We first use the classical method to transform the equations into the corresponding variational formulations, and then apply the T-isomorphism method to show the well-posedness of these variational formulations with some parameters. By applying appropriate isomorphisms, we can conclude the well-posedness of the related variational formulations with certain parameters, which constitute the main findings of this paper. After giving appropriate isomorphisms, we can deduce the well-posedness of the corresponding variational formulations with some parameters, which are our main results in this paper.
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FURUTANI, R., I. KIKUMASA, and H. YOSHIMURA. "ISOMORPHISM OF QF ALGEBRAS OVER ℚ." Journal of Algebra and Its Applications 12, no. 03 (December 20, 2012): 1250166. http://dx.doi.org/10.1142/s0219498812501666.

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We show that the local–global principle (Hasse principle) holds for isomorphisms between commutative local QF algebras over ℚ of dimension five with radical cubed zero, and obtain a criterion for them to be isomorphic by the Hilbert symbol or the Legendre symbol. As a consequence, we give the isomorphism classes of some type of local algebras over ℚ by using a factor group of ℚ*.
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Christensen, Erik, and Allan M. Sinclair. "Completely bounded isomorphisms of injective von Neumann algebras." Proceedings of the Edinburgh Mathematical Society 32, no. 2 (June 1989): 317–27. http://dx.doi.org/10.1017/s0013091500028716.

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Milutin's Theorem states that if X and Y are uncountable metrizable compact Hausdorff spaces, then C(X) and C(Y) are isomorphic as Banach spaces [15, p. 379]. Thus there is only one isomorphism class of such Banach spaces. There is also an extensive theory of the Banach–Mazur distance between various classes of classical Banach spaces with the deepest results depending on probabilistic and asymptotic estimates [18]. Lindenstrauss, Haagerup and possibly others know that as Banach spaceswhere H is the infinite dimensional separable Hilbert space, R is the injective II 1-factor on H, and ≈ denotes Banach space isomorphism. Haagerup informed us of this result, and suggested considering completely bounded isomorphisms; it is a pleasure to acknowledge his suggestion. We replace Banach space isomorphisms by completely bounded isomorphisms that preserve the linear structure and involution, but not the product. One of the two theorems of this paper is a strengthened version of the above result: if N is an injective von Neumann algebra with separable predual and not finite type I of bounded degree, then N is completely boundedly isomorphic to B(H). The methods used are similar to those in Banach space theory with complete boundedness needing a little care at various points in the argument. Extensive use is made of the conditional expectation available for injective algebras, and the methods do not apply to the interesting problems of completely bounded isomorphisms of non-injective von Neumann algebras (see [4] for a study of the completely bounded approximation property).
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Goberstein, Simon M. "Correspondences of completely regular semigroups and -isomorphisms of semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 3 (1995): 625–37. http://dx.doi.org/10.1017/s0308210500032728.

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A correspondence of a semigroup S is any subsemigroup of S × S, and the set of all correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by (S). For semigroups S and T, any isomorphism of (S) onto (T) is called a -isomorphism of S upon T. Similar notion can be introduced for other types of algebras and in the general frame of category theory. The principal goal of this paper is to study -isomorphisms of completely regular semigroups (that is, unions of groups) and of one other interesting class of semigroups.
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Abdeljawad, Ahmed, Sandro Coriasco, and Joachim Toft. "Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators." Analysis and Applications 18, no. 04 (September 18, 2019): 523–83. http://dx.doi.org/10.1142/s0219530519500143.

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We deduce one-parameter group properties for pseudo-differential operators [Formula: see text], where [Formula: see text] belongs to the class [Formula: see text] of certain Gevrey symbols. We use this to show that there are pseudo-differential operators [Formula: see text] and [Formula: see text] which are inverses to each other, where [Formula: see text] and [Formula: see text]. We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions [Formula: see text] moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) [Formula: see text] is an isomorphism from [Formula: see text] to [Formula: see text] for every [Formula: see text].
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Dissertations / Theses on the topic "Isomorphisme de type"

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Bonnet, Jean-Paul. "Un isomorphisme motivique entre deux variétés homogènes projectives sous l'action d'un groupe de type $G_2$." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2003. http://tel.archives-ouvertes.fr/tel-00004214.

