Статті в журналах: "Isomorphisme de type"

1

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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2

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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3

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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4

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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5

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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6

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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7

FURUTANI, R., I. KIKUMASA та H. YOSHIMURA. "ISOMORPHISM OF QF ALGEBRAS OVER ℚ". Journal of Algebra and Its Applications 12, № 03 (20 грудня 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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8

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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9

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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10

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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11

DE LATAILLADE, JOACHIM. "Curry-style type isomorphisms and game semantics." Mathematical Structures in Computer Science 18, no. 4 (August 2008): 647–92. http://dx.doi.org/10.1017/s0960129508006828.

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Curry-style system F, that is, system F with no explicit types in terms, may be viewed as a core presentation of polymorphism from the point of view of programming languages.This paper gives a characterisation of type isomorphisms for this language using a game model, whose intuitions come from both the syntax and the game semantics universe. The model is composed of an untyped part to interpret terms, a notion of arena to interpret types and a typed part to express the fact that an untyped strategy σ plays on an arenaA.By analysing isomorphisms in the model, we prove that the equational system corresponding to type isomorphisms for Curry-style system F is the extension of the equational system for Church-style isomorphisms with a new, non-trivial equation: ∀X.AA[∀Y.Y/X] ifXappears only positively inA.

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12

Traldi, Lorenzo. "Multivariate Alexander quandles, III. Sublinks." Journal of Knot Theory and Its Ramifications 28, no. 14 (December 2019): 1950090. http://dx.doi.org/10.1142/s0218216519500901.

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If [Formula: see text] is a classical link then the multivariate Alexander quandle, [Formula: see text], is a substructure of the multivariate Alexander module, [Formula: see text]. In the first paper of this series, we showed that if two links [Formula: see text] and [Formula: see text] have [Formula: see text], then after an appropriate re-indexing of the components of [Formula: see text] and [Formula: see text], there will be a module isomorphism [Formula: see text] of a particular type, which we call a “Crowell equivalence.” In this paper, we show that [Formula: see text] (up to quandle isomorphism) is a strictly stronger link invariant than [Formula: see text] (up to re-indexing and Crowell equivalence). This result follows from the fact that [Formula: see text] determines the [Formula: see text] quandles of all the sublinks of [Formula: see text], up to quandle isomorphisms.

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13

Dezani-Ciancaglini, Mariangiola, Luca Padovani, and Jovanka Pantovic. "Session Type Isomorphisms." Electronic Proceedings in Theoretical Computer Science 155 (June 12, 2014): 61–71. http://dx.doi.org/10.4204/eptcs.155.9.

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14

COPPO, MARIO, MARIANGIOLA DEZANI-CIANCAGLINI, INES MARGARIA, and MADDALENA ZACCHI. "Isomorphism of intersection and union types." Mathematical Structures in Computer Science 27, no. 5 (August 7, 2015): 603–25. http://dx.doi.org/10.1017/s0960129515000304.

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This paper gives a complete characterisation of type isomorphism definable by terms of a λ-calculus with intersection and union types. Unfortunately, when union is considered the Subject Reduction property does not hold in general. However, it is well known that in the λ-calculus, independently of the considered type system, the isomorphism between two types can be realised only by invertible terms. Notably, all invertible terms are linear terms. In this paper, the isomorphism of intersection and union types is investigated using a relevant type system for linear terms enjoying the Subject Reduction property. To characterise type isomorphism, a similarity between types and a type reduction are introduced. Types have a unique normal form with respect to the reduction rules and two types are isomorphic if and only if their normal forms are similar.

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15

Fixman, Uri, and Frank Okoh. "Preorders on canonical families of modules of finite length." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 1 (August 1992): 64–77. http://dx.doi.org/10.1017/s1446788700035400.

