Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m × n) matrix A and the data vector b. This is in contrast to a least squares solution, where even one large error will typically cause a large error in x. In this paper we give necessary and sufficient conditions that the correct solution is obtained when there are some errors in A and b. Based on the sufficient condition, it is shown that if k rows of [A b] contain large errors, the correct solution is guaranteed if (m – n)/n 2k/, where > 0, is a lower bound of singular values related to A. Since m typically represents the number of measurements, this inequality shows how many data points are needed to guarantee a correct solution in the presence of large errors in some of the data. This inequality is, in fact, an upper bound, and computational results are presented, which show that the correct solution will be obtained, with high probability, for much smaller values of m – n.     

Exotic smooth structures on , Part II

We construct exotic and using the surgery techniques of R. Fintushel and R.J. Stern. We show that these 4-manifolds are irreducible by computing their Seiberg-Witten invariants.

     

Partial-wave decomposition of the ionization continuum accessed by vibrational autoionization of the NO 14s ( nu = 1, N = 20, N(+)(R) = 20) level

Rotationally resolved photoelectron angular distributions from vibrational autoionization of the NO 14s ( nu = 1, N = 20, N(+)(R) = 20) level are measured by photoelectron spectroscopy, and they are analyzed using a theoretical model based on first-order coupling between the Rydberg level and the ionization continuum. The analysis reveals that lambda-changing collisions and l-changing collisions between the molecular-ion core and the outgoing electron are comparable in magnitude and account for 40% of the partial waves produced in the ionization continuum.     

Dimer to monomer phase transition in alkali-metal fullerides: magnetic susceptibility changes

Ab initio calculations have been employed to investigate the peculiar change in magnetic property (from diamagnetic to paramagnetic) of the dianionic C60-dimer phase in a rapidly cooled AC60 samples ( A: alkali metal). We first note that the triplet state of (C60)-22 which was never considered previously is nearly degenerate with the singlet state, and the transition barrier between the two states is reasonably small. This explains the susceptibility increase with an increase in temperature and the magnetic phase transition in the process of the dimer to monomer phase transition.     

Resolution enhancement in a reflection mode near-field optical microscope by second-harmonic modulation signals

The motion of the probe tip in a near-field scanning optical microscope, dithered by vibration of a tuning fork, can modulate the reflection signal from the sample surface not only at the fundamental dithering frequency but also at its second harmonic. By lock-in amplification of these modulated signals, enhanced optical images are obtained, even with an uncoated fiber probe. In particular, accurate optical images with higher resolution are obtained when the second-harmonic signal is detected, which results from the parametric modulation of the tip-sample separation at the double frequency of the horizontal dithering motion of the tip. Using a DVD ROM with a track pitch of 0.74 mum as a test sample, we observed that the sharp edges around the pits are clearly resolved with the second-harmonic signals and obtained enhanced resolution of ~70 nm full width at half-maximum.     

Origin of the high piezoelectric response in PbZr1-xTixO3

High resolution x-ray powder diffraction measurements on poled PbZr1-xTixO3 (PZT) ceramic samples close to the rhombohedral-tetragonal phase boundary (the so-called morphotropic phase boundary) have shown that for both rhombohedral and tetragonal compositions the piezoelectric elongation of the unit cell does not occur along the polar directions but along those directions associated with the monoclinic distortion. This work provides the first direct evidence for the origin of the very high piezoelectricity in PZT.     

Effects of co-substitution on the electrical properties of BiFeO3 thin films prepared by chemical solution deposition

Ferroelectric BiFeO₃ thin films with Nd-Cr (or Sm-Cr) co-substitution (denoted by BNdFCr and BSmFCr, respectively) were deposited on the Pt(2 0 0)/TiO₂/SiO₂/Si(1 0 0) substrates by a chemical solution deposition method. X-ray diffraction patterns revealed the formation of BNdFCr and BSmFCr thin films without any secondary phases. The co-substituted BNdFCr (or BSmFCr) thin films, which were annealed at 550 °C for 30 min in N₂ atmosphere, exhibited enhanced electrical properties compared to BFO thin films with the remanent polarization (2P_r) and coercive electric field (2E_c) of 196, 188 μC/cm² and 600, 570 kV/cm with the electric field of 800 kV/cm, respectively. The leakage current densities of BNdFCr and BSmFCr thin films measured at room temperature were approximately three orders of magnitude lower than that of BFO thin film, and the leakage current at room temperature of the thin films exhibited three distinctive conduction behaviors. Furthermore, the values of pulse polarizations [i.e., +(P*-P^{^}) or −(P*-P^{^})] of BNdFCr and BSmFCr thin films were reasonably unchanged up to 1.4 × 10¹⁰ switching cycles.     

Surface status and size influences of nickel nanoparticles on sulfur compound adsorption

Metallic nickel nanoparticles were incorporated on mesoporous silica to remove sulfur compounds in diesel selectively. In the first method, nickel nanoparticles were formed on mesoporous silica SBA-15 by impregnation and subsequent reduction of nickel nitrate. The sulfur adsorption capacity was strongly dependent on the nickel loading and the average nickel particle size. In the second method, nickel nanoparticles were synthesized in solution in the presence of a capping agent and then incorporated in mesoporous silica MCF by sonication. Although these particles maintain their sizes on the MCF surface after heat treatment, capping agent remaining on the Ni particle surface might interfere the adsorption of sulfur compounds.     

Ignition enhancement by addition of NO and NO2 from a N2/O2 plasma torch in a supersonic flow

The effects of NO and NO₂ produced by using a plasma jet (PJ) of a N₂/O₂ mixture on ignition of hydrogen, methane, and ethylene in a supersonic airflow were experimentally and numerically investigated. Numerical analysis of ignition delay time showed that the addition of a small amount of NO or NO₂ drastically reduced ignition delay times of hydrogen and hydrocarbon fuels at a relatively low initial temperature. In particular, NO and NO₂ were more effective than O radicals for ignition of a CH₄/air mixture at 1200 K or lower. These ignition enhancement effects were examined by including the low temperature chemistry. Ignition tests by a N₂/O₂ PJ in a supersonic flow (M = 1.7) for using hydrogen, methane, and ethylene injected downstream of the PJ were conducted. The results showed that the ignitability of the N₂/O₂ PJ is affected by the composition of the feedstock and that pure O₂ is not the optimum condition for downstream fuel injection. This result of ignition tests with downstream fuel injection demonstrated a significant difference in ignition characteristics of the PJ from the ignition tests with upstream fuel injection.     

Creep Motion in Two-Dimensional Fully Frustrated Coulomb Gas Model

The creep motion in a two-dimensional fully frustrated square lattice Coulomb gas model with disorders is studied by using the Monte Carlo technique. The dependence of charge current density J on electric field E is investigated at low temperature T and at low E. The results show that the creep obeys the Arrhenius law J - C（T） exp[-U（E）/T]. The prefactor C（T） increases with the temperature in a power law relation with an exponent about 3.0. The energy barrier U （ E） increases logarithmically with Ec,/ E as U （ E） - Uo ln（ Ec/ E） with Ec being the critical field at zero temperature.