Erratum to “Lower bounds for the eigenvalues of the basic Dirac operator on a Riemannian foliation” [J. Geom. Phys. 51 (2004) 166–182]

We correct some statements in the paper mentioned in the title.     

Coloring intersection graphs of x-monotone curves in the plane

A class of graphs G is χ-bounded if the chromatic number of the graphs in G is bounded by some function of their clique number. We show that the class of intersection graphs of simple families of x-monotone curves in the plane intersecting a vertical line is χ-bounded. As a corollary, we show that the class of intersection graphs of rays in the plane is χ-bounded, and the class of intersection graphs of unit segments in the plane is χ-bounded.     

Low emissivity Ag/Si/glass thin films deposited by sputtering

Si was deposited on the glass substrate as an interlayer for the 2-D growth of Ag thin films because Si has a strong binding energy against Ag and can lead to a negative surface energy change in Ag/glass. The Si interlayer induced an extremely smooth and flat Ag surface, which effectively reduced the resistance and enhanced the reflectance in the IR region. In particular, Ag (9 nm)/Si (3 nm)/glass showed 0.074 emissivity and ∼91% reflectance in the IR region with 67% transmittance in the visible region.     

Correlation of thermodynamic modeling and molecular simulations for liquid-liquid equilibrium of ternary polymer mixtures based on a phenomenological scaling method

In our previous study [S.Y. Oh, Y.C. Bae, J. Phys. Chem. B 114 (2010) 8948-8953], we presented a new method to predict liquid-liquid equilibria in ternary simple liquid mixtures by using a combination of a thermodynamic model and molecular simulations. As a continuation of that effort, we extend our previously developed method to ternary polymer systems. In the simulations, we used the dummy atoms to calculate the pair interaction energy values between the polymer segments and the solvent molecules. Furthermore, a thermodynamic model scaling concept is introduced to consider the chain length dependence of the energy parameters. This method was applied to ternary mixtures incorporating low to high molecular weight polymers. The method presented here well described the experimental observations using one or no adjustable parameters.     

Determination of Allosteric Effects and Interstrand Bidentate Interactions in DNA‐Peptide Molecular Recognition

To study DNA allostery, quantitative DNase I footprinting studies were carried out on a newly designed peptide His‐Hyp‐Lys‐Lys‐(Py)₄‐Lys‐Lys‐NH₂ (HypKK‐10) containing the XHypKK (Hyp = hydroxyproline) and polyamide motifs. The interconnection of DNA footprints of peptides HypKK‐10 and the parent peptide PyPro‐12 supports the proposal that interaction network cooperativity is preferred in DNA‐peptide interactions between multiple recognition sites. A simple method of determining interstrand bidentate interactions between the peptide moieties and DNA bases is introduced. It is envisaged that interstrand bidentate interactions also participate in the relay of conformational changes to recognition sites on the complementary strands. Circular dichroism studies of the titration of peptide HypKK‐10 with an oligonucleotide duplex indicate that this peptide binds in a dimeric fashion to DNA in the minor groove. This work may prompt the design of new DNA binding ligands for the study of DNA‐peptide allosteric interactions and DNA interaction network.     

Synthesis and properties of phenothiazylene vinylene‐based polymers: New organic semiconductors for field‐effect transistors and solar cells

A series of new phenothiazylene vinylene‐based semiconducting polymers, poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene] ( P1 ), poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene‐alt‐1,4‐phenylene vinylene] ( P2 ), and poly[3,7‐(4′‐dodecyloxyphenyl)phenothiazylene vinylene‐alt‐2,5‐thienylene vinylene] ( P3 ), have been synthesized via a Horner‐Emmons reaction. FTIR and ¹H NMR spectroscopies confirmed that the configurations of the vinylene groups in the polymers were all‐trans (E). The weight‐averaged molecular weights (M_w) of P1 , P2 , and P3 were found to be 27,000, 22,000, and 29,000, with polydispersity indices of 1.91, 2.05, and 2.25, respectively. The thermograms for P1 , P2 , and P3 each contained only a broad glass transition, at 129, 167, and 155 °C, respectively, without the observation of melting features. UV–visible absorption spectra of the polymers showed two strong absorption bands in the ranges 315–370 nm and 450–500 nm, which arose from absorptions of the phenothiazine segments and the conjugated main chains. Solution‐processed field‐effect transistors fabricated from these polymers showed p‐type organic thin‐film transistor characteristics. The field‐effect mobilities of P1 , P2 , and P3 were measured to be 1.0 × 10^?4, 3.6 × 10^?5, and 1.0 × 10^?3 cm² V^?1 s^?1, respectively, and the on/off ratios were in the order of 10² for P1 and P2 , and 10³ for P3 . Atomic force microscopy and X‐ray diffraction analysis of thin films of the polymers show that they have amorphous structures. A photovoltaic device in which a P3 /PC₇₁BM (1/5) blend film was used as the active layer exhibited an open‐circuit voltage (V_OC) of 0.42 V, a short circuit current (J_SC) of 5.17 mA cm^?2, a fill factor of 0.35, and a power conversion efficiency of 0.76% under AM 1.5 G (100 mW cm^?2) illumination. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 635–646, 2010     

Risk in Inventory Models: The Case of the Newsboy Problem — Optimality Conditions

A recent article in this journal employs the capital-asset pricing model for the analysis of the newsboy problem and shows how the covariance risk affects the optimal inventory policy. The purpose of this paper is to sharpen the optimality conditions given by the article and hence to provide a simple method for finding the solution. Under reasonable assumptions, this paper shows that the optimal ordering policy can be described by a single equation, regardless of the sign of the covariance term.     

Synthesis of poly(2‐vinyl pyridine)‐b‐poly(n‐hexyl isocyanate) amphiphilic coil‐rod block copolymer by anionic polymerization

A well‐defined amphiphilic coil‐rod block copolymer, poly(2‐vinyl pyridine)‐b‐poly(n‐hexyl isocyanate) (P2VP‐b‐PHIC), was synthesized with quantitative yields by anionic polymerization. A low reactive one‐directional initiator, potassium diphenyl methane (DPM‐K), was very effective in polymerizing 2‐vinyl pyridine (2VP) without side reactions, leading to perfect control over molecular weight and molecular weight distribution over a broad range of initiator and monomer concentration. Copolymerization of 2VP with n‐hexyl isocyanate (HIC) was carried out in the presence of sodium tetraphenyl borate (NaBPh₄) to prevent backbiting reactions during isocyanate polymerization. Terminating the living end with a suitable end‐capping agent resulted in a P2VP‐b‐PHIC coil‐rod block copolymer with controlled molecular weight and narrow molecular weight distribution. Cast film from a chloroform solution of P2VP‐b‐PHIC displayed microphase separation, characteristic of coil‐rod block copolymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 607–615, 2005