The two-level atom laser: analytical results and the laser transition

The problem of the two-level atom laser is studied analytically. The steady-state solution is expressed as a continued fraction, and allows for accurate approximation by rational functions. Moreover, we show that the abrupt change observed in the pump dependence of the steady-state population is directly connected with the transition to the lasing regime. The condition for a sharp transition to Poissonian statistics is expressed as a scaling limit of vanishing cavity loss and light-matter coupling, $\kappa \to 0$, $g \to 0$, such that $g^2/\kappa$ stays finite and $g^2/\kappa > 2 \gamma$, where $\gamma$ is the rate of atomic losses. The same scaling procedure is also shown to describe a similar change to Poisson distribution in the Scully-Lamb laser model too, suggesting that the low-$\kappa$, low-$g$ asymptotics is of a more general significance for the laser transition.Comment: 23 pages, 3 figures. Extended discussion of the paper aim (in the Introduction) and of the results (Conclusions and Discussion). Results unchange

Exclusive Safeguards and Technology Transfer: Subcontracting Agreements in Eastern Europe's Car Component Industry.

We study the rationale for the use of exclusivity to protect transfer of technology in subcontracting agreements. The legal possibility arises through the EU Notice on Subcontracting. Empirically, the link between exclusive agreements and technology transfer among firms in the automotive supply industry in EU candidate countries is surprisingly weak, although with exclusive-supply or exclusive-buying clauses in subcontracting agreements upstream transfer of technology is more likely. Exclusive agreements are often reciprocal, and are typically passed on. Downstream firms are more likely to face and use vertical restraints. Technology trickles upstream: Multinational final assemblers transfer more technology than lower-tier suppliers.vertical restraints: technology transfer; automotive supply networks; competition policy

Competition Compliance: Limits to Competition Policy Harmonisation in EU Enlargement

The paper analyses the extent of and the reasons behind limits to competition policy harmonisation in EU enlargement. Our focus is on vertical restraints. First, we compare the relevant legal regimes towards vertical agreements in the EU and in Eastern Europe. We then describe competition policy practice in all ten EU candidate countries and point out differences both between East and West and among the candidates. Finally, we examine a large database of inter-firm agreements in Eastern Europe's car industry and use insights from case studies of subcontracting to highlight instances of non-conformity between (1) East European competition law and practice and (2) EU rules and East European competition law enforcement. The conclusion recommends how to improve competition policy practice, and thus compliance, post-enlargement.antitrust law; EU enlargement; empirical studies

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

MicroRNA-200 Family Members Differentially Regulate Morphological Plasticity and Mode of Melanoma Cell Invasion

A functional role of microRNAs (miRNAs or miRs) in neoplasia and metastasis is becoming clear, and the miR-200 family has received much attention for potentially regulating tumor progression. The miRNAs of this family have been shown to suppress epithelial-mesenchymal transition, and their down-regulation in some tumors promotes invasion and metastasis. Interestingly, while miR-200 is down-regulated in some cancers, it is up-regulated in others.We show that levels of miR-200 are increased in melanoma cell lines compared to normal melanocytes and that miR-200 family members play a role in determining modes of tumor cell migration. Individual tumor cells can invade in either elongated, "mesenchymal-type" or rounded, "amoeboid-like" modes and these two modes of invasion are inter-convertible [1]. In melanoma cell lines, expression of miR-200 members does not suppress invasion but rather leads to a switch between modes of invasion. MicroRNA-200c results in a higher proportion of cells adopting the rounded, amoeboid-like mode of invasion, while miR-200a results in a protrusion-associated elongated mode of invasion. Functional target identification studies suggest that the morphological effects of miR-200c may be mediated by reduced expression of MARCKS, which has been linked to formation of cell protrusions. In contrast miR-200a reduces actomyosin contractility, a feature of rounded morphology.Overall our findings call into question the general role of miR-200 in suppressing invasion and metastasis, and highlight novel distinguishing characteristics of individual miR-200 family members

Ramanujan and Extensions and Contractions of Continued Fractions

If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$ we mean a continued fraction $K_{n=1}^{\infty} c_{n}/d_{n}$ whose odd or even part is $K_{n=1}^{\infty} a_{n}/b_{n}$. One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if $K_{n=1}^{\infty}a_{n}/b_{n}$ is the even part); (ii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart.Comment: 16 page

Observations of sunlit N2+ aurora at high altitudes during the RENU2 flight

We present measurements of sunlit aurora during the launch of the Rocket Experiment for Neutral Upwelling 2 (RENU2) on the 13 December 2015, 07:34 UTC. The in situ auroral conditions coincide with those of sunlit aurora and were characterised by the 391.4 and 427.8 nm N2 + emissions. A correlation between several auroral wavelengths, as measured by a meridian-scanning photometer, was used to detect sunlit aurora and indirectly neutral upwelling. These results, based on ground data, agree well with the RENU2 measurements recorded during its pass through the sunlit polar cusp. Using in situ data from RENU2 and the solar photon flux, it was estimated that the sunlit aurora was a major part (≈ 40 %) of the observed 427.8 nm emissio