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     

Domain reversal behavior in perpendicular magnetic nanothin films

We report domain reversal behavior in perpendicular ferromagnetic nanothin films investigated by means of a novel magneto-optical microscope magnetometer, capable of grabbing domain reversal patterns in real time under an applied field as well as simultaneous measurements of 8000 local hysteresis loops with 400-nm special resolution. Three contrasting domain reversal behaviors are found to exist: wall-motion dominant, dendritic-growth dominant, and nucleation dominant reversal. Quantitative analysis reveals that the contrasting reversal behavior is mainly caused by a sensitive change in wall-motion speed and that the reversal ratio of wall-motion speed over nucleation rate is a governing parameter for the contrasting domain reversal dynamics. The activation volumes of the wall-motion and nucleation processes are found generally unequal, and the inequality is closely related with the domain dynamics. The domain reversal pattern is truly coincident with submicron-scale local coercivity variation and local switching time of domain evolution is exponentially dependent on local coercivity governed by a thermal activation relaxation process. The observed domain reversal behavior could be well predicted by a Monte Carlo simulation of a micromagnetic model based on the uniaxial magnetic anisotropy of nanothin films.     

The application of source methods in estimation of an interior sound field

In earlier studies, one has successfully developed three different source methods (SSM, similar source method; IPSM, internal parallel source method; ISM, internal source method) to estimate radiation and scattering sound fields. All these methods are estimations of exterior sound fields. In the present study, the similar source method is modified to estimate an interior sound field. The modification is to move the imaginary sources outside the boundary surface. In addition, general boundary conditions in terms of acoustic admittance or impedance are considered by introducing the suitable least square error functions. Finally, a two-dimensional interior sound field with alternative boundary conditions is evaluated to simulate sound fields inside a car. The results are in agreement with those of boundary integral method.     

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.     

Maximum likelihood estimate for discontinuous parameter in stochastic hyperbolic systems

The purpose of this paper is to study the identification problem of a spatially varying discontinuous parameter in stochastic hyperbolic equations. In previous works, the consistency property of the maximum likelihood estimate (MLE) was explored and the generating algorithm for MLE proposed under the condition that an unknown parameter is in a sufficiently regular space with respect to spatial variables.In order to show the consistency property of the MLE for a discontinuous coefficient, we use the method of sieves, i.e. the admissible class of unknown parameters is projected into a finite-dimensional space. For hyperbolic systems, we cannot obtain a regularity property of the solution with respect to a parameter. So in this paper, the parabolic regularization technique is used. The convergence of the derived finite-dimensional MLE to the infinite-dimensional MLE is justified under some conditions.     

Phase-Only Encryption and Single Path Decryption System Using Phase-Encoded Exclusive-OR Rules in Fourier Domain

A phase-only encryption scheme using phase-encoded exclusive-OR (XOR) rules in a Fourier plane and a single path decryption system are presented. To generate phase-only encrypted data, a zero-padded original image, multiplied by a random phase image, is Fourier transformed and its real-valued data is encrypted with key data by using phase-encoded XOR rules. Since the original information is encrypted on the Fourier plane, the proposed encryption is more tolerant to loss of key information by scratching or cutting than previous XOR encryption in a space domain. A decryption is simply performed based on 2-f setup with spatial filter by Fourier transform for multiplication phase-only encrypted data with phase-only key data. Due to single path architecture without a reference wave, the proposed system is resistant to mechanical vibrations and fluctuation. Numerical simulations have confirmed the validity of the proposed encryption scheme and simple decryption architecture.     

Microlens array diffuser for a light-emitting diode backlight system

Microlens array (MLA) diffusers for light-emitting diode (LED) backlight systems have been developed. A high fill-factor photoresist mold for the MLA was fabricated using three-dimensional diffuser lithography, and the patterns were transferred to a nickel master mold for UV-curable polymer replication. The fabricated microlens had various paraboloidal profiles, and its aspect ratio was controlled from 1.0 to 2.1. The MLA diffuser showed a batwing radiation pattern with a radiation angle of 150 degrees. The fabricated MLA diffuser may greatly enhance the color-mixing characteristics of LED backlight systems and help reduce the number of LEDs required.     

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.