Measurement of ultraweak transitions in the visible region of molecular oxygen

A highly sensitive cavity-enhanced frequency modulation spectroscopy technique has been used to measure ultraweak transitions in molecular oxygen that had not previously been characterized. The self-broadened half-width and line intensity of the measured transitions are reported. We include 12 high J transitions in the band of ¹⁶O₂ (the so-called A band), 59 transitions in the hot band of ¹⁶O₂, and 17 high J transitions in the band of ¹⁶O¹⁸O. Our measurements of line positions of the ¹⁶O¹⁸O transitions are used to determine improved molecular constants for the excited state of ¹⁶O¹⁸O.     

A <Emphasis Type="Italic">QR</Emphasis>–method for computing the singular values via semiseparable matrices

Summary. The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a new method for computing the singular value decomposition of a real matrix. In a first phase, an algorithm for reducing the matrix A into an upper triangular semiseparable matrix by means of orthogonal transformations is described. A remarkable feature of this phase is that, depending on the distribution of the singular values, after few steps of the reduction, the largest singular values are already computed with a precision depending on the gaps between the singular values. An implicit QR–method for upper triangular semiseparable matrices is derived and applied to the latter matrix for computing its singular values. The numerical tests show that the proposed method can compete with the standard method (using an intermediate bidiagonal matrix) for computing the singular values of a matrix.Mathematics Subject Classification (2000): 65F15, 15A18The research of the first two authors was partially supported by the Research Council K.U.Leuven, project OT/00/16 (SLAP: Structured Linear Algebra Package), by the Fund for Scientific Research–Flanders (Belgium), projects G.0078.01 (SMA: Structured Matrices and their Applications), G.0176.02 (ANCILA: Asymptotic aNalysis of the Convergence behavior of Iterative methods in numerical Linear Algebra), G.0184.02 (CORFU: Constructive study of Orthogonal Functions) and G.0455.0 (RHPH: Riemann-Hilbert problems, random matrices and Padé-Hermite approximation), and by the Belgian Programme on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Ministers Office for Science, Technology and Culture, project IUAP V-22 (Dynamical Systems and Control: Computation, Identification & Modelling). The work of the third author was partially supported by MIUR, grant number 2002014121. The scientific responsibility rests with the authors.Acknowledgments.We thank the referees for their suggestions which increased the readability of the paper.     

MRI and x-ray CT study of spatial distribution of core breakdown in 'Conference' pears

Two non-destructive tomographic techniques, X-ray CT imaging and magnetic resonance imaging (MRI), were applied to study the development of core breakdown disorder in 'Conference' pears (Pyrus communis cv. Conference). This disorder, which is characterized by brown discoloration of the tissue and development of cavities, is induced by elevated CO(2) and decreased O(2) levels during controlled atmosphere storage. Tomographic images of pears stored for 10 months under disorder inducing conditions, were acquired with both techniques and compared to the actual slices. Both X-ray and MRI were able to differentiate between unaffected tissue, brown tissue and cavities. A simple image-processing program, based on threshold values, was developed to determine the area percentage of affected and unaffected tissue as well as the cavity and core area per slice. For all three imaging techniques the area percentage brown tissue per slice increased with the diameter of the pear, but was systematically underestimated by 12% and 6% for, respectively, X-ray and MRI, compared to the actual slices. The area percentage cavity corresponded very well for all techniques. It was also found that the contours of the brown tissue were parallel to the fruit boundaries, suggesting a relation between the disorder symptoms and gas diffusion properties of the fruit. It was concluded that MRI is the most appropriate technique to study the development of core breakdown disorder during postharvest storage in future experiments.     

Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains

We use the method of Alexandroff-Serrin to establish the spherical symmetry of the ground domain and of the weak solution to a free boundary problem for a class of quasi-linear parabolic equations in an unbounded cylinder , where , with a simply connected bounded domain. The equations considered are of the type , with modeled on . We consider a solution satisfying the boundary conditions: for , and , as . We show that the overdetermined co-normal condition for , with 0$"> for at least one value , forces the spherical symmetry of the ground domain and of the solution.

     

3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem

We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka–Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only if it is flat.     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

Synthesis and Antiproliferative Effect of Halogenated Coumarin Derivatives

A series of 6- and 6,8-halocoumarin derivatives have been investigated as potential antiproliferative compounds against a panel of tumor and normal cell lines. Cytotoxic effects were determined by the MTT method. To investigate the potential molecular mechanism involved in the cytotoxic effect, apoptosis assay, cell cycle analysis, reactive oxygen species (ROS), and reduced glutathione analysis were performed. Among the screened compounds, coumarins 6,8-dibromo-2-oxo-2H-chromene-3-carbonitrile 2h and 6,8-diiodo-2-oxo-2H-chromene-3-carbonitrile 2k exhibited the most antiproliferative effect in thyroid cancer-derived cells TPC-1. The apoptosis assay showed that both 2h and 2k induced apoptosis in TPC-1 thyroid cancer cells. According to these experiments, both coumarins induced a slight increase in TPC-1 cells in the G2/M phase and a decrease in the S phase. A significant increase in ROS levels was observed in TPC-1 treated with diiodocoumarin 2k, while the dibromocoumarin 2h induced a decrease in ROS in a dose and time-dependent manner.