Saari's conjecture is true for generic vector fields

The simplest non-collision solutions of the -body problem are the ``relative equilibria', in which each body follows a circular orbit around the centre of mass and the shape formed by the bodies is constant. It is easy to see that the moment of inertia of such a solution is constant. In 1970, D. Saari conjectured that the converse is also true for the planar Newtonian -body problem: relative equilibria are the only constant-inertia solutions. A computer-assisted proof for the 3-body case was recently given by R. Moeckel, Trans. Amer. Math. Soc. (2005). We present a different kind of answer: proofs that several generalisations of Saari's conjecture are generically true. Our main tool is jet transversality, including a new version suitable for the study of generic potential functions.

     

Computational analysis and in vivo validation of a microRNA encoded by the IBTK gene,a regulator of B-lymphocytes differentiation and survival

MicroRNAs (miRNAs) are small single-stranded RNA molecules that play an essential role in the regulation of gene expression and cell physiology. Gene rearrangements occurring in the miRNA sequence are associated with cancer. The IBTK genetic locus is located in the genomic sequence 6q14.1 that undergoes chromosomal aberration in lymphoproliferative disorders. The IBTK gene encodes the proteins IBtk-α, β and γ that regulate the B cell receptor signalling through Bruton's tyrosine kinase, which promotes B cell survival and differentiation. Pro-MirII-based analysis predicted four precursors of microRNAs (pre-miR) encoded by introns 17, 21, 26 and the 3′ un-translated region of the IBTK gene. Pre-miR-IBTK3, which was encoded by intron 26, was the effective substrate of RNase III Dicer in vitro as well as the precursor of an IBtk miRNA generated in vivo. By CLUSTALW-based analysis, pre-miR-IBTK3 homologues were found in Pan troglodytes, Pongo pygmaeus and Macaca mulatta, suggesting an evolutionary conserved function in primates.     

Use of a glass residue in the removal of heavy metals from wastewater

The extraction of silica from powdered glass cullet with an aqueous solution of sodium hydroxide has been proposed as an alternative to glass recycling aimed to the low temperature production of sodium silicates. The unextracted residue obtained after a counter current two-step extractive process at approximately 100 degrees C and room pressure is mainly made of calcium and sodium silicate and shows high porosity and a large surface area. We thought that it could be active as an agent for the removal of heavy metals from wastewater. In this paper the capacity of the unextracted residue of removing six metal ions (i.e., Cu2+, Ni2+, Zn2+, Cd2+, Pb2+ e Cr3+) was studied in a stirred batch reactor. The data obtained demonstrate that the removal of metal ions from wastewater is achieved with high capacity in a short time and their concentration is lowered under the legal limits without any appreciable influence from changes of physical and chemical conditions. Sodium and calcium ions take the place of heavy metals in water while pH keeps almost neutral. The exchange mechanism was identified.     

Covariance-based approaches to aeroacoustic noise source analysis

In this paper, several covariance-based approaches are proposed for aeroacoustic noise source analysis under the assumptions of a single dominant source and all observers contaminated solely by uncorrelated noise. The Crame?r-Rao Bounds (CRB) of the unbiased source power estimates are also derived. The proposed methods are evaluated using both simulated data as well as data acquired from an airfoil trailing edge noise experiment in an open-jet aeroacoustic facility. The numerical examples show that the covariance-based algorithms significantly outperform an existing least-squares approach and provide accurate power estimates even under low signal-to-noise ratio (SNR) conditions. Furthermore, the mean-squared-errors (MSEs) of the so-obtained estimates are close to the corresponding CRB especially for a large number of data samples. The experimental results show that the power estimates of the proposed approaches are consistent with one another as long as the core analysis assumptions are obeyed.     

Blood oxygenation monitoring using hyperspectral imaging after flap surgery

In this paper, we present a new method for the assessment of skin flap perfusion based on the non-invasive monitoring of skin blood oxygenation using hyperspectral imaging. This method consists of generation of oxyhemoglobin and deoxyhemoglobin maps in skin flap from hyperspectral image using an analytic model based on Beer–Lambert law. The results obtained on a fasciocutaneous sural flap have revealed that the oxyhemoglobin and deoxyhemoglobin maps facilitate the visualization of some differences between different areas of the flap, an aspect that clinical examination fails to do. In conclusion, the proposed method could provide a new option for a more accurate assessment of flap survival.     

Mass transport controlled oxygen reduction at anthraquinone modified 3D-CNT electrodes with immobilized Trametes hirsuta laccase

Carbon nanotubes covalently modified with anthraquinone were used as an electrode for the immobilization of Trametes hirsuta laccase. The adsorbed laccase is capable of oxygen reduction at a mass transport controlled rate (up to 3.5 mA cm(-2)) in the absence of a soluble mediator. The storage and operational stability of the electrode are excellent.     

Nondegeneracy,from the prospect of wave-wave regular interactions of a gasdynamic type

A parallel is considered between Burnat's “algebraic” approach [restricted to a genuine nonlinearity] and Martin's “differential” approach regarding their contribution to describing some nondegenerate one-dimensional gasdynamic regular interaction solutions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

New integral LEM formulae applied to the nonlinear bar

The linear equivalence method (LEM), introduced by [Bull. Math. Soc. Sci. Math. de la Roumanie 24 (72) (1980) 4417; An. Univ. Bucure ti, ser. Matematica 31 (1982) 75] to get solutions of nonlinear ODEs, was used so far to get differential type representations. New LEM representations of integral type are presented here and used for the study of the nonlinear elastic bar; a good approximating formula for the rotation of the cross-section at the bar end is also obtained, in case of a simply supported bar. A parallel old–new results is made by means of a programming code.