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 $\rho$ of the bounded space online $d$-hypercube bin packing problem, solving an open question raised in 2005. In the classic $d$-hypercube bin packing problem, we are given a sequence of $d$-dimensional hypercubes and we have an unlimited number of bins, each of which is a $d$-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 $d$-hypercube bin packing problem is a variant of the $d$-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 $\rho$ is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$. 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 $d$, using probabilistic arguments. Such packings also lead to lower bounds for the prices of anarchy of the selfish $d$-hypercube bin packing game. We present a lower bound of $\Omega(d/\log d)$ for the pure price of anarchy of this game, and we also give a lower bound of $\Omega(\log d)$ 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