3,460 research outputs found
Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials
We study the low-energy behavior of the Green function for one-dimensional
Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a
formula for the power series expansion of reflection coefficients in terms of
the wave number, and apply it to the low-energy expansion of the Green
function
A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game
We prove a tight lower bound on the asymptotic performance ratio of
the bounded space online -hypercube bin packing problem, solving an open
question raised in 2005. In the classic -hypercube bin packing problem, we
are given a sequence of -dimensional hypercubes and we have an unlimited
number of bins, each of which is a -dimensional unit hypercube. The goal is
to pack (orthogonally) the given hypercubes into the minimum possible number of
bins, in such a way that no two hypercubes in the same bin overlap. The bounded
space online -hypercube bin packing problem is a variant of the
-hypercube bin packing problem, in which the hypercubes arrive online and
each one must be packed in an open bin without the knowledge of the next
hypercubes. Moreover, at each moment, only a constant number of open bins are
allowed (whenever a new bin is used, it is considered open, and it remains so
until it is considered closed, in which case, it is not allowed to accept new
hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448]
showed that is and , and conjectured that
it is . We show that is in fact . To
obtain this result, we elaborate on some ideas presented by those authors, and
go one step further showing how to obtain better (offline) packings of certain
special instances for which one knows how many bins any bounded space algorithm
has to use. Our main contribution establishes the existence of such packings,
for large enough , using probabilistic arguments. Such packings also lead to
lower bounds for the prices of anarchy of the selfish -hypercube bin packing
game. We present a lower bound of for the pure price of
anarchy of this game, and we also give a lower bound of for
its strong price of anarchy
Synthesis of Fullerene Nanowhiskers and Their Electrical and Superconducting Properties
Fullerene nanowhiskers (FNWs) are thin crystalline fibers composed of fullerene molecules such as C60, C70, endohedral fullerenes or other fullerene molecules with functional groups. FNWs are n-type semiconductors with various application examples such as field-effect transistors, solar cells, chemical sensors, photocatalysts and so forth. Alkali metal-doped C60 (fullerene) nanowhiskers (C60NWs) become superconductors. The K-doped C60NWs have the highest superconducting volume fraction as ever have been realized in the alkali metal-doped C60 crystals and a very high critical current density Jc up to a magnetic field of 50 kOe. On the other hand, the growth control of fullerene nanowhiskers is a very important theme for their practical application. This paper reviews the research development of FNWs, focusing on their electrical and superconducting properties as well as their growth mechanism
Properties of contact matrices induced by pairwise interactions in proteins
The total conformational energy is assumed to consist of pairwise interaction
energies between atoms or residues, each of which is expressed as a product of
a conformation-dependent function (an element of a contact matrix, C-matrix)
and a sequence-dependent energy parameter (an element of a contact energy
matrix, E-matrix). Such pairwise interactions in proteins force native
C-matrices to be in a relationship as if the interactions are a Go-like
potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native
C-matrix, because the lowest bound of the total energy function is equal to the
total energy of the native conformation interacting in a Go-like pairwise
potential. This relationship between C- and E-matrices corresponds to (a) a
parallel relationship between the eigenvectors of the C- and E-matrices and a
linear relationship between their eigenvalues, and (b) a parallel relationship
between a contact number vector and the principal eigenvectors of the C- and
E-matrices; the E-matrix is expanded in a series of eigenspaces with an
additional constant term, which corresponds to a threshold of contact energy
that approximately separates native contacts from non-native ones. These
relationships are confirmed in 182 representatives from each family of the SCOP
database by examining inner products between the principal eigenvector of the
C-matrix, that of the E-matrix evaluated with a statistical contact potential,
and a contact number vector. In addition, the spectral representation of C- and
E-matrices reveals that pairwise residue-residue interactions, which depends
only on the types of interacting amino acids but not on other residues in a
protein, are insufficient and other interactions including residue
connectivities and steric hindrance are needed to make native structures the
unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the
present versio
Origin of Tc Enhancement Induced by Doping Yttrium and Hydrogen into LaFeAsO-based Superconductors: 57Fe, 75As, 139La, and 1H-NMR Studies
We report our extensive 57Fe-, 75As-, 139La-, and 1H-NMR studies of
La_{0.8}Y_{0.2}FeAsO_{1-y} (La_{0.8}Y_{0.2}1111) and
LaFeAsO_{1-y}H_{x}(La1111H), where doping yttrium (Y) and hydrogen (H) into
optimally doped LaFeAsO_{1-y} (La1111(OPT)) increases T_c=28 K to 34 and 32 K,
respectively. In the superconducting (SC) state, the measurements of
nuclear-spin lattice-relaxation rate 1/T_1 have revealed in terms of a multiple
fully gapped s_\pm-wave model that the SC gap and T_c in La_{0.8}Y_{0.2}1111
become larger than those in La1111(OPT) without any change in doping level. In
La1111H, the SC gap and T_c also increase slightly even though a decrease in
carrier density and some disorders are significantly introduced. As a
consequence, we suggest that the optimization of both the structural parameters
and the carrier doping level to fill up the bands is crucial for increasing T_c
among these La1111-based compounds through the optimization of the Fermi
surface topology.Comment: 4 pages, 4 figures, 1 table, to be published in J. Phys. Soc. Jpn,
Vol. 79, No. 1
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