784 research outputs found
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 -uniform hypergraph with
edges formed by taking the first sets in the colex ordering of
has the largest Lagrangian of all -uniform hypergraphs
with edges in \cite{FF}. Motzkin and Straus' theorem confirms this
conjecture when . For , it is shown by Talbot in \cite{T} that this
conjecture is true when is in certain ranges. In this paper, we explore the
connection between the clique number and Lagrangians for -uniform
hypergraphs. As an implication of this connection, we prove that the
-uniform hypergraph with edges formed by taking the first sets in
the colex ordering of has the largest Lagrangian of all
-uniform graphs with vertices and edges satisfying for
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
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