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AbstractLet R be an artinian ring. A family, ℳ, of isomorphism types of R-modules of finite length is said to be canonical if every R-module of finite length is a direct sum of modules whose isomorphism types are in ℳ. In this paper we show that ℳ is canonical if the following conditions are simultaneously satisfied: (a) ℳ contains the isomorphism type of every simple R-module; (b) ℳ has a preorder with the property that every nonempty subfamily of ℳ with a common bound on the lengths of its members has a smallest type; (c) if M is a nonsplit extension of a module of isomorphism type II1 by a module of isomorphism type II2, with II1, II2 in ℳ, then M contains a submodule whose type II3 is in ℳ and II1 does not precede II3. We use this result to give another proof of Kronecker's theorem on canonical pairs of matrices under equivalence. If R is a tame hereditary finite-dimensional algebra we show that there is a preorder on the family of isomorphism types of indecomposable R-modules of finite length that satisfies Conditions (b) and (c).

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16

Fontanille, Jacques. "Archéologie et anthropologie de la dimension plastique des sémiotiques visuelles. En hommage à Jean-Marie Floch." Estudos Semióticos 19, no. 2 (August 17, 2023): 87–120. http://dx.doi.org/10.11606/issn.1980-4016.esse.2023.207670.

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L’expression « sémiotique plastique », proposée par Jean-Marie Floch, à la suite de Greimas, est déjà en soi un choix critique. Elle a permis d’éviter le piège des typologies sémiotiques précédentes, fondées sur les canaux sensoriels, car la dimension plastique n’est pas réservée au domaine visuel ! « Sémiotique plastique » implique en effet d’emblée un typede sémiose, doté de ses plans de l’expression et du contenu spécifiques : l’identification d'un plan de l’expression spécifique ne semble pas difficile, mais celle du plan du contenu est plus problématique. Le Groupe μ a consacré une bonne partie de son Traité du signe visuel (1992) à ce qu’il appelle le « signe plastique », mais autant sa description systématique de l’expression plastique semble exhaustive, cohérente et donc convaincante, autant ses propositions concernant le contenu plastique, en défaut par rapport au principe d’hétérotopie (isomorphisme gardé) entre expression et contenu, semblent un peu trop redondantes (ou dépendantes) par rapport à l’expression, et faiblement heuristiques. Précisément, le problème sous-jacent est le statut de la dimension plastique, qui a beaucoup à perdre à être spécialisée dans le visuel, et beaucoup à gagner à être considérée comme un type particulier mais transversal de sémiose (par rapport aux types d’objets, aux canaux sensoriels, et même aux domaines de connaissance). C’est pourquoi la question de la spécificité de ses contenus est décisive, mais seulement si elle est abordée dans une perspective anthropologique et culturelle générale. Il se trouve qu'à cet égard, Greimas, Floch, mais aussi Thürlemann, ont déjà mis en évidence, dans leurs analyses, des contenus plastiques qui prenaient des allures narrativo-mythiques et anthropologiques nettement hétérotopiques par rapport aux expressions plastiques. Pour préciser la dimension plastique, Jean-Marie Floch avait parfaitement identifié une partie de la difficulté — et la possibilité d’une solution — avec les systèmes semi-symboliques : les relations propres à la sémiose plastique seraient caractérisées par la corrélation entre les oppositions de l’expression plastique et les oppositions des contenus plastiques. Mais, si les systèmes semi-symboliques garantissent l’indépendance et l’hétéronomie entre expressions et contenus plastiques, ils ne disent rien sur la nature des contenus en question. Voilà pourquoi notre enquête, qualifiée d’« archéologie de la dimension plastique », s’efforce ici de parcourir les principales typologies où naissent les possibilités de contenus plastiques, qui sont, en fait, différentes propositions en matière de types de signification : celles proposées par la scolastique médiévale (quatre types de signification), celles reformulées par l’iconologie (trois types), celles avancées, enfin, par Barthes (deux ou trois types, selon les versions) et Greimas (deux types) : il en ressort précisément que la particularité des contenus plastiques ne peut être appréhendée que par une approche anthropologique et comparée.

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17

Laskowski, M. C., and S. Shelah. "Forcing isomorphism II." Journal of Symbolic Logic 61, no. 4 (December 1996): 1305–20. http://dx.doi.org/10.2307/2275818.

