Existence of holomorphic sections and perturbation of positive line bundles over qq--concave manifolds

By using asymptotic Morse inequalities we give a lower bound for the space of holomorphic sections of high tensor powers in a positive line bundle over a q-concave domain. The curvature of the positive bundle induces a hermitian metric on the manifold. The bound is given explicitely in terms of the volume of the domain in this metric and a certain integral on the boundary involving the defining function and its Levi form. As application we study the perturbattion of the complex structure of a q-concave manifold.Comment: 18 pages, AmsTe

The Speech Act Theory between Linguistics and Language Philosophy

Of all the issues in the general theory of language usage, speech act theory has probably aroused the widest interest. Psychologists, for example, have suggested that the acquisition of the concepts underlying speech acts may be a prerequisite for the acquisition of language in general, literary critics have looked to speech act theory for an illumination of textual subtleties or for an understanding of the nature of literary genres, anthropologists have hoped to find in the theory some account of the nature of magical incantations, philosophers have seen potential applications to, amongst other things, the status of ethical statements, while linguists have seen the notions of speech act theory as variously applicable to problems in syntax, semantics, second language learning, and elsewhere.speech act theory, presupposition, implicature, deixis

Equidistribution results for singular metrics on line bundles

Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic sections of the p-th tensor powers of L. Assuming that the singular set of the metric is contained in a compact analytic subset of X and that the logarithm of the Bergman kernel function associated to the p-th tensor power of L (defined outside the singular set) grows like o(p) as p tends to infinity, we prove the following: 1) the k-th power of the Fubini-Study currents converge weakly on the whole X to the k-th power of the curvature current of L. 2) the expectations of the common zeros of a random k-tuple of square integrable holomorphic sections converge weakly in the sense of currents to to the k-th power of the curvature current of L. Here k is so that the codimension of the singular set of the metric is greater or equal as k. Our weak asymptotic condition on the Bergman kernel function is known to hold in many cases, as it is a consequence of its asymptotic expansion. We also prove it here in a quite general setting. We then show that many important geometric situations (singular metrics on big line bundles, Kaehler-Einstein metrics on Zariski-open sets, artihmetic quotients) fit into our framework.Comment: 40 page

From Sentence to Text

We are used to applying the term text to any stretch of language which makes coherent sense in the particular context of its use. So conspicuous a linguistic reality, the text may be either spoken or written, either as long as a book or as short as a cry for help. Linguistic form is important but is by no means of itself sufficient to give a stretch of a language the status of text. For example a road – sign reading Dangerous Corner is an adequate text though comprising only a short noun – phrase. It is understood as an existential statement, paraphraseable as something like There is a dangerous corner near by, with such block language features as zero article, that are expected in notices of this kind. By contrast, a sign at the roadside with the same grammatical structure but reading Critical Remark is not an adequate text, because although we recognize the structure and understand the words, the phrase can communicate nothing to us as we drive by, and thus is meaningless.Ellipses , pro – forms, Spatial Relations, Time Relators

Order-of-Magnitude Influence Diagrams

In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an order-of-magnitude approximation of both probabilities and utilities and allows for specifying partially ordered preferences via sets of utility values. We also propose a dedicated variable elimination algorithm that can be applied for solving order-of-magnitude influence diagrams

Berezin-Toeplitz quantization and its kernel expansion

We survey recent results about the asymptotic expansion of Toeplitz operators and their kernels, as well as Berezin-Toeplitz quantization. We deal in particular with calculation of the first coefficients of these expansions.Comment: 34 page

EUROPEAN ECONOMIC MODEL: QUE VADIS UE?

Recent evolutions in Europe raise questions on the viability of the actual economic and social model that defines the European construction project. In this paper, I will try to explain the viability of institutional European model that stick between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the wellbeing for all Europeans. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market which creates the prosperity so long waited for by new member countries?economic model, institutions, economic integration, competition

Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface

We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian