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on the occasion of his *sixtieth* *birthday*

, 2010

"... Rotational symmetry vs. axisymmetry in Shell theory by ..."

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on the Occasion of His *Sixtieth* *Birthday* Editors:

, 1996

"... veröffentlicht Forschungsarbeiten aus allen mathematischen Gebieten und wird in traditioneller Weise referiert. Es wird indiziert durch Mathematical Reviews, Science Citation Index Expanded, Zentralblatt für Mathematik. Artikel können als TEX-Dateien per E-Mail bei einem der Herausgeber eingereic ..."

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veröffentlicht Forschungsarbeiten aus allen mathematischen Gebieten und wird in traditioneller Weise referiert. Es wird indiziert durch Mathematical Reviews, Science Citation Index Expanded, Zentralblatt für Mathematik. Artikel können als TEX-Dateien per E-Mail bei einem der Herausgeber eingereicht werden. Hinweise für die Vorbereitung der Artikel können unter der unten angegebe-nen WWW-Adresse gefunden werden. Documenta Mathematica, Journal der Deutschen Mathematiker-Vereinigung, publishes research manuscripts out of all mathematical fields and is refereed in the traditional manner. It is indexed in Mathematical Reviews, Science Citation Index Expanded, Zentralblatt für Mathematik. Manuscripts should be submitted as TEX-files by e-mail to one of the editors. Hints

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Dedicated to Professor Norio Kikuchi on his *sixtieth* *birthday*

"... known that a family $F $ of all solution curves for an initial value problem $x’=f(t, x) $ , $x(\sigma)=x_{0} $ $(x_{0}\in \mathrm{R}^{n}) $ (1) has the Kneser’s property, namely, a cross section $\{x(\tau);x\in F\} $ of $F $ with the hy-perplane $t=\tau $ is compact and connected if $|\sigma-\tau|& ..."

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known that a family $F $ of all solution curves for an initial value problem $x’=f(t, x) $ , $x(\sigma)=x_{0} $ $(x_{0}\in \mathrm{R}^{n}) $ (1) has the Kneser’s property, namely, a cross section $\{x(\tau);x\in F\} $ of $F $ with the hy-perplane $t=\tau $ is compact and connected if $|\sigma-\tau|>0 $ is sufficiently small. In 1967,

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Dedicated to Octavio Obregón on the occasion of his *sixtieth* *birthday*

, 2006

"... We discuss the Ashtekar formalism from the point of view of twelve dimensions. We first focus on the 2 + 10 spacetime signature and then we consider the transition 2 + 10 → (2 + 2) + (0 + 8). We argue that both sectors 2 + 2 and 0 + 8, which are exceptional signatures, can be analyzed from the point ..."

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We discuss the Ashtekar formalism from the point of view of twelve dimensions. We first focus on the 2 + 10 spacetime signature and then we consider the transition 2 + 10 → (2 + 2) + (0 + 8). We argue that both sectors 2 + 2 and 0 + 8, which are exceptional signatures, can be analyzed from the point of view of a self-dual action associated with the Ashtekar formalism.

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Actions on Subfactors Dedicated to Professor Masamichi Takesaki on his *sixtieth* *birthday* By

"... We define "a crossed product by a paragroup action on a subfactor " as a certain commuting square of type IIj factors and give their complete classification in a strongly amenable case (in the sense of S. Popa) in terms of a new combinatorial object which generalizes Ocneanu's paragro ..."

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We define "a crossed product by a paragroup action on a subfactor " as a certain commuting square of type IIj factors and give their complete classification in a strongly amenable case (in the sense of S. Popa) in terms of a new combinatorial object which generalizes Ocneanu's paragroup. As applications, we show that the subfactor N c M of Goodman-de la Harpe-Jones with index 3 + A/3 is not conjugate to its dual M c M, by showing the fusion algebras of N-N bimodules and M-M bimodules are different, although the principal graph and the dual principal graph are the same. We also make an analogue of the coset construction in RCFT for subfactors in our settings. Our aim in this paper is to introduce a notion of a "crossed product by a paragroup action on a subfactor", which is a certain commuting square of type II1 factors, and classify them in terms of a combinatorial invariant generalizing Ocneanu's paragroup [35]. Roughly speaking, the standard axioms of paragroups

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Presented to Rebecca Posner on the Occasion of her *Sixtieth* *Birthday*. Londres: Routledge.

"... In this atheoretical typological study of the morphosyntactic realisation of argument structure, Lazard defines 'actance ' as 'les faits relatifs aux relations grammaticales qui s'etablissent entre le predicat [verbal] et les termes nominaux qui en dependent ' (p. ix). As fo ..."

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In this atheoretical typological study of the morphosyntactic realisation of argument structure, Lazard defines 'actance ' as 'les faits relatifs aux relations grammaticales qui s'etablissent entre le predicat [verbal] et les termes nominaux qui en dependent ' (p. ix). As for a translation of the term 'actance', the author uses 'actancy ' in the titles of recent work in English, e.g., Lazard (1990, 1995). Chapter 1, 'Les instruments de l'actance ' (1-23), contains an overview of the various means by which languages indicate the relationship between a verb and its arguments, e.g., by overt or non-overt markers on the verb (agreement) and/or on the argument (affixes, adpositions), word order (somewhere between totally free and totally fixed, rarely at either extreme) or coalescence/incorporation (e.g., prendre feulmaintenir) in

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THE MONOIDAL CENTRE AS A LIMIT To Aurelio Carboni for his *sixtieth* *birthday*

"... categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object. Some properties and sufficient conditions for existence of the ..."

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categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object. Some properties and sufficient conditions for existence of the construction are examined. 1.

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DERIVATIONS OF CATEGORICAL GROUPS Dedicated to Aurelio Carboni on the occasion of his *sixtieth* *birthday*

"... Abstract. In this paper we introduce and study the categorical group of derivations,Der(G, A), from a categorical group G into a braided categorical group (A, c) equippedwith a given coherent left action of G. Categorical groups provide a 2-dimensional vision of groups and so this object is a sort o ..."

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Abstract. In this paper we introduce and study the categorical group of derivations,Der(G, A), from a categorical group G into a braided categorical group (A, c) equippedwith a given coherent left action of G. Categorical groups provide a 2-dimensional vision of groups and so this object is a sort of 0-cohomology at a higher level for categoricalgroups. We show that the functor Der(-, A) is corepresentable by the semidirect productA o G and that Der(G,-) preserves homotopy kernels. Well-known cohomology groups,and exact sequences relating these groups, in several different contexts are then obtained

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ON VON NEUMANN VARIETIES To Aurelio Carboni, on his *sixtieth* *birthday*.

"... Abstract. We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras. ..."

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Abstract. We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras.

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ANALYTIC FUNCTORS AND WEAK PULLBACKS For the *sixtieth* *birthday* of Walter Tholen

"... Abstract. For accessible set-valued functors it is well known that weak preservation of limits is equivalent to representability, and weak preservation of connected limits to familial representability. In contrast, preservation of weak wide pullbacks is equivalent to being a coproduct of quotients o ..."

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Abstract. For accessible set-valued functors it is well known that weak preservation of limits is equivalent to representability, and weak preservation of connected limits to familial representability. In contrast, preservation of weak wide pullbacks is equivalent to being a coproduct of quotients of hom-functors modulo groups of automorphisms. For finitary functors this was proved by André Joyal who called these functors analytic. We introduce a generalization of Joyal’s concept from endofunctors of Set to endofunctors of a symmetric monoidal category. 1.