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AbstractIf T has only countably many complete types, yet has a type of infinite multiplicity then there is a c.c.c. forcing notion such that, in any -generic extension of the universe, there are non-isomorphic models M1 and M2 of T that can be forced isomorphic by a c.c.c. forcing. We give examples showing that the hypothesis on the number of complete types is necessary and what happens if ‘c.c.c’ is replaced by other cardinal-preserving adjectives. We also give an example showing that membership in a pseudo-elementary class can be altered by very simple cardinal-preserving forcings.

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18

Chen, Jianke. "Generalized Canonical Isomorphisms on Determinant." Algebra Colloquium 23, no. 02 (March 16, 2016): 239–42. http://dx.doi.org/10.1142/s1005386716000262.

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In this paper we define tensor modules (sheaves) of Schur type and of generalized Schur type associated with given modules (sheaves), using the so-called Schur functors. According to the functorial property, we give a series of tensor modules (sheaves) of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules (sheaves) of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.

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19

Ellis, G. J. "Non-abelian exterior products of groups and exact sequences in the homology of groups." Glasgow Mathematical Journal 29, no. 1 (January 1987): 13–19. http://dx.doi.org/10.1017/s0017089500006637.

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Various authors have obtained an eight term exact sequence in homologyfrom a short exact sequence of groups,the term V varying from author to author (see [7] and [2]; see also [5] for the simpler case where N is central in G, and [6] for the case where N is central and N ⊂ [G, G]). The most satisfying version of the sequence is obtained by Brown and Loday [2] (full details of [2] are in [3]) as a corollary to their van Kampen type theorem for squares of spaces: they give the term V as the kernel of a map G ∧ N → N from a “non-abelian exterior product” of G and N to the group N (the definition of G ∧ N, first published in [2], is recalled below). The two short exact sequencesandwhere F is free, together with the fact that H2(F) = 0 and H3(F) = 0, imply isomorphisms..The isomorphism (2) is essentially the description of H2(G) proved algebraically in [11]. As noted in [2], the isomorphism (3) is the analogue for H3(G) of the Hopf formula for H2(G).

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20

MATTHES, RALPH, and SERGEI SOLOVIEV. "Preface to the special issue: isomorphisms of types and invertibility of lambda terms." Mathematical Structures in Computer Science 18, no. 4 (August 2008): 645–46. http://dx.doi.org/10.1017/s0960129508006798.

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Isomorphisms of types are computational witnesses of logical equivalence with additional properties. The types/formulas A and B are isomorphic if there are functions (in a certain formalism) f : A → B and g : B → A such that g ○ f and f ○ g are equal in a certain sense to the identity on A and B, respectively. Typical such formalisms are extensions of simply typed λ-calculus, with βη-convertibility as equality relation. Another view of a pair of functions f : A → B and g : B → A (besides establishing the logical equivalence of A and B) is that f is invertible with left-inverse g, and it is then natural to relax the above symmetric condition to just g ○ f being equal to the identity on A. In this situation, A is called a retract of B, which is thus a natural generalisation of the notion of an isomorphism, while both these notions are refinements of the concept of logical equivalence in operational terms, that is, in terms of computable functions.

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21

Buss, Sam, Yijia Chen, Jörg Flum, Sy-David Friedman, and Moritz Müller. "Strong isomorphism reductions in complexity theory." Journal of Symbolic Logic 76, no. 4 (December 2011): 1381–402. http://dx.doi.org/10.2178/jsl/1318338855.

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AbstractWe give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

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22

Díaz-Caro, Alejandro, and Gilles Dowek. "Non determinism through type isomorphism." Electronic Proceedings in Theoretical Computer Science 113 (March 28, 2013): 137–44. http://dx.doi.org/10.4204/eptcs.113.13.

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23

Yekutieli, Amnon. "The Continuous Hochschild Cochain Complex of a Scheme." Canadian Journal of Mathematics 54, no. 6 (December 1, 2002): 1319–37. http://dx.doi.org/10.4153/cjm-2002-051-8.

