Some Continued Fractions in Ramanujan’s Lost Notebook

In this paper we first give the value of a periodic continued fraction which was recorded incorrectly by Ramanujan on page 341 of his lost notebook. Next, we describe several pairs of equivalent continued fractions in which one is the odd part of the other. One of the results is for the Rogers-Ramanujan continued fraction which was recently proved by Berndt and Yee. Finally, using the Bauer-Muir transformation we prove the equivalence of two continued fractions. One was recorded on page 44 in Ramanujan’s lost notebook, and the other is found in the unorganized pages at the end of Ramanujan’s second notebook.This work was supported by Yonsei University Research Fund of 2003.     

Molecular lens of the nonresonant dipole force

A cylindrical molecular lens is formed by focusing a nanosecond IR laser pulse. Trajectories of a CS2 molecular beam deflected by the lens are traced using the velocity map imaging technique. The characteristic lens parameters including the focal length, minimum beam width, and distance to the minimum-width position are determined. The laser intensity dependence of the parameters is in good agreement with theoretical predictions. Exciting possibilities for molecular optics and a new type of optical chromatography are opened up.     

Sodium dodecyl sulfate-capillary gel electrophoresis of polyethylene glycolylated interferon alpha

Sodium dodecyl sulfate-capillary gel electrophoresis (SDS-CGE) using a hydrophilic replaceable polymer network matrix was applied to characterize the polyethylene glycol(PEG)ylated interferon alpha (PEG-IFN). The SDS-CGE method resulted in a clearer resolution in both the PEG-IFN species and the native IFN species. The distribution profile of PEGylation determined by SDS-CGE was consistent with that obtained by SDS-polyacrylamide gel electrophoresis (PAGE) with Coomassie blue or barium iodide staining. The result was also compared using matrix-assisted laser desorption/ionization-time of flight-mass spectrometry. SDS-CGE was also useful for monitoring the PEGylation reaction to optimize the reaction conditions, such as reaction molar ratio. This study shows the potential of SDS-CGE as a new method for characterizing the PEGylated proteins with advantages of speed, minimal sample consumption and high resolution.     

Optical implementation of orthogonal phase-code multiplexing

We propose a new optical implementation of orthogonal phase-code multiplexing in which an arbitrary phase shift of theta or theta +pi is used in the reference beam instead of 0 or pi as in the conventional method. To compare the new and the conventional methods, we employ a 2-bit orthogonal phase code and store two binary-data images in a BaTiO(3) crystal with each method. We also employ numerical methods to simulate the 2-bit phase-code multiplexing and show that the signal-to-noise ratio in the restored images is improved by more than one order of magnitude in the new method in our experimental conditions.     

Photopolymerization of liquid carbon disulfide produces nanoscale polythiene films.

Broad band solar or 300--400 nm irradiation (Hg--Xe arc source) of liquid-phase carbon disulfide produces a new carbon--sulfur polymer with the approximate (n = 1.04--1.05) stoichiometry (CS(n))(x). The polymer, from here on called (CS)(x), forms as a approximately 200 nm thick transparent golden membrane as measured by SEM and AFM techniques. IR spectra for this polymer show some similarities with those obtained for the gas-phase photopolymerized (CS(2))(x) and the high-pressure-phase polymer of CS(2), called Bridgman's Black. The observed FT-IR absorptions of (CS)(x) include prominent features at 1431 (s, br), 1298 (m), 1250 (ms), and 1070 cm(-1) (m). In contrast to previous proposals for (CS(2))(x), (13)C labeling and model compound studies of alpha-(C(3)S(5))R(2) and beta-(C(3)S(5))R(2) (R = methyl or benzoyl) suggest that the absorption at 1431 cm(-1) and those at 1298 and 1250 cm(-1) are indicative of carbon--carbon double bonds and carbon--carbon single bonds, respectively. The molecular structure of alpha-(C(3)S(5))(C(O)C(6)H(5))(2), determined at -84 degrees C, belongs to space group P1, with a = 7.486(5) A, b = 13.335(11) A, c = 17.830(13) A, alpha = 105.60(6) degrees, beta = 95.32(6) degrees, gamma = 90.46(6) degrees, Z = 4, V = 1706(2) A(3), R = 0.0785, and R(w) = 0.2323. With use of electron and chemical ionization mass spectrometry, C(4)S(6) and C(6)S(7) were identified as the dominant soluble molecular side-products derived from a putative ethylenedithione (S==C==C==S) precursor. Atomic force microscopy (AFM) provided surface topology information for the thin film (CS)(x) and revealed features that suggested the bulk material is formed from small polymer spheres 20--50 nm in size. Both (CS(2))(x) and (CS)(x) are extensively cross-linked through disulfide linkages and both materials show strong EPR resonances (g > 2.006) indicative of sulfur-centered radicals from incomplete cross-linking. A polymerization mechanism based on the intermediacy of S(2)C=CS(2) is proposed.     