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Dans toute cette thèse, k désigne un corps de caractéristique différente de 2 et par variété nous désignons un k-schéma, séparé et de type fini. Nous allons étudier $X(\alpha_1)$ et $X(\alpha_2)$, les variétés homogènes projectives associées à chacune des deux racines d'un groupes de type $G_(2)$. La pemière d'entre elles, $X(\alpha_1)$, est une quadrique projective de dimension 5 associée à une voisine de Pfister et l'autre, $X(\alpha_2)$, est une variété de Fano (de genre 10). Ces deux variétés ne sont pas isomorphes, pourtant elles le deviennent en tant qu'objets d'une catégorie plus large, à savoir la catégorie des correspondances (et par conséquent également dans la catégorie des motifs de Chow). Nous établissons que ce résultat est vrai que les variétés soient déployées ou non. Dans un premier chapitre, nous rappelons quelques résultats classiques sur les algèbres d'octonions et construisons un modèle d'algèbres d'octonions déployée. Dans le second, nous présentons les variétés mises en jeu et rappelons pour cela des notions essentielles de la théorie des groupes algébriques ainsi que de celle des foncteurs de points. Dans le troisième chapitre, nous construisons une structure cellulaire de $X(\alpha_2)$ lorsqu'elle est déployée, étape essentielle de notre travail. C'est également dans ce chapitre que nous calculons les relations définissant la structure d'anneau de $X(\alpha_2)$. Enfin, dans le quatrième et dernier chapitre, nous introduisons la catégorie des correspondances avant de prouver notre théorème de nilpotence dans le cas particulier de la variété $X(\alpha_2)$, puis nous établissons l'isomorphisme motivique en toute généralité.
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Bonnet, Jean-Paul. "Un isomorphisme motivique entre deux variétés homogènes projectives sous l'action d'un groupe de type G2." Lille 1, 2003. https://ori-nuxeo.univ-lille1.fr/nuxeo/site/esupversions/6a534f30-9098-43a3-8423-d4413bfe78f0.

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Dans toute cette thèse, k désigne un corps de caractéristique différente de 2 et par variété nous désignons un k-schêma, séparé et de type fini. Nous allons étudier X(α1) et X(α2), les variétés homogènes projectives associées à chacune des deux racines d'un groupes de type G2. La pemière d'entre elles, X(α1), est une quadrique projective de dimension 5 associée à une voisine de PFISTER et l'autre, X(α2), est une variété de FANO (de genre 10). Ces deux variétés ne sont pas isomorphes, pourtant elles le deviennent en tant qu'objets d'une catégorie plus large, à savoir la catégorie des correspondances (et par conséquent également dans la catégorie des motifs de CHOW). Nous établissons que ce résultat est vrai que les variétés soient déployées ou non. Dans un premier chapitre, nous rappelons quelques résultats classiques sur les algèbres d'octonions et construisons un modèle d'algèbres d'octonions déployée. Dans le second, nous présentons les variétés mises en jeu et rappelons pour cela des notions essentielles de la théorie des groupes algébriques ainsi que de celle des foncteurs de points. Dans le troisième chapitre, nous construisons une structure cellulaire de X(α2) lorsqu'elle est déployée, étape essentielle de notre travail. C'est également dans ce chapitre que nous calculons les relations définissant la structure d'anneau de X(α2). Enfin, dans le quatrième et dernier chapitre, nous introduisons la catégorie des correspondances avant de prouver notre théorème de nilpotence dans le cas particulier de la variété X(α2), puis, nous établissons l'isomorphisme motivique en toute généralité.
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Stolze, Claude. "Types union, intersection, et dépendants dans le lambda-calcul explicitement typé." Thesis, Université Côte d'Azur (ComUE), 2019. http://www.theses.fr/2019AZUR4104.

