Jurisdictional Issues: The EEC Merger Control Regulation, Member State Laws, and Articles 85 and 86

This Article deals with two main issues. One is the division of powers between the European Economic Community and the Member States with regard to merger control after September 21, 1990. The other is the possible application, by the Commission of the European Communities or by national authorities, of Article 85 and 86 of the Treaty Establishing the European Economic Community to mergers covered by Regulation No. 4064/89. The Article casts a brief look at how the dividing line between merges and operations which do not qualify as mergers within the sense of article 3 of the Regulation will be treated in the future

Non-equilibrium heat capacity of polytetrafluoroethylene at room temperature

Polytetrafluoroethylene can be considered as a model for calorimetric studies of complex systems with thermodynamics transitions at ambient temperature. This polymer exhibits two phase transitions of different nature at 292 K and 303 K. We show that sensitive ac-calorimetry measurements allow us to study the thermodynamic behaviour of polytetrafluoroethylene when it is brought out of thermodynamic equilibrium. Thanks to the thermal modelisation of our calorimetric device, the frequency dependent complex heat capacity of this polymer is extracted. The temperature and frequency variations of the real and imaginary parts of the complex heat capacity are obtained when polytetrafluoroethylene undergoes its first-order structural phase transition at 292 K

Measurement of thermal conductance of silicon nanowires at low temperature

We have performed thermal conductance measurements on individual single crystalline silicon suspended nanowires. The nanowires (130 nm thick and 200 nm wide) are fabricated by e-beam lithography and suspended between two separated pads on Silicon On Insulator (SOI) substrate. We measure the thermal conductance of the phonon wave guide by the 3 method. The cross-section of the nanowire approaches the dominant phonon wavelength in silicon which is of the order of 100 nm at 1K. Above 1.3K the conductance behaves as T3, but a deviation is measured at the lowest temperature which can be attributed to the reduced geometry

Compactness results in Symplectic Field Theory

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [M Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307--347] as well as compactness theorems in Floer homology theory, [A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775--813 and Morse theory for Lagrangian intersections, J. Diff. Geom. 28 (1988) 513--547], and in contact geometry, [H Hofer, Pseudo-holomorphic curves and Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 307--347 and H Hofer, K Wysocki and E Zehnder, Foliations of the Tight Three Sphere, Annals of Mathematics, 157 (2003) 125--255].Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper25.abs.htm

New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Searching for thermal signatures of persistent currents in normal metal rings

We introduce a calorimetric approach to probe persistent currents in normal metal rings. The heat capacity of a large ensemble of silver rings is measured by nanocalorimetry under a varying magnetic field at different temperatures (60 mK, 100 mK and 150 mK). Periodic oscillations versus magnetic field are detected in the phase signal of the temperature oscillations, though not in the amplitude (both of them directly linked to the heat capacity). The period of these oscillations ($\Phi_0/2$, with $\Phi_0 = h/e$ the magnetic flux quantum) and their evolution with temperature are in agreement with theoretical predictions. In contrast, the amplitude of the corresponding heat capacity oscillations (several $k_{\mathrm{B}}$) is two orders of magnitude larger than predicted by theory

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat