Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Spin Axioms in Different Geometries of Relativistic Continuum Physics

The 24 components of the relativistic spin tensor consist of 3 + 3 basic spin fields and 9 + 9 constitutive fields. Empirically only three basic spin fields and nine constitutive fields are known. This empirem can be expressed by two spin axioms, one of them denying purely relativistic spin fields, and the other one relating the three additional basic fields and the nine additional constitutive fields to the known (and measurable) ones. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from six to three basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.     

Large-scale nonlocality in “doubly special relativity” with an energy-dependent speed of light

There are two major alternatives for violating the (usual) Lorentz invariance at large (Planckian) energies or momenta—either not all inertial frames (in the Planck regime) are equivalent (e.g., there is an effectively preferred frame) or the transformations from one frame to another are (nonlinearly) deformed (“doubly special relativity”). We demonstrate that the natural (and reasonable) assumption of an energy-dependent speed of light in the latter method goes along with violations of locality/separability (and even translational invariance) on macroscopic scales.     

A theory of spin fluctuations in the refractory compounds VN and NbN

We calculate the spin fluctuation spectra of VN and NbN in the relevant frequency- and wave vector regime. Significant quantitative differences between the dynamical spin susceptibilities of both substances are found. While in the case of VN their amplitudes are large, especially towards the Brillouin zone boundary and for frequencies below 1 eV, enhancement effects in NbN are of minor importance.     

Siderophore Transport in Mycobacteria Analyzed by Mössbauer Spectroscopy: Possible Routes to Novel Antibiotics against These Organisms?

Iron uptake of the ⁵⁷Fe-siderophores ferricrocin, rhizoferrin and citrate in M. smegmatis was analyzed by in situ Mössbauer spectroscopy. Siderophore dependent uptake and metabolic utilization patterns of ⁵⁷Fe were found. Rhizoferrin is accumulated in the organism and, therefore, represents a suitable candidate for the synthesis of novel siderophore-antibiotics conjugates.     

Lower bounds for the discrepancy of triples of inversive congruential pseudorandom numbers with power of two modulus

This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm ^–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums.     

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