Application of Uniform Asymptotics to the Second Painlevé Transcendent

In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection problems with minimal computational effort. Our method relies on finding uniform approximations of differ ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to the other Painlevé equations, and to the wider problem of the asymptotic behavio ur of the general solution to any of these equations. (Accepted May 15, 1997)     

New Experimental Insight into the Nature of Metal−Metal Bonds in Digallium Compounds: J Coupling between Quadrupolar Nuclei

Multiple bonding between atoms is of ongoing fundamental and applied interest. Here, we report a multinuclear (¹H, ¹³C, and ⁷¹Ga) solid‐state magnetic resonance spectroscopic study of digallium compounds which have been proposed, albeit somewhat controversially, to contain single, double, and triple Ga?Ga bonds. Of particular relevance to the nature of these bonds, we have carried out two‐dimensional ⁷¹Ga J/D‐resolved NMR experiments which provide a direct measurement of J(⁷¹Ga,⁷¹Ga) spin–spin coupling constants across the gallium?gallium bonds. When placed in the context of clear‐cut experimental data for analogous singly, doubly, and triply bonded carbon spin pairs or boron spin pairs, the ⁷¹Ga NMR data clearly support the notion of a different bonding paradigm in the gallium systems. Our findings are consistent with an increasing role across the purported gallane–gallene–gallyne series for classical and/or slipped π‐type bonding orbitals.     

Displacement convexity of entropy and related inequalities on graphs

We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prékopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings. To illustrate through examples, we apply our results to the complete graph and to the hypercube for which our results are optimal—by passing to the limit, we recover the classical log-Sobolev inequality for the standard Gaussian measure with the optimal constant.     

Inclusion complex formation of β-cyclodextrin and Naproxen: a study on exothermic complex formation by differential scanning calorimetry

Inclusion complex formation between β-cyclodextrin and Naproxen was investigated using differential scanning calorimetry (DSC) as a function of the β-cyclodextrin-to-Naproxen molar ratio, ranging from 0:5:1 to 5:1. When these mixtures are heated above the melting temperature of Naproxen, an exothermic peak is observed at a temperature slightly higher than the melting peak of Naproxen. This peak, which has not been previously reported, has been interpreted as an exothermic energy of inclusion complex formation. The magnitude of this complex formation peak was found to be dependent upon the composition of the β-cyclodextrin and Naproxen mixture and increased in magnitude to a maximum value at a β-cyclodextrin:Naproxen molar ratio of 2:1. In addition, Naproxen recrystallization and re-melting peaks seen in the cooling and re-heating scans, respectively, decreased in magnitude with increasing molar ratio and totally disappeared for the mixture with 5:1 of β-cyclodextrin to Naproxen ratio indicative of complete inclusion of Naproxen in the cyclodextrin cavities. Complete inclusion was further reflected by the disappearance of key Naproxen peaks in Fourier transform infrared spectra of samples recovered from DSC experiments. The large excess of β-cyclodextrin needed to fully complex the Naproxen was found to be due to slow kinetics. Increasing the hold time after the initial melting led to inclusion efficiencies up to 95 % even for the 2:1 mixture. These experiments suggest that ratios of β-cyclodextrin:Naproxen 2:1 or greater facilitate the process by increasing the presence of cyclodextrin molecules in the close proximity of the drug molecules and lead to high inclusion efficiencies.     

Assessing calves as carriers of Cryptosporidium and Giardia with zoonotic potential on dairy and beef farms within a water catchment area by mutation scanning