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Le sujet de cette thèse est sur le lambda-calcul décoré avec des types, communément appelé « lambda-calcul typé à la Church ». Nous étudions des versions de ce lambda-calcul muni de types intersections, tels que ceux décrits dans le livre « Lambda-calculus with types » de Barendregt, Dekkers et Statman ; les types unions, qui ont été introduits par Plotkin, MacQueen et Sethi ; et les types dépendants, tels qu'ils ont été décrits par Plotkin, Harper et Honsell lorsqu'ils ont introduit le Logical Framework d'Edinbourgh LF. Les types intersections et unions sont un moyen d'exprimer du polymorphisme ad hoc et sont une alternative au polymorphisme paramétrique de Girard. Les types dépendants ont été introduits pour formaliser la logique intuitionniste avec la correspondance de Curry-Howard. Le système de types obtenu peut être enrichi avec une relation de soutypage décidable. La combinaison de ces trois disciplines de type donne lieu à une famille de calculs qui peuvent être paramétrés et classifiés. Nous appelons le système générique le Delta-calcul. Nous discutons ensuite des décisions de conception qui nous ont amené à la formulation de ces calculs, nous étudions leur métathéorie, et nous présentons divers exemples d'applications avant de présenter une implémentation logicielle du Delta-calcul, avec une description des algorithmes de vérification de type, de raffinement, de soutypage, d'évaluation, ainsi que de l'interface en ligne de commande. Ce travail de recherche peut être vu comme un petit pas franchi dans la direction d'une théorie des types alternative pour définir du polymorphisme dans les langages de programmation et dans les assistants de preuve interactifs
The subject of this thesis is about lambda-calculus decorated with types, usually called "Church-style typed lambda-calculus". We study this lambda-calculus enhanced with Intersection types, as described by Barendregt, Dekkers and Statman in the book "Lambda-calculus with Types"; Union types, as introduced by Plotkin, MacQueen and Sethi; and Dependent types, as described by Plotkin, Harper and Honsell when they introduced the Edinburgh Logical Framework LF. Intersection and union types are a way to express ad hoc polymorphism and are an alternative to the parametric polymorphism of Girard. Dependent types were introduced as a way to formalize intuitionistic logic using the "proof-as-lambda-terms / formulas-as-types" Curry-Howard principle. The resulting type system can be enriched with a decidable subtyping relation. Combining these three type disciplines gives rise to a family of calculi that can be parametrized and classified: we call the resulting system the Delta-calculus. We then discuss the design decisions which have led us to the formulation of these calculi, study their metatheory, and provide various examples of applications; and we finally present a software implementation of the Delta-calculus, with a description of the type checker, the refinement algorithm, the subtyping algorithm, the evaluation algorithm and the command-line interface. This work can be understood as a little step toward an alternative type theory to defining polymorphic programming languages and interactive proof assistants
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Chemouil, David. "Types inductifs, isomorphismes et récriture extensionnelle." Toulouse 3, 2004. http://www.theses.fr/2004TOU30187.

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Cette thèse étudie l'extension du lambda-calcul simplement typé par diverses relations de récriture préservant la terminaison et la confluence. Il s'agit d'assurer, dans un premier temps, que certains types sont isomorphes. Or le problème est indécidable pour les types inductifs : nous avons donc ajouté au calcul des réductions spécifiques résolvant la question dans certains cas, à savoir le codage des types produits et unité et surtout la notion de copie paramétrée. Délaissant ensuite les isomorphismes, nous considérons de nouvelles réductions permettant d'établir des structures algébriques sur les types finis : nous envisageons d'une part la définition d'une catégorie sur un fragment du calcul ; et, d'autre part, la représentation du groupe symétrique par décomposition des permutations en produits de cycles disjoints. Ces résultats sont obtenus par des techniques de récriture abstraite, dont certaines développées spécifiquement pour la thèse
This PhD thesis copes with extensions of the simply-typed lambda-calculus by various rewrite relations preserving termination and confluence. Our first purpose is to ensure that some types become isomorphic. As far as inductive types are concerned, this problem is undecidable: therefore, we added some particular reductions solving it only in peculiar cases, namely the inductive encoding of the product and unit types and, more importantly, the notion of parameterised copy. Next, leaving isomorphims, we consider new reductions enabling to set up some algebraic structures on finite types: firstly, we deal with the definition of a category on a fragment of the calculus; and, secondly, with the representation of the symmetric group by factorisation of permutations as products of disjoint cycles. These results are obtained using techniques from abstract rewriting theory, some of which we have specifically developped for this thesis
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Lasson, Marc. "Réalisabilité et paramétricité dans les systèmes de types purs." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00770669.

