Stability and instability properties of rotating Bose–Einstein condensates

We consider the mean-field dynamics of Bose–Einstein condensates in rotating harmonic traps and establish several stability and instability properties for the corresponding solution. We particularly emphasize the difference between the situation in which the trap is symmetric with respect to the rotation axis and the one where this is not the case.

     

Random Logistic Maps. I

Let {C _i} ₀ be a sequence of independent and identically distributed random variables with vales in [0, 4]. Let {X _n} ₀ be a sequence of random variables with values in [0, 1] defined recursively by X _n+1=C _n+1 X _n(1–X _n). It is shown here that: (i) E ln C ₁<0X _n0 w.p.1. (ii) E ln C ₁=0X _n0 in probability (iii) E ln C ₁>0, E |ln(4–C ₁)| such that (0, 1)=1 and is invariant for {X _n}. (iv) If there exits an invariant probability measure such that {0}=0, then E ln C ₁>0 and – ln(1–x) (dx)=E ln C ₁. (v) E ln C ₁>0, E |ln(4–C ₁)|< and {X _n} is Harris irreducible implies that the probability distribution of X _n converges in the Cesaro sense to a unique probability distribution on (0, 1) for all X ₀0.     

Tetrameric Cubic Structures of Two Solvated Lithium Enolates

The structures of the crystalline lithium enolates derived from 3, 3-dimethyl-2-butanone and from cyclopentanone have been determined by X-ray analysis. Both structures are tetrameric aggregates based on a Li₄O₄-cube, each Li⁺-ion being additionally bonded to the O-atom of a tetrahydrofuran solvent molecule.     

Triangles and tetrahedra: metal directed self-assembly of metallo-supramolecular structures incorporating bis-beta-diketonato ligands

The interaction of six aryl-linked bis-beta-diketones, including a new naphthylene linked species, with copper(II), iron(III) and, in one instance gallium(III), has been investigated with the aim of obtaining metallo-supramolecular assemblies exhibiting different geometries. New examples of two assembly types incorporating the above bis-beta-diketones (L) were generated. The first type is represented by a range of molecular triangles of formula [Cu(3)(L-H(2))(3)](solvent)(n) while the second is given by a corresponding selection of less-common neutral molecular tetrahedra of formula [Fe(4)(L-H(2))(6)](solvent)(n) as well as [Ga(4)(L-H(2))(6)].8.5THF.0.5H(2)O; an example of each type has been characterised by X-ray crystallography. A magnetochemical investigation of [Fe(4)(-H(2))(6)].6THF is reported. The susceptibility is Curie like and consistent with very weak coupling occurring between the iron(III) d(5)(high spin) centres. The X-ray structures of two trinuclear copper(II) as well as a tetranuclear iron(III) and a tetranuclear gallium(III) assembly confirm their discrete triangular and tetrahedral geometries, respectively. The structure of the gallium(III) species is closely related to that of the corresponding iron(III) species. The tetrahedral structures provide rare examples of such assemblies encapsulating guest solvent molecules--in each case tetrahydrofuran is incorporated in the central cavity.     

Application of affinity selection-mass spectrometry assays to purification and affinity-based screening of the chemokine receptor CXCR4

Affinity selection-mass spectrometry (AS-MS) is a sensitive technology for identifying small molecules that bind to target proteins, and assays enabled by AS-MS can be used to delineate relative binding affinities of ligands for proteins. 'Indirect' AS-MS assays employ size-exclusion techniques to separate target-ligand complexes from unbound ligands, and target-associated ligands are then specifically detected by liquid chromatography mass spectrometry. We report how indirect AS-MS binding assays with known reference control compounds were used as guideposts for development of an optimized purification method for CXCR4, a G-protein coupled chemokine receptor, for which we sought novel antagonists. The CXCR4 purification method that was developed was amenable to scale-up and enabled the screening of purified recombinant human CXCR4 against a large combinatorial library of small molecules by high throughput indirect AS-MS. The screen resulted in the discovery of new ligands that competed off binding of reference compounds to CXCR4 in AS-MS binding assays and that antagonized SDF1α-triggered responses and CXCR4-mediated HIV1 viral uptake in cell-based assays. This report provides a methodological paradigm whereby indirect AS-MS-based ligand binding assays may be used to guide optimal integral membrane protein purification methods that enable downstream affinity selection-based applications such as high throughput AS-MS screens.     

Synthesis of marine sponge alkaloid hachijodine B and a comment on the structure of ikimine B and on the absolute configuration of niphatesine D

The syntheses of the proposed structures of hachijodine B 1, ikimine B 2 and niphatesine D 3 from S-citronellol are described. Our results suggest that the gross structures of hachijodine B and niphatesine D are correct, but that ikimine B was incorrectly assigned. We have also established that the previous absolute stereochemical assignment for niphatesine D is unreliable.