Lipschitz conditions in conformally invariant metrics

We consider two conformally invariant metrics in proper subdomains of euclideann-spaceR ⁿ. We show that Lipschitz mappings in these metrics include the class of quasiconformal mappings as a proper subclass, yet these Lipschitz mappings have many properties similar to those of quasiconformal mappings. Research supported in part by the U.S. National Science Foundation and the A.P. Sloan Foundation. Research supported in part by the Alexander von Humboldt Foundation.     

Structure of anionic phospholipid coatings on silica by dissipative quartz crystal microbalance

The adsorption of anionic phospholipids on silica was investigated by the dissipative quartz crystal microbalance (QCM) technique. Liposomes composed of 1 mM 80:20 mol % of 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylcholine (POPC)/phosphatidic acid, POPC/phosphatidylglycerol, or POPC/phosphatidylserine in N-(2-hydroxyethyl)piperazine-N'-(2-ethanesulfonic acid) buffer at pH 7.4 (with or without 3 mM of CaCl2) were examined. We have previously demonstrated that similar phospholipid coatings can be used in capillary electrochromatography as a stationary phase for the separation of analytes. In this work, we focus on the formation of the coatings and on the type of lipid structure formed on silica. The QCM investigation comprised qualitative results based on changes in frequency and resistance, and quantitative modeling of the obtained results. The latter was performed using the dissipative QCM, which measures the quartz crystal impedance, combined with equivalent circuit analysis. A previously developed coating and cleaning procedure for phospholipid-coated fused silica capillaries was adopted in this study, and the same silica-coated crystal was used throughout the QCM study. We will demonstrate in this work that the type of lipid structure formed on silica, that is, a rather rigid supported lipid bilayer or a viscoelastic supported vesicle layer (SVL), is highly dependent on the lipid and solvent composition. We also show for the first time that the modeling of the dissipative QCM data can be used to extract a more quantitative picture of an adsorbed SVL, because, so far, published studies have merely used the QCM data in a qualitative sense.     

High actuation performance offered by simple diene rubbers

Dielectric elastomers are materials well known for their superior actuation behavior under applied electric field. The simplicity of material fabrication and clear working principle of dielectric elastomer actuators (DEAs) can offer various applications of dielectric elastomers. In this work, we have compared a number of different types of commercially available elastomers in terms of actuation performance. It was found that well‐known commercial rubbers like acrylonitrile‐butadiene rubbers (NBR) can offer higher actuation performance in DEAs than the frequently used dielectric elastomers, such as acrylic rubber and silicone. The acrylonitrile content of the NBR was found to play an important role in the dielectric and consequently actuation properties. More interestingly, we observed that addition of organic oil, such as dioctyl adipate, can greatly enhance the actuation performance. Copyright © 2016 John Wiley & Sons, Ltd.     

Functional inequalities for modified Bessel functions

In this paper, our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kind. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact equivalent to the corresponding Turán-type inequalities for these functions. As an application of the results concerning the modified Bessel function of the second kind, we prove that the cumulative distribution function of the gamma–gamma distribution is log-concave. At the end of this paper, several open problems are posed, which may be of interest for further research.     

Comparison theorems for hyperbolic type metrics

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.     

Some properties of the gamma and psi functions, with applications

In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some well-known results for the volume of the unit ball , the surface area of the unit sphere , and some related constants.