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.     

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.     

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

Supramolecular chirogenesis in zinc porphyrins: interaction with bidentate ligands,formation of tweezer structures,and the origin of enhanced optical activity

The complexation behavior, binding properties, and spectral parameters of supramolecular chirality induction in the achiral host molecule, syn (face-to-face conformation) ethane-bridged bis(zinc porphyrin), upon interaction with chiral bidentate guests (diamines and amino alcohols) have been studied by means of UV-vis, CD, fluorescence, (1)H NMR, and ESI MS techniques. It was found that the guest structure plays a decisive role in the chirogenesis pathway. The majority of bidentate ligands (except those geometrically unsuitable) exhibit two major equilibria steps: the first guest ligation leading to formation of the 1:1 host-guest tweezer structure (K(1)) and the second guest molecule ligation (K(2)) forming the anti bis-ligated species (1:2). The second ligation is much weaker (K(1) > K(2)) due to the optimal geometry and stability of the 1:1 tweezer complex. The enhanced conformational stability of the tweezer complex ensures an efficient chirality transfer from the chiral guest to the achiral host, consequently inducing a remarkably high optical activity in the bis-porphyrin.     

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).     

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.