– We study the Casimir effect for the perfect Bose-gase in the slab geometry for various boundary conditions. We show that the grand canonical potential per unit area at the bulk critical chemical potential μ = 0 has the standard asymptotic form with universal Casimir terms. In contrast to the well-known Casimir effect for the photon gas, see e.g. [1], this effect for the massive quantum partic...

Since the chemical evolution of galaxies seems to differ between morphological types and deviates in many details from the standard scenario the question has to be addressed when, how and to what amount metal-enriched ejecta from Supernovae and Planetary Nebulae polute their environment. Since recent observations of dwarf galaxies show no significant metal abundance gradients throughout the gal...

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theory, linear programming and combinatorial optimization. Claude Berge made a conjecture about them, that was proved by Chudnovsky, Robertson, Seymour and Thomas in 2002, and is now called the strong perfect graph theorem. This is a survey about perfect graphs, mostly focused on the strong perfect gr...

We discuss a new mechanism which allows domain walls produced during the primordial electroweak phase transition. We show that the effective surface tension of these domain walls can be made vanishingly small due to a peculiar magnetic condensation induced by fermion zero modes localized on the wall. We find that in the perfect gas approximation the domain wall network behaves like a radiation ...

It is well known that, in steady isentropic expansion of a gas from a reservoir, the maximum mass flux density, pu, occurs at Mach number M=u/a= 1 (p, u, and a are the local values of density, velocity, and speed of sound, respectively; po, 0, and a0 are corresponding reservoir values.) The proof is usually given for the special case of a perfect gas and it does not seem to be well known that t...

We prove global in time existence of solutions of the Euler compressible equations for a Van der Waals gas when the density is small enough in Hm, for m large enough. To do so, we introduce a specific symmetrization allowing areas of null density. Next, we make estimates in H m, using for some terms the estimates done by Grassin, who proved the same theorem in the easier case of a perfect polyt...

We report on a novel resonantly-pumped, erbium (Er)-based, gas-cooled disk laser (GCDL) scalable to highaverage power (HAP). The GCDL uses edge-pumped composite laser disks known for their near perfect pump uniformity and compact configuration. Edge pumping enables a long path for pump absorption, which permits using low Er concentration and limits upconversion losses. Resonant operation reduce...

We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and generalised Chaplygin gas energy–momentum tensors. In each case it leads to a constraint on the scalars thus giving rise to a test of General Relativity. We also...