Non-Extensive Bose-Einstein Condensation Model

The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular it is proved that it has non-extensive Bose-Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground state (k=0) level

The Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page

On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp.Comment: 12 pages, 4 figure

The Approximating Hamiltonian Method for the Imperfect Boson Gas

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.Comment: 7 page

Genes involved in carotene synthesis and mating in Blakeslea trispora

Mating of Blakeslea trispora and other molds of the order Mucorales requires the interaction of mycelia of opposite sex, (+) and (-), leading to the development of specialized structures and to an enhanced accumulation of beta-carotene. Industry obtains beta-carotene by co-cultivating appropriate strains of Blakeslea (mated cultures). Gene transcription in single and mated cultures was assayed by cDNA-AFLP, a technique to observe the differential expression of subsets of mRNA fragments. Overexpression in mated cultures is about ten times more frequent than underexpression. We obtained and sequenced fragments of 97 candidate genes that appeared to be overexpressed during mating and confirmed four of them by reverse transcription and real-time PCR. Comparisons with gene sequences from other organisms suggest functions in carotene biosynthesis (4 genes), energy metabolism (8), cell wall synthesis (1), transfer of acetyl groups (1), and regulatory processes (10). Sodium acetate inhibited sexual overexpression in about two-thirds of the candidate genes and acted as a signal with broad effects on the metabolism and the morphology of mated cultures. Our work offers new materials for the study of carotene biosynthesis and its regulation and for the improvement of carotene production with Mucorales