On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

A generalization of the Hoffman-Lovász upper bound on the independence number of a regular graph

A family of quadratic programming problems whose optimal values are upper bounds on the independence number of a graph is introduced. Among this family, the quadratic programming problem which gives the best upper bound is identified. Also the proof that the upper bound introduced by Hoffman and Lovász for regular graphs is a particular case of this family is given. In addition, some new results characterizing the class of graphs for which the independence number attains the optimal value of the above best upper bound are given. Finally a polynomial-time algorithm for approximating the size of the maximum independent set of an arbitrary graph is described and the computational experiments carried out on 36 DIMACS clique benchmark instances are reported.

A recursive construction of the regular exceptional graphs with least eigenvalue -2

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

Compte rendu: Johann Wolfgang Unger (2013), The Discursive Construction of the Scots Language : Education, Politics and Everyday Life, Amsterdam, John Benjamins, coll. « Discourse Approaches to Politics, Society and Culture, 51 », 178 p. [ISBN : 978-9-027-20642-8]

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How the sublime became "now": time, modernity and aesthetics in Lyotard's rewriting of Kant

Writing in the late 1980s, Nancy gives as examples of the "recent fashion for the sublime" not only the theoreticians of Paris, but the artists of Los Angeles, Berlin, Rome, and Tokyo. At the beginning of the twenty-first century, the sublime may of course no longer seem quite so "now" as it did back then, whether in North America, Europe, or Japan. Simon Critchley, for one, has suggested that, at least as regards the issue of its conceptual coupling to "postmodernism," the "debate" concerning the sublime "has become rather stale and the discussion has moved on." Nonetheless, if that debate has indeed "moved on"-and thankfully so-it is not without its remainder, particularly in the very contemporary context of a resurgence of interest in explicitly philosophical accounts of art, in the wake of an emergent critique of cultural studies and of the apparent waning of poststructuralism's influence-a resurgence that has led to a certain "return to aesthetics" in recent Continental philosophy and to the work of Kant, Schelling, and the German Romantics. Moreover, as Nancy's precise formulations suggest, the "fashion" [mode] through which the sublime "offers itself"-as "a break within or from aesthetics"-clearly contains a significance that Critchley's more straightforward narration of shifts in theoretical chic cannot encompass. At stake in this would be the relation between the mode of fashion and art's "destiny" within modernity itself, from the late eighteenth century onwards. Such a conception of art's "destiny," as inextricably linked to that of the sublime, is not unique to recent French theory. In a brief passage in Aesthetic Theory, Adorno also suggests that the "sublime, which Kant reserved exclusively for nature, later became the historical constituent of art itself.... [I]n a subtle way, after the fall of formal beauty, the sublime was the only aesthetic idea left to modernism." As such, although the term has its classical origins in Longinus, its historical character for "us," both Nancy and Adorno argue, associates it specifically with the emergence of the modern. As another philosopher states: "It is around this name [of the sublime] that the destiny of classical poetics was hazarded and lost; it is in this name that ... romanticism, in other words, modernity, triumphed."

Academics across borders: narratives of linguistic capital, language competence, and communication strategies

This article reports on a study that examined the personal employment paths of six international academics at a British university. To complement previous accounts of difficult migration, it focuses on the successful experiences of such academics, in particular how proficiency in English facilitated their move into employment in higher education (HE), and the linguistic competences and communication strategies they deploy in their daily activities. The article identifies key factors that have facilitated to their academic achievements and contributes to the understanding of the benefits and consequences of skilled migration. In conclusion, it suggests workplace pedagogy and policy responses that could facilitate other international academics' successful experiences in the UK HE sector.

In Support of the Matrix Language Frame Model: Evidence from Igbo-English Intrasentential Codeswitching

This paper explores the morphosyntactic features of mixed nominal expressions in a sample of empirical Igbo-English intrasentential codeswitching data (i.e. codeswitching within a bilingual clause) in terms of the Matrix Language Frame (MLF) model. Since both Igbo and English differ in the relative order of head and complement within the nominal argument phrase, the analysed data seem appropriate for testing the veracity of the principal assumption underpinning the MLF model: the notion that the two languages (in our case Igbo and English) participating in codeswitching do not both contribute equally to the morphosyntactic frame of a mixed constituent. As it turns out, the findings provide both empirical and quantitative support for the basic theoretical view that there is a Matrix Language (ML) versus Embedded Language (EL) hierarchy in classic codeswitching as predicted by the MLF model because both Igbo and English do not simultaneously satisfy the roles of the ML in Igbo-English codeswitching.

The rebirth of an old language: issues of gender equality in Kazakhsstan

The existing language situation in Kazakhstan, while peaceful, is not without some tension. We propose to analyze here some questions we consider relevant in the frame of cultural globalization and gender equality, such as: free from Russian imperialism, could Kazakhstan become an easy prey of Turkey’s “imperialist dream”? Could these traditionally Muslim people be soon facing the end of religious tolerance and gender equality, becoming this new old language an easy instrument for the infiltration in the country of fundamentalism (it has already crossed the boarders of Uzbekistan), leading to a gradual deterioration of its rich multicultural relations? The present structure of the language is still very fragile: there are three main dialects and many academics defend the re-introduction of the Latin alphabet, thus enlarging the possibility of cultural “contamination” by making the transmission of fundamentalist ideas still easier through neighbour countries like Azerbaijan, Uzbekistan and Turkmenistan (their languages belong to the same sub-group of Common Turkic), where the Latin alphabet is already in use, and where the ground for such ideas shown itself very fruitful.