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Cette thèse porte sur l'adaptation de la réalisabilité et la paramétricité au cas des types dépendants dans le cadre des Systèmes de Types Purs. Nous décrivons une méthode systématique pour construire une logique à partir d'un langage de programmation, tous deux décrits comme des systèmes de types purs. Cette logique fournit des formules pour exprimer des propriétés des programmes et elle offre un cadre formel adéquat pour développer une théorie de la réalisabilité au sein de laquelle les réalisateurs des formules sont exactement les programmes du langage de départ. Notre cadre permet alors de considérer les théorèmes de représentation pour le système T de Gödel et le système F de Girard comme deux instances d'un théorème plus général.Puis, nous expliquons comment les relations logiques de la théorie de la paramétricité peuvent s'exprimer en terme de réalisabilité, ce qui montre que la logique engendrée fournit un cadre adéquat pour développer une théorie de la paramétricité du langage de départ. Pour finir, nous montrons comment cette théorie de la paramétricité peut-être adaptée au système sous-jacent à l'assistant de preuve Coq et nous donnons un exemple d'application original de la paramétricité à la formalisation des mathématiques.
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Lataillade, Joachim Guilhem de. "Quantification du second ordre en sémentique des jeux : application aux isomorphismes de types." Paris 7, 2007. http://www.theses.fr/2007PA077228.

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La sémantique des jeux offre un cadre souple et précis pour l'interprétation des langages de programmation. Cette thèse l'illustre à travers d'une part l'étude de la notion de polymorphisme et son pendant logique : la quantification du second ordre, et d'autre part la caractérisation de | certaines propriétés syntaxiques via les modèles de jeux. Le polymorphisme est d'abord envisagé sous sa forme la plus usuelle, le système F à la Church. On en propose un nouveau modèle de jeux, complet, inspiré de travaux antérieurs mais dans lequel il sera cette fois possible d'effectuer des calculs. La question syntaxique de la caractérisation des isomorphismes de typas peut alors être résolue à l'intérieur même de ce modèle, en prouvant l'invariance par isomorphisme d'une structure appelée hyperforêt. Cette approche sémantique permet de retrouver un résultat dû à Roberto Di Cosmo. Une autre variante de la logique du second ordre, le système F à la Curry, est étudiée et modélisée de manière partielle mais suffisamment précise pour permettre là encore la caractérisation des isomorphismes de types par un invariant géométrique. Le système équationnel correspondant enrichit celui des isomorphismes du système F à la. Church d'une nouvelle équation, non triviale. Une extension à la logique classique des résultats obtenus pour te système F à Sa Church est proposée à travers la construction dans les jeux d'une hyperdoctrine de contrôle, structure catégorique adaptée à la logique du second ordre
Game semantics is a flexible and precise framework for interpreting programming languages. The present dissertation illustrates this fact in two ways : first by studying polymorphism and its logical counterpart : second-order quantification, and second by caracterising sorne syntactic properties via game models. Polymorphism is first considered in its most usual form, Church- style System F, We propose a new, complete, game model, inspired by previous works but in which we will be able to do effective calculations. The syntactic question of characterising type isomorphisms can then be solved inside this model, by proving the invariance through isomorphism of some structure called hyperforest. This semantic approach allows to retrieve a result by Roberto Di Cosmo, Another variant of second- order logic, namely Curry- style System F, is studied and modellsed, partially but with enough precision to give once again a characterisation of type isomorphisms through a geometric invariant. The corresponding equationnal system is an enrichment of that of Church-style isomorphisms by a news non-trivial, equation. An extension to classical logic of the results for Church-style System F is proposed, through theconstruction of a game model which results in a control hyperdoctrine, ie a categorical structuresuitable for second- order classical logic
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Herrera, Diana. "Homormophic Images and their Isomorphism Types." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/37.

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In this thesis we have presented original homomorphic images of permutations and monomial progenitors. In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J1 and J2X2 where J1 is the smallest Janko group and J2 is the second Janko sporadic group.
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Ramirez, Jessica Luna. "CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/254.

