The hardy-littlewood maximal function of a sobolev function

We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW ^1,p (R ⁿ ) for 1<p≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.     

Observation of topical catalysis by sphingomyelinase coupled to microspheres

Sphingomyelinase, SMase (EC 3.1.4.12), was coupled onto amino-derivatized acrylate microspheres and was shown to retain its catalytic activity. The immobilized enzyme allows one to carry out topical enzymatic reaction in a controlled manner. Accordingly, these spheres were held with a micropipet and using micromanipulator brought into contact with a giant liposome membrane composed of phosphatidylcholine and sphingomyelin (SOPC/C16:0-SM, 0.75:0.25, molar ratio), representing the substrate for the immobilized enzyme. The macroscopic consequences of the enzyme reaction were visualized using fluorescence microscopy as well as differential interference contrast microscopy. The surface contact of the giant vesicle and immobilized enzyme causes membrane microdomain formation and domain clustering (capping) in the membrane and subsequent shedding of small vesicles from the membrane into the interior of the giant liposome. The method described represents a novel approach to study enzymatic reactions and allows manipulating giant vesicles as well as cultured cells in a spatially controlled manner.     

Cytochrome c–dimyristoylphosphatidylglycerol interactions studied by asymmetrical flow field-flow fractionation

Lipid membranes are well recognized ligands that bind peripheral and integral proteins in a specific manner and regulate their function. Cytochrome c (cyt c) is one of the partner peripheral protein that binds to the lipid membranes via electrostatic and hydrophobic interactions. In this study, asymmetrical flow field-flow fractionation (AsFlFFF) was used to compare the interactions of cyt c with the acidic phospholipid 1,2-dimyristoyl-sn-glycero-3-phospho-rac-glycerol (DMPG), oleic acid (OA), and sodium dodecyl sulfate (SDS). The influence of pH and the cyt c–lipid molar mass ratios were evaluated by monitoring the diffusion coefficients and particle diameter distributions obtained for the free and lipid-bound protein. The hydrodynamic particle diameter of cyt c (pI 10) was 4.1 nm at pH 11.4 and around 4.2 nm at pH 7.0 and 8.0. Standard molar mass marker proteins were used for calibration to obtain the molar masses of free cyt c and its complexes with lipids. AsFlFFF revealed the binding of cyt c to DMPG and to OA to be mainly electrostatic. In the absence of electrostatic interactions, minor complex formation occurred, possibly due to the extended lipid anchorage involving the hydrophobic cavity of cyt c and the hydrocarbon chains of DMPG or SDS. The possibility of the formation of the molten globule state of cyt c, induced by the interaction between cyt c and lipids, is discussed.Electronic Supplementary Material Supplementary material is available for this article at     

Inclusive ϱ0,K *±(892) andf production in\bar p p Interactions at 12 GeV/c

Inclusive production of ?⁰,K ^*±(892), andf is studied in \(\bar p\) p interactions at 12 GeV/c. The inclusive cross sections for ?⁰,K ^*±(892), andf are found to be 6.7±0.3 mb, 1.0±0.2 mb, and 1.4±0.3 mb, respectively. The differential cross sections are presented as a function of c.m. rapidity, Feynmanx and square of the transverse momentump _T ² . Comparison with the correspondingpp data shows some interesting differences which can be attributed to the \(\bar p\) p annihilation. The results are compared with the predictions of the quark fusion model.     

The effect of drying method on the properties and nanoscale structure of cellulose whiskers

Cellulose whiskers were prepared from wood- and cotton-based microcrystalline cellulose and dried by two methods: freeze-drying or air-drying. The effect of drying method on the properties and structure of the whiskers were studied. Furthermore, the influence of the source of cellulose on the nanoscale structure was investigated. Drying method was observed to slightly influence the thermal stability of cellulose whiskers, whereas the char residue varied significantly depending on the drying process performed. Small- and wide-angle X-ray scattering and solid state nuclear magnetic resonance spectroscopy were used to examine the crystallinity and nanoscale structure of the dried whiskers. It was observed that the crystal structure and crystallinity of cellulose whiskers remained during all treatments, whereas their nanoscale structure was significantly influenced by drying method, neutralization, and source of cellulose. Relationships between thermal behavior and nanoscale structure were reported and discussed.     

Nanofibrillated cellulose/carboxymethyl cellulose composite with improved wet strength

In this paper, nanofibrillated cellulose/carboxymethyl cellulose (CMC) composite films were prepared using tape casting. The obtained transparent films showed shear induced partial alignment of fibrils along the casting direction, resulting in birefringence in cross polarized light. The carboxyl groups of CMC could be further utilized to create ionic crosslinking by treatment with glycidyl trimethyl ammonium chloride (GTMA). The GTMA treated composite films had improved mechanical properties both in wet and dry state. The chemical composition and morphologies of composites were analyzed with X-ray photoelectron spectroscopy, elemental analysis, scanning electron microscopy and wide-angle X-ray scattering.     

Fluorescent Temporin B Derivative and its Binding to Liposomes

Temporins are short (10–13 amino acids) and linear antimicrobial peptides first isolated from the skin of the European red frog, Rana temporaria, and are effective against Gram-positive bacteria and Candida albicans. Similarly to other antimicrobial peptides, the association of temporins to lipid membranes has been concluded to underlie their antimicrobial effects. Accordingly, a detailed understanding of their interactions with phospholipids is needed. We conjugated a fluorophore (Texas Red) to a Cys containing derivative of temporin B (temB) and investigated its binding to liposomes by fluorescence spectroscopy. Circular dichroic spectra for the Cys-mutant recorded in the absence and in the presence of phospholipids were essentially similar to those for temB. A blue shift in the emission spectra and diminished quenching by ferrocyanide (FCN) of Texas Red labeled temporin B (TRC-temB) were seen in the presence of liposomes. Both of these changes can be attributed to the insertion of the Texas Red into the hydrophobic region of the bilayer. Resonance energy transfer, steady state anisotropy, and fluorescence lifetimes further demonstrate the interaction of TRC-temB with liposomes to be enhanced by negatively charged phospholipids. Instead, cholesterol attenuates the association of TRC-temB with membranes. The interactions between TRC-temB and liposomes of varying negative surface charge are driven by electrostatics as well as hydrophobicity. Similarly to native temporin B also TRC-temB forms amyloid type fibers in the presence of negatively charged liposomes. This property is likely to relate to the cytotoxic activity of this peptide.     

Rapidity density distributions in antiproton-proton collisions

Data on the density of charged particles in rapidity space for annihilation and non-annihilation p?p interactions at 7.3 and 12 GeV/c are reported. It is shown that the central rapidity density for non-annihilation processes is a simple linear function of $\text{ln}\text{(}\text{s}\text{)}$ from these low energies up to p?p collider energies ($\text{s}\text{=540}\text{GeV}$). Significant differences in density distributions for p?p and e^?e⁺ annihilations at comparable energies are found.     

Langmuir-Blodgett films of hydrophobins HFBI and HFBII

Hydrophobins are small fungal proteins, which have remarkable surface-chemical properties. They self-assemble at hydrophobic/hydrophilic interfaces and work as adhesive agents and coatings. Sixteen layer Langmuir-Blodgett films of hydrophobins HFBI and HFBII from the fungus Trichoderma reesei were prepared and studied using grazing-incidence X-ray diffraction and reflectivity techniques. Both kind of films contain hexagonally ordered crystallites on the substrate with unit cell parameters of a = b = 54 Å (HFBI) and a = b = 55 Å (HFBII). The structure is similar to the structure of monolayer Langmuir-Blodgett films.