A vectorial inverse nodal problem

Consider the vectorial Sturm-Liouville problem:

where is a continuous symmetric matrix-valued function defined on , and and are real symmetric matrices. An eigenfunction of the above problem is said to be of type (CZ) if any isolated zero of its component is a nodal point of . We show that when , there are infinitely many eigenfunctions of type (CZ) if and only if are simultaneously diagonalizable. This indicates that can be reconstructed when all except a finite number of eigenfunctions are of type (CZ). The results supplement a theorem proved by Shen-Shieh (the second author) for Dirichlet boundary conditions. The proof depends on an eigenvalue estimate, which seems to be of independent interest.

     

Observation of plastic deformation in TiAlCN/a -C ceramic nanocomposite coating

Extensive plastic deformation of titanium aluminum carbonitride/amorphous carbon nanocomposite coating at room temperature was observed in this study. Nanoindentation measurement showed that the coating hardness was 24.4 GPa with the plasticity of 57.6%. The critical load of 1.3 m coating in scratch test was beyond 100 N. The depth of the 100 N scratch track identified by microstylus profilometer was 6.7 m, while the thickness of the coating in the center of the scratch track observed by scanning electron microscopy was 0.4 m, which is only about one third of that for the as-deposited coating. The amorphous carbon with sp² hybrid and -bonding is proposed to account for this unique plasticity. PACS 81.15.Gh; 81.07.Bc     

Optimum coasting flight in a horizontal plane

Busemann's concept of optimum altitude for rectilinear coasting flight has been extended to flight in a horizontal plane. The reachable domain of a vehicle in coasting flight in a horizontal plane, starting from an initial velocity, is obtained. It is shown that the area covered first increases with the altitude and then decreases to zero when the ceiling is reached. In particular, there exists an altitude for maximum longitudinal range and another altitude for maximum lateral range. Optimum variations in the lift coefficient and the bank angle to reach the boundary of the footprint are discussed.     

Variational method in the stability analysis of nonconservative problems

Zusammenfassung Das Stabilitätsproblem eines Voigt-Kelvin-Körpers, welcher nichtkonservativen und gyroskopischen Kräften unterworfen ist, wird — ähnlich der bekannten klassischen Methode — als Variationsaufgabe formuliert. Zwei Variationsprinzipien, basierend auf beschränkten zulässigen Verschiebungen, werden aufgestellt und in einem Näherungsverfahren verwendet, das als Verallgemeinerung des vielverwendeten Ritzschen Verfahrens als konservatives Problem gelten kann. Zur Instruktion wird ein Beispiel gegeben.     

A facile synthesis of C2,N3-disubstituted-4-quinazolone

A simple and efficient methodology for the synthesis of C(2),N(3)-disubstituted-4 quinazolones from anilines and N-acylanthranilic acids was developed. The new cyclization conditions are much milder than any other reported protocols and resulted in excellent yields (87-98%) without chromatography.     

Electrocatalytic activities of Nafion/CdSe/Self-doped polyaniline composites to dopamine,uric acid,and ascorbic acid

Composites of Nafion, COOH-capped CdSe, and self-doped polyaniline (SPAN) were used to prepare novel chemical modified glassy carbon electrodes (Nafion/CdSe/SPAN/GCE). The electrocatalytic activities of the modified GCE to the redox reactions of dopamine (DA), uric acid (UA), and ascorbic acid (AA) were investigated by cyclic voltammetry (CV). CV curves revealed that the electrocatalytic activities of Nafion/CdSe/SPAN/GCE to oxidations of the analytes in solution of pH 7 were in the order of DA?>?UA?>?AA. This order was consistent with the strong-to-low extent of interactions between the modified GCE and the analytes. These interactions were consistent with the observations that the oxidation rate of DA followed a diffusion-controlled process whereas that of UA followed a surface adsorption-controlled process. The composites of casting at higher pH levels were found to exhibit better CdSe and SPAN dispersions in films and higher electrocatalytic activities. CdSe and SPAN exhibited insignificant synergistic effects on the oxidations of DA when cast from Nafion solutions of both low and high pHs whereas CdSe and SPAN exhibited much synergistic effects on the oxidations of UA when cast from the Nafion solution of high pH at 12.     

Individually Adapted LC-lens Array for 3D Applications

A low driving voltage with fast response LC-lens was developed. By implementing the LC-lens as an array structure, it can be adaptively used for 2D/3D switching and 3D rotation on auto- stereoscopic display. Additionally, it also can be utilized as a depth sensor for 3D capturing.