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.     

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).     

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.     

MM-PBSA free energy analysis of endo-1,4-xylanase II (XynII)-substrate complexes: binding of the reactive sugar in a skew boat and chair conformation

The binding of xylotetraose in different conformations to the active site of endo-1,4-beta-xylanase II (XynII) from Trichoderma reesei was studied using molecular dynamics (MD) simulations and free energy analyses employing the MM-PBSA (Molecular Mechanics-Poisson-Boltzmann Surface Area) method. MD simulations of 1 ns were done for the substrate xylotetraose having the reactive sugar, which is bound in the -1 subsite of XynII in the 4C1 (chair) and 2So (skew boat) ground state conformations, and for the transition state of the XynII catalysed hydrolysis of the beta-glycosidic linkage. According to the simulations and free energy analysis, XynII binds the substrate with the -1 sugar in the 2So conformation 59.8 kJ mol(-1) tighter than the substrate with the sugar in the 4C1 conformation. The reactive 2So conformation resembles closely the reaction transition state and has the breaking glycosidic bond in a pseudo-axial orientation ready for facile bond cleavage. The transition state was calculated to be bound 77.1 kJ mol(-1) tighter than the 4C1 ground state conformation. The molecular mechanical interaction energy between the enzyme and the reactive pyranoside unit at the -1 subsite was 75.7 kJ mol(-1) more favorable for the binding of the 2So conformation than the 2C1 conformation, explaining the clearly tighter binding of the reactive structure The results of this study indicate that in the Michaelis complex XynII, a member of the family 11 xylanase, the substrate is bound in a skew boat conformation and in the catalytic reaction, the -1 sugar proceeds from the 4C1 conformation through 2So to the transition state with the -1 sugar in the 2,5B conformation.