On the computation of scaling coefficients of Daubechies' wavelets

In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.     

Analysis of the Thermal Stability of Very Thin Surface Layers of Corrosion Inhibitors by Time-of-Flight Secondary Ion Mass Spectrometry

The powerful nature of the secondary ion mass spectrometry (SIMS) technique was explored in order to analyse very thin surface layers that were self-assembled on steel material from acidic solution. These surface layers are adsorbed corrosion inhibitors. The SIMS technique proved useful to characterise the molecular structure and homogeneity of thin surface layers in the nanometre range of specific analytes on the metallic substrate. Using SIMS, the thermal stability of these layers was further investigated and the desorption energy at a certain temperature was determined, where special attention was devoted to the method’s static limit. In order to compare, and for certain cases emphasise, the benefits gained by using SIMS in such surface analysis compared with the X-ray photoelectron spectroscopy (XPS) method, the same samples were also analysed by means of the latter. XPS is usually considered to be the most powerful analytical tool in surface analysis studies, but, as shown herein, it has certain limitations compared to SIMS. Finally, the surface topography was investigated by employing atomic force microscopy (AFM) in order to carry out a comprehensive surface analysis.

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Naphthalene- and perylenediimides with hydroquinones, catechols, boronic esters and imines in the core

The green-fluorescent protein of the jellyfish operates with the most powerful phenolate donors in the push-pull fluorophore. To nevertheless achieve red fluorescence with the same architecture, sea anemone and corals apply oxidative imination, a process that accounts for the chemistry of vision as well. The objective of this study was to apply these lessons from nature to one of the most compact family of panchromatic fluorophores, i.e. core-substituted naphthalenediimides (cNDIs). We report straightforward synthetic access to hydroxylated cNDI and cPDI cores by palladium-catalyzed cleavage of allyloxy substituents. With hydroxylated cNDIs but not cPDIs in water-containing media, excited-state intramolecular proton transfer yields a second bathochromic emission. Deprotonation of hydroquinone, catechol and boronic ester cores provides access to an impressive panchromism up to the NIR frontier at 640 nm. With cNDIs, oxidative imination gives red shifts up to 638 nm, whereas the expanded cPDIs already absorb at 754 nm upon deprotonation of hydroquinone cores. The practical usefulness of hydroquinone cNDIs is exemplified by ratiometric sensing of the purity of DMF with the "naked eye" at a sensitivity far beyond the "naked nose". We conclude that the panchromatic hypersensitivity toward the environment of the new cNDIs is ideal for pattern generation in differential sensing arrays.     

Comprehensive screening of octopus amphiphiles as DNA activators in lipid bilayers: implications on transport, sensing and cellular uptake

Dynamic octopus amphiphiles contain one charged "head," here a guanidinium cation, together several hydrophobic "tails" (or "tentacles") that can be attached and exchanged in situ by reversible hydrazone formation. Quite surprisingly, their ability to activate DNA as transporters in lipid bilayer membranes was found to increase with the number of tails (up to four) as well as with their length (up to eight carbons). Both encouraged and puzzled by these results, we decided that a comprehensive screening of octopus amphiphiles with regard to number (from one to six) and length (from three to eighteen carbons) of their tails would be appropriate at this point. For this purpose, we here report the synthesis of cationic hexahydrazide peptide dendrons together with that of aldehydes with long, saturated, unsaturated and branched hydrophobic tails. Comprehensive screening of the completed collection of tails and heads reveals that the ability of octopus amphiphiles to activate DNA transporters shifts with increasing number of tails to decreasing length of the tails. Moreover, cis-alkenyl and branched alkyl tails are more active than their linear analogs, branched aromatic tails are best. These overall very meaningful trends for octopus amphiphiles will be of importance for sensing applications and fragrant cellular uptake.     

Electro-optic fiber sensor for amplitude and phase detection of radio frequency electromagnetic fields

We present a miniature fiber-optic electromagnetic field (EMF) sensor that is capable of simultaneously detecting the amplitude and phase of an EMF in the range of 0.1-6 GHz. We focus on magnetic field measurements, since the H-field is more significant in our target applications due its direct relation to the current. The sensor is based on an open optical platform to which various antennas can be attached and contains a radio-frequency amplifier for signal conditioning and a vertical-cavity surface-emitting laser as an electro-optic converter. The millimeter size and the full electrical isolation of the sensor allow EMF detection with minimal disturbance. We have characterized the sensor in the near field of a lambda/2 dipole, a rectangular waveguide, and a microstrip line, and we explain the experimental results with a simple theoretical model confirming the mapped near-field distribution of the investigated field source.     

Construction of optimally conditioned cubic spline wavelets on the interval

The paper is concerned with a construction of new spline-wavelet bases on the interval. The resulting bases generate multiresolution analyses on the unit interval with the desired number of vanishing wavelet moments for primal and dual wavelets. Both primal and dual wavelets have compact support. Inner wavelets are translated and dilated versions of well-known wavelets designed by Cohen, Daubechies, and Feauveau. Our objective is to construct interval spline-wavelet bases with the condition number which is close to the condition number of the spline wavelet bases on the real line, especially in the case of the cubic spline wavelets. We show that the constructed set of functions is indeed a Riesz basis for the space L ² ([0, 1]) and for the Sobolev space H ^s ([0, 1]) for a certain range of s. Then we adapt the primal bases to the homogeneous Dirichlet boundary conditions of the first order and the dual bases to the complementary boundary conditions. Quantitative properties of the constructed bases are presented. Finally, we compare the efficiency of an adaptive wavelet scheme for several spline-wavelet bases and we show a superiority of our construction. Numerical examples are presented for the one-dimensional and two-dimensional Poisson equations where the solution has steep gradients.     

An integrated simulation and statistical technique for?investigating the effect of interpenetration polymer brushes in a good solvent

This study presents a novel approach for analyzing the interaction between two parallel surfaces grafted with polymer brushes in a good solvent. In the proposed approach, MD simulations are performed to establish the mean brush height and the standard deviation of the brush height distribution for a given value of the surface separation. The corresponding probability density function (PDF) of the brush height is then determined both with and without the assumption of a brush interpenetration effect, respectively, and a statistical technique is applied to compute the corresponding interaction free energy per unit area of the grafted substrates. Finally, the Derjaguin approximation is employed to determine the corresponding value of the interaction force between the two surfaces. The results obtained for the interaction free energy and interaction force are compared with those derived using the Alexander and de Gennes (AdG) model and the Milner, Witten and Cates (MWC) model, respectively. The value of the normalized interaction free energy computed using the present method is higher than that obtained from the AdG and MWC models at larger surface separations when the brush interpenetration effect is ignored. However, the results obtained by the current method for the interaction force are found to be in better agreement with the experimental data than those obtained using the AdG or MWC models. The enhanced performance of the proposed method is attributed primarily to the use of an adaptive non-Gaussian PDF of the brush height to model the effects of brush interpenetration and fluctuations in the brush conformation at different distances from the grafting plane.