In the present study, we undertook a molecular epidemiological survey of Cryptosporidium and Giardia in calves on three dairy and two beef farms within an open drinking water catchment area (Melbourne, Australia). Faecal samples (n = 474) were collected from calves at two time points (5 months apart) and tested using a PCR‐based mutation scanning‐targeted sequencing phylogenetic approach, employing regions within the genes of small subunit (SSU) of ribosomal RNA (designated partial SSU), 60 kDa glycoprotein (pgp60) and triose phosphate isomerase (ptpi) as genetic markers. Using partial SSU, the C. bovis, C. parvum, C. ryanae and a new genotype of Cryptosporidium were characterised from totals of 74 (15.6%), 35 (7.3%), 37 (7.8%) and 9 (1.9%) samples, respectively. Using pgp60, C. parvum genotype IIa subgenotype A18G3R1 was detected in 29 samples. Using ptpi, G. duodenalis assemblages A and E were detected in totals of 10 (2.1%) and 130 (27.4%) samples, respectively. The present study showed that a considerable proportion of dairy and beef calves in this open water catchment region excreted Cryptosporidium (i.e. subgenotype IIaA18G3R1) and Giardia (e.g. assemblage A) that are consistent with those infecting humans, inferring that they are of zoonotic importance. Future work should focus on exploring, in a temporal and spatial way, whether these parasites occur in the environment and water of the catchment reservoir.     

Oligosiloxane Functionalized with Pendant (1,3‐Bis(9‐carbazolyl)benzene) (mCP) for Solution‐Processed Organic Electronics

A new oligosiloxane derivative (ODCzMSi) functionalized with the well‐known 1,3‐bis(9‐carbazolyl)benzene (mCP) pendant moiety, directly linked to the silicon atom of the oligosiloxane backbone, has been synthesized and characterized. Compared to mCP, the attachment of the oligosiloxane chain significantly improves the thermal and morphological stabilities with a high decomposition temperature (T_d=540 °C) and glass transition temperature (T_g=142 °C). The silicon–oxygen linkage of ODCzMSi disrupts the backbone conjugation and maintains a high triplet energy level (E_T=3.0 eV). A phosphorescent organic light‐emitting diode (PhOLED) using iridium bis(4,6‐difluorophenyl)pyridinato‐N,C² picolinate (FIrpic) as the emitter and ODCzMSi as the host shows a relatively low turn‐on voltage of 5.0 V for solution‐processed PhOLEDs, maximum external quantum efficiency of 9.2 %, and maximum current efficiency of 17.7 cd A^?1. The overall performance of this device is competitive with the best reported solution‐processed blue PhOLEDs. Memory devices using ODCzMSi as an active layer exhibit non‐volatile write‐once read‐many‐times (WORM) characteristics with high stability in retention time up to 10⁴ s and a low switch on voltage. This switching behaviour is explained by different stable conformations of ODCzMSi with high or low conductivity states which are obtained under the action of electric field through a π–π stacking alignment of the pendant aromatic groups. These results with both PhOLEDs and memory devices demonstrate that this oligosiloxane–mCP hybrid structure is promising and versatile for high performance solution‐processed optoelectronic applications.     

Regioregular poly(3‐alkanoylthiophene): Synthesis and electrochemical,photophysical, charge transport,and photovoltaic properties

Head‐to‐tail regioregular poly(3‐heptanoylthiophene) (PHOT) was synthesized by Ni‐catalyzed polycondensation of the 2,2‐dimethyl‐1,3‐propanediol‐protected Grignard monomer followed by deprotection. Cyclic voltammetric (CV) study demonstrates that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of PHOT are 0.5 eV lower in energy than those of the head‐to‐tail poly(3‐hexylthiophene) (HT‐P3HT). Their optical band gaps are essentially the same. Incomplete photoluminescence (PL) quenching was observed in thin films of the 1:1 blend of PHOT and HT‐P3HT. PHOT displayed a glass transition at ～269 °C and decomposed at ～300 °C according to differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). Wide‐angle X‐ray diffraction (WAXD) study showed that PHOT exists in a not highly ordered state in solid films especially in the π‐stacking direction. Only p‐channel activity was observed in field‐effect transistors (FETs) for PHOT. The hole mobility was on the order of 10^?4 cm² V^?1 s^?1. Photovoltaic devices with an active layer of 1:1 blend of PHOT and PC₇₁BM had a power conversion efficiency (PCE) of ～0.5%. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010