Intersection of triadic Cantor sets with their translates— I. Fundamental properties

Motivated by Mandelbrot's [The Fractal Geometry of Nature, Freeman, San Francisco, 1983] idea of referring to lacunarity of Cantor sets in terms of departure from translation invariance, we study the properties of these translation sets and show how they can be used for a classification purpose. This first paper of a series of two will be devoted to set up the fundamental properties of Hausdorff measures of those intersection sets. Using the triadic expansion of the shifting number, we determine the fractal structure of intersection of triadic Cantor sets with their translates. We found that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from those shifting numbers with a finite triadic expansion. We characterize this set of shifting numbers by giving a partition expression of it and the steps of its construction from a fundamental root set. Finally, we prove that intersection of Cantor sets with their translates verify a measure-conservation law with scales. The second paper will take advantage of the properties exposed here in order to utilize them in a classification context. Mainly, it will deal with the use of the discrete spectrum of measures to distinguish two Cantor-like sets of the same fractal dimension.     

An integrated solid-phase extraction system for sub-picomolar detection

A microchip structure etched on a glass substrate for packed column solid-phase extraction (SPE) and capillary electrochromatography (CEC) is described. A 200 microm long, octadecylsilane (ODS) packed column was secured using two different approaches: solvent lock or polymer entrapment. The former method was utilized for SPE while the latter approach was applied for CEC. In SPE, the ODS packed chamber gave a detection limit of 70 fM for a nonpolar BODIPY (493/503) dye when concentrated for 3 min at an electroosmotic flow rate of 4.14 nL/min, compared to 30 pM for this detector without the SPE step. SPE beds showed reproducible, linear calibration curves (R(2) = 0.9989) between 1 and 100 pM BODIPY at fixed preconcentration times. Breakthrough curves for the 330 pL (ODS-packed) bed indicated a capacity for BODIPY dye of 8.1 x 10(-14) mmol, or 0.25 mmol dye per liter of bed. The ODS-chamber could also be used to analyze dilute amino acid and peptide solutions. In the CEC format, two neutral dyes (BODIPY and acridine orange) were baseline-separated in an isocratic run with a theoretical plate count of 84 (420 000 plates/m) and a reduced plate height of about 1. A labeled peptide was also analyzed by CEC, using the acidic eluent (84% acetonitrile, and 26% aqueous trifluoroacetic acid (0.05%)) preferred for peptide separations on ODS-coated silica particles.     

Synthesis of Highly Enantioenriched Sulfonimidoyl Fluorides and Sulfonimidamides by Stereospecific Sulfur–Fluorine Exchange (SuFEx) Reaction

Sulfonimidamides present exciting opportunities as chiral isosteres of sulfonamides, with potential for additional directional interactions. Here, we present the first modular enantioselective synthesis of sulfonimidamides, including the first stereoselective synthesis of enantioenriched sulfonimidoyl fluorides, and studies on their reactivity. A new route to sulfonimidoyl fluorides is presented from solid bench-stable, N-Boc-sulfinamide (Boc=tert-butyloxycarbonyl) salt building blocks. Enantioenriched arylsulfonimidoyl fluorides are shown to be readily racemised by fluoride ions. Conditions are developed, which trap fluoride and enable the stereospecific reaction of sulfonimidoyl fluorides with primary and secondary amines (100 % es, es=enantiospecificity) generating sulfonimidamides with up to 99 % ee. Aryl and alkyl sulfonimidoyl fluoride reagents are suitable for mild late stage functionalisation reactions, exemplified by coupling with a selection of complex amines in marketed drugs.     

General interpolation schemes for the generation of irregular surfaces

We introduce an interpolation scheme to generate a class of irregular surfaces. The analysis is first carried out for a triangleT. We define the function ? on a subsetX, dense inT. In terms of the construction parameters of ?, we establish sufficient conditions for its uniform continuity so that it would be possible to extend it to a continuous function on the whole ofT. We do the same analysis in the case of a rectangleR.     

Towards explicit evaluation of pharmacokinetic outcomes of patient drug intake behaviour

Poor compliance is now well recognized to seriously compromise drug efficacy. Using a probabilistic approach, we established an analytical compliance-pharmacokinetic formalism for common drug administration routes. This work allows to further characterize different levels of drug concentration variations directly inherited from patient compliance. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase stability,mechanical and thermodynamic properties of orthorhombic and trigonal MgSiN2: an ab initio study

Structural stability and mechanical and thermodynamic properties of the orthorhombic and trigonal MgSiN₂ polymorphs (or-MgSiN₂ and tr-MgSiN₂) were investigated through density functional theory and quasi-harmonic Debye model (QHDM). Our calculations show that or-MgSiN₂ is energetically the stable polymorph at low pressure, in agreement with previous experimental and theoretical study. Under pressure, a crystallographic transition from the orthorhombic structure to the trigonal one occurs around 25, 17.45 and 19.05 GPa as obtained from the generalized gradient approximation of Perdew-Wang (GGA-PW91), the generalized gradient approximation parameterized recently by Perdew et al (GGA-PBEsol) and the local density approximation developed by Ceperley and Alder and parameterized by Perdew and Zunger (LDA-CAPZ), respectively. Single-crystalline and polycrystalline elastic constants and related properties, namely Vickers hardness, acoustic Grüneisen parameter, minimum thermal conductivity, isotropic sound velocities and Debye temperature, were numerically estimated for both or-MgSiN₂ and tr-MgSiN₂. We have showed that the hardness of tr-MgSiN₂ is comparable to that of the harder materials like c-BN and B₆O. Temperature and pressure dependencies of volume, bulk modulus, thermal expansion, Grüneisen parameter, heat capacities and Debye temperature were investigated using QHDM.     

