RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications

We discuss the complete convergence of weighted sums for arrays of rowwise negatively dependent random variables (ND r.v.’s) to linear processes. As an application, we obtain the complete convergence of linear processes based on ND r.v.’s which extends the result of Li et al. (Stat. Probab. Lett. 14:111–114, 1992), including the results of Baum and Katz (Trans. Am. Math. Soc. 120:108–123, 1965), from the i.i.d. case to a negatively dependent (ND) setting. We complement the results of Ahmed et al. (Stat. Probab. Lett. 58:185–194, 2002) and confirm their conjecture on linear processes in the ND case.     

Msx2 mediates the inhibitory action of TNF-�� on osteoblast differentiation

TNF-α, a proinflammatory cytokine, inhibits osteoblast differentiation under diverse inflammatory conditions; however, the underlying mechanisms in terms of the TNF-α signaling pathway remain unclear. In this study, we examined the role of Msx2 in TNF-α-mediated inhibition of alkaline phosphatase (ALP) expression and the signaling pathways involved. TNF-α down-regulated ALP expression induced by bone morphogenetic protein 2 (BMP2) in C2C12 and Runx2^-/- calvarial cells. Over-expression of Msx2 suppressed BMP2-induced ALP expression. Furthermore, TNF-α induced Msx2 expression, and the knockdown of Msx2 by small interfering RNAs rescued ALP expression, which was inhibited by TNF-α. TNF-α activated the NF-κB and the JNK pathways. Inhibition of NF-κB or JNK activation reduced the inhibitory effect of TNF-α on ALP expression, whereas TNF-α-induced Msx2 expression was only suppressed by the inhibition of the NF-κB pathway. Taken together, these results indicate that Msx2 mediates the inhibitory action of TNF-α on BMP2-regulated osteoblast differentiation and that the TNF-α-activated NF-κB pathway is responsible for Msx2 induction.     

Palladium-catalyzed synthesis of 3-oxo-1,3-dihydro-1-isobenzofuranyl alkanoates from 2-bromobenzaldehyde and sodium alkanoates

2-Bromobenzaldehyde reacts with sodium alkanoates in acetonitrile under carbon monoxide pressure in the presence of a catalytic amount of bis(triphenylphosphine)palladium(II) chloride to afford the corre sponding 3-oxo-1,3-dihydro-1-isobenzofuranyl alkanoates in moderate to good yields.     

Multifunctional poly(2,5‐benzimidazole)/carbon nanotube composite films

The AB‐monomer, 3,4‐diaminobenzoic acid dihydrochloride, was recrystallized from an aqueous hydrochloric acid solution and used to synthesize high‐molecular‐weight poly(2,5‐benzimidazole) (ABPBI). ABPBI/carbon nanotube (CNT) composites were prepared via in situ polymerization of the AB‐monomer in the presence of single‐walled carbon nanotube (SWCNT) or multiwalled carbon nanotube (MWCNT) in a mildly acidic polyphosphoric acid. The ABPBI/SWCNT and ABPBI/MWCNT composites displayed good solubility in methanesulfonic acid and thus, uniform films could be cast. The morphology of these composite films was studied by X‐ray diffraction, scanning electron microscopy, transmission electron microscopy, and atomic force microscopy. The results showed that both types of CNTs were uniformly dispersed into the ABPBI matrix. Tensile properties of the composite films were significantly improved when compared with ABPBI, and their toughness (～200 MPa) was close to the nature's toughest spider silk (～215 MPa). The electrical conductivities of ABPBI/SWCNT and ABPBI/MWCNT composite films were 9.10 × 10^?5 and 2.53 × 10^?1 S/cm, respectively, whereas that of ABPBI film was 4.81 × 10^?6 S/cm. These values are ～19 and 52,700 times enhanced by the presence of SWCNT and MWCNT, respectively. Finally, without acid impregnation, the ABPBI film was nonconducting while the SWCNT‐ and MWCNT‐based composites were proton conducting with maximum conductivities of 0.018 and 0.017 S/cm, respectively. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1067–1078, 2010     

On the frequency bandwidth change of a servo system with a gear reducer due to backlash and motor input voltage

Summary The paper analyzes how the frequency bandwidth of a servo system is affected by the input voltage of its motor and the magnitude of the total backlash. The bandwidth of the system is defined as the set of antiresonance frequencies, which appears in the frequency-response characteristic. The change in the frequency-response characteristics is investigated depending on motor input voltage and the magnitude of the total backlash. It is shown that at infinite motor input voltage, the servo system has a bandwidth equivalent to that of a backlash-free system. The amount of the systems bandwidth reduction due to the backlash changes greatly with the motor input voltage. It becomes possible then to determine the necessary maximum input voltage of the motor and the admissible magnitude of the total backlash to satisfy the desired bandwidth for a servo system with a gear reducer.     

