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.     

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.     

Initial trace for a doubly nonlinear parabolic equation

This paper studies the Cauchy problem for a doubly nonlinear parabolic equation. The main result shows that if there is a nonnegative solution of the Cauchy problem, then the initial trace of the solution is uniquely given as a nonnegative Borel measure satisfying an exponential growth condition. This extends the known result for the heat equation to the nonlinear case.     

Signature of heavy charged Higgs boson at LHC in the 1 and 3 prong hadronic tau decay channels

We have done a fast simulation analysis of the H^± signal at LHC in 1 and 3 prong hadronic τ-jet channels along with a tt̄ background. The τ polarization was effectively used to suppress the background in both channels. Combining this with appropriate cuts on p_T of the τ-jet, the missing E_T and the azimuthal angle between them reduces the background below the signal level. Consequently, one gets a viable H^± signal up to a mass range of 600–700 GeV at moderate to large tanβ.