Perturbation of systems of linear algebraic equations ∗

A classical perturbation result for nonsingular systems of linear algebraic equations is extended to general consistent systems under any norm. An optimal perturbation result is also obtained for general linear least squares problems under a Euclidean norm.     

Potential energy surface for linear triatomic molecules: An algebraic method

Recently, we proposed a new transformation between the angle of canonical coordinates and the bond angle to describe the bending motion in Potential Energy Surfaces (PES) of bent triatomic molecules. In this work we extend the transformation to include linear triatomic molecules. Results for the linear triatomic molecule N₂O are reported.     

Determination of asperosaponin VI in rat plasma by HPLC‐ESI‐MS and its application to preliminary pharmacokinetic studies

Asperosaponin VI (also named akebia saponin D) is a typical bioactive triterpenoid saponin isolated from the rhizome of Dipsacus asper Wall (Dipsacaceae). In this work, a sensitive high‐performance liquid chromatography–electrospray ionization–mass spectrometry (HPLC‐ESI‐MS) assay has been established for determination of asperosaponin VI in rat plasma. With losartan as the internal standard (IS), plasma samples were prepared by protein precipitation with methanol. Chromatographic separation was performed on a C₁₈ column with a mobile phase of 10 mm ammonium acetate buffer containing 0.05% formic acid–methanol (32 : 68, v/v). The analysis was performed on an ESI in the selected ion monitoring mode using target ions at m/z 951.4 for asperosaponin VI and m/z 423.2 for the IS. The calibration curve was linear over the range 3–1000 ng/mL and the lower limit of quantification was 3.0 ng/mL. The intra‐ and inter‐assay variability values were less than 9.5 and 7.8%, respectively. The accuracies determined at the concentrations of 3.0, 100.0, 300.0 and 1000 ng/mL for asperosaponin VI were within ±15.0%. The validated method was successfully applied to a pharmacokinetic study in rats after oral administration of asperosaponin VI. Copyright © 2009 John Wiley & Sons, Ltd.     

Bifurcations in the optimal elastic foundation for a buckling column

We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.     

The way to high-performance single nanowire photodetectors: problems and prospects

<正>As potential building blocks for micro-nano devices,one-dimensional semiconductor nanowires(NWs)have been widely studied in recent decades.Due to limited dimension and large surface-to-volume ratio,devices based on NWs are more likely to exhibit unique properties.NW photodetectors adopting different materials have been fabricated.However,the performance is greatly affected by several issues such as lattice quality,surface homogeneity,contact electrodes and     

Binary self-assembly of highly symmetric DNA nanocages via sticky-end engineering

Discrete and symmetric three-dimensional(3D)DNA nanocages have been revoked as excellent candidates for various applications,such as guest component encapsulation and organization(e.g.dye molecules,proteins,inorganic nanoparticles,etc.)to construct new materials and devices.To date,a large variety of DNA nanocages has been synthesized through assembling small individual DNA motifs into predesigned structures in a bottom-up fashion.Most of them rely on the assembly using multiple copies of single type of motifs and a few sophisticated nanostructures have been engineered by co-assembling multi-types of DNA tiles simultaneously.However,the availability of complex DNA nanocages is still limited.Herein,we demonstrate that highly symmetric DNA nanocages consisted of binary DNA point-star motifs can be easily assembled by deliberately engineering the sticky-end interaction between the component building blocks.As such,DNA nanocages with new geometries,including elongated tetrahedron(E-TET),rhombic dodecahedron(R-DOD),and rhombic triacontahedron(R-TRI)are successfully synthesized.Moreover,their design principle,assembly process,and structural features are revealed by polyacryalmide gel electrophoresis(PAGE),atomic force microscope(AFM)imaging,and cryogenic transmission electron microscope imaging(cryo-TEM)associated with single particle reconstruction.