Blends of polycarbonate and poly(ϵ‐caprolactone) and the determination of the polymer–polymer interaction parameter of the two polymers

The thermal properties of blends of polycarbonate (PC) and poly(ε‐caprolactone) (PCL) were investigated by differential scanning calorimetry (DSC). From the thermal analysis of PC‐PCL blends, a single glass‐transition temperature (T_g) was observed for all the blend compositions. These results indicate that there is miscibility between the two components. From the modified Lu and Weiss equation, the polymer–polymer interaction parameter (χ₁₂) of the PC‐PCL blends was calculated and found to range from −0.012 to −0.040 with the compositions. The χ₁₂ values calculated from the T_g method decreased with the increase of PC weight fraction. By taking PC‐PCL blend as a model system, the values of χ₁₂ were compared with two different methods, the T_g method and melting point depression method. The two methods are in reasonably good agreement for the χ₁₂ values of the PC‐PCL blends. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2072–2076, 2000     

Patterned immobilization of biomolecules by using ion irradiation‐induced graft polymerization

A new method for biomolecular patterning based on ion irradiation‐induced graft polymerization was demonstrated in this study. Ion irradiation on a polymer surface resulted in the formation of active species, which was further used for surface‐initiated graft polymerization of acrylic acid. The results of the grafting study revealed that the surface graft polymerization using 20 vol % of acrylic acid on the poly(tetrafluoroethylene) (PTFE) film irradiated at the fluence of 1 × 10¹⁵ ions/cm² for 12 h was the optimum graft polymerization condition to achieve the maximum grafting degree. The results of the fluorescence microscopy also revealed that the optimum fluence to achieve the maximum fluorescence intensity was 1 × 10¹⁵ ions/cm². The grafting of acrylic acid on the PTFE surfaces was confirmed by a fluorescence labeling method. The grafted PTFE films were used for the immobilization of amine‐functionalized p‐DNA, followed by hybridization with fluorescently tagged c‐DNA. Biotin‐amine was also immobilized on the acrylic acid grafted PTFE surfaces. Successful biotin‐specific binding of streptavidin further confirmed the potential of this strategy for patterning of various biomolecules. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6124–6134, 2009     

Self‐controlled synthesis of hyperbranched poly(ether‐ketone)s from A2 + B3 approach in poly(phosphoric acid)

Self‐controlled synthesis of hyperbranched poly(ether‐ketone)s (HPEKs) were prepared from “A₂ + B₃” approach by using different monomer solubility in reaction medium. 1,3,5‐Triphenoxybenzene as a hydrophobic B₃ monomer was reacted with commercially available terephthalic acid or 4,4′‐oxybis(benzoic acid) as a hydrophilic A₂ monomer in a hydrophilic reaction medium, polyphosphoric acid (PPA)/phosphorous pentoxide (P₂O₅). The resultant HPEKs were soluble in various common organic solvents and had the weight‐average molecular weight in the range of 3900–13,400 g/mol. The results implied that HPEKs were branched structures instead of crosslinked polymers. The molecular sizes and shapes of HPEKs were further assured by morphological investigation with scanning electron microscopy (SEM) and atomic force microscopy (AFM). Hence, the applied polymerization condition was indeed strong enough to efficiently facilitate polycondensation via “direct” Friedel‐Crafts reaction without gelation. It could be concluded that the polymer forming reaction was kinetically controlled by automatic and slow feeding of the hydrophobic B₃ monomer into the hydrophilic reaction mixture containing hydrophilic comonomer. As a result, hyperbranched structures were formed instead of crosslinked polymers even at full conversion (equifunctional monomer feed ratio). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3326–3336, 2009