Edgeworth Expansions for Semiparametric Averaged Derivatives - (Now published in Econometrica, 68 (2000), pp.931-979.)

A valid Edgeworth expansion is established for the limit distribution of density-weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in magnitude, depending on the choice of bandwidth and kernel order. In general this term has order larger than the n -½ that prevails in standard parametric problems, but we find circumstances in which it is O(n -½), thereby extending the achievement of an n -½ Berry-Essen bound in Robinson (1995). A valid empirical Edgeworth expansion is also established. We also provide theoretical and empirical Edgeworth expansions for a studentized statistic, where the correction terms are different from those for the unstudentized case. We report a Monte Carlo study of finite sample performance.Edgeworth expansion, semiparametric estimates, averaged derivatives

Finite-size-scaling analysis of the XY universality class between two and three dimensions: An application of Novotny's transfer-matrix method

Based on Novotny's transfer-matrix method, we simulated the (stacked) triangular Ising antiferromagnet embedded in the space with the dimensions variable in the range 2 \le d \le 3. Our aim is to investigate the criticality of the XY universality class for 2 \le d \le 3. For that purpose, we employed an extended version of the finite-size-scaling analysis developed by Novotny, who utilized this scheme to survey the Ising criticality (ferromagnet) for 1 \le d \le 3. Diagonalizing the transfer matrix for the system sizes N up to N=17, we calculated the $d$-dependent correlation-length critical exponent \nu(d). Our simulation result \nu(d) appears to interpolate smoothly the known two limiting cases, namely, the KT and d=3 XY universality classes, and the intermediate behavior bears close resemblance to that of the analytical formula via the 1/N-expansion technique. Methodological details including the modifications specific to the present model are reported

Studentization in Edgworth Expansions for Estimates of Semiparametric Index Models - (Now published in C Hsiao, K Morimune and J Powell (eds): Nonlinear Statistical Modeling (Festschrift for Takeshi Amemiya), (Cambridge University Press, 2001), pp.197-240.)

We establish valid theoretical and empirical Edgeworth expansions for density-weighted averaged derivative estimates of semiparametric index models.Edgeworth expansions, semiparametric estimates, averaged derivatives

Time Dependent Pairing Equations for Seniority One Nuclear Systems

When the time dependent Hartree-Fock-Bogoliubov intrinsic equations of motion are solved in the case of seniority one nuclear systems, the unpaired nucleon remains on the same orbital. The blocking effect hinders the possibility to skip from one orbital to another. This unpleasant feature is by-passed with a new set of pairing time dependent equations that allows the possibility that the unpaired nucleon changes its single-particle level. These equations generalize the time dependent Hartree-Fock-Bogoliubov equations of motion by including the Landau-Zener effect. The derivation of these new equations is presented in details. These equations are applied in the case of a superasymmetric fission process, that is, in order to explain the fine structure the 14C emission from 233Ra. A new version of the Woods-Saxon model extended for two-center potentials is used in this context.Comment: 12 pages, 6 figure

Magnetic ordering and fluctuation in kagome lattice antiferromagnets, Fe and Cr jarosites

Jarosite family compounds, KFe_3(OH)_6(SO_4)_2, (abbreviate Fe jarosite), and KCr_3(OH)_6(SO_4)_2, (Cr jarosite), are typical examples of the Heisenberg antiferromagnet on the kagome lattice and have been investigated by means of magnetization and NMR experiments. The susceptibility of Cr jarosite deviates from Curie-Weiss law due to the short-range spin correlation below about 150 K and shows the magnetic transition at 4.2 K, while Fe jarosite has the transition at 65 K. The susceptibility data fit well with the calculated one on the high temperature expansion for the Heisenberg antiferromagnet on the kagome lattice. The values of exchange interaction of Cr jarosite and Fe jarosite are derived to be J_Cr = 4.9 K and J_Fe = 23 K, respectively. The 1H-NMR spectra of Fe jarosite suggest that the ordered spin structure is the q = 0 type with positive chirality of the 120 degrees configuration. The transition is caused by a weak single-ion type anisotropy. The spin-lattice relaxation rate, 1/T_1, of Fe jarosite in the ordered phase decreases sharply with lowering the temperature and can be well explained by the two-magnon process of spin wave with the anisotropy.Comment: REVTeX, 14 pages with 5 figures. Submitted to Canadian Journal of Physic

Superconductivity of the Ternary Boride Li_2Pd_3B Probed by ^{11}B NMR

We report a ^{11}B NMR measurement on the recently discovered superconductor Li_2Pd_3B. The nuclear spin lattice relaxation rate 1/T_1 shows a well-defined coherence peak just below T_c (H=1.46 T)=5.7 K, and the spin susceptibility measured by the Knight shift also decreases below T_c. These results indicate that the superconductivity is of conventional nature, with an isotropic gap. Our results also suggest that the $p$-electrons of boron and the d-electrons of palladium that hybridize with boron $p$-electrons are primarily responsible for the superconductivity.Comment: 4 pages, 5 figure

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure