Shape preservation regions for six-dimensional spaces

We analyze the critical length for design purposes of six-dimensional spaces invariant under translations and reflections containing the functions 1, cos t and sin t. These spaces also contain the first degree polynomials as well as trigonometric and/or hyperbolic functions. We identify the spaces whose critical length for design purposes is greater than 2π and find its maximum 4π. By a change of variables, two biparametric families of spaces arise. We call shape preservation region to the set of admissible parameters in order that the space has shape preserving representations for curves. We describe the shape preserving regions for both families. To our friend Mariano Gasca on occasion of his 60th birthday Research partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

Thermal and dilute-solution properties of zwitterionic copolymers

We report the synthesis, characterization, thermal and dilute-solution properties of zwitterionic copolymers of the sulfobetaine type, where the proportion of ionic groups is varied over a wide range. Two different structures are considered: poly (2-vinyl pyridine sulfopropyl betaine) and poly (4-vinyl pyridine sulfopropyl betaine). Synthesis is carried out to obtain random copolymers which are further characterized and their ionic content determined. At low proportions of ionic groups, the behavior is similar to that observed in ionomers, with substantial differences between the two structures, Increased interaction among the zwitterionic groups at higher charge densities is evidenced, which leads to the formation of clusters and agglomerates. An increase in the intrinsic viscosity with salt content in aqueous solutions is also observed. This behavior is analogous to that of homopolymers with 100% ionic content, but with particular features of interest.     

Quantum Nonlocality of Photon Pairs in Interference in a Mach-Zehnder Interferometer

Nonlocal character of entangled photon pairs generated in spontaneous parametric downconversion is demonstrated. One photon from a pair propagates through a Mach-Zehnder interferometer and is detected in coincidence-count measurement with its twin. Width of the coincidence-count interference pattern (measured for various values of path difference in the Mach-Zehnder interferometer) depends on spectral width of the twin as a result of entanglement of photons in a pair. The experimental setup is analyzed for a Gaussian spectral filter and a Fabry-Perot resonator. It is shown that nonlocal interference is much stronger for cw pumping in comparison with femtosecond pulsed pumping for values of parameters commonly used in spontaneous parametric downconversion experiments.     

EPR investigation of cell membrane fluidity upon external oxidative stimulus

The perturbation of the physical state of cell membranes triggered by an external oxidative stimulus has been studied with sperm cells which were chosen as a model system. Electron paramagnetic resonance (EPR) spectroscopy was applied and three different nitroxides bearing a paramagnetic group on the 5th, 7th and 13th carbon of the stearic acid acyl chain were used to probe different regions of the membrane. The theoretical simulations of the experimental spectra indicate distinct domains in the intact cell plasma membrane where local steric constraints impose different degrees of motional averaging experienced by the reporter group. Upon the external oxidative stimulus the spectral changes were proportional to the accumulated oxidation products and were detected only for the reporter group residing close to the lipid-water interface. The EPR spectra reveal that the motion of the reporter group has slowed down in the oxidized cells and that the oxidatively modified membrane shows up as a more rigid structure as compared with the native state. The results also indicate that the oxidation-induced spectral changes are supressed in the presence of gangliosides.     

Some Landau's type inequalities for infinitesimal generators

Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A ³), the following inequalities hold true: Ax³ 243/8 x²A ³ x, A ² x 24 xA ³ x². Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.     

Comparison of different fibers for the solid-phase microextraction of phthalate esters from water

Solid-phase microextraction (SPME) coupled to gas chromatography-mass spectrometry (GC-MS) has been applied to determine six phthalate esters and one adipate ester in water. The SPME parameters were optimized for several commercially available fibers. A 65-microm polydimethylsiloxane-divinylbenzene (PDMS-DVB) was the fiber selected and was applied to analysis of water from the Ebro river and the industrial port of Tarragona. The studied compounds were found at concentrations ranging from 0.4 microg l(-1) for di-n-butyl phthalate ester (DnBP) to 3.2 microg l(-1) for bis(2-ethylhexyl) phthalate ester (DEHP). The linear range for real samples was from 0.1 to 10 microg l(-1) for most phthalates, and the limits of detection of the method were between 3 and 30 ng l(-1). Repeatability and reproducibility between days (n = 5) for 1 microg l(-1) samples were below 13 and 18%, respectively.