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In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2*7: D14, 2*7 : (7 : 2), 2*6 : S3 x 2, 2*8: S4, 2*72: (32:(2S4)), and 11*2 :m D10. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M11, M12, the 4-fold cover of the Mathieu group M22, 2 x L2(8), and L2(13). Moreover, we have given constructions, by using the technique of double coset enumeration, for some of the images, including M11 and M12. We have given proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that L2(13) over A5, L2(8) over D14, L2(13) over D14, L2(27) over 2D14, and M11 over 2S4 are simple groups. All of the work presented in this thesis is original to the best of our knowledge.
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Di, Guardia Rémi. "Identity of Proofs and Formulas using Proof-Nets in Multiplicative-Additive Linear Logic." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0050.

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Cette thèse s'intéresse à l'égalité des preuves et des formules en logique linéaire, avec des contributions en particulier dans le fragment multiplicatif-additif de cette logique. En logique linéaire, et dans de nombreuses autres logiques (telle que la logique intuitionniste), on dispose de deux transformations sur les preuves : l'élimination des coupures et l'expansion des axiomes. On souhaite très souvent identifier deux preuves reliées par ces transformations, étant donné qu'elles le sont sémantiquement (dans un modèle catégorique par exemple). Cette situation est similaire à celle du λ-calcul où les termes sont identifiés à β-réduction et η-expansion près, opérations qui, par le prisme de la correspondance de Curry-Howard, se rapportent respectivement à l'élimination des coupures et à l'expansion des axiomes. Nous montrons ici que cette identification des preuves correspond exactement à l'identification des preuves à commutation de règle près, qui est une troisième opération sur les preuves bien connue et plus facile à manipuler. Notre démonstration considère uniquement la logique linéaire multiplicative-additive, même si nous conjecturons que ce résultat est vrai pour la logique linéaire dans son entièreté.Non seulement des preuves peuvent être identifiées à élimination des coupures et expansion des axiomes près, mais aussi des formules. Deux formules sont isomorphes si elles sont reliées par des preuves dont les compositions donnent l'identité, toujours à élimination des coupures et expansion des axiomes près. Ces formules sont alors réellement considérées comme les mêmes, et toute utilisation de l'une peut être remplacée par une utilisation de l'autre. Nous donnons une théorie équationnelle caractérisant exactement les formules isomorphes dans la logique linéaire multiplicative-additive. Un problème généralisant les isomorphismes est celui des rétractions, qui intuitivement correspondent aux couples de formules où la première peut être remplacée par la seconde - mais pas nécessairement la seconde par la première, contrairement aux isomorphismes. Étudier les rétractions est bien plus complexe, et nous avons caractérisé les rétractions des atomes dans le fragment multiplicatif de la logique linéaire.Pour l'étude des deux problèmes précédents, la syntaxe usuelle des preuves du calcul des séquents semble mal adaptée, car on considère des preuves à commutation de règle prés. Une partie de la logique linéaire possède une meilleure syntaxe dans ce cas : les réseaux de preuve, qui sont des graphes représentant des preuves quotientées par les commutations de règle. Cette syntaxe fut un outil indispensable pour caractériser isomorphismes et rétractions. Malheureusement, les réseaux de preuve ne sont pas (ou mal) définis en présence des unités. Pour nos problèmes, cette restriction conduit à une étude du cas sans unité dans les réseaux avec le coeur de la démonstration, précédé d'un travail en calcul des séquents pour prendre en compte les unités.Cette thèse développe par ailleurs une partie de la théorie des réseaux de preuve en fournissant une simple