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.     

Strong temperature effect on X-ray photo-etching of polytetrafluoroethylene using a 10 Hz laser-plasma radiation source based on a gas puff target

The first results of experiments on direct photo-etching of heated PTFE using a 10 Hz X-ray source based on a laser-irradiated gas puff target are presented. X-ray radiation in the wavelength range from 6 to 20 nm was produced as a result of irradiation of a double-stream gas puff target with Nd:YAG laser pulses of energy 0.8 J and time duration 3 ns. The resulting X-ray pulses with energy of about 100–200 mJ were used to irradiate samples of PTFE to create microstructures by direct photo-etching. Strong enhancement of the photo-etching process was observed for samples heated up to 300 °C. PACS 52.38.Ph; 81.65.Cf; 61.82.Pv     

Isothermal heat treatment of a thermotropic LCP fiber

The effect of the heat treatment on as-spun fibers made of a commercial liquid crystalline polymer, Vectra®, was examined through tensile properties and differential scanning calorimetry (DSC) measurements. The heat treatment increased the fiber strength considerably, and it also increased the elongation at break. On the other hand, the treatment had a weaker effect on the modulus. In general, the effects of treatment depended on the temperature and on the treatment time used. DSC measurements showed the effect of the treatment on the behavior of the melting endotherm. In light of the development of this endotherm, it seems possible that the structure formed during treatment depends essentially on the treatment temperature. On the whole, an unambiguous correlation between tensile properties and calorimetric quantities could not be concluded.     

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.     

Synthesis and Characterization of Optical Sol–Gel Adhesive for Military Protective Polycarbonate Resin

Sol–gel adhesive material for isostatic hotpressing lamination process was synthesized using 3-aminopropyltrimethoxysilane (APTES), 3-glycidyloxypropyltrimethoxysilane (GPTS) and methacryloxypropyltrimethoxysilane (MPTS) as precursors. Reaction dynamics between APTES and GPTS was followed on-line with Raman spectroscopy. The lamination process was optimized by varying hotpressing times and pressures at the constant temperature. Mechanical shear strength properties were found to be excellent for studied composition, 25–30 kg/cm² at its best. One possible application of laminated polycarbonate (PC) structure is a soldier helmet visor. Therefore, the ballistic protection properties were tested by shooting with 1.1 gram standard fragment, and determining the v₅₀ velocity value, which corresponds to 50% perforation. The laminated structure gave 5.7% better protection compared with the solid polycarbonate. The laminated components were found to have high optical transparency at the visible wavelengths as well as high environmental stability.     

Ab initio molecular orbital calculations on large lattice cluster models: Use of translational symmetry

Summary Translational symmetry has been shown to be useful in the calculation of electronic structures of large lattice models. The number of unique integrals has been derived for cases of different dimensionality. For the unique integrals zero screening and approximation methods are described. The method has been applied to arrays of hydrogen atoms and to a zincblende surface model. When the size of the system is increased the translationally unique integrals are shown to become either zero or they can be calculated by simple coulombic approximations.     

Grafting of functionalized silica particles with poly(acrylic acid)

Two different methods to graft silica particles with poly(acrylic acid) (PAA) were studied. In the first method PAA was reacted with 1,1′‐carbonyldiimidazole to give functionalized PAA. The resulting activated carbonyl group reacted easily with 3‐aminopropyl‐functionalized silica at low temperatures. In the second method 3‐glycidoxypropyl‐functionalized silica particles were reacted directly with PAA by using magnesium chloride as a catalyst. Different molecular weights of PAAs were used in order to investigate the effect of molecular weight on grafting yields in both methods. The grafting yields were determined with thermogravimetric analysis (TGA). All products were also investigated with IR. The results showed that the yields of reactions performed at ambient temperature by using 1,1′‐carbonyldiimidazole‐functionalized PAA were the same as with a direct reaction of unfunctionalized PAA and 3‐aminopropyl‐functionalized silica performed at 153°C. Also in reactions between 3‐glycidoxypropyl‐functionalized silica and PAA the yields were satisfactory. Copyright © 2006 John Wiley & Sons, Ltd.     

The cohomology of invariant variational bicomplexes

Let: E M be a fiber bundle and let be an infinitesimal Lie transformation group acting onE. We announce various new results concerning the cohomology of the invariant variational bicomplex ( ^*,* (J(E)), d_H, d_V) and the associated invariant Euler-Lagrange complex. As one application of our general theory, we completely solve the local invariant inverse problem of the calculus of variations for finite-dimensional infinitesimal Lie transformation groups.     

Skew Brownian motion-type of extensions

We consider a class of possible extensions of a given symmetric Feller processZ _t fromR{0} to the entire real lineR, depending on a parameter [0, 1]. It is proved that the proposed extension exists if =1/2; for 1/2, exists if and only ifZ _t does not jump over 0 (e.g., ifZ _t is a diffusion).     

Supramolecular chirogenesis in zinc porphyrins: equilibria, binding properties, and thermodynamics

Complexation mechanism, binding properties and thermodynamic parameters of supramolecular chirality induction in the achiral host molecule, syn (face-to-face conformation) ethane-bridged bis(zinc porphyrin), upon interaction with chiral monoamine and monoalcohol guests have been studied by means of the UV-vis, CD, (1)H NMR, and ESI MS techniques. It was found that the chirogenesis process includes three major equilibria steps: the first guest ligation to a zinc porphyrin subunit of the host (K(1)), syn to anti conformational switching (K(S)), and further ligation by a second guest molecule to the remaining ligand-free zinc porphyrin subunit (K(2)), thus forming the final bis-ligated species possessing supramolecular chirality. The validity of this equilibria model is confirmed by the excellent match between the calculated and experimentally observed spectral parameters of the bis-ligated species. The second ligation proceeds in a cooperative manner as K(2) > K(1) for all supramolecular systems studied, regardless of the structure of the chiral ligand used. The binding properties are highly dependent on the nature of the functional group (amines are stronger binders than alcohols) and on the structure of the chiral guests (primary and aliphatic amines have overall binding constant values greater than those of secondary and aromatic amines, respectively).