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AbstractLet X be a separated finite type scheme over a noetherian base ring . There is a complex of topological -modules, called the complete Hochschild chain complex of X. To any -module —not necessarily quasi-coherent—we assign the complex of continuous Hochschild cochains with values in . Our first main result is that when X is smooth over there is a functorial isomorphismin the derived category , where .The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard maps induce a quasi-isomorphismWhen this is the quasi-isomorphism underlying the Kontsevich Formality Theorem.Combining the two results above we deduce a decomposition of the globalHochschild cohomologywhere is the relative tangent sheaf.

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24

Di Cosmo, Roberto. "Deciding type isomorphisms in a type-assignment framework." Journal of Functional Programming 3, no. 4 (October 1993): 485–525. http://dx.doi.org/10.1017/s0956796800000861.

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AbstractThis paper provides a formal treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. The results obtained make less justified the commonplace feeling that (the core of) ML is a subset of second order λ-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order λ-calculus. This new isomorphism allows to provide a complete (and decidable) axiomatization of all the types isomorphic in ML style languages, a relevant issue for thetype as specificationsparadigm in library searches. This work is a very extended version of Di Cosmo (1992): we provide both a thorough theoretical treatment of the topic and describe a practical implementation of a library search system so that the paper can be used as a reference both by those interested in the formal theory of ML style languages, and by those simply concerned with implementation issues. The new isomorphism can also be used to extend the usual ML type-inference algorithm, as suggested by Di Cosmo (1992). Building on that proposal, we introduce a better type-inference algorithm that behaves well in the presence of non-functional primitives like references and exceptions. The algorithm described here has been implemented easily as a variation to the Caml-Light 0.4 system.

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25

RAST, RICHARD, and DAVENDER SINGH SAHOTA. "THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES." Journal of Symbolic Logic 82, no. 2 (June 2017): 453–73. http://dx.doi.org/10.1017/jsl.2017.17.

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AbstractGiven a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the isomorphism problem for linear orders into the isomorphism problem for models of T. This is done by constructing models with specific linear orders in the tail of the Archimedean ladder of a suitable nonsimple type.If the theory admits no nonsimple types, then we use Mayer’s characterization of isomorphism for such theories to compute invariants for countable models. If the theory is small, then the invariant is real-valued, and therefore its isomorphism relation is smooth. If not, the invariant corresponds to a countable set of reals, and therefore the isomorphism relation is Borel equivalent to F2.Combining these two results, we conclude that $\left( {{\rm{Mod}}\left( T \right), \cong } \right)$ is either maximally complicated or maximally uncomplicated (subject to completely general model-theoretic lower bounds based on the number of types and the number of countable models).

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26

Katsura, Masashi. "Isomorphisms of group-matrix type automata." Systems and Computers in Japan 18, no. 9 (1987): 10–18. http://dx.doi.org/10.1002/scj.4690180902.

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27

Niggemann, Michael. "An isomorphism of Paley-Wiener type." Journal of Mathematical Analysis and Applications 118, no. 2 (September 1986): 395–409. http://dx.doi.org/10.1016/0022-247x(86)90269-6.

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28

Kossak, Roman, Mark Nadel, and James Schmerl. "A note on the multiplicative semigroup of models of Peano arithmetic." Journal of Symbolic Logic 54, no. 3 (September 1989): 936–40. http://dx.doi.org/10.2307/2274754.

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In a model of Peano arithmetic, the isomorphism type of the multiplicative semigroup uniquely determines the isomorphism type of the additive semigroup. In fact, for any prime p of , the function x ↦ px is an isomorphism of the additive semigroup with the multiplicative subsemigroup of powers of p. It was observed by Jensen and Ehrenfeucht [3] that for countable models of PA, the isomorphism type of the additive semigroup (or even the additive group) determines the isomorphism type of the multiplicative semigroup. (See Theorem 3 below.)In this note we will show that the countability restriction cannot be dropped. First, we show (as Theorem 2) that for uncountable models of PA the isomorphism type of the additive group never determines the isomorphism type of the multiplicative semigroup. Our main result is Theorem 5 in which we show that the isomorphism type of the additive semigroup need not determine the isomorphism type of the multiplicative semigroup, thereby improving upon Harnik [2], where Theorem 5 is proved under the assumption of ♢. For completeness, a sketch of the proof of the Jensen-Ehrenfeucht result is included.The history of this paper begins with Nadel's question, asked in 1981, whether the countability assumption can be eliminated in the Jensen-Ehrenfeucht theorem. Soon afterwards, Nadel obtained the strong counterexample of Theorem 2, which applied to the additive group rather than the additive semigroup. A result of Pabion [8] shows that such a strong result is not possible for the additive semigroup.

