Busemann functions and barrier functions

We show that Busemann functions on a smooth, non-compact, complete, boundaryless, connected Riemannian manifold are viscosity solutions with respect to the Hamilton-Jacobi equation determined by the Riemannian metric and consequently they are locally semi-concave with linear modulus. We also analysis the structure of singularity sets of Busemann functions. Moreover we study barrier functions, which are analogues to Mather's barrier functions in Mather theory, and provide some fundamental properties. Based on barrier functions, we could define some relations on the set of lines and thus classify them. We also discuss some initial relations with the ideal boundary of the Riemannian manifold.Comment: comments are welcome

Hydrogen storage in pillared Li-dispersed boron carbide nanotubes

Ab initio density-functional theory study suggests that pillared Li-dispersed boron carbide nanotubes is capable of storing hydrogen with a mass density higher than 6.0 weight% and a volumetric density higher than 45 g/L. The boron substitution in carbon nanotube greatly enhances the binding energy of Li atom to the nanotube, and this binding energy (~ 2.7 eV) is greater than the cohesive energy of lithium metal (~1.7 eV), preventing lithium from aggregation (or segregation) at high lithium doping concentration. The adsorption energy of hydrogen on the Li-dispersed boron carbide nanotube is in the range of 10 ~24 kJ/mol, suitable for reversible H2 adsorption/desorption at room temperature and near ambient pressure.Comment: 17 pages, 4 figure

On hypergraph Lagrangians

It is conjectured by Frankl and F\"uredi that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform hypergraphs with $m$ edges in \cite{FF}. Motzkin and Straus' theorem confirms this conjecture when $r=2$. For $r=3$, it is shown by Talbot in \cite{T} that this conjecture is true when $m$ is in certain ranges. In this paper, we explore the connection between the clique number and Lagrangians for $r$-uniform hypergraphs. As an implication of this connection, we prove that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform graphs with $t$ vertices and $m$ edges satisfying ${t-1\choose r}\leq m \leq {t-1\choose r}+ {t-2\choose r-1}-[(2r-6)\times2^{r-1}+2^{r-3}+(r-4)(2r-7)-1]({t-2\choose r-2}-1)$ for $r\geq 4.$Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.7529, arXiv:1211.7057, arXiv:1211.6508, arXiv:1311.140

Transmission eigenchannels and the densities of states of random media

We show in microwave measurements and computer simulations that the contribution of each eigenchannel of the transmission matrix to the density of states (DOS) is the derivative with angular frequency of a composite phase shift. The accuracy of the measurement of the DOS determined from transmission eigenchannels is confirmed by the agreement with the DOS found from the decomposition of the field into modes. The distribution of the DOS, which underlies the Thouless number, is substantially broadened in the Anderson localization transition. We find a crossover from constant to exponential scaling of fluctuations of the DOS normalized by its average value. These results illuminate the relationships between scattering, stored energy and dynamics in complex media.Comment: Supplementary Information included at the end of the documen

Exploration of Famille-rose porcelain painting art form

Modern People's understanding of beauty, the exploration and innovation of materials, for our innovation provides infi nite possibilities.Through the understanding of the high-temperature glaze, as well as the exploratory understanding, the rich and variable color glaze characteristics of the kiln change and Famille-rose painting characteristics of the combination, this is based on the understanding of new materials and the improvement of fi ring technology, for the powder porcelain provides a material basis for innovation.Therefore, the combination of high-temperature color glaze and pastel porcelain is an innovative model, which provides a new era contribution to the historical development of pastel. With the further development of ceramic artists, new techniques and techniques of pastel-colored porcelain painting will constantly emerge, and then make the traditional pastel art bloom a new luster