K-Bessel functions associated to 3-rank Jordan algebra

Using Bessel-Muirhead system, we can express the K-bessel function defined on a Jordan algebra as linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for the occasion

Securing EU neighborhood - an ideational approach to EU-neighborhood relations

This paper analyses the interrelationship between internal and external security discourses in the field of European Union's neighbourhood policy. The European Union can be observed to actively use security concepts developed in the internal policy-field of Justice and Home Affairs as guiding principles of its foreign policy. This development can be traced at least to the beginning of the enlargement process in the turn of the 1990s. The paper firstly examines how those discourses infuse the new domain of neighbourhood policy that starts to take shape in the early 2000s. It concludes that especially since the European Security Strategy (2003) started to talk of the neighbourhood as a security issue, the policy can be considered to have become an inherent part of the Union's security priorities. Secondly, the paper examines from a theoretical point of view the role of ideas for institutional identity-building. Using the empirical analysis of the neighbourhood discourses as its departure point, the paper considers what this particular type of discourse can tell about the political entity that has emitted it. The research thus rejects the rationalist assumption of separable structure and agency. Instead it subscribes to the discursive institutionalist theory according to which institutions themselves are ideational structures that cannot be treated separately from actors who constitute them. Building its argument on the theses of critical security studies, the work concludes that by conceptualising the neighbourhood in terms of security threat the Union constructs itself as a political community with societal accountability

Magneto-thermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that growth rate of the condensation modes increases with the electrical charge of the dust particles.Comment: accepted by MNRA