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29

Bruce, Kim B., Roberto Di Cosmo, and Giuseppe Longo. "Provable isomorphisms of types." Mathematical Structures in Computer Science 2, no. 2 (June 1992): 231–47. http://dx.doi.org/10.1017/s0960129500001444.

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A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.

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30

ZHAO, KAIMING. "WEYL TYPE ALGEBRAS FROM QUANTUM TORI." Communications in Contemporary Mathematics 08, no. 02 (April 2006): 135–65. http://dx.doi.org/10.1142/s0219199706002064.

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We introduce and study the quantum version of the differential operator algebra on Laurent polynomials and its associated Lie algebra over a field F of characteristic 0. The q-quantum torus Fq is the unital associative algebra over F generated by [Formula: see text] subject to the defining relations titj = qi,jtjti, where qi,i = 1, [Formula: see text]. Let D be a subspace of [Formula: see text] where ∂i is the derivation on Fq sending [Formula: see text] to [Formula: see text]. Then, the quantum differential operator algebra is the associative algebra Fq[D]. Assume that Fq[D] is simple as an associative algebra. We compute explicitly all 2-cocycles of Fq[D], viewed as a Lie algebra. More precisely, we show that the second cohomology group of Fq[D] has dimension n if D = 0, dimension 1 if dim D = 1, and dimension 0 if dim D > 1. We also determine all isomorphisms and anti-isomorphisms Fq[D] → Fq′[D′] of simple associative algebras, and all isomorphisms Fq[D]/F → Fq′[D′]/F of simple Lie algebras.

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31

GERBER, MARLIES, and PHILIPP KUNDE. "Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli." Ergodic Theory and Dynamical Systems 42, no. 3 (October 1, 2021): 917–73. http://dx.doi.org/10.1017/etds.2021.73.

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AbstractForeman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $\mathcal {F}$ preserves other dynamical properties. We show that $\mathcal {F}$ does not preserve the loosely Bernoulli property by providing positive and zero-entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli.

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32

Altayeva, Assel, and Nobuko Yoshida. "Service Equivalence via Multiparty Session Type Isomorphisms." Electronic Proceedings in Theoretical Computer Science 291 (April 2, 2019): 1–11. http://dx.doi.org/10.4204/eptcs.291.1.

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33

de Lataillade, Joachim. "Second-order type isomorphisms through game semantics." Annals of Pure and Applied Logic 151, no. 2-3 (February 2008): 115–50. http://dx.doi.org/10.1016/j.apal.2007.10.008.

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34

Han, Sang-Eon. "The Most Refined Axiom for a Digital Covering Space and Its Utilities." Mathematics 8, no. 11 (October 27, 2020): 1868. http://dx.doi.org/10.3390/math8111868.

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This paper is devoted to establishing the most refined axiom for a digital covering space which remains open. The crucial step in making our approach is to simplify the notions of several types of earlier versions of local (k0,k1)-isomorphisms and use the most simplified local (k0,k1)-isomorphism. This approach is indeed a key step to make the axioms for a digital covering space very refined. In this paper, the most refined local (k0,k1)-isomorphism is proved to be a (k0,k1)-covering map, which implies that the earlier axioms for a digital covering space are significantly simplified with one axiom. This finding facilitates the calculations of digital fundamental groups of digital images using the unique lifting property and the homotopy lifting theorem. In addition, consider a simple closed k:=k(t,n)-curve with five elements in Zn, denoted by SCkn,5. After introducing the notion of digital topological imbedding, we investigate some properties of SCkn,5, where k:=k(t,n),3≤t≤n. Since SCkn,5 is the minimal and simple closed k-curve with odd elements in Zn which is not k-contractible, we strongly study some properties of it associated with generalized digital wedges from the viewpoint of fixed point theory. Finally, after introducing the notion of generalized digital wedge, we further address some issues which remain open. The present paper only deals with k-connected digital images.

