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     

Effects of diamines and their fluorinated groups on the color lightness and preparation of organosoluble aromatic polyimides from 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]‐hexafluoropropane

To investigate the position and amount of the CF₃ group affecting the coloration of polyimides (PIs), we prepared 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]hexafluoropropane ( 2 ) with four CF₃ groups with 2‐chloro‐5‐nitrobenzotrifluoride and 2,2‐bis(4‐hydroxyphenol)hexafluoropropane. A series of soluble and light‐colored fluorinated PIs ( 5 ) were synthesized from 2 and various aromatic dianhydrides ( 3a – 3f ). 5a – 5f had inherent viscosities ranging from 0.80 to 1.19 dL/g and were soluble in amide polar solvents and even in less polar solvents. The glass‐transition temperatures of 5 were 221–265 °C, and the 10% weight‐loss temperatures were above 493 °C. Their films had cutoff wavelengths between 343 and 390 nm, b* values (a yellowness index) ranging from 5 to 41, dielectric constants of 2.68–3.01 (1 MHz), and moisture absorptions of 0.03–0.29 wt %. In a comparison of the PI series 6 – 8 based on 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane, 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]propane, and 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane, we found that the CF₃ group close to the imide group was more effective in lowering the color; this means that CF₃ of 5 , 7 , and 8f was more effective than that of 6c . The color intensity of the four PI series was lowered in the following order: 5 > 7 > 6 > 8 . The PI 5f , synthesized from diamine 2 and 4,4′‐hexafluoroisopropylidenediphthalic anhydride, had six CF₃ groups in a repeated segment, so it exhibited the lightest color among the four series. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 922–938, 2003     

A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

Generation of highly stable amidate anion in anionic polymerization of 3‐(triethylsilyl)propyl isocyanate

To study living anionic polymerization, 3‐(triethylsilyl)propyl isocyanate (TEtSPI) monomer was synthesized by hydrosilylation of allylamine with triethylsilane and treatment of the resulting amine with triphosgene. The polymerization of TEtSPI was performed with sodium naphthalenide (Na‐Naph) as an initiator and in the absence and presence of sodium tetraphenylborate (NaBPh₄) as an additive in tetrahydrofuran (THF) at ?78 and at ?98 °C. A highly stabilized amidate anion for living polymerization of isocyanates was generated for the first time with the combined effect of the bulky substituent and the shielding action of the additive NaBPh₄, extending the living character at least up to 120 min at ?98 °C. Even the anion could exist at ?78 °C for 10 min. A block copolymer, poly(n‐hexyl isocyanate)‐b‐poly[(3‐triethylsilyl)propyl isocyanate]‐b‐poly(n‐hexyl isocyanate), was synthesized with quantitative yields and controlled molecular weights via living anionic polymerization in THF at ?78 °C for TEtSPI and ?98 °C for n‐hexyl isocyanate, respectively, with Na‐Naph with three times of NaBPh₄ as a common ion salt. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 933–940, 2004     

Intramolecular energy transferable (2,2‐diphenylvinyl)phenyl substituted poly(p‐phenylenevinylene) derivative with efficient photoluminescence and electroluminescence

A poly(p‐phenylenevinylene) (PPV) derivative containing a bulky (2,2‐diphenylvinyl)phenyl group in the side chain, EHDVP‐PPV, was synthesized by Gilch route. The reduced tolane‐bisbenzyl (TBB) defects, as well as the structure of the polymer, was confirmed by various spectroscopic methods. The intramolecular energy transfer from the (2,2‐diphenylvinyl)phenyl side group to the PPV backbone was studied by UV‐vis and photoluminescence (PL) of the obtained polymer and model compound. The polymer film showed maximum absorption and emission peaks at 454 and 546 nm, respectively, and high PL efficiency of 57%. A yellow electroluminescence (λ_max = 548 nm) was obtained with intensities of 6479 cd/m² when the light‐emitting diodes of ITO/PEDOT/EHDVP‐PPV/LiF/Al were fabricated. The maximum power efficiency of the devices was 0.729 lm/W with a turn‐on voltage of 3.6 V. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5636–5646, 2004     

A possibility of parallel and anti-parallel diffraction measurements on neutron diffractometer employing bent perfect crystal monochromator at the monochromatic focusing condition

In a conventional diffractometer having single monochromator, only one position, parallel position, is used for the diffraction experiment (i.e. detection) because the resolution property of the other one, anti-parallel position, is very poor. However, a bent perfect crystal (BPC) monochromator at monochromatic focusing condition can provide a quite flat and equal resolution property at both parallel and anti-parallel positions and thus one can have a chance to use both sides for the diffraction experiment. From the data of the FWHM and the Δd/d measured on three diffraction geometries (symmetric, asymmetric compression and asymmetric expansion), we can conclude that the simultaneous diffraction measurement in both parallel and anti-parallel positions can be achieved.     

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.     

Electrochemical behavior of Li intercalation processes into a Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2 cathode

Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂ (X=0.17, 0.25, 0.33, 0.5) compounds are prepared by a simple combustion method. The Rietvelt analysis shows that these compounds could be classified as having the α-NaFeO₂ structure. The initial charge-discharge and irreversible capacity increases with the decrease of x in Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂. Indeed, Li[Ni_0.50Mn_0.50]O₂ compound shows relatively low initial discharge capacity of 200 mAh/g and large capacity loss during cycling, with Li[Ni_0.17Li_0.22Mn_0.61]O₂ and Li[Ni_0.25Li_0.17Mn₀.₅₈]O₂ compounds exhibit high initial discharge capacity over 245 mAh/g and stable cycle performance in the voltage range of 4.8 -2.0 V. On the other hand, XANES analysis shows that the oxidation state of Ni ion reversibly changes between Ni²⁺ and about Ni³⁺, while the oxidation state of Mn ion sustains Mn⁴⁺ during charge-discharge process. This result does not agree with the previously reported ‘electrochemistry model’ of Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂, in which Ni ion changes between Ni²⁺ and NI⁴⁺. Based on these results, we modified oxidation-state change of Mn and Ni ion during charge-discharge process.     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Phase Measurement Algorithm in Wavelength Scanned Fizeau Interferometer

Wavelength scanned interferometry allows the simultaneous measurement of top surface shape and optical thickness variation of a transparent object consisting of several parallel surfaces. Interference signals from these surfaces can be separated in frequency space, and their phases are detected by discrete Fourier analysis. However, these signal frequencies are shifted from the detection frequency by the refractive index dispersion of the object and a nonlinearity of the wavelength scanning. The Fourier analysis is sensitive to the detuning of the signal frequency and suffers from the multiple-beam interference noise. Conventional error-compensating algorithms cannot be applied to an object consisting of more than three reflecting surfaces. We derive a new 2N-1 sample error-compensating algorithm, which allows the phase detection of any order of harmonic frequency among the interference signals. The new algorithm suppresses the effect of signal frequency detuning as well as the multiple-beam interference noise and can be applied to the measurement of complex objects consisting of more than three reflecting surfaces.