Development of multianalyte sensor arrays composed of chemically derivatized polymeric microspheres localized in micromachined cavities.

The development of a chip-based sensor array composed of individually addressable polystyrene-poly(ethylene glycol) and agarose microspheres has been demonstrated. The microspheres are selectively arranged in micromachined cavities localized on silicon wafers. These cavities are created with an anisotropic etch and serve as miniaturized reaction vessels and analysis chambers. A single drop of fluid provides sufficient analysis media to complete approximately 100 assays in these microetch pits. The cavities possess pyramidal pit shapes with trans-wafer openings that allows for both fluid flow through the microreactors/analysis chambers and optical access to the chemically sensitive microspheres. Identification and quantitation of analytes occurs via colorimetric and fluorescence changes to receptor and indicator molecules that are covalently attached to termination sites on the polymeric microspheres. Spectral data are extracted from the array efficiently using a charge-coupled device allowing for the near-real-time digital analysis of complex fluids. The power and utility of this new microbead array detection methodology is demonstrated here for the analysis of complex fluids containing a variety of important classes of analytes including acids, bases, metal cations, metabolic cofactors, and antibody reagents.     

Polymer-based multi-layer conductive electrode film for plastic LCD applications

Thin films of polymer-based multi-layer conductive electrode to be used as a substrate for a plastic liquid crystal display (LCD) have been prepared by a DC magnetron roll-to-roll sputtering method. The conductive layer is composed of three layers, ITO/Ag/ITO or ITO/APC/ITO, where APC is Ag-Pd-Cu alloy, on the polymer substrate (Arton?), which has been treated with hard-coat and gas-barrier layers. The properties of the conductive electrode for the plastic LCD were the following: (1) sheet resistance is 6 Ω/square; (2) transparency is 88% at 550 nm; (3) H₂O gas permeation through the plastics is 0.35 g/m² in 24 h; (4) durability against solvents is good for 5% NaOH solution, IPA, methanol, NMP, acetone, etc.; (5) the irreversible shrinkage and the compaction rate are both less than 3 ppm/h after annealing for 100 h at 150 °C. Received: 22 January 2001 / Accepted: 30 January 2001 / Published online: 26 April 2001     

Template‐Assisted Synthesis of Self‐Doped Polyaniline: Morphological Effects of Templates on the Conductivity

Self‐doped sulfonated polyaniline (PSA) has been synthesized on the surface of micellar nanoparticles made from positively charged surfactants by biocatalysis. The conformation forced by the electrostatic charge interactions between the positively charged micelle and the negatively charged PSA increases the conductivity of the PSA by three orders of magnitude. The pure PSA recovered from ion exchange, however, shows quite similar electrical properties compared with sulfonated polyanilines reported earlier. The increased conductivity of PSA complexes is as a result of the increased charge carrier concentration caused by a certain conformational locking.