Vibrational spectra of triiodomesitylene: combination of DFT calculations and experimental studies. Effects of the environment

A study of the internal vibrations of triiodomesitylene (TIM) is presented. It is known from X-rays diffraction at 293 K that the molecule has nearly D(3h) symmetry because of the large delocalization of the methyl protons. By using Raman and infrared spectra recorded at room temperature, a first assignment is done by comparing TIM vibrations with those of 1,3,5-triiodo- and 1,3,5-trimethyl-benzene. This assignment is supported by DFT calculations by using the MPW1PW91 functional with the LanL2DZ(d,p) basis set and assuming C(3h) symmetry. The agreement between the calculated and experimental frequencies is very good: always better than 97% for the observed skeletal vibrations. The calculations overestimate the methyl frequencies by 7%, and experiment shows only broad features for these excitations. Because a neutron diffraction study had established that the TIM conformation at 14 K is not exactly trigonal, new theoretical calculations were done with C(s) symmetry. This shows that all previous E' and E' modes of vibration are split by 2-12 cm(-1). This is confirmed by infrared, Raman, and inelastic neutron scattering spectra recorded below 10 K. Apart from two frequencies, all the TIM skeleton vibrations have been detected and assigned by using C(s) symmetry. For the methyl vibrations, experiment has confirmed the splitting of the previously degenerate modes; only some small discrepancies remain in the assignment. This is partly due to the difference of the model conformation used in the calculations and the crystallographic one. All these results confirm that each of the three methyl groups has not only its own tunnel splitting but also a different specific spectroscopic behavior for all the molecular modes.     

Aggregation of sodium dodecyl sulfate in micellar solution of β-casein analyzed by 1H NMR self-diffusion, relaxation and Fourier transform IR spectroscopy

Micellization of anionic sodium dodecyl sulfate (SDS) in the presence of -casein (-CN) micelles in aqueous media was studied by ¹H NMR and Fourier transform IR spectroscopy. At low concentrations SDS molecules incorporate into -CN micelles and modify the protein secondary structure, increasing the portion of helical domains. It was shown that SDS micelles do not appear until binding sites located in the hydrophobic core of -CN micelles are saturated.     

Fluorimetric Determination of Some Sulfur Containing Compounds Through Complex Formation with Terbium (Tb<Superscript>+3</Superscript>) and Uranium (U<Superscript>+3</Superscript>)

Two simple, sensitive and specific fluorimetric methods have been developed for the determination of some sulphur containing compounds namely, Acetylcysteine (Ac), Carbocisteine (Cc) and Thioctic acid (Th) using terbium Tb⁺³ and uranium U⁺³ ions as fluorescent probes. The proposed methods involve the formation of a ternary complex with Tb⁺³ in presence of Tris-buffer method (I) and a binary complex with aqueous uranyl acetate solution method (II). The fluorescence quenching of Tb⁺³ at 510, 488 and 540 nm (λ_ex 250, 241 and 268 nm) and of uranyl acetate at 512 nm (λ_ex 240 nm) due to the complex formation was quantitatively measured for Ac, Cc and Th, respectively. The reaction conditions and the fluorescence spectral properties of the complexes have been investigated. Under the described conditions, the proposed methods were applicable over the concentration range (0.2–2.5 μg ml⁻¹), (1–4 μg ml⁻¹) and (0.5–3.5 μg ml⁻¹) with mean percentage recoveries 99.74±0.36, 99.70±0.52 and 99.43±0.23 for method (I) and (0.5–6 μg ml⁻¹), (0.5–5 μg ml⁻¹), and (1–6 μg ml⁻¹) with mean percentage recoveries 99.38±0.20, 99.82±0.28 and 99.93±0.32 for method (II), for the three cited drugs, respectively. The proposed methods were successfully applied for the determination of the studied compounds in bulk powders and in pharmaceutical formulations, as well as in presence of their related substances. The results obtained were found to be in agree statistically with those obtained by official and reported ones. The two methods were validated according to USP guidelines and also assessed by applying the standard addition technique.     

Discrete Fourier Transform with Denoise Model Based Least Square Wiener Channel Estimator for Channel Estimation in MIMO-OFDM

Multiple-input Multiple-Output (MIMO) systems require orthogonal frequency division multiplexing to operate efficiently in multipath communication (OFDM). Channel estimation (C.E.) is used in channel conditions where time-varying features are required. The existing channel estimation techniques are highly complicated. A channel estimation algorithm is needed to estimate the received signal’s correctness. In order to resolve this complexity in C.E. methodologies, this paper developed an Improved Channel Estimation Algorithm integrated with DFT-LS-WIENER (ICEA-DA). The Least Square (L.S.) and Minimum Mean Square Error (MMSE) algorithms also use the Discrete Fourier Transform (DFT)-based channel estimation method. The DFT-LS-WIENER channel estimation approach is recommended for better BER performance. The input signal is modulated in the transmitter module using the Quadrature Phase Shift Keying (QPSK) technique, pulse modeling, and least squares concepts. The L.S. Estimation technique needs the channel consistent throughout the estimation period. DFT joined with L.S. gives higher estimation precision and limits M.S.E. and BER. Experimental analysis of the proposed state-of-the-art method shows that DFT-LS-WIENER provides superior performance in terms of symbol error rate (S.E.R.), bit error rate (BER), channel capacity (CC), and peak signal-to-noise (PSNR). At 15 dB SNR, the proposed DFT-LS-WIENER techniques reduce the BER of 48.19%, 38.19%, 14.8%, and 14.03% compared to L.S., LS-DFT, MMSE, and MMSE-DFT. Compared to the conventional algorithm, the proposed DFT-LS-WIENER outperform them.