Nilpotent center conditions in cubic switching polynomial Li\'enard systems by higher-order analysis

The aim of this paper is to investigate two classical problems related to nilpotent center conditions and bifurcation of limit cycles in switching polynomial systems. Due to the difficulty in calculating the Lyapunov constants of switching polynomial systems at non-elementary singular points, it is extremely difficult to use the existing Poincar\'e-Lyapunov method to study these two problems. In this paper, we develop a higher-order Poincar\'e-Lyapunov method to consider the nilpotent center problem in switching polynomial systems, with particular attention focused on cubic switching Li\'enard systems. With proper perturbations, explicit center conditions are derived for switching Li\'enard systems at a nilpotent center, which is characterized as global. Moreover, with Bogdanov-Takens bifurcation theory, the existence of five limit cycles around the nilpotent center is proved for a class of switching Li\'enard systems, which is a new lower bound of cyclicity for such polynomial systems around a nilpotent center

A solution processed flexible nanocomposite electrode with efficient light extraction for organic light emitting diodes.

Highly efficient organic light emitting diodes (OLEDs) based on multiple layers of vapor evaporated small molecules, indium tin oxide transparent electrode, and glass substrate have been extensively investigated and are being commercialized. The light extraction from the exciton radiative decay is limited to less than 30% due to plasmonic quenching on the metallic cathode and the waveguide in the multi-layer sandwich structure. Here we report a flexible nanocomposite electrode comprising single-walled carbon nanotubes and silver nanowires stacked and embedded in the surface of a polymer substrate. Nanoparticles of barium strontium titanate are dispersed within the substrate to enhance light extraction efficiency. Green polymer OLED (PLEDs) fabricated on the nanocomposite electrode exhibit a maximum current efficiency of 118 cd/A at 10,000 cd/m(2) with the calculated external quantum efficiency being 38.9%. The efficiencies of white PLEDs are 46.7 cd/A and 30.5%, respectively. The devices can be bent to 3 mm radius repeatedly without significant loss of electroluminescent performance. The nanocomposite electrode could pave the way to high-efficiency flexible OLEDs with simplified device structure and low fabrication cost

Envelopes of legendre curves in the unit spherical bundle over the unit sphere

In this paper, we introduce a one-parameter family of Legendre curves in the unit spherical bundle over the unit sphere and the curvature. We give the existence and uniqueness theorems for one-parameter families of spherical Legendre curves by using the curvatures. Then we define an envelope for the one-parameter family of Legendre curves in the unit spherical bundle. We also consider the parallel curves and evolutes of one-parameter families of Legendre curves in the unit spherical bundle and their envelopes. Moreover, we give relationships among one-parameter families of Legendre curves in the unit spherical bundle over the unit sphere and one-parameter families of Legendre curves in the unit tangent bundle over the Euclidean plane

Association of tissue lineage and gene expression: conservatively and differentially expressed genes define common and special functions of tissues

<p>Abstract</p> <p>Background</p> <p>Embryogenesis is the process by which the embryo is formed, develops, and establishes developmental hierarchies of tissues. The recent advance in microarray technology made it possible to investigate the tissue specific patterns of gene expression and their relationship with tissue lineages. This study is focused on how tissue specific functions, tissue lineage, and cell differentiation are correlated, which is essential to understand embryonic development and organism complexity.</p> <p>Results</p> <p>We performed individual gene and gene set based analysis on multiple tissue expression data, in association with the classic topology of mammalian fate maps of embryogenesis. For each sub-group of tissues on the fate map, conservatively, differentially and correlatively expressed genes or gene sets were identified. Tissue distance was found to correlate with gene expression divergence. Tissues of the ectoderm or mesoderm origins from the same segments on the fate map shared more similar expression pattern than those from different origins. Conservatively expressed genes or gene sets define common functions in a tissue group and are related to tissue specific diseases, which is supported by results from Gene Ontology and KEGG pathway analysis. Gene expression divergence is larger in certain human tissues than in the mouse homologous tissues.</p> <p>Conclusion</p> <p>The results from tissue lineage and gene expression analysis indicate that common function features of neighbor tissue groups were defined by the conservatively expressed genes and were related to tissue specific diseases, and differentially expressed genes contribute to the functional divergence of tissues. The difference of gene expression divergence in human and mouse homologous tissues reflected the organism complexity, i.e. distinct neural development levels and different body sizes.</p