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35

BECKER, HOWARD. "ASSIGNING AN ISOMORPHISM TYPE TO A HYPERDEGREE." Journal of Symbolic Logic 85, no. 1 (December 10, 2019): 325–37. http://dx.doi.org/10.1017/jsl.2019.81.

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AbstractLet L be a computable vocabulary, let XL be the space of L-structures with universe ω and let $f:{2^\omega } \to {X_L}$ be a hyperarithmetic function such that for all $x,y \in {2^\omega }$, if $x{ \equiv _h}y$ then $f\left( x \right) \cong f\left( y \right)$. One of the following two properties must hold. (1) The Scott rank of f (0) is $\omega _1^{CK} + 1$. (2) For all $x \in {2^\omega },f\left( x \right) \cong f\left( 0 \right)$.

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36

Tinhofer, G. "Graph isomorphism and theorems of Birkhoff type." Computing 36, no. 4 (December 1986): 285–300. http://dx.doi.org/10.1007/bf02240204.

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37

ARNOLD, DAVID M., ADOLF MADER, OTTO MUTZBAUER, and EBRU SOLAK. "THE CLASS OF (2, 2)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT HAS BOUNDED REPRESENTATION TYPE." Journal of the Australian Mathematical Society 99, no. 1 (December 4, 2014): 12–29. http://dx.doi.org/10.1017/s1446788714000652.

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The class of almost completely decomposable groups with a critical typeset of type$(2,2)$and a homocyclic regulator quotient of exponent $p^{3}$is shown to be of bounded representation type. There are only$16$isomorphism at$p$types of indecomposables, all of rank $8$or lower.

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38

Kurniawan, Dedy, and Rusdi Akbar. "The Evaluation of Performance Indicators Development: A Study on Indonesian Financial Transaction Report and Analysis Center (PPATK)." Journal of Accounting and Investment 22, no. 3 (June 15, 2021): 426–59. http://dx.doi.org/10.18196/jai.v22i3.11157.

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Research aims: This research aims to evaluate the development of performance indicators using the performance blueprint analysis tools and know what factors are instrumental in the development of performance indicators for public organizations in Indonesia using Institutional Isomorphism point of view.Design/Methodology/Approach: The study comprised qualitative research undertaken at one public organization, the Indonesian Financial Transaction Reports and Analysis Center (PPATK) in Jakarta.Research findings: This study revealed that the PPATK business process was still not optimally aligned with the performance blueprint analysis tools. This study also uncovered eleven factors that play a role in the development of performance indicators: mindset, business process, comfort zone, technical competence, regulation, activity plan, process, drafting, management commitments, monitoring and evaluation, reward and punishment, and performance data management.Theoretical contribution/Originality: This study contributes to knowledge of the institutional isomorphism’s influence, primarily normative isomorphism at a public organization. Also, this research is the first research to use the performance blueprint more thoroughly, with six types of analysis.Practitioner/Policy implication: This study has implications for ministries/institutions and regulatory agencies to implement the performance blueprint in the development process of performance indicators.Research limitation/Implication: The limitations of this study are that the results of the performance blueprint analysis tools did not yet have the criteria as the basis for assessment of findings, and this research only employed a qualitative method; therefore, the resultant conclusions are still minimum.

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39

Ricci, Paolo Emilio. "Laguerre-Type Exponentials, Laguerre Derivatives and Applications. A Survey." Mathematics 8, no. 11 (November 18, 2020): 2054. http://dx.doi.org/10.3390/math8112054.

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Laguerrian derivatives and related autofunctions are presented that allow building new special functions determined by the action of a differential isomorphism within the space of analytical functions. Such isomorphism can be iterated every time, so that the resulting construction can be re-submitted endlessly in a cyclic way. Some applications of this theory are made in the field of population dynamics and in the solution of Cauchy’s problems for particular linear dynamical systems.