preuve du théorème de séquentialisation, qui relie les deux syntaxes des réseaux de preuve et du calcul des séquents, justifiant qu'elles décrivent les mêmes objets sous-jacents. Cette nouvelle démonstration s'obtient comme corollaire d'une généralisation du théorème de Yeo. Ce dernier résultat s'exprime entièrement dans la théorie des graphes aux arêtes colorées, et permet de déduire des preuves de sequentialisation pour différentes définitions de réseaux de preuve. Enfin, nous avons aussi formalisé les réseaux de preuve du fragment multiplicatif de la logique linéaire dans l'assistant de preuve Coq, avec en particulier une implémentation de notre nouvelle preuve de séquentialisation
This study is concerned with the equality of proofs and formulas in linear logic, with in particular contributions for the multiplicative-additive fragment of this logic. In linear logic, and as in many other logics (such as intuitionistic logic), there are two transformations on proofs: cut-elimination and axiom-expansion. One often wishes to identify two proofs related by these transformations, as it is the case semantically (in a categorical model for instance). This situation is similar to the one in the λ-calculus where terms are identified up to β-reduction and η-expansion, operations that, through the prism of the Curry-Howard correspondence, are related respectively to cut-elimination and axiom-expansion. We show here that this identification corresponds exactly to identifying proofs up to rule commutation, a third well-known operation on proofs which is easier to manipulate. We prove so only in multiplicative-additive linear logic, even if we conjecture such a result holds in full linear logic.Not only proofs but also formulas can be identified up to cut-elimination and axiom-expansion. Two formulas are isomorphic if there are proofs between them whose compositions yield identities, still up to cut-elimination and axiom-expansion. These formulas are then really considered to be the same, and every use of one can be replaced with one use of the other. We give an equational theory characterizing exactly isomorphic formulas in multiplicative-additive linear logic. A generalization of an isomorphism is a retraction, which intuitively corresponds to a couple of formulas where the first can be replaced by the second -- but not necessarily the other way around, contrary to an isomorphism. Studying retractions is more complicated, and we characterize retractions to an atom in the multiplicative fragment of linear logic.When studying the two previous problems, the usual syntax of proofs from sequent calculus seems ill-suited because we consider proofs up to rule commutation. Part of linear logic can be expressed in a better adapted syntax in this case: proof-nets, which are graphs representing proofs quotiented by rule commutation. This syntax was an instrumental tool for the characterization of isomorphisms and retractions. Unfortunately, proof-nets are not (or badly) defined with units. Concerning our issues, this restriction leads to a study of the unit-free case by means of proof-nets with the crux of the demonstration, preceded by a work in sequent calculus to handle the units. Besides, this thesis also develops part of the theory of proof-nets by providing a simple proof of the sequentialization theorem, which relates the two syntaxes of proof-net and sequent calculus, substantiating that they describe the same underlying objects. This new demonstration is obtained as a corollary of a generalization of Yeo's theorem. This last result is fully expressed in the theory of edge-colored graphs, and allows to recover proofs of sequentialization for various definitions of proof-nets. Finally, we also formalized proof-nets for the multiplicative fragment of linear logic in the proof assistant Coq, with notably an implementation of our new sequentialization proof
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Lengrand, Stéphane. "Normalisation & equivalence in proof theory & type theory /." St Andrews, 2007. http://hdl.handle.net/10023/319.

