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

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

Embeddability of some strongly pseudoconvex CR manifolds

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.Comment: 12 pages, AMSLate

Berezin-Toeplitz quantization on Kaehler manifolds

We study the Berezin-Toeplitz quantization on Kaehler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the Berezin-Toeplitz operators, and of the composition of two Berezin-Toeplitz operators. As application we estimate the norm of Donaldson's Q-operator.Comment: 45 pages, footnote at page 3 and Remark 0.5 added; v.3 is a final update to agree with the published pape

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

Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles

In this paper we study the asymptotic behaviour of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. This implies a full asymptotic expansion of this function on the set where the curvature of the line bundle is non-degenerate. As application we obtain the Bergman kernel asymptotics for adjoint semi-positive line bundles over complete Kaehler manifolds, on the set where the curvature is positive. We also prove the asymptotics for big line bundles endowed with singular Hermitian metrics with strictly positive curvature current. In this case the full asymptotics holds outside the singular locus of the metric.Comment: 71 pages; v.2 is a final update to agree with the published pape