Nonexistence of time‐periodic solutions of the Dirac equation in an axisymmetric black hole geometry

We prove that in the nonextreme Kerr‐Newman black hole geometry, the Dirac equation has no normalizable, time‐periodic solutions. A key tool is Chan‐drasekhar's separation of the Dirac equation in this geometry. A similar nonexistence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast to the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity. © 2000 John Wiley & Sons, Inc.     

Morphology and glass transition behavior of polycarbonate–phenoxy system: Effects of trans-reactions in domain interface regions

Effects of trans reactions on the morphology, glass transition, and phase behavior in a classical blend system of a poly(hydroxyl ether bisphenol-A) (phenoxy) with bisphenol-A polycarbonate (PC) were investigated by differential scanning calorimetry (DSC) and optical microscopy. Although two T_gs were observed in the as-prepared PC/phenoxy blends, an apparently single, but broadened, T_g was found in the blends after heating at high temperatures, typically 200–250°C for short times. The optical microscopy results indicated that same scales of heterogeneity did exist in post-heated PC/phenoxy blends as well as unheated blends. Explanations were provided. After heating-induced interchange reactions ( OH and carbonate), randomly linked polymer chains might form at the numerous interfaces of the mutually occluded/included micro-domains. The majority of the chains in the micro-domains are forced to relax in coordinated motion modes after heating, thus showing a single T_g. A mechanism of trans reactions in interfacial regions was briefly discussed in supplement to earlier reports in the literature. © 1997 John Wiley & Sons, Inc.     

Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass

The definition of quasi-local mass for a bounded space-like region Ω in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface \({\Sigma=\partial \Omega}\) and should be independent of whichever space-like region \({\Sigma}\) bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been taken by Brown-York [4,5] and Liu-Yau [16,17] (see also related works [3,6,9,12,14,15,28,32]) to define such notions using the isometric embedding theorem into the Euclidean three space. However, there exist surfaces in the Minkowski space whose quasilocal mass is strictly positive [19]. It appears that the momentum information needs to be accounted for to reconcile the difference. In order to fully capture this information, we use isometric embeddings into the Minkowski space as references. In this article, we first prove an existence and uniqueness theorem for such isometric embeddings. We then solve the boundary value problem for Jang’s [13] equation as a procedure to recognize such a surface in the Minkowski space. In doing so, we discover a new expression of quasi-local mass for a large class of “admissible” surfaces (see Theorem A and Remark 1.1). The new mass is positive when the ambient space-time satisfies the dominant energy condition and vanishes on surfaces in the Minkowski space. It also has the nice asymptotic behavior at spatial infinity and null infinity. Some of these results were announced in [29].     

Coherently Aligned Porphyrin‐Appended Polynorbornenes

You can append on me! Porphyrin‐appended polynorbornenes derived from 5,6‐endo‐fused N‐arylpyrrolidenonorbornenes have been shown to have coherently aligned pendant groups that exhibit exciton coupling and fluorescence quenching in the absorption and emission profiles (see figure).

     

Determination of senkirkine and senecionine in Tussilago farfara using microwave-assisted extraction and pressurized hot water extraction with liquid chromatography tandem mass spectrometry

Tussilago farfara (Kuan Donghua) is an important Chinese herbal medicine which has been shown to contain many bioactive compounds and widely used to relieve cough and resolve phlegm. However, besides therapeutic bioactive compounds, this herb has been found to contain toxic pyrrolizidine alkaloids (PAs), mainly senkirkine and traces of senecionine. In this report, conditions for microwave-assisted extraction (MAE) and pressurized hot water extraction (PHWE) were optimized for the extraction of the PAs. The results were compared against heating under reflux. It was found that the binary mixture of MeOH:H₂O (1:1) acidified using HCl to pH 2-3 was the optimal solvent for the extraction of the PAs in the plant materials. Liquid chromatography (LC) with ultra-violet (UV) detection and electrospray ionization mass spectrometry (ESI-MS) in the positive mode was used for the determination and quantitation of senkirkine and senecionine in the botanical extract. The proposed extraction methods with LC/MS allow for the rapid detection of the major and the minor alkaloids in T. farfara in the presence of co-eluting peaks. With LC/MS, the quantitative analysis of PAs in the extract was done using internal standard calibration and the precision was found to vary from 0.6% to 5.4% on different days. The limits of detection (LODs) and limits of quantitation (LOQs) for MAE and PHWE were found to vary from 0.26 μg/g to 1.04 μg/g and 1.32 μg/g to 5.29 μg/g, respectively. The method precision of MAE and PHWE were found to vary from 3.7% to 10.4% on different days. The results showed that major and minor alkaloids extracted using MAE and PHWE were comparable to that by heating under reflux. Our data also showed that significant ion suppression was not observed in the analysis of senkirkine and senecionine in the botanical extracts with co-eluting peaks.     