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Books on the topic "Isomorphisme de type"

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Philippe, De Groote, and Université catholique de Louvain (1970- ). Départment de philosophie., eds. The Curry-Howard isomorphism. Louvain-la-Neuve: Academia, 1995.

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Di Cosmo, Roberto. Isomorphisms of Types: from λ-calculus to information retrieval and language design. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2572-0.

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Simmons, Harold. Derivation and computation: Taking the Curry-Howard correspondence seriously. Cambridge: Cambridge University Press, 2000.

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Elatskov, Aleksey. General Geopolitics: Theoretical and Methodological Issues in Geographical Interpretation. ru: INFRA-M Academic Publishing LLC., 2024. http://dx.doi.org/10.12737/2033550.

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This text is dedicated to the development of the general theory of geopolitics as a scientific discipline. The author discusses what geopolitics is, as well as its content and methodology, and investigates the principles of geopolitical zoning and modelling, the content and essence of geopolitical relations, geographical and geopolitical spaces, geopolitical thinking and geopolitical idealised models. Activity-geospatial and geo-adaptation approaches are utilised while considering geopolitical phenomena. The first focuses attention on the geopolitical relations existing between political activity and geographical space. This forms the methodological basis of the concept of the geospatial self-organisation of a society as a new theoretical paradigm regarding political geography and geopolitics. The book consists of the Introduction, four chapters and contains 41 figures, 9 tables and an extensive reference list. The first chapter deals with the basic theoretical questions of political geography and geopolitics: the concept of geopolitics, the essence of politics and political actors, the concept and structure of geographical space, as well as geopolitical space as a set of geopolitical relations. The author describes several types of geopolitical relations with sensitivity to distance and borders. It has been proven that the “geopolitical relations” category forms the basis for both geopolitics and political geography theories. The second chapter is dedicated to discussing the study of geopolitical space. The geo-adaptation (geoadaptation) approach is proposed for the study of geopolitics and related problems. Geopolitics is understood as a political type of geo-adaptation of society. The author argues that any geopolitical relations represent a kind of societal geo-adaptational relations. The author also discusses the concept of territory (in the Russian sense) and zoning principles. An extended typology of geographical regions has been proposed, which more accurately reflects specific geopolitical phenomena. Along with nodal (functional) and uniform (formal) regions, the author also proposes relational ones. In addition, the concept of geopolitical field as a field of geopolitical relations is described. The author examines the assessment types of fragmentation and integration of geopolitical spaces or fields, and also discusses the principles of research geopolitical location of a country. The third chapter examines the essence, genesis, levels, and types of geopolitical thinking from the viewpoint of the proposed approach. The author notes the principles of critical geopolitics and discusses the place of geopolitics in the system of scientific knowledge and its relation to current political geography, as well as the categorical framework of scientific geopolitics, the principles of forecasting and expert assessment, and special education issues. The fourth chapter discusses the essence of scientific geopolitical laws and principles of modelling. The author argues that the majority of "geopolitics laws" are statements that describe various types of geopolitical strategies. In addition, the author considers numerous idealised geopolitical models of natural-geographic, human-geographic, spatial-activity, functional-activity and chrono-geopolitical types in terms of the geo-adaptation approach. The effect of geographic isomorphisms in geopolitical models is also discussed. The fundamental concepts of physical geography and geomorphology may be used in conceptualising geopolitics. The book is intended for scientists, researchers, and students in the field of geopolitics and political geography. The book is available online at the electronic library system Znanium.com.
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Dicosmo, Roberto. Isomorphisms of Types. Island Press, 1994.

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Button, Tim, and Sean Walsh. Modelism and mathematical doxology. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0006.

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This chapter outlines a certain attitude to model theory called ‘modelism’. The modelist idea is that structure-talk, as used informally by mathematicians, is to be understood in terms of isomorphism, in the model theorist's sense. For example, modelists will want to explicate talk of ‘the natural numbers' in terms of a particular isomorphism type. As such, modelists face an important doxological question: ‘How can we pick out particular isomorphism types?’ This chapter examines various versions of this question, and in particular what it means to say that it is a doxological question. We also distinguish between objectual and conceptual versions of this question, and show how they relate to Shapiro’s and Hellman’s different versions of structuralism.
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Kraus, Alain, and Nuno Freitas. On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves. American Mathematical Society, 2022.

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Isomorphisms of Types: From ? -calculus to information retrieval and language design. Birkhäuser Boston, 2011.

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DiCosmo, Roberto. Isomorphisms of Types: From ?-Calculus to Information Retrieval and Language Design. Birkhauser Verlag, 2012.

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Tits, Jacques. Buildings of Spherical Type and Finite Bn-Pairs (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete). Springer, 1986.

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Book chapters on the topic "Isomorphisme de type"

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Thatte, Satish R. "Coercive type isomorphism." In Functional Programming Languages and Computer Architecture, 29–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3540543961_3.

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Atanassow, Frank, and Johan Jeuring. "Inferring Type Isomorphisms Generically." In Lecture Notes in Computer Science, 32–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-27764-4_4.

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Aponte, María Virginia, and Roberto Cosmo. "Type isomorphisms for module signatures." In Lecture Notes in Computer Science, 334–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61756-6_95.

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Gaifman, Haim, and E. P. Specker. "Isomorphism Types of Trees." In Ernst Specker Selecta, 202–8. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-9259-9_18.

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Di Cosmo, Roberto. "Isomorphisms for ML." In Isomorphisms of Types: from λ-calculus to information retrieval and language design, 165–204. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-2572-0_6.

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Barthe, Gilles, and Olivier Pons. "Type Isomorphisms and Proof Reuse in Dependent Type Theory." In Lecture Notes in Computer Science, 57–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45315-6_4.

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Xu, Xiaoping. "Isomorphisms, Conjugacy and Exceptional Types." In Representations of Lie Algebras and Partial Differential Equations, 95–123. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6391-6_4.

