On Beckenbach–Radó type integral inequalities

Beckenbach and Radó characterized logarithmically subharmonic functions in the plane in terms of integral inequalities involving spherical averages. In this work we generalize this result to higher dimensions and thus answer to a question raised by Beckenbach and Radó. We also consider generalizations of integral inequalities suggested by Beckenbach and Radó and discuss connections to reverse Hölder inequalities and Muckenhoupt weights.     

Tracing Lysozyme-Lipid Interactions with Long-Wavelength Squaraine Dyes

The applicability of the two newly commercial available squaraine labels Square-670-NHS and Seta-635-NHS to exploring protein-lipid interactions has been evaluated. The labels were conjugated to lysozyme (Lz) (squaraine-lysozyme conjugates below referred to as Square-670-Lz and Seta-635-Lz), a structurally well-characterized small globular protein displaying the ability to interact both, electrostatically and hydrophobically with lipids. The lipid component of the model systems was represented by lipid vesicles composed of zwitterionic lipids egg yolk phosphatidylcholine (PC) and 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC), and their mixtures with anionic lipids either beef heart cardiolipin (CL) or 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG), respectively. Fluorescence intensity of Square-670-Lz was found to decrease upon association with lipid bilayer, while the fluorescence intensity of Seta-635-Lz displayed more complex behavior depending on lipid-to-protein molar ratio. Covalent coupling of squaraine labels to lysozyme exerts different influence on the properties of dye-protein conjugate. It was suggested that Square-670-NHS covalent attachment to Lz molecule enhances protein propensity for self-association, while squaraine label Seta-635-NHS is sensitive to different modes of lysozyme-lipid interactions—within the L:P range 6–11, when hydrophobic protein-lipid interactions are predominant, an aggregation of membrane-bound protein molecules takes place, thereby decreasing the fluorescence intensity of Seta-635-Lz. At higher L:P values (from 22 to 148) when electrostatic interactions are enhanced fluorescence intensity of Seta-635-Lz increases with increasing lipid concentrations.     

Thermal phase behavior of DMPG: the exclusion of continuous network and dense aggregates

1,2-Dimyristoyl-sn-glycero-3-phospho-rac-glycerol has been suggested to form at intermediate temperatures and at high concentrations in low-salt solutions as a continuous sponge phase (Heimburg, T.; Biltonen, R. L. Biochemistry 1994, 33, 9477-9488). In the present study, the changes in signals seen for a range of fluorescent probes during phase transformations of this phospholipid indicate continuous melting and a change in lipid packing, in accordance with previous reports. However, in accordance with Lamy-Freund and Riske (Lamy-Freund, M. T.; Riske, K. A. Chem. Phys. Lipids 2003, 122, 19-32), no enhancement of lipid mixing within the putative sponge phase region was seen, suggesting a lack of a connected lipid surface. Accordingly, a typical sponge phase cannot account for the properties of the intermediate phase. The low scattering intensities of the latter have also been taken as evidence for disaggregation. While dynamic light scattering and data for membranes containing poly(ethylene glycol)-ylated lipids could lend credence to disaggregation, the most likely explanation for the scattering data would appear to be a shape transition without significant changes in neither vesicle aggregation nor bilayer connectivity. An abrupt change in light scattering and signals from some of the fluorescent probes used reveals a new transition at Tt approximately 43 degrees C, with the formation of a more ordered interface.     

An existence result for superparabolic functions

We study superparabolic functions related to nonlinear parabolic equations. They are defined by means of a parabolic comparison principle with respect to solutions. We show that every superparabolic function satisfies the equation with a positive Radon measure on the right-hand side, and conversely, for every finite positive Radon measure there exists a superparabolic function which is solution to the corresponding equation with measure data.     

The BV-capacity in metric spaces

We study basic properties of the BV-capacity and Sobolev capacity of order one in a complete metric space equipped with a doubling measure and supporting a weak Poincaré inequality. In particular, we show that the BV-capacity is a Choquet capacity and the Sobolev 1-capacity is not. However, these quantities are equivalent by two sided estimates and they have the same null sets as the Hausdorff measure of codimension one. The theory of functions of bounded variation plays an essential role in our arguments. The main tool is a modified version of the boxing inequality.     

A risk approach by credibility theory

This paper attempts to treat some topics of risk theory by means of credibility theory. We study the risk aversion of an agent faced with a situation of uncertainty represented by a discrete fuzzy variable, the relationship between stochastic dominance and credibilistic dominance, and an index of riskiness of discrete credibilistic gambles. In the framework of an optimal saving credibilistic model, the way the presence of risk modifies the level of optimal saving is studied. The main tool of our investigation is an operator defined by B. Liu and Y. K. Liu by which to a discrete fuzzy variable one associates a discrete random variable with the same expected value as the former.     

Sobolev space properties of superharmonic functions on metric spaces

Our objective is to study regularity of superharmonic functions of a nonlinear potential theory on metric measure spaces. In particular, we are interested in the local integrability properties of a superharmonic function and its derivative. We show that every superharmonic function has a weak upper gradient and provide sharp local integrability estimates. In addition, we study absolute continuity of a superharmonic function.     

Local behaviour of solutions to doubly nonlinear parabolic equations

We give a relatively simple and transparent proof for Harnack’s inequality for certain degenerate doubly nonlinear parabolic equations. We consider the case where the Lebesgue measure is replaced with a doubling Borel measure which supports a Poincaré inequality.     

Harnack’s principle for quasiminimizers

Abstract We study Harnack type properties of quasiminimizers of the -Dirichlet integral on metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. We show that an increasing sequence of quasiminimizers converges locally uniformly to a quasiminimizer, provided the limit function is finite at some point, even if the quasiminimizing constant and the boundary values are allowed to vary in a bounded way. If the quasiminimizing constants converge to one, then the limit function is the unique minimizer of the -Dirichlet integral. In the Euclidean case with the Lebesgue measure we obtain convergence also in the Sobolev norm. Keywords: Metric space, doubling measure, Poincaré inequality, Newtonian space, Harnack inequality, Harnack convergence theorem Mathematics Subject Classification (2000): 49J52, 35J60, 49J27     

Glucose-induced changes in the optical properties of Intralipid

Photoacoustic and optical measurement techniques were used in this paper to study glucose-induced changes in Intralipid suspensions. Optical energy was provided by a Nd:YAG laser at 1064 and 532 nm and a picosecond laser module at 906 nm. As detectors, the setup employed a photoacoustic detector, PIN diode, and streak camera. Increasing the glucose content of the suspensions increased the refractive indices of the studied media. This served to decrease the refractive index mismatch between the background and the scattering particles and led consequently to decreased scattering, which then affected both the peak-to-peak value of the photoacoustic signals and the transmitted optical pulses. At 1064 nm, glucose changed the peak-to-peak value of the photoacoustic signal more in 1% than in 2% Intralipid. In addition, the glucose-induced change in the transmitted pulse amplitude was less noticeable at 532 than at 1064 nm in 1% Intralipid. The text was submitted by the authors in English.