On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators

 We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials. In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin. Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002     

Using Gd-EOB-DTPA-enhanced 3-T MRI for the differentiation of infiltrative hepatocellular carcinoma and focal confluent fibrosis in liver cirrhosis

Purpose

The purpose of the study was to determine significant imaging features to differentiate between infiltrative hepatocellular carcinoma (HCC) and confluent fibrosis (CF) in liver cirrhosis using Gd-EOB-DTPA-enhanced 3-T magnetic resonance imaging.

Material and methods

Nineteen infiltrative HCCs and eight CFs were included. We evaluated the difference in imaging findings and apparent diffusion coefficient (ADC) between the two entities. We compared T2-weighted image (WI) and hepatobiliary phase (HBP) in terms of the clarity of the lesion outer margin.

Results

Seventeen infiltrative HCCs showed lobulated margin, while focal CFs showed either straight (n = 3) or irregular margins (n = 5) (P = .001). All infiltrative HCCs had intact or bulging contours, and all focal CFs showed capsular retraction (P = .001). Fourteen infiltrative HCCs and two focal CFs showed arterial enhancement (P = .035). The ADC of infiltrative HCCs was significantly lower than that of CFs (P = .001). Satellite nodules were noted in 10 infiltrative HCCs. In terms of outer margin clarity, infiltrative HCCs showed a more distinct margin on HBP than on T2-WI (P = .005), while these two sequences were not significantly different in focal CFs (P = 1.000).

Conclusion

HBP improved the imaging characteristics of infiltrative HCC, allowing it to be distinguished from focal CF. Infiltrative HCC showed lower ADC values than focal CF. Lobular configuration, contour bulging, enhancement pattern, associated satellite nodules and portal vein thrombosis were still found to be highly suggestive MR findings for infiltrative HCC.     

Transformation mechanism of n-butyl terminated Si nanoparticles embedded into Si1−xCx nanocomposites mixed with Si nanoparticles and C atoms

Bright-field transmission electron microscopy (TEM) images, high-resolution TEM (HRTEM) images, and fast-Fourier transformed electron-diffraction patterns showed that n-butyl terminated Si nanoparticles were aggregated. The formation of Si_1−xC_x nanocomposites was mixed with Si nanoparticles and C atoms embedded in a SiO₂ layer due to the diffusion of C atoms from n-butyl termination shells into aggregated Si nanoparticles. Atomic force microscopy (AFM) images showed that the Si_1−xC_x nanocomposites mixed with Si nanoparticles and C atoms existed in almost all regions of the SiO₂ layer. The formation mechanism of Si nanoparticles and the transformation mechanism of n-butyl terminated Si nanoparticles embedded into Si_1−xC_x nanocomposites mixed with Si nanoparticles and C atoms are described on the basis of the TEM, HRTEM, and AFM results. These results can help to improve the understanding of the formation mechanism of Si nanoparticles.     

Vibration analysis of a circular arch with variable cross-section using differential transformation and generalized differential quadrature

Vibration analysis of circular arches is an important subject in mechanics due to its various applications. In particular, circular arches with variable cross-section have been widely used to satisfy modern architectural and structural requirements. Recently, the generalized differential quadrature method (GDQM) and differential transformation method (DTM) were proposed by Shu and Zhou, respectively. In this study, GDQM and DTM are applied to vibration analysis of circular arches with variable cross-section. The governing equation of motion is derived and the non-dimensional natural frequencies are obtained for various boundary conditions. The concepts of differential transformation and generalized differential quadrature are briefly introduced. The results obtained by these methods are compared with previously published works. GDQM and DTM showed fast convergence, accuracy and validity in solving the vibration problem for circular arches with variable cross-sections.     

Beam Recombination Characteristics in Array Laser Amplification Using Stimulated Brillouin Scattering Phase Conjugation

Beam recombination characteristics were numerically investigated in array laser amplification using stimulated Brillouin scattering phase conjugation. To clarify the effect of piston errors due to imperfect phase locking, spatial intensity profiles of the beam recombination output were calculated in both the near and the far field on the basis of Rayleigh-Sommerfeld diffraction theory. The analyses indicate that piston errors are seriously detrimental to the quality of a beam recombination output and should be eliminated by a proper phase locking. It is also found that the gap between the beam splitting-combining wedges has a negligible effect.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

Studies of the out-of-plane emission of pions in symmetric heavy-ion collisions

Triple differential cross-sections of midrapidity pions from ²⁰⁹Bi+²⁰⁹Bi collisions were measured with the Kaon Spectrometer at SIS at incident energies of 400, 700 and 1000 AMeV. The azimuthal emission pattern of the pions has been investigated in dependence of beam energy and impact parameter. An enhanced emission of pions perpendicular to the reaction plane is observed. The strength of the anisotropy increases with beam energy and pion transverse momentum. In contrast to the nucleons the anisotropy varies only little with the impact parameter. No difference in the behaviour of positive and negative pions is observed.     

Investigation of the Li1+xV3O8 electrode–organic electrolyte interface by scanning photoelectron microscopy

To investigate the formation of a solid electrolyte interface (SEI) on the Li_1+xV₃O₈ electrode surface in the thermodynamic stability range of the organic electrolyte, we applied scanning photoelectron microscopy (SPEM) to a pristine electrode and to an electrode after ten cycles. The F K-edge absorption spectrum of the cycled electrode showed that LiF forms on the electrode surface during the lithium insertion–extraction process in the Li_1+xV₃O₈/Li cell. The photoelectron spectrum for the cycled electrode showed intense spectral features corresponding to Li 1s, F 2s, F 2p, and P 2p electron signals, whereas these spectral features were of negligible intensity for the pristine electrode. The above results give strong support for the formation of an SEI that consists of LiF and compounds containing phosphorus during operation of the battery. The SPEM images also revealed that the fluorine distribution on the surface of the cycled electrode was inhomogeneous.     

Determination of the debris produced from poly(ethylene terephthalate) during KrF excimer laser ablation

Pulsed UV laser beams, which are widely used in the processing of polymers, have many advantages because their photon energy is higher than the binding energy of polymers. Fabricating polymers with a UV laser process is faster, cleaner, and more convenient than with other processes. Nevertheless, some problems occur in the precision microprocessing of polymers. For example, the formation and deposition of surface debris, which is produced from the breakdown of either polymer chains or radical bonds.To determine the formation and origin of surface debris, a KrF excimer laser beam (248 nm) was used in the processing of poly(ethylene terephthalate) (PET). The investigation of the debris formation was facilitated by UV-vis spectroscopy, ATR FT-IR spectroscopy, and NMR spectroscopy. The UV-vis absorption peak indicates that the primary chromophore in the PET is benzoate. Furthermore, because benzoate causes the primary absorption, the absorbed energy is transferred by heat generation to an unsaturated ester. The ATR FT-IR spectrometer measurements show that the phenyl systems in the benzoate are demolished by ablation. This phenomenon indicates that the photochemical reaction causes the benzoate bonds to break down, and this breakdown in turn causes the carbonization to leave debris on the PET.