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.     

Headspace solvent microextraction of trihalomethane compounds into a single drop

Headspace solvent microextraction (HSME) into a single drop is developed for the determination of six trihalomethanes, CH2Cl2, CHCl3, C4H9Cl, CCl4, C2HCl3, and C2Cl4, in aqueous solution. A drop of benzyl alcohol containing bromoform, as an internal standard, is used for extraction. The analytes are extracted by suspending a 3-microL drop directly from the needle of a microsyringe. The needle passes through the septum of a vessel, and the needle tip appears above the surface of the solution. After the prescribed extraction time, the drop is drawn back into the syringe. The syringe is then removed, and its content is injected directly into a gas chromatography column for analysis. The main parameters affecting the HSME process, such as stirring speed, microdrop volume, sample solution temperature, microsyringe needle temperature, sample volume, solution pH, extracting solvent, and ionic strength of the solution, are studied. Also, the linear range and precision of the method are examined.     

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.     

Simultaneous determination of cobalt, nickel and palladium in micellar media using partial least square regression and direct orthogonal signal correction

A simple, novel and sensitive spectrophotometric method was described for the simultaneous determination of cobalt, nickel and palladium. The method is based on the complex formation of Co, Ni and Pd with 1-(2-pyridylazo)-2-naphtol (PAN) in Tween-80 micellar media. All factors affecting on the sensitivity were optimized and the linear dynamic range for determination of Co, Ni and Pd was found. The experimental calibration matrix was designed by measuring the absorbance over the range of 520-700 nm for 21 samples of 0.10-1.0, 0.050-0.50 and 0.050-4.0 microg ml(-1) of Co, Ni and Pd, respectively. The partial least square (PLS) modeling based on singular value decomposition (SVD) was used for the multivariate calibration of the spectrophotometric data. The direct orthogonal signal correction was used for pre-processing of data matrices and the prediction results of model, with and without using direct orthogonal signal correction, were statistically compared. The effects of various anions and cations on selectivity of the method were investigated. The proposed method was successfully applied to the determination of Co, Ni and Pd in water and alloy samples.     

Complexation of palladium cyanide with imidazolidine-2-thione and its derivatives

Summary Pd(CN)₂ reacts with imidazolidine-2-thione (Imt), 1,3-diazinane-2-thione(Diaz), 1,3-diazipnane-2-thione (Diap) and their derivatives to yield complexes of stoichiometry [PdL₂(CN)₂] or [PdL(CN)₂] (L = Imt, Diaz or Diap and L = Imt having N-Me, Et or Pr substituents), which were characterized by elemental analysis, i.r., ¹H and ¹³C n.m.r. spectroscopy. Both mono- and bis ligand complexes are thought to be square planar with the monoligand binding to metal via sulphur (bridging) and the bis ligand via the monodentate thione group. The ¹³C enriched Pd(¹³CN)₂ complex was prepared and the ¹³C n.m.r. recorded. The C-2 resonance of ¹³C n.m.r. of Imt, Diaz or Diap complexes of the copper(I), silver(I), gold(I) and palladium(II) were compared.     

Electronic and Structural Properties of Neutral, Anionic, and Cationic Rh x Cu4−x (x = 0–4) Small Clusters: A DFT Study

In this study, electronic structure, stability, and tendency to exchange electron of neutral, anionic, and cationic Rh _x Cu_4?x (x = 0–4) small clusters were investigated by density functional theory calculations. For neutral small clusters, it was found that the most stable structures of Rh₄, Rh₃Cu and Rh₂Cu₂ have distorted tetrahedral shape while the most stable structures of RhCu₃ and Cu₄ have quasi-planer shape. Adding charges to the clusters, caused shapes of the most stable structures undergo variations. Stabilities of the neutral, anionic, and cationic clusters decrease linearly with increasing the copper content. In addition, calculated chemical harnesses indicated that the small cluster with 75 % copper content has the least chemical hardness. Interestingly, prevailing number of electronegative (Rh) and electropositive (Cu) atoms in the anionic and cationic clusters coincides with high dipole moment in these species that occur at 25 and 75 % copper respectively.     

Selective Oxidative Cleavage of Benzylic Carbon-Nitrogen Double Bonds Under Non-Aqueous Condition with Tetrakis(pyridine)-Silver Dichromate [(Py)2Ag]2 Cr2O7

Carbonyl derivatives of phenylhydrazine, 2-nitrophenylhydrazine, 2, 4-dinitrophenazine, semicarbozone, and hydroxylamine are converted to their corresponding carbonyl compounds with tetrakis(pyridine)silver dichromate in benzene. Selectivity is also observed for benzylic C = N cleavage.     

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.     

DFT computational study towards investigating Cladribine anticancer drug adsorption on the graphene and functionalized graphene

Structural Chemistry - Density functional theory calculations at the M06-2X/6-31G** level have been carried out to examine the adsorption behavior of Cladribine drug on the graphene and graphene...     

Generalized Bessel functions: Theory and their applications

This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.