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40

GIL, JOSEPH (YOSSI), and YOAV ZIBIN. "Randomised algorithms for isomorphisms of simple types." Mathematical Structures in Computer Science 17, no. 3 (June 2007): 565–84. http://dx.doi.org/10.1017/s0960129507006068.

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We give the first linear time (randomised) algorithm for the first order isomorphism problem, that is, the isomorphism of non-recursive types involving product- and function-type constructors, under the axioms of commutativity and associativity of products, currying and distributivity of functions over products. This problem can also be thought of as the problem of formal equality-testing of multi-variate expressions involving only multiplications and exponentiation. Previous work gave a deterministic O(n log2n) time and O(n) space algorithm for the problem (n being the input size). Our specific contribution includes two randomised algorithms for the problem: (i)an O(n) time Monte Carlo algorithm (that is, with a small probability it may decide erroneously that the two types are isomorphic), and(ii)an O(n log n) expected time and O(n) space Las Vegas algorithm (that is, with a small probability it may execute long). The algorithms rely on a preprocessing stage, which computes the sequence of the first n primes in O(n log n/log log n) time and space.

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41

Frąckiewicz, Piotr. "Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games." Advances in Mathematical Physics 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/4180864.

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The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form.

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42

Yan, Rong. "Isomorphisms between affine Hecke algebras of type A2˜." Journal of Algebra 324, no. 5 (September 2010): 984–99. http://dx.doi.org/10.1016/j.jalgebra.2010.03.004.

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43

Cameron, J., E. Christensen, A. M. Sinclair, R. R. Smith, S. A. White, and A. D. Wiggins. "Type II1 factors satisfying the spatial isomorphism conjecture." Proceedings of the National Academy of Sciences 109, no. 50 (November 26, 2012): 20338–43. http://dx.doi.org/10.1073/pnas.1217792109.

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44

Paris, Luis. "Artin groups of spherical type up to isomorphism." Journal of Algebra 281, no. 2 (November 2004): 666–78. http://dx.doi.org/10.1016/j.jalgebra.2004.04.021.

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45

Yani, Ni Putu Ratih Kesuma, Herkulanus Bambang Suprasto, Maria Mediatrix Ratna Sari, and I. Gusti Ayu Made Asri Dwija Putri. "Influence of industry type, profitability and size on corporate social responsibility reports isomorphism stage in Indonesia." International research journal of management, IT and social sciences 6, no. 4 (June 7, 2019): 17–30. http://dx.doi.org/10.21744/irjmis.v6n4.649.

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This research examines the influence of industry type, profitability, and size on corporate social responsibility reporting in Indonesian into three stages of isomorphism. The method purposive sampling of companies listed in Kompas100 Index from 2009 to 2016 resulting 327 coercive, 317 normative and 217 mimetic samples. Data were analyzed using binary logistic regression. The results show that only size affected on firm’s tendency to adopted corporate social responsibility reporting by publishing sustainability report in coercive isomorphism stage. Meanwhile industry type, profitability, and size affected on firm’s tendency to adopted corporate social reporting by publishing sustainability report in normative isomorphism stage. The result also showed that industry type and size affected on a firm’s tendency to adopted corporate social responsibility reporting by publishing a sustainability report in mimetic isomorphism stage. The only size is constantly influenced by corporate social responsibility reporting. We can conclude that size as the most important factor to firm considers in issuing a sustainability report in Indonesia.

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46

KHOUSSAINOV, BAKHADYR, STEFFEN LEMPP, and THEODORE A. SLAMAN. "COMPUTABLY ENUMERABLE ALGEBRAS, THEIR EXPANSIONS, AND ISOMORPHISMS." International Journal of Algebra and Computation 15, no. 03 (June 2005): 437–54. http://dx.doi.org/10.1142/s0218196705002281.