Cohomology with coefficients for operadic coalgebras

Corepresentations of a coalgebra over a quadratic operad are defined, and various characterizations of them are given. Cohomology of such an operadic coalgebra with coefficients in a corepresentation is then studied.     

Electrodeposition of Au monolayer on Pt(111) mediated by self-assembled monolayers

In-situ scanning tunneling microscopy (STM), cyclic voltammetry (CV), and infrared reflection-adsorption spectroscopy (IRRAS) have been used to examine the electrodeposition of gold onto Pt(111) electrodes modified with benzenethiol (BT) and benzene-1,2-dithiol (BDT) in 0.1 M HClO4 containing 10 microM HAuCl4. Both BT and BDT were attached to Pt(111) via one sulfur headgroup. STM and IRRAS results indicated that the other SH group of BDT was pendant in the electrolyte. Both BT and BDT formed (2 x 2) structures at the coverage of 0.25, and they were transformed into (square root(3) x square root(3))R30 degrees as the coverage was raised to 0.33. These two organic surface modifiers resulted in 3D and 2D gold islands at BT- and BDT-coated Pt(111) electrodes, respectively. The pendant SH group of BDT could interact specifically with gold adspecies to immobilize gold adatoms on the Pt(111) substrate, which yields a 2D growth of gold deposition. Molecular resolution STM revealed an ordered array of (6 x 2 square root(13)) after a full monolayer of gold was plated on the BDT/Pt(111) electrode. Since BDT was strongly adsorbed on Pt(111), gold adatoms only occupied free sites between BDT admolecules on Pt(111). This is supported by a stripping voltammetric analysis, which reveals no reductive desorption of BDT admolecules at a gold-deposited BDT/Pt(111) electrode. It seems that the BDT adlayer acted as the template for gold deposit on Pt(111). In contrast, a BT adlayer yielded 3D gold deposit on Pt(111). This study demonstrates unambiguously that organic surface modifiers could contribute greatly to the electrodeposition of metal adatoms.     

Carbon nanotube-enhanced separation of DNA fragments by a portable capillary electrophoresis system with contactless conductivity detection

It was demonstrated that separation of DNA fragments by a CE-contactless conductivity detection system (CE-CCD) could be enhanced with multiple-wall carbon nanotubes (MWCNs) as buffer additive. For HaeIII digest of PhiX174 DNA, optimized MWCN concentration was obtained when the MWCN was above its threshold concentration, at which MWCN could form a network in the buffer as pseudostationary phase to provide additional interaction sites. In the case of larger DNA, MWCN near or below its threshold concentration was enough to provide great improvement of the resolution, which was shown by the separation of the 2-Log DNA ladder. Furthermore, the buffer containing MWCN could provide a more stable baseline in the CE-CCD system, owing to less fluctuation of its conductivity. Compared with CE-UV, CE-CCD with MWCN could provide lower LODs as well as better resolution.     

Determination of tobramycin in human serum by capillary electrophoresis with contactless conductivity detection

A study on the determination of the antibiotic tobramycin by CE with capacitively coupled contactless conductivity detection is presented. This method enabled the direct quantification of the non-UV-absorbing species without incurring the disadvantages of the indirect approaches which would be needed for optical detection. The separation of tobramycin from inorganic cations present in serum samples was achieved by optimizing the composition of the acetic acid buffer. Field-amplified sample stacking was employed to enhance the sensitivity of the method and a detection limit of 50 microg/L (S/N = 3) was reached. The RSDs obtained for migration time and peak area using kanamycin B as internal standard were typically 0.12 and 4%, respectively. The newly developed method was validated by measuring the concentration of tobramycin in serum standards containing typical therapeutic concentrations of 2 and 10 mg/L. The recoveries were 96 and 97% for the two concentrations, respectively.     

Limit of Quasilocal Mass at Spatial Infinity

We study the limit of quasilocal mass defined in [4 and 5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spatial infinity. The limit for coordinate spheres of a boosted slice of the Schwarzchild solution is computed explicitly and shown to give the expected energy-momentum four-vector.