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Dezani-Ciancaglini, Mariangiola, Roberto Di Cosmo, Elio Giovannetti, and Makoto Tatsuta. "On Isomorphisms of Intersection Types." In Computer Science Logic, 461–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-87531-4_33.

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Balat, Vincent, and Roberto Di Cosmo. "A Linear Logical View of Linear Type Isomorphisms." In Computer Science Logic, 250–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-48168-0_18.

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Nuida, Koji. "On the Isomorphism Problem for Coxeter Groups and Related Topics." In Groups of Exceptional Type, Coxeter Groups and Related Geometries, 217–38. New Delhi: Springer India, 2014. http://dx.doi.org/10.1007/978-81-322-1814-2_12.

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Conference papers on the topic "Isomorphisme de type"

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Balyo, Tomáš, Martin Suda, Lukáš Chrpa, Dominik Šafránek, Stephan Gocht, Filip Dvořák, Roman Barták, and G. Michael Youngblood. "Planning Domain Model Acquisition from State Traces without Action Parameters." In 21st International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}, 812–22. California: International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/kr.2024/76.

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Existing planning action domain model acquisition approaches consider different types of state traces from which they learn. The differences in state traces refer to the level of observability of state changes (from full to none) and whether the observations have some noise (the state changes might be inaccurately logged). However, to the best of our knowledge, all the existing approaches consider state traces in which each state change corresponds to an action specified by its name and all its parameters (all objects that are relevant to the action). Furthermore, the names and types of all the parameters of the actions to be learned are given. These assumptions are too strong. In this paper, we propose a method that learns action schema from state traces with fully observable state changes but without the parameters of actions responsible for the state changes (only action names are part of the state traces). Although we can easily deduce the number (and names) of the actions that will be in the learned domain model, we still need to deduce the number and types of the parameters of each action alongside its precondition and effects. We show that this task is at least as hard as graph isomorphism. However, our experimental evaluation on a large collection of IPC benchmarks shows that our approach is still practical as the number of required parameters is usually small. Compared to the state-of-the-art learning tools SAM and Extended SAM our new algorithm can provide better results in terms of learning action models more similar to reference models, even though it uses less information and has fewer restrictions on the input traces.
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Cosmo, Robero Di. "Type isomorphisms in a type-assignment framework." In the 19th ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/143165.143208.

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Aloupis, Greg, John Iacono, Stefan Langerman, Özgür Ozkan, and Stefanie Wuhrer. "The Complexity of Order Type Isomorphism." In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973402.30.

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Fiore, Marcelo. "Isomorphisms of generic recursive polynomial types." In the 31st ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/964001.964008.

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Zibin, Yoav, Joseph (Yossi) Gil, and Jeffrey Considine. "Efficient algorithms for isomorphisms of simple types." In the 30th ACM SIGPLAN-SIGACT symposium. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/604131.604146.

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Ilik, Danko. "Axioms and decidability for type isomorphism in the presence of sums." In CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2603088.2603115.

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Tarau, Paul. "Isomorphisms, hylomorphisms and hereditarily finite data types in Haskell." In the 2009 ACM symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1529282.1529706.

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Clairambault, Pierre. "Isomorphisms of Types in the Presence of Higher-Order References." In 2011 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011). IEEE, 2011. http://dx.doi.org/10.1109/lics.2011.32.

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Bruce, K. B., and G. Longo. "Provable isomorphisms and domain equations in models of typed languages." In the seventeenth annual ACM symposium. New York, New York, USA: ACM Press, 1985. http://dx.doi.org/10.1145/22145.22175.

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Forster, Yannick, Felix Jahn, and Gert Smolka. "A Computational Cantor-Bernstein and Myhill’s Isomorphism Theorem in Constructive Type Theory (Proof Pearl)." In CPP '23: 12th ACM SIGPLAN International Conference on Certified Programs and Proofs. New York, NY, USA: ACM, 2023. http://dx.doi.org/10.1145/3573105.3575690.

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Reports on the topic "Isomorphisme de type"

1

Gross, Jonathan L. Topological Representation of Graph Isomorphism Types. Fort Belvoir, VA: Defense Technical Information Center, November 1991. http://dx.doi.org/10.21236/ada243528.

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