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Computably enumerable algebras are the ones whose positive atomic diagrams are computably enumerable. Computable algebras are the ones whose atomic diagrams are computable. In this paper we investigate computably enumerable algebras and provide several algebraic and computable theoretic distinctions of these algebras from the class of computable algebras. We give a characterization of computably enumerable but not computable algebras in terms of congruences and effective conjunctions of [Formula: see text]-sentences. Our characterization, for example, shows that computable conjunctions of negative atomic formulas true in a given c.e. algebra can be preserved in infinitely many of its homomorphic images. We also study questions on how expansions of algebras by finitely many new functions affect computable isomorphism types. In particular, we construct a c.e. algebra with unique computable isomorphism type but which has no finitely generated c.e. expansion.

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47

Choudhury, Vikraman, Jacek Karwowski, and Amr Sabry. "Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages." Proceedings of the ACM on Programming Languages 6, POPL (January 16, 2022): 1–32. http://dx.doi.org/10.1145/3498667.

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The Pi family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic data types. In this paper, we give a denotational semantics for this language, using weak groupoids à la Homotopy Type Theory, and show how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of type isomorphisms. We establish a correspondence between the syntactic groupoid of the language and a formally presented univalent subuniverse of finite types. The correspondence relates 1-combinators to 1-paths, and 2-combinators to 2-paths in the universe, which is shown to be sound and complete for both levels, forming an equivalence of groupoids. We use this to establish a Curry-Howard-Lambek correspondence between Reversible Logic, Reversible Programming Languages, and Symmetric Rig Groupoids, by showing that the syntax of Pi is presented by the free symmetric rig groupoid, given by finite sets and bijections. Using the formalisation of our results, we perform normalisation-by-evaluation, verification and synthesis of reversible logic gates, motivated by examples from quantum computing. We also show how to reason about and transfer theorems between different representations of reversible circuits.

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48

Todorović, Dejan. "In defense of neuro-perceptual isomorphism." Behavioral and Brain Sciences 21, no. 6 (December 1998): 774–75. http://dx.doi.org/10.1017/s0140525x98521759.

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It is argued that the notion of bridge locus is compatible with distributed representation and brain interconnectivity. Isomorphism is not a dogmatic condition on explanatory adequacy but a refutable hypothesis, superior to Dennett's proposed alternatives. The assumption of type-type neuro-perceptual correspondences is more parsimonious than multiple realizability.

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49

Baldwin, J. T., M. C. Laskowski, and S. Shelah. "Forcing isomorphism." Journal of Symbolic Logic 58, no. 4 (December 1993): 1291–301. http://dx.doi.org/10.2307/2275144.

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If two models of a first-order theory are isomorphic, then they remain isomorphic in any forcing extension of the universe of sets. In general however, such a forcing extension may create new isomorphisms. For example, any forcing that collapses cardinals may easily make formerly nonisomorphic models isomorphic. However, if we place restrictions on the partially-ordered set to ensure that the forcing extension preserves certain invariants, then the ability to force nonisomorphic models of some theory T to be isomorphic implies that the invariants are not sufficient to characterize the models of T.A countable first-order theory is said to be classifiable if it is superstable and does not have either the dimensional order property (DOP) or the omitting types order property (OTOP). If T is not classifiable, Shelah has shown in [5] that sentences in L∞,λ do not characterize models of T of power λ. By contrast, in [8] Shelah showed that if a theory T is classifiable, then each model of cardinality λ is described by a sentence of L∞,λ. In fact, this sentence can be chosen in the . ( is the result of enriching the language by adding for each μ < λ a quantifier saying the dimension of a dependence structure is greater than μ) Further work ([3], [2]) shows that ⊐+ can be replaced by ℵ1.

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50

Bavard, Juliette, Spencer Dowdall, and Kasra Rafi. "Isomorphisms Between Big Mapping Class Groups." International Mathematics Research Notices 2020, no. 10 (May 25, 2018): 3084–99. http://dx.doi.org/10.1093/imrn/rny093.

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Abstract We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these “big” mapping class groups and shows that each finite-index subgroup has finite outer automorphism group. As a key ingredient, we prove that all simplicial automorphisms between curve complexes of infinite-type orientable surfaces are induced by homeomorphisms.

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